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authorHans Bolinder <[email protected]>2016-09-16 11:54:57 +0200
committerHans Bolinder <[email protected]>2016-10-06 16:37:59 +0200
commit87a13c257bfd5a53b6803bc2d714afb13106c243 (patch)
treece5b5882e1889649c57ed3466d26c03ec3cfd92d /lib/dialyzer/test
parent5acfcf3758f89ba32d44807cd8cb406a55d39836 (diff)
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dialyzer: Fix opaque bugs
t_from_form() sometimes returned a more general type than it should have done due to a bug in from_form_loop(): it stopped when the limit was exceeded, which could mean a collapsed type. Returning a type with smaller depth should fix this. is_specialization() now handles opaque types before unions, which should fix another problem. The bugs reported by Kostis.
Diffstat (limited to 'lib/dialyzer/test')
-rw-r--r--lib/dialyzer/test/opaque_SUITE_data/dialyzer_options2
-rw-r--r--lib/dialyzer/test/opaque_SUITE_data/src/recrec/cerl.erl4602
-rw-r--r--lib/dialyzer/test/opaque_SUITE_data/src/recrec/core_parse.hrl122
-rw-r--r--lib/dialyzer/test/opaque_SUITE_data/src/recrec/dialyzer.hrl180
-rw-r--r--lib/dialyzer/test/opaque_SUITE_data/src/recrec/dialyzer_dataflow.erl3802
-rw-r--r--lib/dialyzer/test/opaque_SUITE_data/src/recrec/dialyzer_races.erl2494
-rw-r--r--lib/dialyzer/test/opaque_SUITE_data/src/recrec/erl_types.erl5741
7 files changed, 16942 insertions, 1 deletions
diff --git a/lib/dialyzer/test/opaque_SUITE_data/dialyzer_options b/lib/dialyzer/test/opaque_SUITE_data/dialyzer_options
index ffdf8270c8..06ed52043a 100644
--- a/lib/dialyzer/test/opaque_SUITE_data/dialyzer_options
+++ b/lib/dialyzer/test/opaque_SUITE_data/dialyzer_options
@@ -1,2 +1,2 @@
{dialyzer_options, [{warnings, [no_unused, no_return]}]}.
-{time_limit, 2}.
+{time_limit, 20}.
diff --git a/lib/dialyzer/test/opaque_SUITE_data/src/recrec/cerl.erl b/lib/dialyzer/test/opaque_SUITE_data/src/recrec/cerl.erl
new file mode 100644
index 0000000000..a4fdbfd5f0
--- /dev/null
+++ b/lib/dialyzer/test/opaque_SUITE_data/src/recrec/cerl.erl
@@ -0,0 +1,4602 @@
+%%
+%% %CopyrightBegin%
+%%
+%% Copyright Ericsson AB 2001-2016. All Rights Reserved.
+%%
+%% Licensed under the Apache License, Version 2.0 (the "License");
+%% you may not use this file except in compliance with the License.
+%% You may obtain a copy of the License at
+%%
+%% http://www.apache.org/licenses/LICENSE-2.0
+%%
+%% Unless required by applicable law or agreed to in writing, software
+%% distributed under the License is distributed on an "AS IS" BASIS,
+%% WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+%% See the License for the specific language governing permissions and
+%% limitations under the License.
+%%
+%% %CopyrightEnd%
+
+%% =====================================================================
+%% @doc Core Erlang abstract syntax trees.
+%%
+%% <p> This module defines an abstract data type for representing Core
+%% Erlang source code as syntax trees.</p>
+%%
+%% <p>A recommended starting point for the first-time user is the
+%% documentation of the function <a
+%% href="#type-1"><code>type/1</code></a>.</p>
+%%
+%% <h3><b>NOTES:</b></h3>
+%%
+%% <p>This module deals with the composition and decomposition of
+%% <em>syntactic</em> entities (as opposed to semantic ones); its
+%% purpose is to hide all direct references to the data structures
+%% used to represent these entities. With few exceptions, the
+%% functions in this module perform no semantic interpretation of
+%% their inputs, and in general, the user is assumed to pass
+%% type-correct arguments - if this is not done, the effects are not
+%% defined.</p>
+%%
+%% <p>Currently, the internal data structure used is the same as
+%% the record-based data structures used traditionally in the Beam
+%% compiler.</p>
+%%
+%% <p>The internal representations of abstract syntax trees are
+%% subject to change without notice, and should not be documented
+%% outside this module. Furthermore, we do not give any guarantees on
+%% how an abstract syntax tree may or may not be represented, <em>with
+%% the following exceptions</em>: no syntax tree is represented by a
+%% single atom, such as <code>none</code>, by a list constructor
+%% <code>[X | Y]</code>, or by the empty list <code>[]</code>. This
+%% can be relied on when writing functions that operate on syntax
+%% trees.</p>
+%%
+%% @type cerl(). An abstract Core Erlang syntax tree.
+%%
+%% <p>Every abstract syntax tree has a <em>type</em>, given by the
+%% function <a href="#type-1"><code>type/1</code></a>. In addition,
+%% each syntax tree has a list of <em>user annotations</em> (cf. <a
+%% href="#get_ann-1"><code>get_ann/1</code></a>), which are included
+%% in the Core Erlang syntax.</p>
+
+-module(cerl).
+
+-export([abstract/1, add_ann/2, alias_pat/1, alias_var/1,
+ ann_abstract/2, ann_c_alias/3, ann_c_apply/3, ann_c_atom/2,
+ ann_c_call/4, ann_c_case/3, ann_c_catch/2, ann_c_char/2,
+ ann_c_clause/3, ann_c_clause/4, ann_c_cons/3, ann_c_float/2,
+ ann_c_fname/3, ann_c_fun/3, ann_c_int/2, ann_c_let/4,
+ ann_c_letrec/3, ann_c_module/4, ann_c_module/5, ann_c_nil/1,
+ ann_c_cons_skel/3, ann_c_tuple_skel/2, ann_c_primop/3,
+ ann_c_receive/2, ann_c_receive/4, ann_c_seq/3, ann_c_string/2,
+ ann_c_try/6, ann_c_tuple/2, ann_c_values/2, ann_c_var/2,
+ ann_make_data/3, ann_make_list/2, ann_make_list/3,
+ ann_make_data_skel/3, ann_make_tree/3, apply_args/1,
+ apply_arity/1, apply_op/1, atom_lit/1, atom_name/1, atom_val/1,
+ c_alias/2, c_apply/2, c_atom/1, c_call/3, c_case/2, c_catch/1,
+ c_char/1, c_clause/2, c_clause/3, c_cons/2, c_float/1,
+ c_fname/2, c_fun/2, c_int/1, c_let/3, c_letrec/2, c_module/3,
+ c_module/4, c_nil/0, c_cons_skel/2, c_tuple_skel/1, c_primop/2,
+ c_receive/1, c_receive/3, c_seq/2, c_string/1, c_try/5,
+ c_tuple/1, c_values/1, c_var/1, call_args/1, call_arity/1,
+ call_module/1, call_name/1, case_arg/1, case_arity/1,
+ case_clauses/1, catch_body/1, char_lit/1, char_val/1,
+ clause_arity/1, clause_body/1, clause_guard/1, clause_pats/1,
+ clause_vars/1, concrete/1, cons_hd/1, cons_tl/1, copy_ann/2,
+ data_arity/1, data_es/1, data_type/1, float_lit/1, float_val/1,
+ fname_arity/1, fname_id/1, fold_literal/1, from_records/1,
+ fun_arity/1, fun_body/1, fun_vars/1, get_ann/1, int_lit/1,
+ int_val/1, is_c_alias/1, is_c_apply/1, is_c_atom/1,
+ is_c_call/1, is_c_case/1, is_c_catch/1, is_c_char/1,
+ is_c_clause/1, is_c_cons/1, is_c_float/1, is_c_fname/1,
+ is_c_fun/1, is_c_int/1, is_c_let/1, is_c_letrec/1, is_c_list/1,
+ is_c_module/1, is_c_nil/1, is_c_primop/1, is_c_receive/1,
+ is_c_seq/1, is_c_string/1, is_c_try/1, is_c_tuple/1,
+ is_c_values/1, is_c_var/1, is_data/1, is_leaf/1, is_literal/1,
+ is_literal_term/1, is_print_char/1, is_print_string/1,
+ let_arg/1, let_arity/1, let_body/1, let_vars/1, letrec_body/1,
+ letrec_defs/1, letrec_vars/1, list_elements/1, list_length/1,
+ make_data/2, make_list/1, make_list/2, make_data_skel/2,
+ make_tree/2, meta/1, module_attrs/1, module_defs/1,
+ module_exports/1, module_name/1, module_vars/1,
+ pat_list_vars/1, pat_vars/1, primop_args/1, primop_arity/1,
+ primop_name/1, receive_action/1, receive_clauses/1,
+ receive_timeout/1, seq_arg/1, seq_body/1, set_ann/2,
+ string_lit/1, string_val/1, subtrees/1, to_records/1,
+ try_arg/1, try_body/1, try_vars/1, try_evars/1, try_handler/1,
+ tuple_arity/1, tuple_es/1, type/1, unfold_literal/1,
+ update_c_alias/3, update_c_apply/3, update_c_call/4,
+ update_c_case/3, update_c_catch/2, update_c_clause/4,
+ update_c_cons/3, update_c_cons_skel/3, update_c_fname/2,
+ update_c_fname/3, update_c_fun/3, update_c_let/4,
+ update_c_letrec/3, update_c_module/5, update_c_primop/3,
+ update_c_receive/4, update_c_seq/3, update_c_try/6,
+ update_c_tuple/2, update_c_tuple_skel/2, update_c_values/2,
+ update_c_var/2, update_data/3, update_list/2, update_list/3,
+ update_data_skel/3, update_tree/2, update_tree/3,
+ values_arity/1, values_es/1, var_name/1, c_binary/1,
+ update_c_binary/2, ann_c_binary/2, is_c_binary/1,
+ binary_segments/1, c_bitstr/3, c_bitstr/4, c_bitstr/5,
+ update_c_bitstr/5, update_c_bitstr/6, ann_c_bitstr/5,
+ ann_c_bitstr/6, is_c_bitstr/1, bitstr_val/1, bitstr_size/1,
+ bitstr_bitsize/1, bitstr_unit/1, bitstr_type/1, bitstr_flags/1,
+
+ %% keep map exports here for now
+ c_map_pattern/1,
+ is_c_map/1,
+ is_c_map_pattern/1,
+ map_es/1,
+ map_arg/1,
+ update_c_map/3,
+ c_map/1, is_c_map_empty/1,
+ ann_c_map/2, ann_c_map/3,
+ ann_c_map_pattern/2,
+ map_pair_op/1,map_pair_key/1,map_pair_val/1,
+ update_c_map_pair/4,
+ c_map_pair/2, c_map_pair_exact/2,
+ ann_c_map_pair/4
+ ]).
+
+-export_type([c_binary/0, c_bitstr/0, c_call/0, c_clause/0, c_cons/0, c_fun/0,
+ c_let/0, c_literal/0, c_map/0, c_map_pair/0,
+ c_module/0, c_tuple/0,
+ c_values/0, c_var/0, cerl/0,
+ anns/0, attrs/0, defs/0, litval/0, var_name/0]).
+
+-include("core_parse.hrl").
+
+-type c_alias() :: #c_alias{}.
+-type c_apply() :: #c_apply{}.
+-type c_binary() :: #c_binary{}.
+-type c_bitstr() :: #c_bitstr{}.
+-type c_call() :: #c_call{}.
+-type c_case() :: #c_case{}.
+-type c_catch() :: #c_catch{}.
+-type c_clause() :: #c_clause{}.
+-type c_cons() :: #c_cons{}.
+-type c_fun() :: #c_fun{}.
+-type c_let() :: #c_let{}.
+-type c_letrec() :: #c_letrec{}.
+-type c_literal() :: #c_literal{}.
+-type c_map() :: #c_map{}.
+-type c_map_pair() :: #c_map_pair{}.
+-type c_module() :: #c_module{}.
+-type c_primop() :: #c_primop{}.
+-type c_receive() :: #c_receive{}.
+-type c_seq() :: #c_seq{}.
+-type c_try() :: #c_try{}.
+-type c_tuple() :: #c_tuple{}.
+-type c_values() :: #c_values{}.
+-type c_var() :: #c_var{}.
+
+-type cerl() :: c_alias() | c_apply() | c_binary() | c_bitstr()
+ | c_call() | c_case() | c_catch() | c_clause() | c_cons()
+ | c_fun() | c_let() | c_letrec() | c_literal()
+ | c_map() | c_map_pair()
+ | c_module() | c_primop() | c_receive() | c_seq()
+ | c_try() | c_tuple() | c_values() | c_var().
+
+-type anns() :: [term()].
+-type attr() :: {c_literal(), c_literal()}.
+-type attrs() :: [attr()].
+-type def() :: {c_var(), c_fun()}.
+-type defs() :: [def()].
+
+-type litval() :: atom() | bitstring() | map() | number()
+ | string() | tuple() | [litval()].
+
+-type var_name() :: integer() | atom() | {atom(), arity()}.
+
+
+%% =====================================================================
+%% Representation (general)
+%%
+%% All nodes are represented by tuples of arity 2 or (generally)
+%% greater, whose first element is an atom which uniquely identifies the
+%% type of the node, and whose second element is a (proper) list of
+%% annotation terms associated with the node - this is by default empty.
+%%
+%% For most node constructor functions, there are analogous functions
+%% named 'ann_...', taking one extra argument 'As' (always the first
+%% argument), specifying an annotation list at node creation time.
+%% Similarly, there are also functions named 'update_...', taking one
+%% extra argument 'Old', specifying a node from which all fields not
+%% explicitly given as arguments should be copied (generally, this is
+%% the annotation field only).
+%% =====================================================================
+
+%% @spec type(Node::cerl()) -> atom()
+%%
+%% @doc Returns the type tag of <code>Node</code>. Current node types
+%% are:
+%%
+%% <p><center><table border="1">
+%% <tr>
+%% <td>alias</td>
+%% <td>apply</td>
+%% <td>binary</td>
+%% <td>bitstr</td>
+%% <td>call</td>
+%% <td>case</td>
+%% <td>catch</td>
+%% <td>clause</td>
+%% </tr><tr>
+%% <td>cons</td>
+%% <td>fun</td>
+%% <td>let</td>
+%% <td>letrec</td>
+%% <td>literal</td>
+%% <td>map</td>
+%% <td>map_pair</td>
+%% <td>module</td>
+%% </tr><tr>
+%% <td>primop</td>
+%% <td>receive</td>
+%% <td>seq</td>
+%% <td>try</td>
+%% <td>tuple</td>
+%% <td>values</td>
+%% <td>var</td>
+%% </tr>
+%% </table></center></p>
+%%
+%% <p>Note: The name of the primary constructor function for a node
+%% type is always the name of the type itself, prefixed by
+%% "<code>c_</code>"; recognizer predicates are correspondingly
+%% prefixed by "<code>is_c_</code>". Furthermore, to simplify
+%% preservation of annotations (cf. <code>get_ann/1</code>), there are
+%% analogous constructor functions prefixed by "<code>ann_c_</code>"
+%% and "<code>update_c_</code>", for setting the annotation list of
+%% the new node to either a specific value or to the annotations of an
+%% existing node, respectively.</p>
+%%
+%% @see abstract/1
+%% @see c_alias/2
+%% @see c_apply/2
+%% @see c_binary/1
+%% @see c_bitstr/5
+%% @see c_call/3
+%% @see c_case/2
+%% @see c_catch/1
+%% @see c_clause/3
+%% @see c_cons/2
+%% @see c_fun/2
+%% @see c_let/3
+%% @see c_letrec/2
+%% @see c_module/3
+%% @see c_primop/2
+%% @see c_receive/1
+%% @see c_seq/2
+%% @see c_try/5
+%% @see c_tuple/1
+%% @see c_values/1
+%% @see c_var/1
+%% @see get_ann/1
+%% @see to_records/1
+%% @see from_records/1
+%% @see data_type/1
+%% @see subtrees/1
+%% @see meta/1
+
+-type ctype() :: 'alias' | 'apply' | 'binary' | 'bitrst' | 'call' | 'case'
+ | 'catch' | 'clause' | 'cons' | 'fun' | 'let' | 'letrec'
+ | 'literal' | 'map' | 'map_pair' | 'module' | 'primop'
+ | 'receive' | 'seq' | 'try' | 'tuple' | 'values' | 'var'.
+
+-spec type(cerl()) -> ctype().
+
+type(#c_alias{}) -> alias;
+type(#c_apply{}) -> apply;
+type(#c_binary{}) -> binary;
+type(#c_bitstr{}) -> bitstr;
+type(#c_call{}) -> call;
+type(#c_case{}) -> 'case';
+type(#c_catch{}) -> 'catch';
+type(#c_clause{}) -> clause;
+type(#c_cons{}) -> cons;
+type(#c_fun{}) -> 'fun';
+type(#c_let{}) -> 'let';
+type(#c_letrec{}) -> letrec;
+type(#c_literal{}) -> literal;
+type(#c_map{}) -> map;
+type(#c_map_pair{}) -> map_pair;
+type(#c_module{}) -> module;
+type(#c_primop{}) -> primop;
+type(#c_receive{}) -> 'receive';
+type(#c_seq{}) -> seq;
+type(#c_try{}) -> 'try';
+type(#c_tuple{}) -> tuple;
+type(#c_values{}) -> values;
+type(#c_var{}) -> var.
+
+
+%% @spec is_leaf(Node::cerl()) -> boolean()
+%%
+%% @doc Returns <code>true</code> if <code>Node</code> is a leaf node,
+%% otherwise <code>false</code>. The current leaf node types are
+%% <code>literal</code> and <code>var</code>.
+%%
+%% <p>Note: all literals (cf. <code>is_literal/1</code>) are leaf
+%% nodes, even if they represent structured (constant) values such as
+%% <code>{foo, [bar, baz]}</code>. Also note that variables are leaf
+%% nodes but not literals.</p>
+%%
+%% @see type/1
+%% @see is_literal/1
+
+-spec is_leaf(cerl()) -> boolean().
+
+is_leaf(Node) ->
+ case type(Node) of
+ literal -> true;
+ var -> true;
+ _ -> false
+ end.
+
+
+%% @spec get_ann(cerl()) -> anns()
+%%
+%% @doc Returns the list of user annotations associated with a syntax
+%% tree node. For a newly created node, this is the empty list. The
+%% annotations may be any terms.
+%%
+%% @see set_ann/2
+
+-spec get_ann(cerl()) -> anns().
+
+get_ann(Node) ->
+ element(2, Node).
+
+
+%% @spec set_ann(Node::cerl(), Annotations::anns()) -> cerl()
+%%
+%% @doc Sets the list of user annotations of <code>Node</code> to
+%% <code>Annotations</code>.
+%%
+%% @see get_ann/1
+%% @see add_ann/2
+%% @see copy_ann/2
+
+-spec set_ann(cerl(), anns()) -> cerl().
+
+set_ann(Node, List) ->
+ setelement(2, Node, List).
+
+
+%% @spec add_ann(Annotations::anns(), Node::cerl()) -> cerl()
+%%
+%% @doc Appends <code>Annotations</code> to the list of user
+%% annotations of <code>Node</code>.
+%%
+%% <p>Note: this is equivalent to <code>set_ann(Node, Annotations ++
+%% get_ann(Node))</code>, but potentially more efficient.</p>
+%%
+%% @see get_ann/1
+%% @see set_ann/2
+
+-spec add_ann(anns(), cerl()) -> cerl().
+
+add_ann(Terms, Node) ->
+ set_ann(Node, Terms ++ get_ann(Node)).
+
+
+%% @spec copy_ann(Source::cerl(), Target::cerl()) -> cerl()
+%%
+%% @doc Copies the list of user annotations from <code>Source</code>
+%% to <code>Target</code>.
+%%
+%% <p>Note: this is equivalent to <code>set_ann(Target,
+%% get_ann(Source))</code>, but potentially more efficient.</p>
+%%
+%% @see get_ann/1
+%% @see set_ann/2
+
+-spec copy_ann(cerl(), cerl()) -> cerl().
+
+copy_ann(Source, Target) ->
+ set_ann(Target, get_ann(Source)).
+
+
+%% @spec abstract(Term::litval()) -> cerl()
+%%
+%% @doc Creates a syntax tree corresponding to an Erlang term.
+%% <code>Term</code> must be a literal term, i.e., one that can be
+%% represented as a source code literal. Thus, it may not contain a
+%% process identifier, port, reference or function value as a subterm.
+%%
+%% <p>Note: This is a constant time operation.</p>
+%%
+%% @see ann_abstract/2
+%% @see concrete/1
+%% @see is_literal/1
+%% @see is_literal_term/1
+
+-spec abstract(litval()) -> c_literal().
+
+abstract(T) ->
+ #c_literal{val = T}.
+
+
+%% @spec ann_abstract(Annotations::anns(), Term::litval()) -> cerl()
+%% @see abstract/1
+
+-spec ann_abstract(anns(), litval()) -> c_literal().
+
+ann_abstract(As, T) ->
+ #c_literal{val = T, anno = As}.
+
+
+%% @spec is_literal_term(Term::term()) -> boolean()
+%%
+%% @doc Returns <code>true</code> if <code>Term</code> can be
+%% represented as a literal, otherwise <code>false</code>. This
+%% function takes time proportional to the size of <code>Term</code>.
+%%
+%% @see abstract/1
+
+-spec is_literal_term(term()) -> boolean().
+
+is_literal_term(T) when is_integer(T) -> true;
+is_literal_term(T) when is_float(T) -> true;
+is_literal_term(T) when is_atom(T) -> true;
+is_literal_term([]) -> true;
+is_literal_term([H | T]) ->
+ is_literal_term(H) andalso is_literal_term(T);
+is_literal_term(T) when is_tuple(T) ->
+ is_literal_term_list(tuple_to_list(T));
+is_literal_term(B) when is_bitstring(B) -> true;
+is_literal_term(M) when is_map(M) ->
+ is_literal_term_list(maps:to_list(M));
+is_literal_term(_) ->
+ false.
+
+-spec is_literal_term_list([term()]) -> boolean().
+
+is_literal_term_list([T | Ts]) ->
+ case is_literal_term(T) of
+ true ->
+ is_literal_term_list(Ts);
+ false ->
+ false
+ end;
+is_literal_term_list([]) ->
+ true.
+
+
+%% @spec concrete(Node::c_literal()) -> litval()
+%%
+%% @doc Returns the Erlang term represented by a syntax tree. An
+%% exception is thrown if <code>Node</code> does not represent a
+%% literal term.
+%%
+%% <p>Note: This is a constant time operation.</p>
+%%
+%% @see abstract/1
+%% @see is_literal/1
+
+%% Because the normal tuple and list constructor operations always
+%% return a literal if the arguments are literals, 'concrete' and
+%% 'is_literal' never need to traverse the structure.
+
+-spec concrete(c_literal()) -> litval().
+
+concrete(#c_literal{val = V}) ->
+ V.
+
+
+%% @spec is_literal(Node::cerl()) -> boolean()
+%%
+%% @doc Returns <code>true</code> if <code>Node</code> represents a
+%% literal term, otherwise <code>false</code>. This function returns
+%% <code>true</code> if and only if the value of
+%% <code>concrete(Node)</code> is defined.
+%%
+%% <p>Note: This is a constant time operation.</p>
+%%
+%% @see abstract/1
+%% @see concrete/1
+%% @see fold_literal/1
+
+-spec is_literal(cerl()) -> boolean().
+
+is_literal(#c_literal{}) ->
+ true;
+is_literal(_) ->
+ false.
+
+
+%% @spec fold_literal(Node::cerl()) -> cerl()
+%%
+%% @doc Assures that literals have a compact representation. This is
+%% occasionally useful if <code>c_cons_skel/2</code>,
+%% <code>c_tuple_skel/1</code> or <code>unfold_literal/1</code> were
+%% used in the construction of <code>Node</code>, and you want to revert
+%% to the normal "folded" representation of literals. If
+%% <code>Node</code> represents a tuple or list constructor, its
+%% elements are rewritten recursively, and the node is reconstructed
+%% using <code>c_cons/2</code> or <code>c_tuple/1</code>, respectively;
+%% otherwise, <code>Node</code> is not changed.
+%%
+%% @see is_literal/1
+%% @see c_cons_skel/2
+%% @see c_tuple_skel/1
+%% @see c_cons/2
+%% @see c_tuple/1
+%% @see unfold_literal/1
+
+-spec fold_literal(cerl()) -> cerl().
+
+fold_literal(Node) ->
+ case type(Node) of
+ tuple ->
+ update_c_tuple(Node, fold_literal_list(tuple_es(Node)));
+ cons ->
+ update_c_cons(Node, fold_literal(cons_hd(Node)),
+ fold_literal(cons_tl(Node)));
+ _ ->
+ Node
+ end.
+
+fold_literal_list([E | Es]) ->
+ [fold_literal(E) | fold_literal_list(Es)];
+fold_literal_list([]) ->
+ [].
+
+
+%% @spec unfold_literal(Node::cerl()) -> cerl()
+%%
+%% @doc Assures that literals have a fully expanded representation. If
+%% <code>Node</code> represents a literal tuple or list constructor, its
+%% elements are rewritten recursively, and the node is reconstructed
+%% using <code>c_cons_skel/2</code> or <code>c_tuple_skel/1</code>,
+%% respectively; otherwise, <code>Node</code> is not changed. The {@link
+%% fold_literal/1} can be used to revert to the normal compact
+%% representation.
+%%
+%% @see is_literal/1
+%% @see c_cons_skel/2
+%% @see c_tuple_skel/1
+%% @see c_cons/2
+%% @see c_tuple/1
+%% @see fold_literal/1
+
+-spec unfold_literal(cerl()) -> cerl().
+
+unfold_literal(Node) ->
+ case type(Node) of
+ literal ->
+ copy_ann(Node, unfold_concrete(concrete(Node)));
+ _ ->
+ Node
+ end.
+
+unfold_concrete(Val) ->
+ case Val of
+ _ when is_tuple(Val) ->
+ c_tuple_skel(unfold_concrete_list(tuple_to_list(Val)));
+ [H|T] ->
+ c_cons_skel(unfold_concrete(H), unfold_concrete(T));
+ _ ->
+ abstract(Val)
+ end.
+
+unfold_concrete_list([E | Es]) ->
+ [unfold_concrete(E) | unfold_concrete_list(Es)];
+unfold_concrete_list([]) ->
+ [].
+
+
+%% ---------------------------------------------------------------------
+
+%% @spec c_module(Name::c_literal(), Exports, Definitions) -> c_module()
+%%
+%% Exports = [c_var()]
+%% Definitions = defs()
+%%
+%% @equiv c_module(Name, Exports, [], Definitions)
+
+-spec c_module(c_literal(), [c_var()], defs()) -> c_module().
+
+c_module(Name, Exports, Defs) ->
+ #c_module{name = Name, exports = Exports, attrs = [], defs = Defs}.
+
+
+%% @spec c_module(Name::c_literal(), Exports, Attributes, Definitions) ->
+%% c_module()
+%%
+%% Exports = [c_var()]
+%% Attributes = attrs()
+%% Definitions = defs()
+%%
+%% @doc Creates an abstract module definition. The result represents
+%% <pre>
+%% module <em>Name</em> [<em>E1</em>, ..., <em>Ek</em>]
+%% attributes [<em>K1</em> = <em>T1</em>, ...,
+%% <em>Km</em> = <em>Tm</em>]
+%% <em>V1</em> = <em>F1</em>
+%% ...
+%% <em>Vn</em> = <em>Fn</em>
+%% end</pre>
+%%
+%% if <code>Exports</code> = <code>[E1, ..., Ek]</code>,
+%% <code>Attributes</code> = <code>[{K1, T1}, ..., {Km, Tm}]</code>,
+%% and <code>Definitions</code> = <code>[{V1, F1}, ..., {Vn,
+%% Fn}]</code>.
+%%
+%% <p><code>Name</code> and all the <code>Ki</code> must be atom
+%% literals, and all the <code>Ti</code> must be constant literals. All
+%% the <code>Vi</code> and <code>Ei</code> must have type
+%% <code>var</code> and represent function names. All the
+%% <code>Fi</code> must have type <code>'fun'</code>.</p>
+%%
+%% @see c_module/3
+%% @see module_name/1
+%% @see module_exports/1
+%% @see module_attrs/1
+%% @see module_defs/1
+%% @see module_vars/1
+%% @see ann_c_module/4
+%% @see ann_c_module/5
+%% @see update_c_module/5
+%% @see c_atom/1
+%% @see c_var/1
+%% @see c_fun/2
+%% @see is_literal/1
+
+-spec c_module(c_literal(), [c_var()], attrs(), defs()) -> c_module().
+
+c_module(Name, Exports, Attrs, Defs) ->
+ #c_module{name = Name, exports = Exports, attrs = Attrs, defs = Defs}.
+
+
+%% @spec ann_c_module(As::anns(), Name::c_literal(), Exports,
+%% Definitions) -> c_module()
+%%
+%% Exports = [c_var()]
+%% Definitions = defs()
+%%
+%% @see c_module/3
+%% @see ann_c_module/5
+
+-spec ann_c_module(anns(), c_literal(), [c_var()], defs()) -> c_module().
+
+ann_c_module(As, Name, Exports, Defs) ->
+ #c_module{name = Name, exports = Exports, attrs = [], defs = Defs,
+ anno = As}.
+
+
+%% @spec ann_c_module(As::anns(), Name::c_literal(), Exports,
+%% Attributes, Definitions) -> c_module()
+%%
+%% Exports = [c_var()]
+%% Attributes = attrs()
+%% Definitions = defs()
+%%
+%% @see c_module/4
+%% @see ann_c_module/4
+
+-spec ann_c_module(anns(), c_literal(), [c_var()], attrs(), defs()) ->
+ c_module().
+
+ann_c_module(As, Name, Exports, Attrs, Defs) ->
+ #c_module{name = Name, exports = Exports, attrs = Attrs, defs = Defs,
+ anno = As}.
+
+
+%% @spec update_c_module(Old::cerl(), Name::c_literal(), Exports,
+%% Attributes, Definitions) -> c_module()
+%%
+%% Exports = [c_var()]
+%% Attributes = attrs()
+%% Definitions = defs()
+%%
+%% @see c_module/4
+
+-spec update_c_module(c_module(), c_literal(), [c_var()], attrs(), defs()) ->
+ c_module().
+
+update_c_module(Node, Name, Exports, Attrs, Defs) ->
+ #c_module{name = Name, exports = Exports, attrs = Attrs, defs = Defs,
+ anno = get_ann(Node)}.
+
+
+%% @spec is_c_module(Node::cerl()) -> boolean()
+%%
+%% @doc Returns <code>true</code> if <code>Node</code> is an abstract
+%% module definition, otherwise <code>false</code>.
+%%
+%% @see type/1
+
+-spec is_c_module(cerl()) -> boolean().
+
+is_c_module(#c_module{}) ->
+ true;
+is_c_module(_) ->
+ false.
+
+
+%% @spec module_name(Node::c_module()) -> c_literal()
+%%
+%% @doc Returns the name subtree of an abstract module definition.
+%%
+%% @see c_module/4
+
+-spec module_name(c_module()) -> c_literal().
+
+module_name(Node) ->
+ Node#c_module.name.
+
+
+%% @spec module_exports(Node::c_module()) -> [c_var()]
+%%
+%% @doc Returns the list of exports subtrees of an abstract module
+%% definition.
+%%
+%% @see c_module/4
+
+-spec module_exports(c_module()) -> [c_var()].
+
+module_exports(Node) ->
+ Node#c_module.exports.
+
+
+%% @spec module_attrs(Node::c_module()) -> [{cerl(), cerl()}]
+%%
+%% @doc Returns the list of pairs of attribute key/value subtrees of
+%% an abstract module definition.
+%%
+%% @see c_module/4
+
+-spec module_attrs(c_module()) -> attrs().
+
+module_attrs(Node) ->
+ Node#c_module.attrs.
+
+
+%% @spec module_defs(Node::c_module()) -> defs()
+%%
+%% @doc Returns the list of function definitions of an abstract module
+%% definition.
+%%
+%% @see c_module/4
+
+-spec module_defs(c_module()) -> defs().
+
+module_defs(Node) ->
+ Node#c_module.defs.
+
+
+%% @spec module_vars(Node::c_module()) -> [c_var()]
+%%
+%% @doc Returns the list of left-hand side function variable subtrees
+%% of an abstract module definition.
+%%
+%% @see c_module/4
+
+-spec module_vars(c_module()) -> [c_var()].
+
+module_vars(Node) ->
+ [F || {F, _} <- module_defs(Node)].
+
+
+%% ---------------------------------------------------------------------
+
+%% @spec c_int(Value::integer()) -> c_literal()
+%%
+%% @doc Creates an abstract integer literal. The lexical
+%% representation is the canonical decimal numeral of
+%% <code>Value</code>.
+%%
+%% @see ann_c_int/2
+%% @see is_c_int/1
+%% @see int_val/1
+%% @see int_lit/1
+%% @see c_char/1
+
+-spec c_int(integer()) -> c_literal().
+
+c_int(Value) ->
+ #c_literal{val = Value}.
+
+
+%% @spec ann_c_int(As::anns(), Value::integer()) -> c_literal()
+%% @see c_int/1
+
+-spec ann_c_int(anns(), integer()) -> c_literal().
+
+ann_c_int(As, Value) ->
+ #c_literal{val = Value, anno = As}.
+
+
+%% @spec is_c_int(Node::cerl()) -> boolean()
+%%
+%% @doc Returns <code>true</code> if <code>Node</code> represents an
+%% integer literal, otherwise <code>false</code>.
+%% @see c_int/1
+
+-spec is_c_int(cerl()) -> boolean().
+
+is_c_int(#c_literal{val = V}) when is_integer(V) ->
+ true;
+is_c_int(_) ->
+ false.
+
+
+%% @spec int_val(c_literal()) -> integer()
+%%
+%% @doc Returns the value represented by an integer literal node.
+%% @see c_int/1
+
+-spec int_val(c_literal()) -> integer().
+
+int_val(Node) ->
+ Node#c_literal.val.
+
+
+%% @spec int_lit(c_literal()) -> string()
+%%
+%% @doc Returns the numeral string represented by an integer literal
+%% node.
+%% @see c_int/1
+
+-spec int_lit(c_literal()) -> string().
+
+int_lit(Node) ->
+ integer_to_list(int_val(Node)).
+
+
+%% ---------------------------------------------------------------------
+
+%% @spec c_float(Value::float()) -> c_literal()
+%%
+%% @doc Creates an abstract floating-point literal. The lexical
+%% representation is the decimal floating-point numeral of
+%% <code>Value</code>.
+%%
+%% @see ann_c_float/2
+%% @see is_c_float/1
+%% @see float_val/1
+%% @see float_lit/1
+
+%% Note that not all floating-point numerals can be represented with
+%% full precision.
+
+-spec c_float(float()) -> c_literal().
+
+c_float(Value) ->
+ #c_literal{val = Value}.
+
+
+%% @spec ann_c_float(As::anns(), Value::float()) -> c_literal()
+%% @see c_float/1
+
+-spec ann_c_float(anns(), float()) -> c_literal().
+
+ann_c_float(As, Value) ->
+ #c_literal{val = Value, anno = As}.
+
+
+%% @spec is_c_float(Node::cerl()) -> boolean()
+%%
+%% @doc Returns <code>true</code> if <code>Node</code> represents a
+%% floating-point literal, otherwise <code>false</code>.
+%% @see c_float/1
+
+-spec is_c_float(cerl()) -> boolean().
+
+is_c_float(#c_literal{val = V}) when is_float(V) ->
+ true;
+is_c_float(_) ->
+ false.
+
+
+%% @spec float_val(c_literal()) -> float()
+%%
+%% @doc Returns the value represented by a floating-point literal
+%% node.
+%% @see c_float/1
+
+-spec float_val(c_literal()) -> float().
+
+float_val(Node) ->
+ Node#c_literal.val.
+
+
+%% @spec float_lit(c_literal()) -> string()
+%%
+%% @doc Returns the numeral string represented by a floating-point
+%% literal node.
+%% @see c_float/1
+
+-spec float_lit(c_literal()) -> string().
+
+float_lit(Node) ->
+ float_to_list(float_val(Node)).
+
+
+%% ---------------------------------------------------------------------
+
+%% @spec c_atom(Name) -> c_literal()
+%% Name = atom() | string()
+%%
+%% @doc Creates an abstract atom literal. The print name of the atom
+%% is the character sequence represented by <code>Name</code>.
+%%
+%% <p>Note: passing a string as argument to this function causes a
+%% corresponding atom to be created for the internal representation.</p>
+%%
+%% @see ann_c_atom/2
+%% @see is_c_atom/1
+%% @see atom_val/1
+%% @see atom_name/1
+%% @see atom_lit/1
+
+-spec c_atom(atom() | string()) -> c_literal().
+
+c_atom(Name) when is_atom(Name) ->
+ #c_literal{val = Name};
+c_atom(Name) ->
+ #c_literal{val = list_to_atom(Name)}.
+
+
+%% @spec ann_c_atom(As::anns(), Name) -> cerl()
+%% Name = atom() | string()
+%% @see c_atom/1
+
+-spec ann_c_atom(anns(), atom() | string()) -> c_literal().
+
+ann_c_atom(As, Name) when is_atom(Name) ->
+ #c_literal{val = Name, anno = As};
+ann_c_atom(As, Name) ->
+ #c_literal{val = list_to_atom(Name), anno = As}.
+
+
+%% @spec is_c_atom(Node::cerl()) -> boolean()
+%%
+%% @doc Returns <code>true</code> if <code>Node</code> represents an
+%% atom literal, otherwise <code>false</code>.
+%%
+%% @see c_atom/1
+
+-spec is_c_atom(cerl()) -> boolean().
+
+is_c_atom(#c_literal{val = V}) when is_atom(V) ->
+ true;
+is_c_atom(_) ->
+ false.
+
+%% @spec atom_val(c_literal()) -> atom()
+%%
+%% @doc Returns the value represented by an abstract atom.
+%%
+%% @see c_atom/1
+
+-spec atom_val(c_literal()) -> atom().
+
+atom_val(Node) ->
+ Node#c_literal.val.
+
+
+%% @spec atom_name(c_literal()) -> string()
+%%
+%% @doc Returns the printname of an abstract atom.
+%%
+%% @see c_atom/1
+
+-spec atom_name(c_literal()) -> string().
+
+atom_name(Node) ->
+ atom_to_list(atom_val(Node)).
+
+
+%% @spec atom_lit(cerl()) -> string()
+%%
+%% @doc Returns the literal string represented by an abstract
+%% atom. This always includes surrounding single-quote characters.
+%%
+%% <p>Note that an abstract atom may have several literal
+%% representations, and that the representation yielded by this
+%% function is not fixed; e.g.,
+%% <code>atom_lit(c_atom("a\012b"))</code> could yield the string
+%% <code>"\'a\\nb\'"</code>.</p>
+%%
+%% @see c_atom/1
+
+%% TODO: replace the use of the unofficial 'write_string/2'.
+
+-spec atom_lit(cerl()) -> nonempty_string().
+
+atom_lit(Node) ->
+ io_lib:write_string(atom_name(Node), $'). %' stupid Emacs.
+
+
+%% ---------------------------------------------------------------------
+
+%% @spec c_char(Value) -> c_literal()
+%%
+%% Value = char() | integer()
+%%
+%% @doc Creates an abstract character literal. If the local
+%% implementation of Erlang defines <code>char()</code> as a subset of
+%% <code>integer()</code>, this function is equivalent to
+%% <code>c_int/1</code>. Otherwise, if the given value is an integer,
+%% it will be converted to the character with the corresponding
+%% code. The lexical representation of a character is
+%% "<code>$<em>Char</em></code>", where <code>Char</code> is a single
+%% printing character or an escape sequence.
+%%
+%% @see c_int/1
+%% @see c_string/1
+%% @see ann_c_char/2
+%% @see is_c_char/1
+%% @see char_val/1
+%% @see char_lit/1
+%% @see is_print_char/1
+
+-spec c_char(non_neg_integer()) -> c_literal().
+
+c_char(Value) when is_integer(Value), Value >= 0 ->
+ #c_literal{val = Value}.
+
+
+%% @spec ann_c_char(As::anns(), Value::char()) -> c_literal()
+%% @see c_char/1
+
+-spec ann_c_char(anns(), char()) -> c_literal().
+
+ann_c_char(As, Value) ->
+ #c_literal{val = Value, anno = As}.
+
+
+%% @spec is_c_char(Node::c_literal()) -> boolean()
+%%
+%% @doc Returns <code>true</code> if <code>Node</code> may represent a
+%% character literal, otherwise <code>false</code>.
+%%
+%% <p>If the local implementation of Erlang defines
+%% <code>char()</code> as a subset of <code>integer()</code>, then
+%% <code>is_c_int(<em>Node</em>)</code> will also yield
+%% <code>true</code>.</p>
+%%
+%% @see c_char/1
+%% @see is_print_char/1
+
+-spec is_c_char(c_literal()) -> boolean().
+
+is_c_char(#c_literal{val = V}) when is_integer(V), V >= 0 ->
+ is_char_value(V);
+is_c_char(_) ->
+ false.
+
+
+%% @spec is_print_char(Node::cerl()) -> boolean()
+%%
+%% @doc Returns <code>true</code> if <code>Node</code> may represent a
+%% "printing" character, otherwise <code>false</code>. (Cf.
+%% <code>is_c_char/1</code>.) A "printing" character has either a
+%% given graphical representation, or a "named" escape sequence such
+%% as "<code>\n</code>". Currently, only ISO 8859-1 (Latin-1)
+%% character values are recognized.
+%%
+%% @see c_char/1
+%% @see is_c_char/1
+
+-spec is_print_char(cerl()) -> boolean().
+
+is_print_char(#c_literal{val = V}) when is_integer(V), V >= 0 ->
+ is_print_char_value(V);
+is_print_char(_) ->
+ false.
+
+
+%% @spec char_val(c_literal()) -> char()
+%%
+%% @doc Returns the value represented by an abstract character literal.
+%%
+%% @see c_char/1
+
+-spec char_val(c_literal()) -> char().
+
+char_val(Node) ->
+ Node#c_literal.val.
+
+
+%% @spec char_lit(c_literal()) -> string()
+%%
+%% @doc Returns the literal string represented by an abstract
+%% character. This includes a leading <code>$</code>
+%% character. Currently, all characters that are not in the set of ISO
+%% 8859-1 (Latin-1) "printing" characters will be escaped.
+%%
+%% @see c_char/1
+
+-spec char_lit(c_literal()) -> nonempty_string().
+
+char_lit(Node) ->
+ io_lib:write_char(char_val(Node)).
+
+
+%% ---------------------------------------------------------------------
+
+%% @spec c_string(Value::string()) -> c_literal()
+%%
+%% @doc Creates an abstract string literal. Equivalent to creating an
+%% abstract list of the corresponding character literals
+%% (cf. <code>is_c_string/1</code>), but is typically more
+%% efficient. The lexical representation of a string is
+%% "<code>"<em>Chars</em>"</code>", where <code>Chars</code> is a
+%% sequence of printing characters or spaces.
+%%
+%% @see c_char/1
+%% @see ann_c_string/2
+%% @see is_c_string/1
+%% @see string_val/1
+%% @see string_lit/1
+%% @see is_print_string/1
+
+-spec c_string(string()) -> c_literal().
+
+c_string(Value) ->
+ #c_literal{val = Value}.
+
+
+%% @spec ann_c_string(As::anns(), Value::string()) -> c_literal()
+%% @see c_string/1
+
+-spec ann_c_string(anns(), string()) -> c_literal().
+
+ann_c_string(As, Value) ->
+ #c_literal{val = Value, anno = As}.
+
+
+%% @spec is_c_string(Node::cerl()) -> boolean()
+%%
+%% @doc Returns <code>true</code> if <code>Node</code> may represent a
+%% string literal, otherwise <code>false</code>. Strings are defined
+%% as lists of characters; see <code>is_c_char/1</code> for details.
+%%
+%% @see c_string/1
+%% @see is_c_char/1
+%% @see is_print_string/1
+
+-spec is_c_string(cerl()) -> boolean().
+
+is_c_string(#c_literal{val = V}) ->
+ is_char_list(V);
+is_c_string(_) ->
+ false.
+
+
+%% @spec is_print_string(Node::cerl()) -> boolean()
+%%
+%% @doc Returns <code>true</code> if <code>Node</code> may represent a
+%% string literal containing only "printing" characters, otherwise
+%% <code>false</code>. See <code>is_c_string/1</code> and
+%% <code>is_print_char/1</code> for details. Currently, only ISO
+%% 8859-1 (Latin-1) character values are recognized.
+%%
+%% @see c_string/1
+%% @see is_c_string/1
+%% @see is_print_char/1
+
+-spec is_print_string(cerl()) -> boolean().
+
+is_print_string(#c_literal{val = V}) ->
+ is_print_char_list(V);
+is_print_string(_) ->
+ false.
+
+
+%% @spec string_val(cerl()) -> string()
+%%
+%% @doc Returns the value represented by an abstract string literal.
+%%
+%% @see c_string/1
+
+-spec string_val(c_literal()) -> string().
+
+string_val(Node) ->
+ Node#c_literal.val.
+
+
+%% @spec string_lit(cerl()) -> string()
+%%
+%% @doc Returns the literal string represented by an abstract string.
+%% This includes surrounding double-quote characters
+%% <code>"..."</code>. Currently, characters that are not in the set
+%% of ISO 8859-1 (Latin-1) "printing" characters will be escaped,
+%% except for spaces.
+%%
+%% @see c_string/1
+
+-spec string_lit(c_literal()) -> nonempty_string().
+
+string_lit(Node) ->
+ io_lib:write_string(string_val(Node)).
+
+
+%% ---------------------------------------------------------------------
+
+%% @spec c_nil() -> cerl()
+%%
+%% @doc Creates an abstract empty list. The result represents
+%% "<code>[]</code>". The empty list is traditionally called "nil".
+%%
+%% @see ann_c_nil/1
+%% @see is_c_list/1
+%% @see c_cons/2
+
+-spec c_nil() -> c_literal().
+
+c_nil() ->
+ #c_literal{val = []}.
+
+
+%% @spec ann_c_nil(As::anns()) -> cerl()
+%% @see c_nil/0
+
+-spec ann_c_nil(anns()) -> c_literal().
+
+ann_c_nil(As) ->
+ #c_literal{val = [], anno = As}.
+
+
+%% @spec is_c_nil(Node::cerl()) -> boolean()
+%%
+%% @doc Returns <code>true</code> if <code>Node</code> is an abstract
+%% empty list, otherwise <code>false</code>.
+
+-spec is_c_nil(cerl()) -> boolean().
+
+is_c_nil(#c_literal{val = []}) ->
+ true;
+is_c_nil(_) ->
+ false.
+
+
+%% ---------------------------------------------------------------------
+
+%% @spec c_cons(Head::cerl(), Tail::cerl()) -> cerl()
+%%
+%% @doc Creates an abstract list constructor. The result represents
+%% "<code>[<em>Head</em> | <em>Tail</em>]</code>". Note that if both
+%% <code>Head</code> and <code>Tail</code> have type
+%% <code>literal</code>, then the result will also have type
+%% <code>literal</code>, and annotations on <code>Head</code> and
+%% <code>Tail</code> are lost.
+%%
+%% <p>Recall that in Erlang, the tail element of a list constructor is
+%% not necessarily a list.</p>
+%%
+%% @see ann_c_cons/3
+%% @see update_c_cons/3
+%% @see c_cons_skel/2
+%% @see is_c_cons/1
+%% @see cons_hd/1
+%% @see cons_tl/1
+%% @see is_c_list/1
+%% @see c_nil/0
+%% @see list_elements/1
+%% @see list_length/1
+%% @see make_list/2
+
+%% *Always* collapse literals.
+
+-spec c_cons(cerl(), cerl()) -> c_literal() | c_cons().
+
+c_cons(#c_literal{val = Head}, #c_literal{val = Tail}) ->
+ #c_literal{val = [Head | Tail]};
+c_cons(Head, Tail) ->
+ #c_cons{hd = Head, tl = Tail}.
+
+
+%% @spec ann_c_cons(As::anns(), Head::cerl(), Tail::cerl()) -> cerl()
+%% @see c_cons/2
+
+-spec ann_c_cons(anns(), cerl(), cerl()) -> c_literal() | c_cons().
+
+ann_c_cons(As, #c_literal{val = Head}, #c_literal{val = Tail}) ->
+ #c_literal{val = [Head | Tail], anno = As};
+ann_c_cons(As, Head, Tail) ->
+ #c_cons{hd = Head, tl = Tail, anno = As}.
+
+
+%% @spec update_c_cons(Old::cerl(), Head::cerl(), Tail::cerl()) ->
+%% cerl()
+%% @see c_cons/2
+
+-spec update_c_cons(c_literal() | c_cons(), cerl(), cerl()) ->
+ c_literal() | c_cons().
+
+update_c_cons(Node, #c_literal{val = Head}, #c_literal{val = Tail}) ->
+ #c_literal{val = [Head | Tail], anno = get_ann(Node)};
+update_c_cons(Node, Head, Tail) ->
+ #c_cons{hd = Head, tl = Tail, anno = get_ann(Node)}.
+
+
+%% @spec c_cons_skel(Head::cerl(), Tail::cerl()) -> c_cons()
+%%
+%% @doc Creates an abstract list constructor skeleton. Does not fold
+%% constant literals, i.e., the result always has type
+%% <code>cons</code>, representing "<code>[<em>Head</em> |
+%% <em>Tail</em>]</code>".
+%%
+%% <p>This function is occasionally useful when it is necessary to have
+%% annotations on the subnodes of a list constructor node, even when the
+%% subnodes are constant literals. Note however that
+%% <code>is_literal/1</code> will yield <code>false</code> and
+%% <code>concrete/1</code> will fail if passed the result from this
+%% function.</p>
+%%
+%% <p><code>fold_literal/1</code> can be used to revert a node to the
+%% normal-form representation.</p>
+%%
+%% @see ann_c_cons_skel/3
+%% @see update_c_cons_skel/3
+%% @see c_cons/2
+%% @see is_c_cons/1
+%% @see is_c_list/1
+%% @see c_nil/0
+%% @see is_literal/1
+%% @see fold_literal/1
+%% @see concrete/1
+
+%% *Never* collapse literals.
+
+-spec c_cons_skel(cerl(), cerl()) -> c_cons().
+
+c_cons_skel(Head, Tail) ->
+ #c_cons{hd = Head, tl = Tail}.
+
+
+%% @spec ann_c_cons_skel(As::anns(), Head::cerl(), Tail::cerl()) ->
+%% c_cons()
+%% @see c_cons_skel/2
+
+-spec ann_c_cons_skel(anns(), cerl(), cerl()) -> c_cons().
+
+ann_c_cons_skel(As, Head, Tail) ->
+ #c_cons{hd = Head, tl = Tail, anno = As}.
+
+
+%% @spec update_c_cons_skel(Old::cerl(), Head::cerl(), Tail::cerl()) ->
+%% c_cons()
+%% @see c_cons_skel/2
+
+-spec update_c_cons_skel(c_cons() | c_literal(), cerl(), cerl()) -> c_cons().
+
+update_c_cons_skel(Node, Head, Tail) ->
+ #c_cons{hd = Head, tl = Tail, anno = get_ann(Node)}.
+
+
+%% @spec is_c_cons(Node::cerl()) -> boolean()
+%%
+%% @doc Returns <code>true</code> if <code>Node</code> is an abstract
+%% list constructor, otherwise <code>false</code>.
+
+-spec is_c_cons(cerl()) -> boolean().
+
+is_c_cons(#c_cons{}) ->
+ true;
+is_c_cons(#c_literal{val = [_ | _]}) ->
+ true;
+is_c_cons(_) ->
+ false.
+
+
+%% @spec cons_hd(cerl()) -> cerl()
+%%
+%% @doc Returns the head subtree of an abstract list constructor.
+%%
+%% @see c_cons/2
+
+-spec cons_hd(c_cons() | c_literal()) -> cerl().
+
+cons_hd(#c_cons{hd = Head}) ->
+ Head;
+cons_hd(#c_literal{val = [Head | _]}) ->
+ #c_literal{val = Head}.
+
+
+%% @spec cons_tl(c_cons() | c_literal()) -> cerl()
+%%
+%% @doc Returns the tail subtree of an abstract list constructor.
+%%
+%% <p>Recall that the tail does not necessarily represent a proper
+%% list.</p>
+%%
+%% @see c_cons/2
+
+-spec cons_tl(c_cons() | c_literal()) -> cerl().
+
+cons_tl(#c_cons{tl = Tail}) ->
+ Tail;
+cons_tl(#c_literal{val = [_ | Tail]}) ->
+ #c_literal{val = Tail}.
+
+
+%% @spec is_c_list(Node::cerl()) -> boolean()
+%%
+%% @doc Returns <code>true</code> if <code>Node</code> represents a
+%% proper list, otherwise <code>false</code>. A proper list is either
+%% the empty list <code>[]</code>, or a cons cell <code>[<em>Head</em> |
+%% <em>Tail</em>]</code>, where recursively <code>Tail</code> is a
+%% proper list.
+%%
+%% <p>Note: Because <code>Node</code> is a syntax tree, the actual
+%% run-time values corresponding to its subtrees may often be partially
+%% or completely unknown. Thus, if <code>Node</code> represents e.g.
+%% "<code>[... | Ns]</code>" (where <code>Ns</code> is a variable), then
+%% the function will return <code>false</code>, because it is not known
+%% whether <code>Ns</code> will be bound to a list at run-time. If
+%% <code>Node</code> instead represents e.g. "<code>[1, 2, 3]</code>" or
+%% "<code>[A | []]</code>", then the function will return
+%% <code>true</code>.</p>
+%%
+%% @see c_cons/2
+%% @see c_nil/0
+%% @see list_elements/1
+%% @see list_length/1
+
+-spec is_c_list(cerl()) -> boolean().
+
+is_c_list(#c_cons{tl = Tail}) ->
+ is_c_list(Tail);
+is_c_list(#c_literal{val = V}) ->
+ is_proper_list(V);
+is_c_list(_) ->
+ false.
+
+is_proper_list([_ | Tail]) ->
+ is_proper_list(Tail);
+is_proper_list([]) ->
+ true;
+is_proper_list(_) ->
+ false.
+
+%% @spec list_elements(c_cons() | c_literal()) -> [cerl()]
+%%
+%% @doc Returns the list of element subtrees of an abstract list.
+%% <code>Node</code> must represent a proper list. E.g., if
+%% <code>Node</code> represents "<code>[<em>X1</em>, <em>X2</em> |
+%% [<em>X3</em>, <em>X4</em> | []]</code>", then
+%% <code>list_elements(Node)</code> yields the list <code>[X1, X2, X3,
+%% X4]</code>.
+%%
+%% @see c_cons/2
+%% @see c_nil/0
+%% @see is_c_list/1
+%% @see list_length/1
+%% @see make_list/2
+
+-spec list_elements(c_cons() | c_literal()) -> [cerl()].
+
+list_elements(#c_cons{hd = Head, tl = Tail}) ->
+ [Head | list_elements(Tail)];
+list_elements(#c_literal{val = V}) ->
+ abstract_list(V).
+
+abstract_list([X | Xs]) ->
+ [abstract(X) | abstract_list(Xs)];
+abstract_list([]) ->
+ [].
+
+
+%% @spec list_length(Node::c_cons() | c_literal()) -> integer()
+%%
+%% @doc Returns the number of element subtrees of an abstract list.
+%% <code>Node</code> must represent a proper list. E.g., if
+%% <code>Node</code> represents "<code>[X1 | [X2, X3 | [X4, X5,
+%% X6]]]</code>", then <code>list_length(Node)</code> returns the
+%% integer 6.
+%%
+%% <p>Note: this is equivalent to
+%% <code>length(list_elements(Node))</code>, but potentially more
+%% efficient.</p>
+%%
+%% @see c_cons/2
+%% @see c_nil/0
+%% @see is_c_list/1
+%% @see list_elements/1
+
+-spec list_length(c_cons() | c_literal()) -> non_neg_integer().
+
+list_length(L) ->
+ list_length(L, 0).
+
+list_length(#c_cons{tl = Tail}, A) ->
+ list_length(Tail, A + 1);
+list_length(#c_literal{val = V}, A) ->
+ A + length(V).
+
+
+%% @spec make_list(List) -> Node
+%% @equiv make_list(List, none)
+
+-spec make_list([cerl()]) -> cerl().
+
+make_list(List) ->
+ ann_make_list([], List).
+
+
+%% @spec make_list(List::[cerl()], Tail) -> cerl()
+%%
+%% Tail = cerl() | none
+%%
+%% @doc Creates an abstract list from the elements in <code>List</code>
+%% and the optional <code>Tail</code>. If <code>Tail</code> is
+%% <code>none</code>, the result will represent a nil-terminated list,
+%% otherwise it represents "<code>[... | <em>Tail</em>]</code>".
+%%
+%% @see c_cons/2
+%% @see c_nil/0
+%% @see ann_make_list/3
+%% @see update_list/3
+%% @see list_elements/1
+
+-spec make_list([cerl()], cerl() | 'none') -> cerl().
+
+make_list(List, Tail) ->
+ ann_make_list([], List, Tail).
+
+
+%% @spec update_list(Old::cerl(), List::[cerl()]) -> cerl()
+%% @equiv update_list(Old, List, none)
+
+-spec update_list(cerl(), [cerl()]) -> cerl().
+
+update_list(Node, List) ->
+ ann_make_list(get_ann(Node), List).
+
+
+%% @spec update_list(Old::cerl(), List::[cerl()], Tail) -> cerl()
+%%
+%% Tail = cerl() | none
+%%
+%% @see make_list/2
+%% @see update_list/2
+
+-spec update_list(cerl(), [cerl()], cerl() | 'none') -> cerl().
+
+update_list(Node, List, Tail) ->
+ ann_make_list(get_ann(Node), List, Tail).
+
+
+%% @spec ann_make_list(As::anns(), List::[cerl()]) -> cerl()
+%% @equiv ann_make_list(As, List, none)
+
+-spec ann_make_list(anns(), [cerl()]) -> cerl().
+
+ann_make_list(As, List) ->
+ ann_make_list(As, List, none).
+
+
+%% @spec ann_make_list(As::anns(), List::[cerl()], Tail) -> cerl()
+%%
+%% Tail = cerl() | none
+%%
+%% @see make_list/2
+%% @see ann_make_list/2
+
+-spec ann_make_list(anns(), [cerl()], cerl() | 'none') -> cerl().
+
+ann_make_list(As, [H | T], Tail) ->
+ ann_c_cons(As, H, make_list(T, Tail)); % `c_cons' folds literals
+ann_make_list(As, [], none) ->
+ ann_c_nil(As);
+ann_make_list(_, [], Node) ->
+ Node.
+
+
+%% ---------------------------------------------------------------------
+%% maps
+
+%% @spec is_c_map(Node::cerl()) -> boolean()
+%%
+%% @doc Returns <code>true</code> if <code>Node</code> is an abstract
+%% map constructor, otherwise <code>false</code>.
+
+-spec is_c_map(cerl()) -> boolean().
+
+is_c_map(#c_map{}) ->
+ true;
+is_c_map(#c_literal{val = V}) when is_map(V) ->
+ true;
+is_c_map(_) ->
+ false.
+
+-spec map_es(c_map() | c_literal()) -> [c_map_pair()].
+
+map_es(#c_literal{anno=As,val=M}) when is_map(M) ->
+ [ann_c_map_pair(As,
+ #c_literal{anno=As,val='assoc'},
+ #c_literal{anno=As,val=K},
+ #c_literal{anno=As,val=V}) || {K,V} <- maps:to_list(M)];
+map_es(#c_map{es = Es}) ->
+ Es.
+
+-spec map_arg(c_map() | c_literal()) -> c_map() | c_literal().
+
+map_arg(#c_literal{anno=As,val=M}) when is_map(M) ->
+ #c_literal{anno=As,val=#{}};
+map_arg(#c_map{arg=M}) ->
+ M.
+
+-spec c_map([c_map_pair()]) -> c_map().
+
+c_map(Pairs) ->
+ ann_c_map([], Pairs).
+
+-spec c_map_pattern([c_map_pair()]) -> c_map().
+
+c_map_pattern(Pairs) ->
+ #c_map{es=Pairs, is_pat=true}.
+
+-spec ann_c_map_pattern([term()], [c_map_pair()]) -> c_map().
+
+ann_c_map_pattern(As, Pairs) ->
+ #c_map{anno=As, es=Pairs, is_pat=true}.
+
+-spec is_c_map_empty(c_map() | c_literal()) -> boolean().
+
+is_c_map_empty(#c_map{ es=[] }) -> true;
+is_c_map_empty(#c_literal{val=M}) when is_map(M),map_size(M) =:= 0 -> true;
+is_c_map_empty(_) -> false.
+
+-spec is_c_map_pattern(c_map()) -> boolean().
+
+is_c_map_pattern(#c_map{is_pat=IsPat}) ->
+ IsPat.
+
+-spec ann_c_map([term()], [c_map_pair()]) -> c_map() | c_literal().
+
+ann_c_map(As, Es) ->
+ ann_c_map(As, #c_literal{val=#{}}, Es).
+
+-spec ann_c_map(anns(), c_map() | c_literal(), [c_map_pair()]) -> c_map() | c_literal().
+
+ann_c_map(As, #c_literal{val=M}, Es) when is_map(M) ->
+ fold_map_pairs(As,Es,M);
+ann_c_map(As, M, Es) ->
+ #c_map{arg=M, es=Es, anno=As}.
+
+fold_map_pairs(As,[],M) -> #c_literal{anno=As,val=M};
+%% M#{ K => V}
+fold_map_pairs(As,[#c_map_pair{op=#c_literal{val=assoc},key=Ck,val=Cv}=E|Es],M) ->
+ case is_lit_list([Ck,Cv]) of
+ true ->
+ [K,V] = lit_list_vals([Ck,Cv]),
+ fold_map_pairs(As,Es,maps:put(K,V,M));
+ false ->
+ #c_map{arg=#c_literal{val=M,anno=As}, es=[E|Es], anno=As}
+ end;
+%% M#{ K := V}
+fold_map_pairs(As,[#c_map_pair{op=#c_literal{val=exact},key=Ck,val=Cv}=E|Es],M) ->
+ case is_lit_list([Ck,Cv]) of
+ true ->
+ [K,V] = lit_list_vals([Ck,Cv]),
+ case maps:is_key(K,M) of
+ true -> fold_map_pairs(As,Es,maps:put(K,V,M));
+ false ->
+ #c_map{arg=#c_literal{val=M,anno=As}, es=[E|Es], anno=As }
+ end;
+ false ->
+ #c_map{arg=#c_literal{val=M,anno=As}, es=[E|Es], anno=As }
+ end.
+
+-spec update_c_map(c_map(), cerl(), [cerl()]) -> c_map() | c_literal().
+
+update_c_map(#c_map{is_pat=true}=Old, M, Es) ->
+ Old#c_map{arg=M, es=Es};
+update_c_map(#c_map{is_pat=false}=Old, M, Es) ->
+ ann_c_map(get_ann(Old), M, Es).
+
+map_pair_key(#c_map_pair{key=K}) -> K.
+map_pair_val(#c_map_pair{val=V}) -> V.
+map_pair_op(#c_map_pair{op=Op}) -> Op.
+
+-spec c_map_pair(cerl(), cerl()) -> c_map_pair().
+
+c_map_pair(Key,Val) ->
+ #c_map_pair{op=#c_literal{val=assoc},key=Key,val=Val}.
+
+-spec c_map_pair_exact(cerl(), cerl()) -> c_map_pair().
+
+c_map_pair_exact(Key,Val) ->
+ #c_map_pair{op=#c_literal{val=exact},key=Key,val=Val}.
+
+-spec ann_c_map_pair(anns(), cerl(), cerl(), cerl()) ->
+ c_map_pair().
+
+ann_c_map_pair(As,Op,K,V) ->
+ #c_map_pair{op = Op, key = K, val = V, anno = As}.
+
+update_c_map_pair(Old,Op,K,V) ->
+ #c_map_pair{op = Op, key = K, val = V, anno = get_ann(Old)}.
+
+
+%% ---------------------------------------------------------------------
+
+%% @spec c_tuple(Elements::[cerl()]) -> cerl()
+%%
+%% @doc Creates an abstract tuple. If <code>Elements</code> is
+%% <code>[E1, ..., En]</code>, the result represents
+%% "<code>{<em>E1</em>, ..., <em>En</em>}</code>". Note that if all
+%% nodes in <code>Elements</code> have type <code>literal</code>, or if
+%% <code>Elements</code> is empty, then the result will also have type
+%% <code>literal</code> and annotations on nodes in
+%% <code>Elements</code> are lost.
+%%
+%% <p>Recall that Erlang has distinct 1-tuples, i.e., <code>{X}</code>
+%% is always distinct from <code>X</code> itself.</p>
+%%
+%% @see ann_c_tuple/2
+%% @see update_c_tuple/2
+%% @see is_c_tuple/1
+%% @see tuple_es/1
+%% @see tuple_arity/1
+%% @see c_tuple_skel/1
+
+%% *Always* collapse literals.
+
+-spec c_tuple([cerl()]) -> c_tuple() | c_literal().
+
+c_tuple(Es) ->
+ case is_lit_list(Es) of
+ false ->
+ #c_tuple{es = Es};
+ true ->
+ #c_literal{val = list_to_tuple(lit_list_vals(Es))}
+ end.
+
+
+%% @spec ann_c_tuple(As::anns(), Elements::[cerl()]) -> cerl()
+%% @see c_tuple/1
+
+-spec ann_c_tuple(anns(), [cerl()]) -> c_tuple() | c_literal().
+
+ann_c_tuple(As, Es) ->
+ case is_lit_list(Es) of
+ false ->
+ #c_tuple{es = Es, anno = As};
+ true ->
+ #c_literal{val = list_to_tuple(lit_list_vals(Es)), anno = As}
+ end.
+
+
+%% @spec update_c_tuple(Old::cerl(), Elements::[cerl()]) -> cerl()
+%% @see c_tuple/1
+
+-spec update_c_tuple(c_tuple() | c_literal(), [cerl()]) -> c_tuple() | c_literal().
+
+update_c_tuple(Node, Es) ->
+ case is_lit_list(Es) of
+ false ->
+ #c_tuple{es = Es, anno = get_ann(Node)};
+ true ->
+ #c_literal{val = list_to_tuple(lit_list_vals(Es)),
+ anno = get_ann(Node)}
+ end.
+
+
+%% @spec c_tuple_skel(Elements::[cerl()]) -> cerl()
+%%
+%% @doc Creates an abstract tuple skeleton. Does not fold constant
+%% literals, i.e., the result always has type <code>tuple</code>,
+%% representing "<code>{<em>E1</em>, ..., <em>En</em>}</code>", if
+%% <code>Elements</code> is <code>[E1, ..., En]</code>.
+%%
+%% <p>This function is occasionally useful when it is necessary to have
+%% annotations on the subnodes of a tuple node, even when all the
+%% subnodes are constant literals. Note however that
+%% <code>is_literal/1</code> will yield <code>false</code> and
+%% <code>concrete/1</code> will fail if passed the result from this
+%% function.</p>
+%%
+%% <p><code>fold_literal/1</code> can be used to revert a node to the
+%% normal-form representation.</p>
+%%
+%% @see ann_c_tuple_skel/2
+%% @see update_c_tuple_skel/2
+%% @see c_tuple/1
+%% @see tuple_es/1
+%% @see is_c_tuple/1
+%% @see is_literal/1
+%% @see fold_literal/1
+%% @see concrete/1
+
+%% *Never* collapse literals.
+
+-spec c_tuple_skel([cerl()]) -> c_tuple().
+
+c_tuple_skel(Es) ->
+ #c_tuple{es = Es}.
+
+
+%% @spec ann_c_tuple_skel(As::anns(), Elements::[cerl()]) -> cerl()
+%% @see c_tuple_skel/1
+
+-spec ann_c_tuple_skel(anns(), [cerl()]) -> c_tuple().
+
+ann_c_tuple_skel(As, Es) ->
+ #c_tuple{es = Es, anno = As}.
+
+
+%% @spec update_c_tuple_skel(Old::cerl(), Elements::[cerl()]) -> cerl()
+%% @see c_tuple_skel/1
+
+-spec update_c_tuple_skel(c_tuple(), [cerl()]) -> c_tuple().
+
+update_c_tuple_skel(Old, Es) ->
+ #c_tuple{es = Es, anno = get_ann(Old)}.
+
+
+%% @spec is_c_tuple(Node::cerl()) -> boolean()
+%%
+%% @doc Returns <code>true</code> if <code>Node</code> is an abstract
+%% tuple, otherwise <code>false</code>.
+%%
+%% @see c_tuple/1
+
+-spec is_c_tuple(cerl()) -> boolean().
+
+is_c_tuple(#c_tuple{}) ->
+ true;
+is_c_tuple(#c_literal{val = V}) when is_tuple(V) ->
+ true;
+is_c_tuple(_) ->
+ false.
+
+
+%% @spec tuple_es(cerl()) -> [cerl()]
+%%
+%% @doc Returns the list of element subtrees of an abstract tuple.
+%%
+%% @see c_tuple/1
+
+-spec tuple_es(c_tuple() | c_literal()) -> [cerl()].
+
+tuple_es(#c_tuple{es = Es}) ->
+ Es;
+tuple_es(#c_literal{val = V}) ->
+ make_lit_list(tuple_to_list(V)).
+
+
+%% @spec tuple_arity(Node::cerl()) -> integer()
+%%
+%% @doc Returns the number of element subtrees of an abstract tuple.
+%%
+%% <p>Note: this is equivalent to <code>length(tuple_es(Node))</code>,
+%% but potentially more efficient.</p>
+%%
+%% @see tuple_es/1
+%% @see c_tuple/1
+
+-spec tuple_arity(c_tuple() | c_literal()) -> non_neg_integer().
+
+tuple_arity(#c_tuple{es = Es}) ->
+ length(Es);
+tuple_arity(#c_literal{val = V}) when is_tuple(V) ->
+ tuple_size(V).
+
+
+%% ---------------------------------------------------------------------
+
+%% @spec c_var(Name::var_name()) -> cerl()
+%%
+%% var_name() = integer() | atom() | {atom(), arity()}
+%%
+%% @doc Creates an abstract variable. A variable is identified by its
+%% name, given by the <code>Name</code> parameter.
+%%
+%% <p>If a name is given by a single atom, it should either be a
+%% "simple" atom which does not need to be single-quoted in Erlang, or
+%% otherwise its print name should correspond to a proper Erlang
+%% variable, i.e., begin with an uppercase character or an
+%% underscore. Names on the form <code>{A, N}</code> represent
+%% function name variables "<code><em>A</em>/<em>N</em></code>"; these
+%% are special variables which may be bound only in the function
+%% definitions of a module or a <code>letrec</code>. They may not be
+%% bound in <code>let</code> expressions and cannot occur in clause
+%% patterns. The atom <code>A</code> in a function name may be any
+%% atom; the integer <code>N</code> must be nonnegative. The functions
+%% <code>c_fname/2</code> etc. are utilities for handling function
+%% name variables.</p>
+%%
+%% <p>When printing variable names, they must have the form of proper
+%% Core Erlang variables and function names. E.g., a name represented
+%% by an integer such as <code>42</code> could be formatted as
+%% "<code>_42</code>", an atom <code>'Xxx'</code> simply as
+%% "<code>Xxx</code>", and an atom <code>foo</code> as
+%% "<code>_foo</code>". However, one must assure that any two valid
+%% distinct names are never mapped to the same strings. Tuples such
+%% as <code>{foo, 2}</code> representing function names can simply by
+%% formatted as "<code>'foo'/2</code>", with no risk of conflicts.</p>
+%%
+%% @see ann_c_var/2
+%% @see update_c_var/2
+%% @see is_c_var/1
+%% @see var_name/1
+%% @see c_fname/2
+%% @see c_module/4
+%% @see c_letrec/2
+
+-spec c_var(var_name()) -> c_var().
+
+c_var(Name) ->
+ #c_var{name = Name}.
+
+
+%% @spec ann_c_var(As::anns(), Name::var_name()) -> c_var()
+%%
+%% @see c_var/1
+
+-spec ann_c_var(anns(), var_name()) -> c_var().
+
+ann_c_var(As, Name) ->
+ #c_var{name = Name, anno = As}.
+
+%% @spec update_c_var(Old::cerl(), Name::var_name()) -> c_var()
+%%
+%% @see c_var/1
+
+-spec update_c_var(c_var(), var_name()) -> c_var().
+
+update_c_var(Node, Name) ->
+ #c_var{name = Name, anno = get_ann(Node)}.
+
+
+%% @spec is_c_var(Node::cerl()) -> boolean()
+%%
+%% @doc Returns <code>true</code> if <code>Node</code> is an abstract
+%% variable, otherwise <code>false</code>.
+%%
+%% @see c_var/1
+
+-spec is_c_var(cerl()) -> boolean().
+
+is_c_var(#c_var{}) ->
+ true;
+is_c_var(_) ->
+ false.
+
+
+%% @spec c_fname(Name::atom(), Arity::arity()) -> c_var()
+%% @equiv c_var({Name, Arity})
+%% @see fname_id/1
+%% @see fname_arity/1
+%% @see is_c_fname/1
+%% @see ann_c_fname/3
+%% @see update_c_fname/3
+
+-spec c_fname(atom(), arity()) -> c_var().
+
+c_fname(Atom, Arity) ->
+ c_var({Atom, Arity}).
+
+
+%% @spec ann_c_fname(As::anns(), Name::atom(), Arity::arity()) -> c_var()
+%%
+%% @equiv ann_c_var(As, {Atom, Arity})
+%% @see c_fname/2
+
+-spec ann_c_fname(anns(), atom(), arity()) -> c_var().
+
+ann_c_fname(As, Atom, Arity) ->
+ ann_c_var(As, {Atom, Arity}).
+
+
+%% @spec update_c_fname(Old::c_var(), Name::atom()) -> c_var()
+%% @doc Like <code>update_c_fname/3</code>, but takes the arity from
+%% <code>Node</code>.
+%% @see update_c_fname/3
+%% @see c_fname/2
+
+-spec update_c_fname(c_var(), atom()) -> c_var().
+
+update_c_fname(#c_var{name = {_, Arity}, anno = As}, Atom) ->
+ #c_var{name = {Atom, Arity}, anno = As}.
+
+
+%% @spec update_c_fname(Old::var(), Name::atom(), Arity::arity()) -> c_var()
+%%
+%% @equiv update_c_var(Old, {Atom, Arity})
+%% @see update_c_fname/2
+%% @see c_fname/2
+
+-spec update_c_fname(c_var(), atom(), arity()) -> c_var().
+
+update_c_fname(Node, Atom, Arity) ->
+ update_c_var(Node, {Atom, Arity}).
+
+
+%% @spec is_c_fname(Node::cerl()) -> boolean()
+%%
+%% @doc Returns <code>true</code> if <code>Node</code> is an abstract
+%% function name variable, otherwise <code>false</code>.
+%%
+%% @see c_fname/2
+%% @see c_var/1
+%% @see var_name/1
+
+-spec is_c_fname(cerl()) -> boolean().
+
+is_c_fname(#c_var{name = {A, N}}) when is_atom(A), is_integer(N), N >= 0 ->
+ true;
+is_c_fname(_) ->
+ false.
+
+
+%% @spec var_name(c_var()) -> var_name()
+%%
+%% @doc Returns the name of an abstract variable.
+%%
+%% @see c_var/1
+
+-spec var_name(c_var()) -> var_name().
+
+var_name(Node) ->
+ Node#c_var.name.
+
+
+%% @spec fname_id(c_var()) -> atom()
+%%
+%% @doc Returns the identifier part of an abstract function name
+%% variable.
+%%
+%% @see fname_arity/1
+%% @see c_fname/2
+
+-spec fname_id(c_var()) -> atom().
+
+fname_id(#c_var{name={A,_}}) ->
+ A.
+
+
+%% @spec fname_arity(c_var()) -> arity()
+%%
+%% @doc Returns the arity part of an abstract function name variable.
+%%
+%% @see fname_id/1
+%% @see c_fname/2
+
+-spec fname_arity(c_var()) -> arity().
+
+fname_arity(#c_var{name={_,N}}) ->
+ N.
+
+
+%% ---------------------------------------------------------------------
+
+%% @spec c_values(Elements::[cerl()]) -> c_values()
+%%
+%% @doc Creates an abstract value list. If <code>Elements</code> is
+%% <code>[E1, ..., En]</code>, the result represents
+%% "<code>&lt;<em>E1</em>, ..., <em>En</em>&gt;</code>".
+%%
+%% @see ann_c_values/2
+%% @see update_c_values/2
+%% @see is_c_values/1
+%% @see values_es/1
+%% @see values_arity/1
+
+-spec c_values([cerl()]) -> c_values().
+
+c_values(Es) ->
+ #c_values{es = Es}.
+
+
+%% @spec ann_c_values(As::anns(), Elements::[cerl()]) -> c_values()
+%% @see c_values/1
+
+-spec ann_c_values(anns(), [cerl()]) -> c_values().
+
+ann_c_values(As, Es) ->
+ #c_values{es = Es, anno = As}.
+
+
+%% @spec update_c_values(Old::cerl(), Elements::[cerl()]) -> c_values()
+%% @see c_values/1
+
+-spec update_c_values(c_values(), [cerl()]) -> c_values().
+
+update_c_values(Node, Es) ->
+ #c_values{es = Es, anno = get_ann(Node)}.
+
+
+%% @spec is_c_values(Node::cerl()) -> boolean()
+%%
+%% @doc Returns <code>true</code> if <code>Node</code> is an abstract
+%% value list; otherwise <code>false</code>.
+%%
+%% @see c_values/1
+
+-spec is_c_values(cerl()) -> boolean().
+
+is_c_values(#c_values{}) ->
+ true;
+is_c_values(_) ->
+ false.
+
+
+%% @spec values_es(c_values()) -> [cerl()]
+%%
+%% @doc Returns the list of element subtrees of an abstract value
+%% list.
+%%
+%% @see c_values/1
+%% @see values_arity/1
+
+-spec values_es(c_values()) -> [cerl()].
+
+values_es(Node) ->
+ Node#c_values.es.
+
+
+%% @spec values_arity(Node::c_values()) -> non_neg_integer()
+%%
+%% @doc Returns the number of element subtrees of an abstract value
+%% list.
+%%
+%% <p>Note: This is equivalent to
+%% <code>length(values_es(Node))</code>, but potentially more
+%% efficient.</p>
+%%
+%% @see c_values/1
+%% @see values_es/1
+
+-spec values_arity(c_values()) -> non_neg_integer().
+
+values_arity(Node) ->
+ length(values_es(Node)).
+
+
+%% ---------------------------------------------------------------------
+
+%% @spec c_binary(Segments::[c_bitstr()]) -> c_binary()
+%%
+%% @doc Creates an abstract binary-template. A binary object is a
+%% sequence of 8-bit bytes. It is specified by zero or more bit-string
+%% template <em>segments</em> of arbitrary lengths (in number of bits),
+%% such that the sum of the lengths is evenly divisible by 8. If
+%% <code>Segments</code> is <code>[S1, ..., Sn]</code>, the result
+%% represents "<code>#{<em>S1</em>, ..., <em>Sn</em>}#</code>". All the
+%% <code>Si</code> must have type <code>bitstr</code>.
+%%
+%% @see ann_c_binary/2
+%% @see update_c_binary/2
+%% @see is_c_binary/1
+%% @see binary_segments/1
+%% @see c_bitstr/5
+
+-spec c_binary([c_bitstr()]) -> c_binary().
+
+c_binary(Segments) ->
+ #c_binary{segments = Segments}.
+
+
+%% @spec ann_c_binary(As::anns(), Segments::[c_bitstr()]) -> c_binary()
+%% @see c_binary/1
+
+-spec ann_c_binary(anns(), [c_bitstr()]) -> c_binary().
+
+ann_c_binary(As, Segments) ->
+ #c_binary{segments = Segments, anno = As}.
+
+
+%% @spec update_c_binary(Old::cerl(), Segments::[c_bitstr()]) -> cerl()
+%% @see c_binary/1
+
+-spec update_c_binary(c_binary(), [c_bitstr()]) -> c_binary().
+
+update_c_binary(Node, Segments) ->
+ #c_binary{segments = Segments, anno = get_ann(Node)}.
+
+
+%% @spec is_c_binary(Node::cerl()) -> boolean()
+%%
+%% @doc Returns <code>true</code> if <code>Node</code> is an abstract
+%% binary-template; otherwise <code>false</code>.
+%%
+%% @see c_binary/1
+
+-spec is_c_binary(cerl()) -> boolean().
+
+is_c_binary(#c_binary{}) ->
+ true;
+is_c_binary(_) ->
+ false.
+
+
+%% @spec binary_segments(cerl()) -> [c_bitstr()]
+%%
+%% @doc Returns the list of segment subtrees of an abstract
+%% binary-template.
+%%
+%% @see c_binary/1
+%% @see c_bitstr/5
+
+-spec binary_segments(c_binary()) -> [c_bitstr()].
+
+binary_segments(Node) ->
+ Node#c_binary.segments.
+
+
+%% @spec c_bitstr(Value::cerl(), Size::cerl(), Unit::cerl(),
+%% Type::cerl(), Flags::cerl()) -> c_bitstr()
+%%
+%% @doc Creates an abstract bit-string template. These can only occur as
+%% components of an abstract binary-template (see {@link c_binary/1}).
+%% The result represents "<code>#&lt;<em>Value</em>&gt;(<em>Size</em>,
+%% <em>Unit</em>, <em>Type</em>, <em>Flags</em>)</code>", where
+%% <code>Unit</code> must represent a positive integer constant,
+%% <code>Type</code> must represent a constant atom (one of
+%% <code>'integer'</code>, <code>'float'</code>, or
+%% <code>'binary'</code>), and <code>Flags</code> must represent a
+%% constant list <code>"[<em>F1</em>, ..., <em>Fn</em>]"</code> where
+%% all the <code>Fi</code> are atoms.
+%%
+%% @see c_binary/1
+%% @see ann_c_bitstr/6
+%% @see update_c_bitstr/6
+%% @see is_c_bitstr/1
+%% @see bitstr_val/1
+%% @see bitstr_size/1
+%% @see bitstr_unit/1
+%% @see bitstr_type/1
+%% @see bitstr_flags/1
+
+-spec c_bitstr(cerl(), cerl(), cerl(), cerl(), cerl()) -> c_bitstr().
+
+c_bitstr(Val, Size, Unit, Type, Flags) ->
+ #c_bitstr{val = Val, size = Size, unit = Unit, type = Type,
+ flags = Flags}.
+
+
+%% @spec c_bitstr(Value::cerl(), Size::cerl(), Type::cerl(),
+%% Flags::cerl()) -> c_bitstr()
+%% @equiv c_bitstr(Value, Size, abstract(1), Type, Flags)
+
+-spec c_bitstr(cerl(), cerl(), cerl(), cerl()) -> c_bitstr().
+
+c_bitstr(Val, Size, Type, Flags) ->
+ c_bitstr(Val, Size, abstract(1), Type, Flags).
+
+
+%% @spec c_bitstr(Value::cerl(), Type::cerl(),
+%% Flags::cerl()) -> c_bitstr()
+%% @equiv c_bitstr(Value, abstract(all), abstract(1), Type, Flags)
+
+-spec c_bitstr(cerl(), cerl(), cerl()) -> c_bitstr().
+
+c_bitstr(Val, Type, Flags) ->
+ c_bitstr(Val, abstract(all), abstract(1), Type, Flags).
+
+
+%% @spec ann_c_bitstr(As::anns(), Value::cerl(), Size::cerl(),
+%% Unit::cerl(), Type::cerl(), Flags::cerl()) -> cerl()
+%% @see c_bitstr/5
+%% @see ann_c_bitstr/5
+
+-spec ann_c_bitstr(anns(), cerl(), cerl(), cerl(), cerl(), cerl()) ->
+ c_bitstr().
+
+ann_c_bitstr(As, Val, Size, Unit, Type, Flags) ->
+ #c_bitstr{val = Val, size = Size, unit = Unit, type = Type,
+ flags = Flags, anno = As}.
+
+%% @spec ann_c_bitstr(As::anns(), Value::cerl(), Size::cerl(),
+%% Type::cerl(), Flags::cerl()) -> c_bitstr()
+%% @equiv ann_c_bitstr(As, Value, Size, abstract(1), Type, Flags)
+
+-spec ann_c_bitstr(anns(), cerl(), cerl(), cerl(), cerl()) -> c_bitstr().
+
+ann_c_bitstr(As, Value, Size, Type, Flags) ->
+ ann_c_bitstr(As, Value, Size, abstract(1), Type, Flags).
+
+
+%% @spec update_c_bitstr(Old::c_bitstr(), Value::cerl(), Size::cerl(),
+%% Unit::cerl(), Type::cerl(), Flags::cerl()) -> c_bitstr()
+%% @see c_bitstr/5
+%% @see update_c_bitstr/5
+
+-spec update_c_bitstr(c_bitstr(), cerl(), cerl(), cerl(), cerl(), cerl()) ->
+ c_bitstr().
+
+update_c_bitstr(Node, Val, Size, Unit, Type, Flags) ->
+ #c_bitstr{val = Val, size = Size, unit = Unit, type = Type,
+ flags = Flags, anno = get_ann(Node)}.
+
+
+%% @spec update_c_bitstr(Old::c_bitstr(), Value::cerl(), Size::cerl(),
+%% Type::cerl(), Flags::cerl()) -> c_bitstr()
+%% @equiv update_c_bitstr(Node, Value, Size, abstract(1), Type, Flags)
+
+-spec update_c_bitstr(c_bitstr(), cerl(), cerl(), cerl(), cerl()) -> c_bitstr().
+
+update_c_bitstr(Node, Value, Size, Type, Flags) ->
+ update_c_bitstr(Node, Value, Size, abstract(1), Type, Flags).
+
+%% @spec is_c_bitstr(Node::cerl()) -> boolean()
+%%
+%% @doc Returns <code>true</code> if <code>Node</code> is an abstract
+%% bit-string template; otherwise <code>false</code>.
+%%
+%% @see c_bitstr/5
+
+-spec is_c_bitstr(cerl()) -> boolean().
+
+is_c_bitstr(#c_bitstr{}) ->
+ true;
+is_c_bitstr(_) ->
+ false.
+
+
+%% @spec bitstr_val(c_bitstr()) -> cerl()
+%%
+%% @doc Returns the value subtree of an abstract bit-string template.
+%%
+%% @see c_bitstr/5
+
+-spec bitstr_val(c_bitstr()) -> cerl().
+
+bitstr_val(Node) ->
+ Node#c_bitstr.val.
+
+
+%% @spec bitstr_size(c_bitstr()) -> cerl()
+%%
+%% @doc Returns the size subtree of an abstract bit-string template.
+%%
+%% @see c_bitstr/5
+
+-spec bitstr_size(c_bitstr()) -> cerl().
+
+bitstr_size(Node) ->
+ Node#c_bitstr.size.
+
+
+%% @spec bitstr_bitsize(c_bitstr()) -> any | all | utf | integer()
+%%
+%% @doc Returns the total size in bits of an abstract bit-string
+%% template. If the size field is an integer literal, the result is the
+%% product of the size and unit values; if the size field is the atom
+%% literal <code>all</code>, the atom <code>all</code> is returned.
+%% If the size is not a literal, the atom <code>any</code> is returned.
+%%
+%% @see c_bitstr/5
+
+-spec bitstr_bitsize(c_bitstr()) -> 'all' | 'any' | 'utf' | non_neg_integer().
+
+bitstr_bitsize(Node) ->
+ Size = Node#c_bitstr.size,
+ case is_literal(Size) of
+ true ->
+ case concrete(Size) of
+ all ->
+ all;
+ undefined ->
+ %% just an assertion below
+ "utf" ++ _ = atom_to_list(concrete(Node#c_bitstr.type)),
+ utf;
+ S when is_integer(S) ->
+ S * concrete(Node#c_bitstr.unit)
+ end;
+ false ->
+ any
+ end.
+
+
+%% @spec bitstr_unit(c_bitstr()) -> cerl()
+%%
+%% @doc Returns the unit subtree of an abstract bit-string template.
+%%
+%% @see c_bitstr/5
+
+-spec bitstr_unit(c_bitstr()) -> cerl().
+
+bitstr_unit(Node) ->
+ Node#c_bitstr.unit.
+
+
+%% @spec bitstr_type(c_bitstr()) -> cerl()
+%%
+%% @doc Returns the type subtree of an abstract bit-string template.
+%%
+%% @see c_bitstr/5
+
+-spec bitstr_type(c_bitstr()) -> cerl().
+
+bitstr_type(Node) ->
+ Node#c_bitstr.type.
+
+
+%% @spec bitstr_flags(c_bitstr()) -> cerl()
+%%
+%% @doc Returns the flags subtree of an abstract bit-string template.
+%%
+%% @see c_bitstr/5
+
+-spec bitstr_flags(c_bitstr()) -> cerl().
+
+bitstr_flags(Node) ->
+ Node#c_bitstr.flags.
+
+
+%% ---------------------------------------------------------------------
+
+%% @spec c_fun(Variables::[c_var()], Body::cerl()) -> c_fun()
+%%
+%% @doc Creates an abstract fun-expression. If <code>Variables</code>
+%% is <code>[V1, ..., Vn]</code>, the result represents "<code>fun
+%% (<em>V1</em>, ..., <em>Vn</em>) -> <em>Body</em></code>". All the
+%% <code>Vi</code> must have type <code>var</code>.
+%%
+%% @see ann_c_fun/3
+%% @see update_c_fun/3
+%% @see is_c_fun/1
+%% @see fun_vars/1
+%% @see fun_body/1
+%% @see fun_arity/1
+
+-spec c_fun([c_var()], cerl()) -> c_fun().
+
+c_fun(Variables, Body) ->
+ #c_fun{vars = Variables, body = Body}.
+
+
+%% @spec ann_c_fun(As::anns(), Variables::[c_var()], Body::cerl()) ->
+%% c_fun()
+%% @see c_fun/2
+
+-spec ann_c_fun(anns(), [c_var()], cerl()) -> c_fun().
+
+ann_c_fun(As, Variables, Body) ->
+ #c_fun{vars = Variables, body = Body, anno = As}.
+
+
+%% @spec update_c_fun(Old::c_fun(), Variables::[c_var()],
+%% Body::cerl()) -> c_fun()
+%% @see c_fun/2
+
+-spec update_c_fun(c_fun(), [c_var()], cerl()) -> c_fun().
+
+update_c_fun(Node, Variables, Body) ->
+ #c_fun{vars = Variables, body = Body, anno = get_ann(Node)}.
+
+
+%% @spec is_c_fun(Node::cerl()) -> boolean()
+%%
+%% @doc Returns <code>true</code> if <code>Node</code> is an abstract
+%% fun-expression, otherwise <code>false</code>.
+%%
+%% @see c_fun/2
+
+-spec is_c_fun(cerl()) -> boolean().
+
+is_c_fun(#c_fun{}) ->
+ true; % Now this is fun!
+is_c_fun(_) ->
+ false.
+
+
+%% @spec fun_vars(c_fun()) -> [c_var()]
+%%
+%% @doc Returns the list of parameter subtrees of an abstract
+%% fun-expression.
+%%
+%% @see c_fun/2
+%% @see fun_arity/1
+
+-spec fun_vars(c_fun()) -> [c_var()].
+
+fun_vars(Node) ->
+ Node#c_fun.vars.
+
+
+%% @spec fun_body(c_fun()) -> cerl()
+%%
+%% @doc Returns the body subtree of an abstract fun-expression.
+%%
+%% @see c_fun/2
+
+-spec fun_body(c_fun()) -> cerl().
+
+fun_body(Node) ->
+ Node#c_fun.body.
+
+
+%% @spec fun_arity(Node::c_fun()) -> arity()
+%%
+%% @doc Returns the number of parameter subtrees of an abstract
+%% fun-expression.
+%%
+%% <p>Note: this is equivalent to <code>length(fun_vars(Node))</code>,
+%% but potentially more efficient.</p>
+%%
+%% @see c_fun/2
+%% @see fun_vars/1
+
+-spec fun_arity(c_fun()) -> arity().
+
+fun_arity(Node) ->
+ length(fun_vars(Node)).
+
+
+%% ---------------------------------------------------------------------
+
+%% @spec c_seq(Argument::cerl(), Body::cerl()) -> c_seq()
+%%
+%% @doc Creates an abstract sequencing expression. The result
+%% represents "<code>do <em>Argument</em> <em>Body</em></code>".
+%%
+%% @see ann_c_seq/3
+%% @see update_c_seq/3
+%% @see is_c_seq/1
+%% @see seq_arg/1
+%% @see seq_body/1
+
+-spec c_seq(cerl(), cerl()) -> c_seq().
+
+c_seq(Argument, Body) ->
+ #c_seq{arg = Argument, body = Body}.
+
+
+%% @spec ann_c_seq(As::anns(), Argument::cerl(), Body::cerl()) -> c_seq()
+%%
+%% @see c_seq/2
+
+-spec ann_c_seq(anns(), cerl(), cerl()) -> c_seq().
+
+ann_c_seq(As, Argument, Body) ->
+ #c_seq{arg = Argument, body = Body, anno = As}.
+
+
+%% @spec update_c_seq(Old::c_seq(), Argument::cerl(), Body::cerl()) ->
+%% c_seq()
+%% @see c_seq/2
+
+-spec update_c_seq(c_seq(), cerl(), cerl()) -> c_seq().
+
+update_c_seq(Node, Argument, Body) ->
+ #c_seq{arg = Argument, body = Body, anno = get_ann(Node)}.
+
+
+%% @spec is_c_seq(Node::cerl()) -> boolean()
+%%
+%% @doc Returns <code>true</code> if <code>Node</code> is an abstract
+%% sequencing expression, otherwise <code>false</code>.
+%%
+%% @see c_seq/2
+
+-spec is_c_seq(cerl()) -> boolean().
+
+is_c_seq(#c_seq{}) ->
+ true;
+is_c_seq(_) ->
+ false.
+
+
+%% @spec seq_arg(c_seq()) -> cerl()
+%%
+%% @doc Returns the argument subtree of an abstract sequencing
+%% expression.
+%%
+%% @see c_seq/2
+
+-spec seq_arg(c_seq()) -> cerl().
+
+seq_arg(Node) ->
+ Node#c_seq.arg.
+
+
+%% @spec seq_body(c_seq()) -> cerl()
+%%
+%% @doc Returns the body subtree of an abstract sequencing expression.
+%%
+%% @see c_seq/2
+
+-spec seq_body(c_seq()) -> cerl().
+
+seq_body(Node) ->
+ Node#c_seq.body.
+
+
+%% ---------------------------------------------------------------------
+
+%% @spec c_let(Variables::[c_var()], Argument::cerl(), Body::cerl()) ->
+%% c_let()
+%%
+%% @doc Creates an abstract let-expression. If <code>Variables</code>
+%% is <code>[V1, ..., Vn]</code>, the result represents "<code>let
+%% &lt;<em>V1</em>, ..., <em>Vn</em>&gt; = <em>Argument</em> in
+%% <em>Body</em></code>". All the <code>Vi</code> must have type
+%% <code>var</code>.
+%%
+%% @see ann_c_let/4
+%% @see update_c_let/4
+%% @see is_c_let/1
+%% @see let_vars/1
+%% @see let_arg/1
+%% @see let_body/1
+%% @see let_arity/1
+
+-spec c_let([c_var()], cerl(), cerl()) -> c_let().
+
+c_let(Variables, Argument, Body) ->
+ #c_let{vars = Variables, arg = Argument, body = Body}.
+
+
+%% ann_c_let(As, Variables, Argument, Body) -> c_let()
+%% @see c_let/3
+
+-spec ann_c_let(anns(), [c_var()], cerl(), cerl()) -> c_let().
+
+ann_c_let(As, Variables, Argument, Body) ->
+ #c_let{vars = Variables, arg = Argument, body = Body, anno = As}.
+
+
+%% update_c_let(Old, Variables, Argument, Body) -> c_let()
+%% @see c_let/3
+
+-spec update_c_let(c_let(), [c_var()], cerl(), cerl()) -> c_let().
+
+update_c_let(Node, Variables, Argument, Body) ->
+ #c_let{vars = Variables, arg = Argument, body = Body,
+ anno = get_ann(Node)}.
+
+
+%% @spec is_c_let(Node::cerl()) -> boolean()
+%%
+%% @doc Returns <code>true</code> if <code>Node</code> is an abstract
+%% let-expression, otherwise <code>false</code>.
+%%
+%% @see c_let/3
+
+-spec is_c_let(cerl()) -> boolean().
+
+is_c_let(#c_let{}) ->
+ true;
+is_c_let(_) ->
+ false.
+
+
+%% @spec let_vars(c_let()) -> [c_var()]
+%%
+%% @doc Returns the list of left-hand side variables of an abstract
+%% let-expression.
+%%
+%% @see c_let/3
+%% @see let_arity/1
+
+-spec let_vars(c_let()) -> [c_var()].
+
+let_vars(Node) ->
+ Node#c_let.vars.
+
+
+%% @spec let_arg(c_let()) -> cerl()
+%%
+%% @doc Returns the argument subtree of an abstract let-expression.
+%%
+%% @see c_let/3
+
+-spec let_arg(c_let()) -> cerl().
+
+let_arg(Node) ->
+ Node#c_let.arg.
+
+
+%% @spec let_body(c_let()) -> cerl()
+%%
+%% @doc Returns the body subtree of an abstract let-expression.
+%%
+%% @see c_let/3
+
+-spec let_body(c_let()) -> cerl().
+
+let_body(Node) ->
+ Node#c_let.body.
+
+
+%% @spec let_arity(Node::c_let()) -> non_neg_integer()
+%%
+%% @doc Returns the number of left-hand side variables of an abstract
+%% let-expression.
+%%
+%% <p>Note: this is equivalent to <code>length(let_vars(Node))</code>,
+%% but potentially more efficient.</p>
+%%
+%% @see c_let/3
+%% @see let_vars/1
+
+-spec let_arity(c_let()) -> non_neg_integer().
+
+let_arity(Node) ->
+ length(let_vars(Node)).
+
+
+%% ---------------------------------------------------------------------
+
+%% @spec c_letrec(Definitions::defs(), Body::cerl()) -> c_letrec()
+%%
+%% @doc Creates an abstract letrec-expression. If
+%% <code>Definitions</code> is <code>[{V1, F1}, ..., {Vn, Fn}]</code>,
+%% the result represents "<code>letrec <em>V1</em> = <em>F1</em>
+%% ... <em>Vn</em> = <em>Fn</em> in <em>Body</em></code>. All the
+%% <code>Vi</code> must have type <code>var</code> and represent
+%% function names. All the <code>Fi</code> must have type
+%% <code>'fun'</code>.
+%%
+%% @see ann_c_letrec/3
+%% @see update_c_letrec/3
+%% @see is_c_letrec/1
+%% @see letrec_defs/1
+%% @see letrec_body/1
+%% @see letrec_vars/1
+
+-spec c_letrec(defs(), cerl()) -> c_letrec().
+
+c_letrec(Defs, Body) ->
+ #c_letrec{defs = Defs, body = Body}.
+
+
+%% @spec ann_c_letrec(As::anns(), Definitions::defs(),
+%% Body::cerl()) -> c_letrec()
+%% @see c_letrec/2
+
+-spec ann_c_letrec(anns(), defs(), cerl()) -> c_letrec().
+
+ann_c_letrec(As, Defs, Body) ->
+ #c_letrec{defs = Defs, body = Body, anno = As}.
+
+
+%% @spec update_c_letrec(Old::c_letrec(), Definitions::defs(),
+%% Body::cerl()) -> c_letrec()
+%% @see c_letrec/2
+
+-spec update_c_letrec(c_letrec(), defs(), cerl()) -> c_letrec().
+
+update_c_letrec(Node, Defs, Body) ->
+ #c_letrec{defs = Defs, body = Body, anno = get_ann(Node)}.
+
+
+%% @spec is_c_letrec(Node::cerl()) -> boolean()
+%%
+%% @doc Returns <code>true</code> if <code>Node</code> is an abstract
+%% letrec-expression, otherwise <code>false</code>.
+%%
+%% @see c_letrec/2
+
+-spec is_c_letrec(cerl()) -> boolean().
+
+is_c_letrec(#c_letrec{}) ->
+ true;
+is_c_letrec(_) ->
+ false.
+
+
+%% @spec letrec_defs(Node::c_letrec()) -> defs()
+%%
+%% @doc Returns the list of definitions of an abstract
+%% letrec-expression. If <code>Node</code> represents "<code>letrec
+%% <em>V1</em> = <em>F1</em> ... <em>Vn</em> = <em>Fn</em> in
+%% <em>Body</em></code>", the returned value is <code>[{V1, F1}, ...,
+%% {Vn, Fn}]</code>.
+%%
+%% @see c_letrec/2
+
+-spec letrec_defs(c_letrec()) -> defs().
+
+letrec_defs(Node) ->
+ Node#c_letrec.defs.
+
+
+%% @spec letrec_body(c_letrec()) -> cerl()
+%%
+%% @doc Returns the body subtree of an abstract letrec-expression.
+%%
+%% @see c_letrec/2
+
+-spec letrec_body(c_letrec()) -> cerl().
+
+letrec_body(Node) ->
+ Node#c_letrec.body.
+
+
+%% @spec letrec_vars(c_letrec()) -> [cerl()]
+%%
+%% @doc Returns the list of left-hand side function variable subtrees
+%% of a letrec-expression. If <code>Node</code> represents
+%% "<code>letrec <em>V1</em> = <em>F1</em> ... <em>Vn</em> =
+%% <em>Fn</em> in <em>Body</em></code>", the returned value is
+%% <code>[V1, ..., Vn]</code>.
+%%
+%% @see c_letrec/2
+
+-spec letrec_vars(c_letrec()) -> [cerl()].
+
+letrec_vars(Node) ->
+ [F || {F, _} <- letrec_defs(Node)].
+
+
+%% ---------------------------------------------------------------------
+
+%% @spec c_case(Argument::cerl(), Clauses::[cerl()]) -> c_case()
+%%
+%% @doc Creates an abstract case-expression. If <code>Clauses</code>
+%% is <code>[C1, ..., Cn]</code>, the result represents "<code>case
+%% <em>Argument</em> of <em>C1</em> ... <em>Cn</em>
+%% end</code>". <code>Clauses</code> must not be empty.
+%%
+%% @see ann_c_case/3
+%% @see update_c_case/3
+%% @see is_c_case/1
+%% @see c_clause/3
+%% @see case_arg/1
+%% @see case_clauses/1
+%% @see case_arity/1
+
+-spec c_case(cerl(), [cerl()]) -> c_case().
+
+c_case(Expr, Clauses) ->
+ #c_case{arg = Expr, clauses = Clauses}.
+
+
+%% @spec ann_c_case(As::anns(), Argument::cerl(),
+%% Clauses::[cerl()]) -> c_case()
+%% @see c_case/2
+
+-spec ann_c_case(anns(), cerl(), [cerl()]) -> c_case().
+
+ann_c_case(As, Expr, Clauses) ->
+ #c_case{arg = Expr, clauses = Clauses, anno = As}.
+
+
+%% @spec update_c_case(Old::cerl(), Argument::cerl(),
+%% Clauses::[cerl()]) -> c_case()
+%% @see c_case/2
+
+-spec update_c_case(c_case(), cerl(), [cerl()]) -> c_case().
+
+update_c_case(Node, Expr, Clauses) ->
+ #c_case{arg = Expr, clauses = Clauses, anno = get_ann(Node)}.
+
+
+%% is_c_case(Node) -> boolean()
+%%
+%% Node = cerl()
+%%
+%% @doc Returns <code>true</code> if <code>Node</code> is an abstract
+%% case-expression; otherwise <code>false</code>.
+%%
+%% @see c_case/2
+
+-spec is_c_case(cerl()) -> boolean().
+
+is_c_case(#c_case{}) ->
+ true;
+is_c_case(_) ->
+ false.
+
+
+%% @spec case_arg(c_case()) -> cerl()
+%%
+%% @doc Returns the argument subtree of an abstract case-expression.
+%%
+%% @see c_case/2
+
+-spec case_arg(c_case()) -> cerl().
+
+case_arg(Node) ->
+ Node#c_case.arg.
+
+
+%% @spec case_clauses(c_case()) -> [cerl()]
+%%
+%% @doc Returns the list of clause subtrees of an abstract
+%% case-expression.
+%%
+%% @see c_case/2
+%% @see case_arity/1
+
+-spec case_clauses(c_case()) -> [cerl()].
+
+case_clauses(Node) ->
+ Node#c_case.clauses.
+
+
+%% @spec case_arity(Node::c_case()) -> non_neg_integer()
+%%
+%% @doc Equivalent to
+%% <code>clause_arity(hd(case_clauses(Node)))</code>, but potentially
+%% more efficient.
+%%
+%% @see c_case/2
+%% @see case_clauses/1
+%% @see clause_arity/1
+
+-spec case_arity(c_case()) -> non_neg_integer().
+
+case_arity(Node) ->
+ clause_arity(hd(case_clauses(Node))).
+
+
+%% ---------------------------------------------------------------------
+
+%% @spec c_clause(Patterns::[cerl()], Body::cerl()) -> c_clause()
+%% @equiv c_clause(Patterns, c_atom(true), Body)
+%% @see c_atom/1
+
+-spec c_clause([cerl()], cerl()) -> c_clause().
+
+c_clause(Patterns, Body) ->
+ c_clause(Patterns, c_atom(true), Body).
+
+
+%% @spec c_clause(Patterns::[cerl()], Guard::cerl(), Body::cerl()) ->
+%% c_clause()
+%%
+%% @doc Creates an an abstract clause. If <code>Patterns</code> is
+%% <code>[P1, ..., Pn]</code>, the result represents
+%% "<code>&lt;<em>P1</em>, ..., <em>Pn</em>&gt; when <em>Guard</em> ->
+%% <em>Body</em></code>".
+%%
+%% @see c_clause/2
+%% @see ann_c_clause/4
+%% @see update_c_clause/4
+%% @see is_c_clause/1
+%% @see c_case/2
+%% @see c_receive/3
+%% @see clause_pats/1
+%% @see clause_guard/1
+%% @see clause_body/1
+%% @see clause_arity/1
+%% @see clause_vars/1
+
+-spec c_clause([cerl()], cerl(), cerl()) -> c_clause().
+
+c_clause(Patterns, Guard, Body) ->
+ #c_clause{pats = Patterns, guard = Guard, body = Body}.
+
+
+%% @spec ann_c_clause(As::anns(), Patterns::[cerl()],
+%% Body::cerl()) -> c_clause()
+%% @equiv ann_c_clause(As, Patterns, c_atom(true), Body)
+%% @see c_clause/3
+
+-spec ann_c_clause(anns(), [cerl()], cerl()) -> c_clause().
+
+ann_c_clause(As, Patterns, Body) ->
+ ann_c_clause(As, Patterns, c_atom(true), Body).
+
+
+%% @spec ann_c_clause(As::anns(), Patterns::[cerl()], Guard::cerl(),
+%% Body::cerl()) -> c_clause()
+%% @see ann_c_clause/3
+%% @see c_clause/3
+
+-spec ann_c_clause(anns(), [cerl()], cerl(), cerl()) -> c_clause().
+
+ann_c_clause(As, Patterns, Guard, Body) ->
+ #c_clause{pats = Patterns, guard = Guard, body = Body, anno = As}.
+
+
+%% @spec update_c_clause(Old::c_clause(), Patterns::[cerl()],
+%% Guard::cerl(), Body::cerl()) -> c_clause()
+%% @see c_clause/3
+
+-spec update_c_clause(c_clause(), [cerl()], cerl(), cerl()) -> c_clause().
+
+update_c_clause(Node, Patterns, Guard, Body) ->
+ #c_clause{pats = Patterns, guard = Guard, body = Body,
+ anno = get_ann(Node)}.
+
+
+%% @spec is_c_clause(Node::cerl()) -> boolean()
+%%
+%% @doc Returns <code>true</code> if <code>Node</code> is an abstract
+%% clause, otherwise <code>false</code>.
+%%
+%% @see c_clause/3
+
+-spec is_c_clause(cerl()) -> boolean().
+
+is_c_clause(#c_clause{}) ->
+ true;
+is_c_clause(_) ->
+ false.
+
+
+%% @spec clause_pats(c_clause()) -> [cerl()]
+%%
+%% @doc Returns the list of pattern subtrees of an abstract clause.
+%%
+%% @see c_clause/3
+%% @see clause_arity/1
+
+-spec clause_pats(c_clause()) -> [cerl()].
+
+clause_pats(Node) ->
+ Node#c_clause.pats.
+
+
+%% @spec clause_guard(c_clause()) -> cerl()
+%%
+%% @doc Returns the guard subtree of an abstract clause.
+%%
+%% @see c_clause/3
+
+-spec clause_guard(c_clause()) -> cerl().
+
+clause_guard(Node) ->
+ Node#c_clause.guard.
+
+
+%% @spec clause_body(c_clause()) -> cerl()
+%%
+%% @doc Returns the body subtree of an abstract clause.
+%%
+%% @see c_clause/3
+
+-spec clause_body(c_clause()) -> cerl().
+
+clause_body(Node) ->
+ Node#c_clause.body.
+
+
+%% @spec clause_arity(Node::c_clause()) -> non_neg_integer()
+%%
+%% @doc Returns the number of pattern subtrees of an abstract clause.
+%%
+%% <p>Note: this is equivalent to
+%% <code>length(clause_pats(Node))</code>, but potentially more
+%% efficient.</p>
+%%
+%% @see c_clause/3
+%% @see clause_pats/1
+
+-spec clause_arity(c_clause()) -> non_neg_integer().
+
+clause_arity(Node) ->
+ length(clause_pats(Node)).
+
+
+%% @spec clause_vars(c_clause()) -> [cerl()]
+%%
+%% @doc Returns the list of all abstract variables in the patterns of
+%% an abstract clause. The order of listing is not defined.
+%%
+%% @see c_clause/3
+%% @see pat_list_vars/1
+
+-spec clause_vars(c_clause()) -> [cerl()].
+
+clause_vars(Clause) ->
+ pat_list_vars(clause_pats(Clause)).
+
+
+%% @spec pat_vars(Pattern::cerl()) -> [cerl()]
+%%
+%% @doc Returns the list of all abstract variables in a pattern. An
+%% exception is thrown if <code>Node</code> does not represent a
+%% well-formed Core Erlang clause pattern. The order of listing is not
+%% defined.
+%%
+%% @see pat_list_vars/1
+%% @see clause_vars/1
+
+-spec pat_vars(cerl()) -> [cerl()].
+
+pat_vars(Node) ->
+ pat_vars(Node, []).
+
+pat_vars(Node, Vs) ->
+ case type(Node) of
+ var ->
+ [Node | Vs];
+ literal ->
+ Vs;
+ cons ->
+ pat_vars(cons_hd(Node), pat_vars(cons_tl(Node), Vs));
+ tuple ->
+ pat_list_vars(tuple_es(Node), Vs);
+ map ->
+ pat_list_vars(map_es(Node), Vs);
+ map_pair ->
+ %% map_pair_key is not a pattern var, excluded
+ pat_list_vars([map_pair_op(Node),map_pair_val(Node)],Vs);
+ binary ->
+ pat_list_vars(binary_segments(Node), Vs);
+ bitstr ->
+ %% bitstr_size is not a pattern var, excluded
+ pat_vars(bitstr_val(Node), Vs);
+ alias ->
+ pat_vars(alias_pat(Node), [alias_var(Node) | Vs])
+ end.
+
+
+%% @spec pat_list_vars(Patterns::[cerl()]) -> [cerl()]
+%%
+%% @doc Returns the list of all abstract variables in the given
+%% patterns. An exception is thrown if some element in
+%% <code>Patterns</code> does not represent a well-formed Core Erlang
+%% clause pattern. The order of listing is not defined.
+%%
+%% @see pat_vars/1
+%% @see clause_vars/1
+
+-spec pat_list_vars([cerl()]) -> [cerl()].
+
+pat_list_vars(Ps) ->
+ pat_list_vars(Ps, []).
+
+pat_list_vars([P | Ps], Vs) ->
+ pat_list_vars(Ps, pat_vars(P, Vs));
+pat_list_vars([], Vs) ->
+ Vs.
+
+
+%% ---------------------------------------------------------------------
+
+%% @spec c_alias(Variable::c_var(), Pattern::cerl()) -> c_alias()
+%%
+%% @doc Creates an abstract pattern alias. The result represents
+%% "<code><em>Variable</em> = <em>Pattern</em></code>".
+%%
+%% @see ann_c_alias/3
+%% @see update_c_alias/3
+%% @see is_c_alias/1
+%% @see alias_var/1
+%% @see alias_pat/1
+%% @see c_clause/3
+
+-spec c_alias(c_var(), cerl()) -> c_alias().
+
+c_alias(Var, Pattern) ->
+ #c_alias{var = Var, pat = Pattern}.
+
+
+%% @spec ann_c_alias(As::anns(), Variable::c_var(),
+%% Pattern::cerl()) -> c_alias()
+%% @see c_alias/2
+
+-spec ann_c_alias(anns(), c_var(), cerl()) -> c_alias().
+
+ann_c_alias(As, Var, Pattern) ->
+ #c_alias{var = Var, pat = Pattern, anno = As}.
+
+
+%% @spec update_c_alias(Old::cerl(), Variable::c_var(),
+%% Pattern::cerl()) -> c_alias()
+%% @see c_alias/2
+
+-spec update_c_alias(c_alias(), c_var(), cerl()) -> c_alias().
+
+update_c_alias(Node, Var, Pattern) ->
+ #c_alias{var = Var, pat = Pattern, anno = get_ann(Node)}.
+
+
+%% @spec is_c_alias(Node::cerl()) -> boolean()
+%%
+%% @doc Returns <code>true</code> if <code>Node</code> is an abstract
+%% pattern alias, otherwise <code>false</code>.
+%%
+%% @see c_alias/2
+
+-spec is_c_alias(cerl()) -> boolean().
+
+is_c_alias(#c_alias{}) ->
+ true;
+is_c_alias(_) ->
+ false.
+
+
+%% @spec alias_var(c_alias()) -> c_var()
+%%
+%% @doc Returns the variable subtree of an abstract pattern alias.
+%%
+%% @see c_alias/2
+
+-spec alias_var(c_alias()) -> c_var().
+
+alias_var(Node) ->
+ Node#c_alias.var.
+
+
+%% @spec alias_pat(c_alias()) -> cerl()
+%%
+%% @doc Returns the pattern subtree of an abstract pattern alias.
+%%
+%% @see c_alias/2
+
+-spec alias_pat(c_alias()) -> cerl().
+
+alias_pat(Node) ->
+ Node#c_alias.pat.
+
+
+%% ---------------------------------------------------------------------
+
+%% @spec c_receive(Clauses::[cerl()]) -> c_receive()
+%% @equiv c_receive(Clauses, c_atom(infinity), c_atom(true))
+%% @see c_atom/1
+
+-spec c_receive([cerl()]) -> c_receive().
+
+c_receive(Clauses) ->
+ c_receive(Clauses, c_atom(infinity), c_atom(true)).
+
+
+%% @spec c_receive(Clauses::[cerl()], Timeout::cerl(),
+%% Action::cerl()) -> c_receive()
+%%
+%% @doc Creates an abstract receive-expression. If
+%% <code>Clauses</code> is <code>[C1, ..., Cn]</code>, the result
+%% represents "<code>receive <em>C1</em> ... <em>Cn</em> after
+%% <em>Timeout</em> -> <em>Action</em> end</code>".
+%%
+%% @see c_receive/1
+%% @see ann_c_receive/4
+%% @see update_c_receive/4
+%% @see is_c_receive/1
+%% @see receive_clauses/1
+%% @see receive_timeout/1
+%% @see receive_action/1
+
+-spec c_receive([cerl()], cerl(), cerl()) -> c_receive().
+
+c_receive(Clauses, Timeout, Action) ->
+ #c_receive{clauses = Clauses, timeout = Timeout, action = Action}.
+
+
+%% @spec ann_c_receive(As::anns(), Clauses::[cerl()]) -> c_receive()
+%% @equiv ann_c_receive(As, Clauses, c_atom(infinity), c_atom(true))
+%% @see c_receive/3
+%% @see c_atom/1
+
+-spec ann_c_receive(anns(), [cerl()]) -> c_receive().
+
+ann_c_receive(As, Clauses) ->
+ ann_c_receive(As, Clauses, c_atom(infinity), c_atom(true)).
+
+
+%% @spec ann_c_receive(As::anns(), Clauses::[cerl()],
+%% Timeout::cerl(), Action::cerl()) -> c_receive()
+%% @see ann_c_receive/2
+%% @see c_receive/3
+
+-spec ann_c_receive(anns(), [cerl()], cerl(), cerl()) -> c_receive().
+
+ann_c_receive(As, Clauses, Timeout, Action) ->
+ #c_receive{clauses = Clauses, timeout = Timeout, action = Action,
+ anno = As}.
+
+
+%% @spec update_c_receive(Old::cerl(), Clauses::[cerl()],
+%% Timeout::cerl(), Action::cerl()) -> c_receive()
+%% @see c_receive/3
+
+-spec update_c_receive(c_receive(), [cerl()], cerl(), cerl()) -> c_receive().
+
+update_c_receive(Node, Clauses, Timeout, Action) ->
+ #c_receive{clauses = Clauses, timeout = Timeout, action = Action,
+ anno = get_ann(Node)}.
+
+
+%% @spec is_c_receive(Node::cerl()) -> boolean()
+%%
+%% @doc Returns <code>true</code> if <code>Node</code> is an abstract
+%% receive-expression, otherwise <code>false</code>.
+%%
+%% @see c_receive/3
+
+-spec is_c_receive(cerl()) -> boolean().
+
+is_c_receive(#c_receive{}) ->
+ true;
+is_c_receive(_) ->
+ false.
+
+
+%% @spec receive_clauses(c_receive()) -> [cerl()]
+%%
+%% @doc Returns the list of clause subtrees of an abstract
+%% receive-expression.
+%%
+%% @see c_receive/3
+
+-spec receive_clauses(c_receive()) -> [cerl()].
+
+receive_clauses(Node) ->
+ Node#c_receive.clauses.
+
+
+%% @spec receive_timeout(c_receive()) -> cerl()
+%%
+%% @doc Returns the timeout subtree of an abstract receive-expression.
+%%
+%% @see c_receive/3
+
+-spec receive_timeout(c_receive()) -> cerl().
+
+receive_timeout(Node) ->
+ Node#c_receive.timeout.
+
+
+%% @spec receive_action(c_receive()) -> cerl()
+%%
+%% @doc Returns the action subtree of an abstract receive-expression.
+%%
+%% @see c_receive/3
+
+-spec receive_action(c_receive()) -> cerl().
+
+receive_action(Node) ->
+ Node#c_receive.action.
+
+
+%% ---------------------------------------------------------------------
+
+%% @spec c_apply(Operator::c_var(), Arguments::[cerl()]) -> c_apply()
+%%
+%% @doc Creates an abstract function application. If
+%% <code>Arguments</code> is <code>[A1, ..., An]</code>, the result
+%% represents "<code>apply <em>Operator</em>(<em>A1</em>, ...,
+%% <em>An</em>)</code>".
+%%
+%% @see ann_c_apply/3
+%% @see update_c_apply/3
+%% @see is_c_apply/1
+%% @see apply_op/1
+%% @see apply_args/1
+%% @see apply_arity/1
+%% @see c_call/3
+%% @see c_primop/2
+
+-spec c_apply(c_var(), [cerl()]) -> c_apply().
+
+c_apply(Operator, Arguments) ->
+ #c_apply{op = Operator, args = Arguments}.
+
+
+%% @spec ann_c_apply(As::anns(), Operator::c_var(),
+%% Arguments::[cerl()]) -> c_apply()
+%% @see c_apply/2
+
+-spec ann_c_apply(anns(), c_var(), [cerl()]) -> c_apply().
+
+ann_c_apply(As, Operator, Arguments) ->
+ #c_apply{op = Operator, args = Arguments, anno = As}.
+
+
+%% @spec update_c_apply(Old::c_apply(), Operator::cerl(),
+%% Arguments::[cerl()]) -> c_apply()
+%% @see c_apply/2
+
+-spec update_c_apply(c_apply(), c_var(), [cerl()]) -> c_apply().
+
+update_c_apply(Node, Operator, Arguments) ->
+ #c_apply{op = Operator, args = Arguments, anno = get_ann(Node)}.
+
+
+%% @spec is_c_apply(Node::cerl()) -> boolean()
+%%
+%% @doc Returns <code>true</code> if <code>Node</code> is an abstract
+%% function application, otherwise <code>false</code>.
+%%
+%% @see c_apply/2
+
+-spec is_c_apply(cerl()) -> boolean().
+
+is_c_apply(#c_apply{}) ->
+ true;
+is_c_apply(_) ->
+ false.
+
+
+%% @spec apply_op(c_apply()) -> c_var()
+%%
+%% @doc Returns the operator subtree of an abstract function
+%% application.
+%%
+%% @see c_apply/2
+
+-spec apply_op(c_apply()) -> c_var().
+
+apply_op(Node) ->
+ Node#c_apply.op.
+
+
+%% @spec apply_args(c_apply()) -> [cerl()]
+%%
+%% @doc Returns the list of argument subtrees of an abstract function
+%% application.
+%%
+%% @see c_apply/2
+%% @see apply_arity/1
+
+-spec apply_args(c_apply()) -> [cerl()].
+
+apply_args(Node) ->
+ Node#c_apply.args.
+
+
+%% @spec apply_arity(Node::c_apply()) -> arity()
+%%
+%% @doc Returns the number of argument subtrees of an abstract
+%% function application.
+%%
+%% <p>Note: this is equivalent to
+%% <code>length(apply_args(Node))</code>, but potentially more
+%% efficient.</p>
+%%
+%% @see c_apply/2
+%% @see apply_args/1
+
+-spec apply_arity(c_apply()) -> arity().
+
+apply_arity(Node) ->
+ length(apply_args(Node)).
+
+
+%% ---------------------------------------------------------------------
+
+%% @spec c_call(Module::cerl(), Name::cerl(), Arguments::[cerl()]) ->
+%% c_call()
+%%
+%% @doc Creates an abstract inter-module call. If
+%% <code>Arguments</code> is <code>[A1, ..., An]</code>, the result
+%% represents "<code>call <em>Module</em>:<em>Name</em>(<em>A1</em>,
+%% ..., <em>An</em>)</code>".
+%%
+%% @see ann_c_call/4
+%% @see update_c_call/4
+%% @see is_c_call/1
+%% @see call_module/1
+%% @see call_name/1
+%% @see call_args/1
+%% @see call_arity/1
+%% @see c_apply/2
+%% @see c_primop/2
+
+-spec c_call(cerl(), cerl(), [cerl()]) -> c_call().
+
+c_call(Module, Name, Arguments) ->
+ #c_call{module = Module, name = Name, args = Arguments}.
+
+
+%% @spec ann_c_call(As::anns(), Module::cerl(), Name::cerl(),
+%% Arguments::[cerl()]) -> c_call()
+%% @see c_call/3
+
+-spec ann_c_call(anns(), cerl(), cerl(), [cerl()]) -> c_call().
+
+ann_c_call(As, Module, Name, Arguments) ->
+ #c_call{module = Module, name = Name, args = Arguments, anno = As}.
+
+
+%% @spec update_c_call(Old::cerl(), Module::cerl(), Name::cerl(),
+%% Arguments::[cerl()]) -> c_call()
+%% @see c_call/3
+
+-spec update_c_call(cerl(), cerl(), cerl(), [cerl()]) -> c_call().
+
+update_c_call(Node, Module, Name, Arguments) ->
+ #c_call{module = Module, name = Name, args = Arguments,
+ anno = get_ann(Node)}.
+
+
+%% @spec is_c_call(Node::cerl()) -> boolean()
+%%
+%% @doc Returns <code>true</code> if <code>Node</code> is an abstract
+%% inter-module call expression; otherwise <code>false</code>.
+%%
+%% @see c_call/3
+
+-spec is_c_call(cerl()) -> boolean().
+
+is_c_call(#c_call{}) ->
+ true;
+is_c_call(_) ->
+ false.
+
+
+%% @spec call_module(c_call()) -> cerl()
+%%
+%% @doc Returns the module subtree of an abstract inter-module call.
+%%
+%% @see c_call/3
+
+-spec call_module(c_call()) -> cerl().
+
+call_module(Node) ->
+ Node#c_call.module.
+
+
+%% @spec call_name(c_call()) -> cerl()
+%%
+%% @doc Returns the name subtree of an abstract inter-module call.
+%%
+%% @see c_call/3
+
+-spec call_name(c_call()) -> cerl().
+
+call_name(Node) ->
+ Node#c_call.name.
+
+
+%% @spec call_args(c_call()) -> [cerl()]
+%%
+%% @doc Returns the list of argument subtrees of an abstract
+%% inter-module call.
+%%
+%% @see c_call/3
+%% @see call_arity/1
+
+-spec call_args(c_call()) -> [cerl()].
+
+call_args(Node) ->
+ Node#c_call.args.
+
+
+%% @spec call_arity(Node::c_call()) -> arity()
+%%
+%% @doc Returns the number of argument subtrees of an abstract
+%% inter-module call.
+%%
+%% <p>Note: this is equivalent to
+%% <code>length(call_args(Node))</code>, but potentially more
+%% efficient.</p>
+%%
+%% @see c_call/3
+%% @see call_args/1
+
+-spec call_arity(c_call()) -> arity().
+
+call_arity(Node) ->
+ length(call_args(Node)).
+
+
+%% ---------------------------------------------------------------------
+
+%% @spec c_primop(Name::c_literal(), Arguments::[cerl()]) -> c_primop()
+%%
+%% @doc Creates an abstract primitive operation call. If
+%% <code>Arguments</code> is <code>[A1, ..., An]</code>, the result
+%% represents "<code>primop <em>Name</em>(<em>A1</em>, ...,
+%% <em>An</em>)</code>". <code>Name</code> must be an atom literal.
+%%
+%% @see ann_c_primop/3
+%% @see update_c_primop/3
+%% @see is_c_primop/1
+%% @see primop_name/1
+%% @see primop_args/1
+%% @see primop_arity/1
+%% @see c_apply/2
+%% @see c_call/3
+
+-spec c_primop(c_literal(), [cerl()]) -> c_primop().
+
+c_primop(Name, Arguments) ->
+ #c_primop{name = Name, args = Arguments}.
+
+
+%% @spec ann_c_primop(As::anns(), Name::c_literal(),
+%% Arguments::[cerl()]) -> c_primop()
+%% @see c_primop/2
+
+-spec ann_c_primop(anns(), c_literal(), [cerl()]) -> c_primop().
+
+ann_c_primop(As, Name, Arguments) ->
+ #c_primop{name = Name, args = Arguments, anno = As}.
+
+
+%% @spec update_c_primop(Old::cerl(), Name::c_literal(),
+%% Arguments::[cerl()]) -> c_primop()
+%% @see c_primop/2
+
+-spec update_c_primop(cerl(), c_literal(), [cerl()]) -> c_primop().
+
+update_c_primop(Node, Name, Arguments) ->
+ #c_primop{name = Name, args = Arguments, anno = get_ann(Node)}.
+
+
+%% @spec is_c_primop(Node::cerl()) -> boolean()
+%%
+%% @doc Returns <code>true</code> if <code>Node</code> is an abstract
+%% primitive operation call, otherwise <code>false</code>.
+%%
+%% @see c_primop/2
+
+-spec is_c_primop(cerl()) -> boolean().
+
+is_c_primop(#c_primop{}) ->
+ true;
+is_c_primop(_) ->
+ false.
+
+
+%% @spec primop_name(c_primop()) -> c_literal()
+%%
+%% @doc Returns the name subtree of an abstract primitive operation
+%% call.
+%%
+%% @see c_primop/2
+
+-spec primop_name(c_primop()) -> c_literal().
+
+primop_name(Node) ->
+ Node#c_primop.name.
+
+
+%% @spec primop_args(c_primop()) -> [cerl()]
+%%
+%% @doc Returns the list of argument subtrees of an abstract primitive
+%% operation call.
+%%
+%% @see c_primop/2
+%% @see primop_arity/1
+
+-spec primop_args(c_primop()) -> [cerl()].
+
+primop_args(Node) ->
+ Node#c_primop.args.
+
+
+%% @spec primop_arity(Node::c_primop()) -> arity()
+%%
+%% @doc Returns the number of argument subtrees of an abstract
+%% primitive operation call.
+%%
+%% <p>Note: this is equivalent to
+%% <code>length(primop_args(Node))</code>, but potentially more
+%% efficient.</p>
+%%
+%% @see c_primop/2
+%% @see primop_args/1
+
+-spec primop_arity(c_primop()) -> arity().
+
+primop_arity(Node) ->
+ length(primop_args(Node)).
+
+
+%% ---------------------------------------------------------------------
+
+%% @spec c_try(Argument::cerl(), Variables::[c_var()], Body::cerl(),
+%% ExceptionVars::[c_var()], Handler::cerl()) -> c_try()
+%%
+%% @doc Creates an abstract try-expression. If <code>Variables</code> is
+%% <code>[V1, ..., Vn]</code> and <code>ExceptionVars</code> is
+%% <code>[X1, ..., Xm]</code>, the result represents "<code>try
+%% <em>Argument</em> of &lt;<em>V1</em>, ..., <em>Vn</em>&gt; ->
+%% <em>Body</em> catch &lt;<em>X1</em>, ..., <em>Xm</em>&gt; ->
+%% <em>Handler</em></code>". All the <code>Vi</code> and <code>Xi</code>
+%% must have type <code>var</code>.
+%%
+%% @see ann_c_try/6
+%% @see update_c_try/6
+%% @see is_c_try/1
+%% @see try_arg/1
+%% @see try_vars/1
+%% @see try_body/1
+%% @see c_catch/1
+
+-spec c_try(cerl(), [c_var()], cerl(), [c_var()], cerl()) -> c_try().
+
+c_try(Expr, Vs, Body, Evs, Handler) ->
+ #c_try{arg = Expr, vars = Vs, body = Body,
+ evars = Evs, handler = Handler}.
+
+
+%% @spec ann_c_try(As::[term()], Expression::cerl(),
+%% Variables::[c_var()], Body::cerl(),
+%% EVars::[c_var()], Handler::cerl()) -> c_try()
+%% @see c_try/5
+
+-spec ann_c_try(anns(), cerl(), [c_var()], cerl(), [c_var()], cerl()) ->
+ c_try().
+
+ann_c_try(As, Expr, Vs, Body, Evs, Handler) ->
+ #c_try{arg = Expr, vars = Vs, body = Body,
+ evars = Evs, handler = Handler, anno = As}.
+
+
+%% @spec update_c_try(Old::c_try(), Expression::cerl(),
+%% Variables::[c_var()], Body::cerl(),
+%% EVars::[c_var()], Handler::cerl()) -> cerl()
+%% @see c_try/5
+
+-spec update_c_try(c_try(), cerl(), [c_var()], cerl(), [c_var()], cerl()) ->
+ c_try().
+
+update_c_try(Node, Expr, Vs, Body, Evs, Handler) ->
+ #c_try{arg = Expr, vars = Vs, body = Body,
+ evars = Evs, handler = Handler, anno = get_ann(Node)}.
+
+
+%% @spec is_c_try(Node::cerl()) -> boolean()
+%%
+%% @doc Returns <code>true</code> if <code>Node</code> is an abstract
+%% try-expression, otherwise <code>false</code>.
+%%
+%% @see c_try/5
+
+-spec is_c_try(cerl()) -> boolean().
+
+is_c_try(#c_try{}) ->
+ true;
+is_c_try(_) ->
+ false.
+
+
+%% @spec try_arg(c_try()) -> cerl()
+%%
+%% @doc Returns the expression subtree of an abstract try-expression.
+%%
+%% @see c_try/5
+
+-spec try_arg(c_try()) -> cerl().
+
+try_arg(Node) ->
+ Node#c_try.arg.
+
+
+%% @spec try_vars(c_try()) -> [c_var()]
+%%
+%% @doc Returns the list of success variable subtrees of an abstract
+%% try-expression.
+%%
+%% @see c_try/5
+
+-spec try_vars(c_try()) -> [c_var()].
+
+try_vars(Node) ->
+ Node#c_try.vars.
+
+
+%% @spec try_body(c_try()) -> cerl()
+%%
+%% @doc Returns the success body subtree of an abstract try-expression.
+%%
+%% @see c_try/5
+
+-spec try_body(c_try()) -> cerl().
+
+try_body(Node) ->
+ Node#c_try.body.
+
+
+%% @spec try_evars(c_try()) -> [c_var()]
+%%
+%% @doc Returns the list of exception variable subtrees of an abstract
+%% try-expression.
+%%
+%% @see c_try/5
+
+-spec try_evars(c_try()) -> [c_var()].
+
+try_evars(Node) ->
+ Node#c_try.evars.
+
+
+%% @spec try_handler(c_try()) -> cerl()
+%%
+%% @doc Returns the exception body subtree of an abstract
+%% try-expression.
+%%
+%% @see c_try/5
+
+-spec try_handler(c_try()) -> cerl().
+
+try_handler(Node) ->
+ Node#c_try.handler.
+
+
+%% ---------------------------------------------------------------------
+
+%% @spec c_catch(Body::cerl()) -> c_catch()
+%%
+%% @doc Creates an abstract catch-expression. The result represents
+%% "<code>catch <em>Body</em></code>".
+%%
+%% <p>Note: catch-expressions can be rewritten as try-expressions, and
+%% will eventually be removed from Core Erlang.</p>
+%%
+%% @see ann_c_catch/2
+%% @see update_c_catch/2
+%% @see is_c_catch/1
+%% @see catch_body/1
+%% @see c_try/5
+
+-spec c_catch(cerl()) -> c_catch().
+
+c_catch(Body) ->
+ #c_catch{body = Body}.
+
+
+%% @spec ann_c_catch(As::anns(), Body::cerl()) -> c_catch()
+%% @see c_catch/1
+
+-spec ann_c_catch(anns(), cerl()) -> c_catch().
+
+ann_c_catch(As, Body) ->
+ #c_catch{body = Body, anno = As}.
+
+
+%% @spec update_c_catch(Old::c_catch(), Body::cerl()) -> c_catch()
+%% @see c_catch/1
+
+-spec update_c_catch(c_catch(), cerl()) -> c_catch().
+
+update_c_catch(Node, Body) ->
+ #c_catch{body = Body, anno = get_ann(Node)}.
+
+
+%% @spec is_c_catch(Node::cerl()) -> boolean()
+%%
+%% @doc Returns <code>true</code> if <code>Node</code> is an abstract
+%% catch-expression, otherwise <code>false</code>.
+%%
+%% @see c_catch/1
+
+-spec is_c_catch(cerl()) -> boolean().
+
+is_c_catch(#c_catch{}) ->
+ true;
+is_c_catch(_) ->
+ false.
+
+
+%% @spec catch_body(Node::c_catch()) -> cerl()
+%%
+%% @doc Returns the body subtree of an abstract catch-expression.
+%%
+%% @see c_catch/1
+
+-spec catch_body(c_catch()) -> cerl().
+
+catch_body(Node) ->
+ Node#c_catch.body.
+
+
+%% ---------------------------------------------------------------------
+
+%% @spec to_records(Tree::cerl()) -> record(record_types())
+%%
+%% @doc Translates an abstract syntax tree to a corresponding explicit
+%% record representation. The records are defined in the file
+%% "<code>cerl.hrl</code>".
+%%
+%% @see type/1
+%% @see from_records/1
+
+-spec to_records(cerl()) -> cerl().
+
+to_records(Node) ->
+ Node.
+
+%% @spec from_records(Tree::record(record_types())) -> cerl()
+%%
+%% record_types() = c_alias | c_apply | c_binary | c_bitstr | c_call |
+%% c_case | c_catch | c_clause | c_cons | c_fun |
+%% c_let | c_letrec | c_literal | c_map | c_map_pair |
+%% c_module | c_primop | c_receive | c_seq |
+%% c_try | c_tuple | c_values | c_var
+%%
+%% @doc Translates an explicit record representation to a
+%% corresponding abstract syntax tree. The records are defined in the
+%% file "<code>core_parse.hrl</code>".
+%%
+%% @see type/1
+%% @see to_records/1
+
+-spec from_records(cerl()) -> cerl().
+
+from_records(Node) ->
+ Node.
+
+
+%% ---------------------------------------------------------------------
+
+%% @spec is_data(Node::cerl()) -> boolean()
+%%
+%% @doc Returns <code>true</code> if <code>Node</code> represents a
+%% data constructor, otherwise <code>false</code>. Data constructors
+%% are cons cells, tuples, and atomic literals.
+%%
+%% @see data_type/1
+%% @see data_es/1
+%% @see data_arity/1
+
+-spec is_data(cerl()) -> boolean().
+
+is_data(#c_literal{}) ->
+ true;
+is_data(#c_cons{}) ->
+ true;
+is_data(#c_tuple{}) ->
+ true;
+is_data(_) ->
+ false.
+
+
+%% @spec data_type(Node::cerl()) -> dtype()
+%%
+%% dtype() = cons | tuple | {atomic, Value}
+%% Value = integer() | float() | atom() | []
+%%
+%% @doc Returns a type descriptor for a data constructor
+%% node. (Cf. <code>is_data/1</code>.) This is mainly useful for
+%% comparing types and for constructing new nodes of the same type
+%% (cf. <code>make_data/2</code>). If <code>Node</code> represents an
+%% integer, floating-point number, atom or empty list, the result is
+%% <code>{atomic, Value}</code>, where <code>Value</code> is the value
+%% of <code>concrete(Node)</code>, otherwise the result is either
+%% <code>cons</code> or <code>tuple</code>.
+%%
+%% <p>Type descriptors can be compared for equality or order (in the
+%% Erlang term order), but remember that floating-point values should
+%% in general never be tested for equality.</p>
+%%
+%% @see is_data/1
+%% @see make_data/2
+%% @see type/1
+%% @see concrete/1
+
+-type value() :: integer() | float() | atom() | [].
+-type dtype() :: 'cons' | 'tuple' | {'atomic', value()}.
+-type c_lct() :: c_literal() | c_cons() | c_tuple().
+
+-spec data_type(c_lct()) -> dtype().
+
+data_type(#c_literal{val = V}) ->
+ case V of
+ [_ | _] ->
+ cons;
+ _ when is_tuple(V) ->
+ tuple;
+ _ ->
+ {atomic, V}
+ end;
+data_type(#c_cons{}) ->
+ cons;
+data_type(#c_tuple{}) ->
+ tuple.
+
+%% @spec data_es(Node::cerl()) -> [cerl()]
+%%
+%% @doc Returns the list of subtrees of a data constructor node. If
+%% the arity of the constructor is zero, the result is the empty list.
+%%
+%% <p>Note: if <code>data_type(Node)</code> is <code>cons</code>, the
+%% number of subtrees is exactly two. If <code>data_type(Node)</code>
+%% is <code>{atomic, Value}</code>, the number of subtrees is
+%% zero.</p>
+%%
+%% @see is_data/1
+%% @see data_type/1
+%% @see data_arity/1
+%% @see make_data/2
+
+-spec data_es(c_lct()) -> [cerl()].
+
+data_es(#c_literal{val = V}) ->
+ case V of
+ [Head | Tail] ->
+ [#c_literal{val = Head}, #c_literal{val = Tail}];
+ _ when is_tuple(V) ->
+ make_lit_list(tuple_to_list(V));
+ _ ->
+ []
+ end;
+data_es(#c_cons{hd = H, tl = T}) ->
+ [H, T];
+data_es(#c_tuple{es = Es}) ->
+ Es.
+
+%% @spec data_arity(Node::cerl()) -> non_neg_integer()
+%%
+%% @doc Returns the number of subtrees of a data constructor
+%% node. This is equivalent to <code>length(data_es(Node))</code>, but
+%% potentially more efficient.
+%%
+%% @see is_data/1
+%% @see data_es/1
+
+-spec data_arity(c_lct()) -> non_neg_integer().
+
+data_arity(#c_literal{val = V}) ->
+ case V of
+ [_ | _] ->
+ 2;
+ _ when is_tuple(V) ->
+ tuple_size(V);
+ _ ->
+ 0
+ end;
+data_arity(#c_cons{}) ->
+ 2;
+data_arity(#c_tuple{es = Es}) ->
+ length(Es).
+
+
+%% @spec make_data(Type::dtype(), Elements::[cerl()]) -> cerl()
+%%
+%% @doc Creates a data constructor node with the specified type and
+%% subtrees. (Cf. <code>data_type/1</code>.) An exception is thrown
+%% if the length of <code>Elements</code> is invalid for the given
+%% <code>Type</code>; see <code>data_es/1</code> for arity constraints
+%% on constructor types.
+%%
+%% @see data_type/1
+%% @see data_es/1
+%% @see ann_make_data/3
+%% @see update_data/3
+%% @see make_data_skel/2
+
+-spec make_data(dtype(), [cerl()]) -> c_lct().
+
+make_data(CType, Es) ->
+ ann_make_data([], CType, Es).
+
+
+%% @spec ann_make_data(As::anns(), Type::dtype(),
+%% Elements::[cerl()]) -> cerl()
+%% @see make_data/2
+
+-spec ann_make_data(anns(), dtype(), [cerl()]) -> c_lct().
+
+ann_make_data(As, {atomic, V}, []) -> #c_literal{val = V, anno = As};
+ann_make_data(As, cons, [H, T]) -> ann_c_cons(As, H, T);
+ann_make_data(As, tuple, Es) -> ann_c_tuple(As, Es).
+
+%% @spec update_data(Old::cerl(), Type::dtype(),
+%% Elements::[cerl()]) -> cerl()
+%% @see make_data/2
+
+-spec update_data(cerl(), dtype(), [cerl()]) -> c_lct().
+
+update_data(Node, CType, Es) ->
+ ann_make_data(get_ann(Node), CType, Es).
+
+
+%% @spec make_data_skel(Type::dtype(), Elements::[cerl()]) -> cerl()
+%%
+%% @doc Like <code>make_data/2</code>, but analogous to
+%% <code>c_tuple_skel/1</code> and <code>c_cons_skel/2</code>.
+%%
+%% @see ann_make_data_skel/3
+%% @see update_data_skel/3
+%% @see make_data/2
+%% @see c_tuple_skel/1
+%% @see c_cons_skel/2
+
+-spec make_data_skel(dtype(), [cerl()]) -> c_lct().
+
+make_data_skel(CType, Es) ->
+ ann_make_data_skel([], CType, Es).
+
+
+%% @spec ann_make_data_skel(As::anns(), Type::dtype(),
+%% Elements::[cerl()]) -> cerl()
+%% @see make_data_skel/2
+
+-spec ann_make_data_skel(anns(), dtype(), [cerl()]) -> c_lct().
+
+ann_make_data_skel(As, {atomic, V}, []) -> #c_literal{val = V, anno = As};
+ann_make_data_skel(As, cons, [H, T]) -> ann_c_cons_skel(As, H, T);
+ann_make_data_skel(As, tuple, Es) -> ann_c_tuple_skel(As, Es).
+
+
+%% @spec update_data_skel(Old::cerl(), Type::dtype(),
+%% Elements::[cerl()]) -> cerl()
+%% @see make_data_skel/2
+
+-spec update_data_skel(cerl(), dtype(), [cerl()]) -> c_lct().
+
+update_data_skel(Node, CType, Es) ->
+ ann_make_data_skel(get_ann(Node), CType, Es).
+
+
+%% ---------------------------------------------------------------------
+
+%% @spec subtrees(Node::cerl()) -> [[cerl()]]
+%%
+%% @doc Returns the grouped list of all subtrees of a node. If
+%% <code>Node</code> is a leaf node (cf. <code>is_leaf/1</code>), this
+%% is the empty list, otherwise the result is always a nonempty list,
+%% containing the lists of subtrees of <code>Node</code>, in
+%% left-to-right order as they occur in the printed program text, and
+%% grouped by category. Often, each group contains only a single
+%% subtree.
+%%
+%% <p>Depending on the type of <code>Node</code>, the size of some
+%% groups may be variable (e.g., the group consisting of all the
+%% elements of a tuple), while others always contain the same number
+%% of elements - usually exactly one (e.g., the group containing the
+%% argument expression of a case-expression). Note, however, that the
+%% exact structure of the returned list (for a given node type) should
+%% in general not be depended upon, since it might be subject to
+%% change without notice.</p>
+%%
+%% <p>The function <code>subtrees/1</code> and the constructor functions
+%% <code>make_tree/2</code> and <code>update_tree/2</code> can be a
+%% great help if one wants to traverse a syntax tree, visiting all its
+%% subtrees, but treat nodes of the tree in a uniform way in most or all
+%% cases. Using these functions makes this simple, and also assures that
+%% your code is not overly sensitive to extensions of the syntax tree
+%% data type, because any node types not explicitly handled by your code
+%% can be left to a default case.</p>
+%%
+%% <p>For example:
+%% <pre>
+%% postorder(F, Tree) ->
+%% F(case subtrees(Tree) of
+%% [] -> Tree;
+%% List -> update_tree(Tree,
+%% [[postorder(F, Subtree)
+%% || Subtree &lt;- Group]
+%% || Group &lt;- List])
+%% end).
+%% </pre>
+%% maps the function <code>F</code> on <code>Tree</code> and all its
+%% subtrees, doing a post-order traversal of the syntax tree. (Note
+%% the use of <code>update_tree/2</code> to preserve annotations.) For
+%% a simple function like:
+%% <pre>
+%% f(Node) ->
+%% case type(Node) of
+%% atom -> atom("a_" ++ atom_name(Node));
+%% _ -> Node
+%% end.
+%% </pre>
+%% the call <code>postorder(fun f/1, Tree)</code> will yield a new
+%% representation of <code>Tree</code> in which all atom names have
+%% been extended with the prefix "a_", but nothing else (including
+%% annotations) has been changed.</p>
+%%
+%% @see is_leaf/1
+%% @see make_tree/2
+%% @see update_tree/2
+
+-spec subtrees(cerl()) -> [[cerl()]].
+
+subtrees(T) ->
+ case is_leaf(T) of
+ true ->
+ [];
+ false ->
+ case type(T) of
+ values ->
+ [values_es(T)];
+ binary ->
+ [binary_segments(T)];
+ bitstr ->
+ [[bitstr_val(T)], [bitstr_size(T)],
+ [bitstr_unit(T)], [bitstr_type(T)],
+ [bitstr_flags(T)]];
+ cons ->
+ [[cons_hd(T)], [cons_tl(T)]];
+ tuple ->
+ [tuple_es(T)];
+ map ->
+ [map_es(T)];
+ map_pair ->
+ [[map_pair_op(T)],[map_pair_key(T)],[map_pair_val(T)]];
+ 'let' ->
+ [let_vars(T), [let_arg(T)], [let_body(T)]];
+ seq ->
+ [[seq_arg(T)], [seq_body(T)]];
+ apply ->
+ [[apply_op(T)], apply_args(T)];
+ call ->
+ [[call_module(T)], [call_name(T)],
+ call_args(T)];
+ primop ->
+ [[primop_name(T)], primop_args(T)];
+ 'case' ->
+ [[case_arg(T)], case_clauses(T)];
+ clause ->
+ [clause_pats(T), [clause_guard(T)],
+ [clause_body(T)]];
+ alias ->
+ [[alias_var(T)], [alias_pat(T)]];
+ 'fun' ->
+ [fun_vars(T), [fun_body(T)]];
+ 'receive' ->
+ [receive_clauses(T), [receive_timeout(T)],
+ [receive_action(T)]];
+ 'try' ->
+ [[try_arg(T)], try_vars(T), [try_body(T)],
+ try_evars(T), [try_handler(T)]];
+ 'catch' ->
+ [[catch_body(T)]];
+ letrec ->
+ Es = unfold_tuples(letrec_defs(T)),
+ [Es, [letrec_body(T)]];
+ module ->
+ As = unfold_tuples(module_attrs(T)),
+ Es = unfold_tuples(module_defs(T)),
+ [[module_name(T)], module_exports(T), As, Es]
+ end
+ end.
+
+
+%% @spec update_tree(Old::cerl(), Groups::[[cerl()]]) -> cerl()
+%%
+%% @doc Creates a syntax tree with the given subtrees, and the same
+%% type and annotations as the <code>Old</code> node. This is
+%% equivalent to <code>ann_make_tree(get_ann(Node), type(Node),
+%% Groups)</code>, but potentially more efficient.
+%%
+%% @see update_tree/3
+%% @see ann_make_tree/3
+%% @see get_ann/1
+%% @see type/1
+
+-spec update_tree(cerl(), [[cerl()],...]) -> cerl().
+
+update_tree(Node, Gs) ->
+ ann_make_tree(get_ann(Node), type(Node), Gs).
+
+
+%% @spec update_tree(Old::cerl(), Type::ctype(), Groups::[[cerl()]]) ->
+%% cerl()
+%%
+%% @doc Creates a syntax tree with the given type and subtrees, and
+%% the same annotations as the <code>Old</code> node. This is
+%% equivalent to <code>ann_make_tree(get_ann(Node), Type,
+%% Groups)</code>, but potentially more efficient.
+%%
+%% @see update_tree/2
+%% @see ann_make_tree/3
+%% @see get_ann/1
+
+-spec update_tree(cerl(), ctype(), [[cerl()],...]) -> cerl().
+
+update_tree(Node, Type, Gs) ->
+ ann_make_tree(get_ann(Node), Type, Gs).
+
+
+%% @spec make_tree(Type::ctype(), Groups::[[cerl()]]) -> cerl()
+%%
+%% @doc Creates a syntax tree with the given type and subtrees.
+%% <code>Type</code> must be a node type name
+%% (cf. <code>type/1</code>) that does not denote a leaf node type
+%% (cf. <code>is_leaf/1</code>). <code>Groups</code> must be a
+%% <em>nonempty</em> list of groups of syntax trees, representing the
+%% subtrees of a node of the given type, in left-to-right order as
+%% they would occur in the printed program text, grouped by category
+%% as done by <code>subtrees/1</code>.
+%%
+%% <p>The result of <code>ann_make_tree(get_ann(Node), type(Node),
+%% subtrees(Node))</code> (cf. <code>update_tree/2</code>) represents
+%% the same source code text as the original <code>Node</code>,
+%% assuming that <code>subtrees(Node)</code> yields a nonempty
+%% list. However, it does not necessarily have the exact same data
+%% representation as <code>Node</code>.</p>
+%%
+%% @see ann_make_tree/3
+%% @see type/1
+%% @see is_leaf/1
+%% @see subtrees/1
+%% @see update_tree/2
+
+-spec make_tree(ctype(), [[cerl()],...]) -> cerl().
+
+make_tree(Type, Gs) ->
+ ann_make_tree([], Type, Gs).
+
+
+%% @spec ann_make_tree(As::anns(), Type::ctype(),
+%% Groups::[[cerl()]]) -> cerl()
+%%
+%% @doc Creates a syntax tree with the given annotations, type and
+%% subtrees. See <code>make_tree/2</code> for details.
+%%
+%% @see make_tree/2
+
+-spec ann_make_tree(anns(), ctype(), [[cerl()],...]) -> cerl().
+
+ann_make_tree(As, values, [Es]) -> ann_c_values(As, Es);
+ann_make_tree(As, binary, [Ss]) -> ann_c_binary(As, Ss);
+ann_make_tree(As, bitstr, [[V],[S],[U],[T],[Fs]]) ->
+ ann_c_bitstr(As, V, S, U, T, Fs);
+ann_make_tree(As, cons, [[H], [T]]) -> ann_c_cons(As, H, T);
+ann_make_tree(As, tuple, [Es]) -> ann_c_tuple(As, Es);
+ann_make_tree(As, map, [Es]) -> ann_c_map(As, Es);
+ann_make_tree(As, map, [[A], Es]) -> ann_c_map(As, A, Es);
+ann_make_tree(As, map_pair, [[Op], [K], [V]]) -> ann_c_map_pair(As, Op, K, V);
+ann_make_tree(As, 'let', [Vs, [A], [B]]) -> ann_c_let(As, Vs, A, B);
+ann_make_tree(As, seq, [[A], [B]]) -> ann_c_seq(As, A, B);
+ann_make_tree(As, apply, [[Op], Es]) -> ann_c_apply(As, Op, Es);
+ann_make_tree(As, call, [[M], [N], Es]) -> ann_c_call(As, M, N, Es);
+ann_make_tree(As, primop, [[N], Es]) -> ann_c_primop(As, N, Es);
+ann_make_tree(As, 'case', [[A], Cs]) -> ann_c_case(As, A, Cs);
+ann_make_tree(As, clause, [Ps, [G], [B]]) -> ann_c_clause(As, Ps, G, B);
+ann_make_tree(As, alias, [[V], [P]]) -> ann_c_alias(As, V, P);
+ann_make_tree(As, 'fun', [Vs, [B]]) -> ann_c_fun(As, Vs, B);
+ann_make_tree(As, 'receive', [Cs, [T], [A]]) ->
+ ann_c_receive(As, Cs, T, A);
+ann_make_tree(As, 'try', [[E], Vs, [B], Evs, [H]]) ->
+ ann_c_try(As, E, Vs, B, Evs, H);
+ann_make_tree(As, 'catch', [[B]]) -> ann_c_catch(As, B);
+ann_make_tree(As, letrec, [Es, [B]]) ->
+ ann_c_letrec(As, fold_tuples(Es), B);
+ann_make_tree(As, module, [[N], Xs, Es, Ds]) ->
+ ann_c_module(As, N, Xs, fold_tuples(Es), fold_tuples(Ds)).
+
+
+%% ---------------------------------------------------------------------
+
+%% @spec meta(Tree::cerl()) -> cerl()
+%%
+%% @doc Creates a meta-representation of a syntax tree. The result
+%% represents an Erlang expression "<code><em>MetaTree</em></code>"
+%% which, if evaluated, will yield a new syntax tree representing the
+%% same source code text as <code>Tree</code> (although the actual
+%% data representation may be different). The expression represented
+%% by <code>MetaTree</code> is <em>implementation independent</em>
+%% with regard to the data structures used by the abstract syntax tree
+%% implementation.
+%%
+%% <p>Any node in <code>Tree</code> whose node type is
+%% <code>var</code> (cf. <code>type/1</code>), and whose list of
+%% annotations (cf. <code>get_ann/1</code>) contains the atom
+%% <code>meta_var</code>, will remain unchanged in the resulting tree,
+%% except that exactly one occurrence of <code>meta_var</code> is
+%% removed from its annotation list.</p>
+%%
+%% <p>The main use of the function <code>meta/1</code> is to transform
+%% a data structure <code>Tree</code>, which represents a piece of
+%% program code, into a form that is <em>representation independent
+%% when printed</em>. E.g., suppose <code>Tree</code> represents a
+%% variable named "V". Then (assuming a function <code>print/1</code>
+%% for printing syntax trees), evaluating
+%% <code>print(abstract(Tree))</code> - simply using
+%% <code>abstract/1</code> to map the actual data structure onto a
+%% syntax tree representation - would output a string that might look
+%% something like "<code>{var, ..., 'V'}</code>", which is obviously
+%% dependent on the implementation of the abstract syntax trees. This
+%% could e.g. be useful for caching a syntax tree in a file. However,
+%% in some situations like in a program generator generator (with two
+%% "generator"), it may be unacceptable. Using
+%% <code>print(meta(Tree))</code> instead would output a
+%% <em>representation independent</em> syntax tree generating
+%% expression; in the above case, something like
+%% "<code>cerl:c_var('V')</code>".</p>
+%%
+%% <p>The implementation tries to generate compact code with respect
+%% to literals and lists.</p>
+%%
+%% @see abstract/1
+%% @see type/1
+%% @see get_ann/1
+
+-spec meta(cerl()) -> cerl().
+
+meta(Node) ->
+ %% First of all we check for metavariables:
+ case type(Node) of
+ var ->
+ case lists:member(meta_var, get_ann(Node)) of
+ false ->
+ meta_0(var, Node);
+ true ->
+ %% A meta-variable: remove the first found
+ %% 'meta_var' annotation, but otherwise leave
+ %% the node unchanged.
+ set_ann(Node, lists:delete(meta_var, get_ann(Node)))
+ end;
+ Type ->
+ meta_0(Type, Node)
+ end.
+
+meta_0(Type, Node) ->
+ case get_ann(Node) of
+ [] ->
+ meta_1(Type, Node);
+ As ->
+ meta_call(set_ann, [meta_1(Type, Node), abstract(As)])
+ end.
+
+meta_1(literal, Node) ->
+ %% We handle atomic literals separately, to get a bit
+ %% more compact code. For the rest, we use 'abstract'.
+ case concrete(Node) of
+ V when is_atom(V) ->
+ meta_call(c_atom, [Node]);
+ V when is_integer(V) ->
+ meta_call(c_int, [Node]);
+ V when is_float(V) ->
+ meta_call(c_float, [Node]);
+ [] ->
+ meta_call(c_nil, []);
+ _ ->
+ meta_call(abstract, [Node])
+ end;
+meta_1(var, Node) ->
+ %% A normal variable or function name.
+ meta_call(c_var, [abstract(var_name(Node))]);
+meta_1(values, Node) ->
+ meta_call(c_values,
+ [make_list(meta_list(values_es(Node)))]);
+meta_1(binary, Node) ->
+ meta_call(c_binary,
+ [make_list(meta_list(binary_segments(Node)))]);
+meta_1(bitstr, Node) ->
+ meta_call(c_bitstr,
+ [meta(bitstr_val(Node)),
+ meta(bitstr_size(Node)),
+ meta(bitstr_unit(Node)),
+ meta(bitstr_type(Node)),
+ meta(bitstr_flags(Node))]);
+meta_1(cons, Node) ->
+ %% The list is split up if some sublist has annotatations. If
+ %% we get exactly one element, we generate a 'c_cons' call
+ %% instead of 'make_list' to reconstruct the node.
+ case split_list(Node) of
+ {[H], Node1} ->
+ meta_call(c_cons, [meta(H), meta(Node1)]);
+ {L, Node1} ->
+ meta_call(make_list,
+ [make_list(meta_list(L)), meta(Node1)])
+ end;
+meta_1(tuple, Node) ->
+ meta_call(c_tuple,
+ [make_list(meta_list(tuple_es(Node)))]);
+meta_1('let', Node) ->
+ meta_call(c_let,
+ [make_list(meta_list(let_vars(Node))),
+ meta(let_arg(Node)), meta(let_body(Node))]);
+meta_1(seq, Node) ->
+ meta_call(c_seq,
+ [meta(seq_arg(Node)), meta(seq_body(Node))]);
+meta_1(apply, Node) ->
+ meta_call(c_apply,
+ [meta(apply_op(Node)),
+ make_list(meta_list(apply_args(Node)))]);
+meta_1(call, Node) ->
+ meta_call(c_call,
+ [meta(call_module(Node)), meta(call_name(Node)),
+ make_list(meta_list(call_args(Node)))]);
+meta_1(primop, Node) ->
+ meta_call(c_primop,
+ [meta(primop_name(Node)),
+ make_list(meta_list(primop_args(Node)))]);
+meta_1('case', Node) ->
+ meta_call(c_case,
+ [meta(case_arg(Node)),
+ make_list(meta_list(case_clauses(Node)))]);
+meta_1(clause, Node) ->
+ meta_call(c_clause,
+ [make_list(meta_list(clause_pats(Node))),
+ meta(clause_guard(Node)),
+ meta(clause_body(Node))]);
+meta_1(alias, Node) ->
+ meta_call(c_alias,
+ [meta(alias_var(Node)), meta(alias_pat(Node))]);
+meta_1('fun', Node) ->
+ meta_call(c_fun,
+ [make_list(meta_list(fun_vars(Node))),
+ meta(fun_body(Node))]);
+meta_1('receive', Node) ->
+ meta_call(c_receive,
+ [make_list(meta_list(receive_clauses(Node))),
+ meta(receive_timeout(Node)),
+ meta(receive_action(Node))]);
+meta_1('try', Node) ->
+ meta_call(c_try,
+ [meta(try_arg(Node)),
+ make_list(meta_list(try_vars(Node))),
+ meta(try_body(Node)),
+ make_list(meta_list(try_evars(Node))),
+ meta(try_handler(Node))]);
+meta_1('catch', Node) ->
+ meta_call(c_catch, [meta(catch_body(Node))]);
+meta_1(letrec, Node) ->
+ meta_call(c_letrec,
+ [make_list([c_tuple([meta(N), meta(F)])
+ || {N, F} <- letrec_defs(Node)]),
+ meta(letrec_body(Node))]);
+meta_1(module, Node) ->
+ meta_call(c_module,
+ [meta(module_name(Node)),
+ make_list(meta_list(module_exports(Node))),
+ make_list([c_tuple([meta(A), meta(V)])
+ || {A, V} <- module_attrs(Node)]),
+ make_list([c_tuple([meta(N), meta(F)])
+ || {N, F} <- module_defs(Node)])]).
+
+meta_call(F, As) ->
+ c_call(c_atom(?MODULE), c_atom(F), As).
+
+meta_list([T | Ts]) ->
+ [meta(T) | meta_list(Ts)];
+meta_list([]) ->
+ [].
+
+split_list(Node) ->
+ split_list(set_ann(Node, []), []).
+
+split_list(Node, L) ->
+ A = get_ann(Node),
+ case type(Node) of
+ cons when A =:= [] ->
+ split_list(cons_tl(Node), [cons_hd(Node) | L]);
+ _ ->
+ {lists:reverse(L), Node}
+ end.
+
+
+%% ---------------------------------------------------------------------
+
+%% General utilities
+
+is_lit_list([#c_literal{} | Es]) ->
+ is_lit_list(Es);
+is_lit_list([_ | _]) ->
+ false;
+is_lit_list([]) ->
+ true.
+
+lit_list_vals([#c_literal{val = V} | Es]) ->
+ [V | lit_list_vals(Es)];
+lit_list_vals([]) ->
+ [].
+
+-spec make_lit_list([litval()]) -> [c_literal()].
+
+make_lit_list([V | Vs]) ->
+ [#c_literal{val = V} | make_lit_list(Vs)];
+make_lit_list([]) ->
+ [].
+
+%% The following tests are the same as done by 'io_lib:char_list' and
+%% 'io_lib:printable_list', respectively, but for a single character.
+
+is_char_value(V) when V >= $\000, V =< $\377 -> true;
+is_char_value(_) -> false.
+
+is_print_char_value(V) when V >= $\040, V =< $\176 -> true;
+is_print_char_value(V) when V >= $\240, V =< $\377 -> true;
+is_print_char_value(V) when V =:= $\b -> true;
+is_print_char_value(V) when V =:= $\d -> true;
+is_print_char_value(V) when V =:= $\e -> true;
+is_print_char_value(V) when V =:= $\f -> true;
+is_print_char_value(V) when V =:= $\n -> true;
+is_print_char_value(V) when V =:= $\r -> true;
+is_print_char_value(V) when V =:= $\s -> true;
+is_print_char_value(V) when V =:= $\t -> true;
+is_print_char_value(V) when V =:= $\v -> true;
+is_print_char_value(V) when V =:= $\" -> true;
+is_print_char_value(V) when V =:= $\' -> true; %' stupid Emacs.
+is_print_char_value(V) when V =:= $\\ -> true;
+is_print_char_value(_) -> false.
+
+is_char_list([V | Vs]) when is_integer(V) ->
+ is_char_value(V) andalso is_char_list(Vs);
+is_char_list([]) ->
+ true;
+is_char_list(_) ->
+ false.
+
+is_print_char_list([V | Vs]) when is_integer(V) ->
+ is_print_char_value(V) andalso is_print_char_list(Vs);
+is_print_char_list([]) ->
+ true;
+is_print_char_list(_) ->
+ false.
+
+unfold_tuples([{X, Y} | Ps]) ->
+ [X, Y | unfold_tuples(Ps)];
+unfold_tuples([]) ->
+ [].
+
+fold_tuples([X, Y | Es]) ->
+ [{X, Y} | fold_tuples(Es)];
+fold_tuples([]) ->
+ [].
diff --git a/lib/dialyzer/test/opaque_SUITE_data/src/recrec/core_parse.hrl b/lib/dialyzer/test/opaque_SUITE_data/src/recrec/core_parse.hrl
new file mode 100644
index 0000000000..5823622f05
--- /dev/null
+++ b/lib/dialyzer/test/opaque_SUITE_data/src/recrec/core_parse.hrl
@@ -0,0 +1,122 @@
+%%
+%% %CopyrightBegin%
+%%
+%% Copyright Ericsson AB 1999-2016. All Rights Reserved.
+%%
+%% Licensed under the Apache License, Version 2.0 (the "License");
+%% you may not use this file except in compliance with the License.
+%% You may obtain a copy of the License at
+%%
+%% http://www.apache.org/licenses/LICENSE-2.0
+%%
+%% Unless required by applicable law or agreed to in writing, software
+%% distributed under the License is distributed on an "AS IS" BASIS,
+%% WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+%% See the License for the specific language governing permissions and
+%% limitations under the License.
+%%
+%% %CopyrightEnd%
+%%
+%% Purpose : Core Erlang syntax trees as records.
+
+%% It would be nice to incorporate some generic functions as well but
+%% this could make including this file difficult.
+
+%% Note: the annotation list is *always* the first record field.
+%% Thus it is possible to define the macros:
+%% -define(get_ann(X), element(2, X)).
+%% -define(set_ann(X, Y), setelement(2, X, Y)).
+
+%% The record definitions appear alphabetically
+
+-record(c_alias, {anno=[] :: cerl:anns(),
+ var :: cerl:c_var(),
+ pat :: cerl:cerl()}).
+
+-record(c_apply, {anno=[] :: cerl:anns(),
+ op :: cerl:c_var(),
+ args :: [cerl:cerl()]}).
+
+-record(c_binary, {anno=[] :: cerl:anns(),
+ segments :: [cerl:c_bitstr()]}).
+
+-record(c_bitstr, {anno=[], val, % val :: Tree,
+ size, % size :: Tree,
+ unit, % unit :: Tree,
+ type, % type :: Tree,
+ flags}). % flags :: Tree
+
+-record(c_call, {anno=[], module, % module :: cerl:cerl(),
+ name, % name :: cerl:cerl(),
+ args}). % args :: [cerl:cerl()]
+
+-record(c_case, {anno=[] :: cerl:anns(),
+ arg :: cerl:cerl(),
+ clauses :: [cerl:cerl()]}).
+
+-record(c_catch, {anno=[] :: cerl:anns(), body :: cerl:cerl()}).
+
+-record(c_clause, {anno=[] :: cerl:anns(),
+ pats, % :: [cerl:cerl()], % pats :: [Tree],
+ guard, % :: cerl:cerl(), % guard :: Tree,
+ body}). % :: cerl:cerl()}). % body :: Tree
+
+-record(c_cons, {anno=[] :: cerl:anns(),
+ hd :: cerl:cerl(),
+ tl :: cerl:cerl()}).
+
+-record(c_fun, {anno=[] :: cerl:anns(),
+ vars :: [cerl:c_var()],
+ body :: cerl:cerl()}).
+
+-record(c_let, {anno=[] :: cerl:anns(),
+ vars :: [cerl:c_var()],
+ arg :: cerl:cerl(),
+ body :: cerl:cerl()}).
+
+-record(c_letrec, {anno=[] :: cerl:anns(),
+ defs :: cerl:defs(),
+ body :: cerl:cerl()}).
+
+-record(c_literal, {anno=[] :: cerl:anns(), val :: cerl:litval()}).
+
+-record(c_map, {anno=[] :: cerl:anns(),
+ arg=#c_literal{val=#{}} :: cerl:c_var() | cerl:c_literal(),
+ es :: [cerl:c_map_pair()],
+ is_pat=false :: boolean()}).
+
+-record(c_map_pair, {anno=[] :: cerl:anns(),
+ op, %:: #c_literal{val::'assoc'} | #c_literal{val::'exact'},
+ key,
+ val}).
+
+-record(c_module, {anno=[] :: cerl:anns(),
+ name :: cerl:c_literal(),
+ exports :: [cerl:c_var()],
+ attrs :: cerl:attrs(),
+ defs :: cerl:defs()}).
+
+-record(c_primop, {anno=[] :: cerl:anns(),
+ name :: cerl:c_literal(),
+ args :: [cerl:cerl()]}).
+
+-record(c_receive, {anno=[]:: cerl:anns(),
+ clauses, % clauses :: [Tree],
+ timeout, % timeout :: Tree,
+ action}). % action :: Tree
+
+-record(c_seq, {anno=[] :: cerl:anns(),
+ arg, % arg :: cerl:cerl(),
+ body}). % body :: cerl:cerl()
+
+-record(c_try, {anno=[], arg, % arg :: cerl:cerl(),
+ vars, % vars :: [cerl:c_var()],
+ body, % body :: cerl:cerl(),
+ evars, % evars :: [cerl:c_var()],
+ handler}). % handler :: cerl:cerl()
+
+-record(c_tuple, {anno=[] :: cerl:anns(), es :: [cerl:cerl()]}).
+
+-record(c_values, {anno=[] :: cerl:anns(), es :: [cerl:cerl()]}).
+
+-record(c_var, {anno=[] :: cerl:anns(), name :: cerl:var_name()}).
diff --git a/lib/dialyzer/test/opaque_SUITE_data/src/recrec/dialyzer.hrl b/lib/dialyzer/test/opaque_SUITE_data/src/recrec/dialyzer.hrl
new file mode 100644
index 0000000000..ea6a71217c
--- /dev/null
+++ b/lib/dialyzer/test/opaque_SUITE_data/src/recrec/dialyzer.hrl
@@ -0,0 +1,180 @@
+%%% This is an -*- Erlang -*- file.
+%%%
+%%% %CopyrightBegin%
+%%%
+%%% Copyright Ericsson AB 2006-2015. All Rights Reserved.
+%%%
+%%% Licensed under the Apache License, Version 2.0 (the "License");
+%%% you may not use this file except in compliance with the License.
+%%% You may obtain a copy of the License at
+%%%
+%%% http://www.apache.org/licenses/LICENSE-2.0
+%%%
+%%% Unless required by applicable law or agreed to in writing, software
+%%% distributed under the License is distributed on an "AS IS" BASIS,
+%%% WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+%%% See the License for the specific language governing permissions and
+%%% limitations under the License.
+%%%
+%%% %CopyrightEnd%
+%%%
+%%%-------------------------------------------------------------------
+%%% File : dialyzer.hrl
+%%% Author : Tobias Lindahl <[email protected]>
+%%% Kostis Sagonas <[email protected]>
+%%% Description : Header file for Dialyzer.
+%%%
+%%% Created : 1 Oct 2004 by Kostis Sagonas <[email protected]>
+%%%-------------------------------------------------------------------
+
+-define(RET_NOTHING_SUSPICIOUS, 0).
+-define(RET_INTERNAL_ERROR, 1).
+-define(RET_DISCREPANCIES, 2).
+
+-type dial_ret() :: ?RET_NOTHING_SUSPICIOUS
+ | ?RET_INTERNAL_ERROR
+ | ?RET_DISCREPANCIES.
+
+%%--------------------------------------------------------------------
+%% Warning classification
+%%--------------------------------------------------------------------
+
+-define(WARN_RETURN_NO_RETURN, warn_return_no_exit).
+-define(WARN_RETURN_ONLY_EXIT, warn_return_only_exit).
+-define(WARN_NOT_CALLED, warn_not_called).
+-define(WARN_NON_PROPER_LIST, warn_non_proper_list).
+-define(WARN_FUN_APP, warn_fun_app).
+-define(WARN_MATCHING, warn_matching).
+-define(WARN_OPAQUE, warn_opaque).
+-define(WARN_FAILING_CALL, warn_failing_call).
+-define(WARN_BIN_CONSTRUCTION, warn_bin_construction).
+-define(WARN_CONTRACT_TYPES, warn_contract_types).
+-define(WARN_CONTRACT_SYNTAX, warn_contract_syntax).
+-define(WARN_CONTRACT_NOT_EQUAL, warn_contract_not_equal).
+-define(WARN_CONTRACT_SUBTYPE, warn_contract_subtype).
+-define(WARN_CONTRACT_SUPERTYPE, warn_contract_supertype).
+-define(WARN_CONTRACT_RANGE, warn_contract_range).
+-define(WARN_CALLGRAPH, warn_callgraph).
+-define(WARN_UNMATCHED_RETURN, warn_umatched_return).
+-define(WARN_RACE_CONDITION, warn_race_condition).
+-define(WARN_BEHAVIOUR, warn_behaviour).
+-define(WARN_UNDEFINED_CALLBACK, warn_undefined_callbacks).
+-define(WARN_UNKNOWN, warn_unknown).
+-define(WARN_MAP_CONSTRUCTION, warn_map_construction).
+
+%%
+%% The following type has double role:
+%% 1. It is the set of warnings that will be collected.
+%% 2. It is also the set of tags for warnings that will be returned.
+%%
+-type dial_warn_tag() :: ?WARN_RETURN_NO_RETURN | ?WARN_RETURN_ONLY_EXIT
+ | ?WARN_NOT_CALLED | ?WARN_NON_PROPER_LIST
+ | ?WARN_MATCHING | ?WARN_OPAQUE | ?WARN_FUN_APP
+ | ?WARN_FAILING_CALL | ?WARN_BIN_CONSTRUCTION
+ | ?WARN_CONTRACT_TYPES | ?WARN_CONTRACT_SYNTAX
+ | ?WARN_CONTRACT_NOT_EQUAL | ?WARN_CONTRACT_SUBTYPE
+ | ?WARN_CONTRACT_SUPERTYPE | ?WARN_CALLGRAPH
+ | ?WARN_UNMATCHED_RETURN | ?WARN_RACE_CONDITION
+ | ?WARN_BEHAVIOUR | ?WARN_CONTRACT_RANGE
+ | ?WARN_UNDEFINED_CALLBACK | ?WARN_UNKNOWN
+ | ?WARN_MAP_CONSTRUCTION.
+
+%%
+%% This is the representation of each warning as they will be returned
+%% to dialyzer's callers
+%%
+-type file_line() :: {file:filename(), non_neg_integer()}.
+-type dial_warning() :: {dial_warn_tag(), file_line(), {atom(), [term()]}}.
+
+%%
+%% This is the representation of each warning before suppressions have
+%% been applied
+%%
+-type m_or_mfa() :: module() % warnings not associated with any function
+ | mfa().
+-type warning_info() :: {file:filename(), non_neg_integer(), m_or_mfa()}.
+-type raw_warning() :: {dial_warn_tag(), warning_info(), {atom(), [term()]}}.
+
+%%
+%% This is the representation of dialyzer's internal errors
+%%
+-type dial_error() :: any(). %% XXX: underspecified
+
+%%--------------------------------------------------------------------
+%% Basic types used either in the record definitions below or in other
+%% parts of the application
+%%--------------------------------------------------------------------
+
+-type anal_type() :: 'succ_typings' | 'plt_build'.
+-type anal_type1() :: anal_type() | 'plt_add' | 'plt_check' | 'plt_remove'.
+-type contr_constr() :: {'subtype', erl_types:erl_type(), erl_types:erl_type()}.
+-type contract_pair() :: {erl_types:erl_type(), [contr_constr()]}.
+-type dial_define() :: {atom(), term()}.
+-type dial_option() :: {atom(), term()}.
+-type dial_options() :: [dial_option()].
+-type fopt() :: 'basename' | 'fullpath'.
+-type format() :: 'formatted' | 'raw'.
+-type label() :: non_neg_integer().
+-type dial_warn_tags():: ordsets:ordset(dial_warn_tag()).
+-type rep_mode() :: 'quiet' | 'normal' | 'verbose'.
+-type start_from() :: 'byte_code' | 'src_code'.
+-type mfa_or_funlbl() :: label() | mfa().
+-type solver() :: 'v1' | 'v2'.
+
+%%--------------------------------------------------------------------
+%% Record declarations used by various files
+%%--------------------------------------------------------------------
+
+-type doc_plt() :: 'undefined' | dialyzer_plt:plt().
+
+-record(analysis, {analysis_pid :: pid() | 'undefined',
+ type = succ_typings :: anal_type(),
+ defines = [] :: [dial_define()],
+ doc_plt :: doc_plt(),
+ files = [] :: [file:filename()],
+ include_dirs = [] :: [file:filename()],
+ start_from = byte_code :: start_from(),
+ plt :: dialyzer_plt:plt(),
+ use_contracts = true :: boolean(),
+ race_detection = false :: boolean(),
+ behaviours_chk = false :: boolean(),
+ timing = false :: boolean() | 'debug',
+ timing_server = none :: dialyzer_timing:timing_server(),
+ callgraph_file = "" :: file:filename(),
+ solvers :: [solver()]}).
+
+-record(options, {files = [] :: [file:filename()],
+ files_rec = [] :: [file:filename()],
+ analysis_type = succ_typings :: anal_type1(),
+ timing = false :: boolean() | 'debug',
+ defines = [] :: [dial_define()],
+ from = byte_code :: start_from(),
+ get_warnings = maybe :: boolean() | 'maybe',
+ init_plts = [] :: [file:filename()],
+ include_dirs = [] :: [file:filename()],
+ output_plt = none :: 'none' | file:filename(),
+ legal_warnings = ordsets:new() :: dial_warn_tags(),
+ report_mode = normal :: rep_mode(),
+ erlang_mode = false :: boolean(),
+ use_contracts = true :: boolean(),
+ output_file = none :: 'none' | file:filename(),
+ output_format = formatted :: format(),
+ filename_opt = basename :: fopt(),
+ callgraph_file = "" :: file:filename(),
+ check_plt = true :: boolean(),
+ solvers = [] :: [solver()]}).
+
+-record(contract, {contracts = [] :: [contract_pair()],
+ args = [] :: [erl_types:erl_type()],
+ forms = [] :: [{_, _}]}).
+
+%%--------------------------------------------------------------------
+
+-define(timing(Server, Msg, Var, Expr),
+ begin
+ dialyzer_timing:start_stamp(Server, Msg),
+ Var = Expr,
+ dialyzer_timing:end_stamp(Server),
+ Var
+ end).
+-define(timing(Server, Msg, Expr), ?timing(Server, Msg, _T, Expr)).
diff --git a/lib/dialyzer/test/opaque_SUITE_data/src/recrec/dialyzer_dataflow.erl b/lib/dialyzer/test/opaque_SUITE_data/src/recrec/dialyzer_dataflow.erl
new file mode 100644
index 0000000000..9399789464
--- /dev/null
+++ b/lib/dialyzer/test/opaque_SUITE_data/src/recrec/dialyzer_dataflow.erl
@@ -0,0 +1,3802 @@
+%% -*- erlang-indent-level: 2 -*-
+%%--------------------------------------------------------------------
+%% %CopyrightBegin%
+%%
+%% Copyright Ericsson AB 2006-2016. All Rights Reserved.
+%%
+%% Licensed under the Apache License, Version 2.0 (the "License");
+%% you may not use this file except in compliance with the License.
+%% You may obtain a copy of the License at
+%%
+%% http://www.apache.org/licenses/LICENSE-2.0
+%%
+%% Unless required by applicable law or agreed to in writing, software
+%% distributed under the License is distributed on an "AS IS" BASIS,
+%% WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+%% See the License for the specific language governing permissions and
+%% limitations under the License.
+%%
+%% %CopyrightEnd%
+%%
+
+%%%-------------------------------------------------------------------
+%%% File : dialyzer_dataflow.erl
+%%% Author : Tobias Lindahl <[email protected]>
+%%% Description :
+%%%
+%%% Created : 19 Apr 2005 by Tobias Lindahl <[email protected]>
+%%%-------------------------------------------------------------------
+
+-module(dialyzer_dataflow).
+
+-export([get_fun_types/5, get_warnings/5, format_args/3]).
+
+%% Data structure interfaces.
+-export([state__add_warning/2, state__cleanup/1,
+ state__duplicate/1, dispose_state/1,
+ state__get_callgraph/1, state__get_races/1,
+ state__get_records/1, state__put_callgraph/2,
+ state__put_races/2, state__records_only/1,
+ state__find_function/2]).
+
+-export_type([state/0]).
+
+-include("dialyzer.hrl").
+
+-import(erl_types,
+ [t_inf/2, t_inf/3, t_inf_lists/2, t_inf_lists/3,
+ t_inf_lists/3, t_is_equal/2, t_is_subtype/2, t_subtract/2,
+ t_sup/1, t_sup/2]).
+
+-import(erl_types,
+ [any_none/1, t_any/0, t_atom/0, t_atom/1, t_atom_vals/1, t_atom_vals/2,
+ t_binary/0, t_boolean/0,
+ t_bitstr/0, t_bitstr/2, t_bitstr_concat/1, t_bitstr_match/2,
+ t_cons/0, t_cons/2, t_cons_hd/2, t_cons_tl/2,
+ t_contains_opaque/2,
+ t_find_opaque_mismatch/3, t_float/0, t_from_range/2, t_from_term/1,
+ t_fun/0, t_fun/2, t_fun_args/1, t_fun_args/2, t_fun_range/1,
+ t_fun_range/2, t_integer/0, t_integers/1,
+ t_is_any/1, t_is_atom/1, t_is_atom/2, t_is_any_atom/3,
+ t_is_boolean/2,
+ t_is_integer/2, t_is_list/1,
+ t_is_nil/2, t_is_none/1, t_is_none_or_unit/1,
+ t_is_number/2, t_is_reference/2, t_is_pid/2, t_is_port/2,
+ t_is_unit/1,
+ t_limit/2, t_list/0, t_list_elements/2,
+ t_maybe_improper_list/0, t_module/0,
+ t_none/0, t_non_neg_integer/0, t_number/0, t_number_vals/2,
+ t_pid/0, t_port/0, t_product/1, t_reference/0,
+ t_to_string/2, t_to_tlist/1,
+ t_tuple/0, t_tuple/1, t_tuple_args/1, t_tuple_args/2,
+ t_tuple_subtypes/2,
+ t_unit/0, t_unopaque/2,
+ t_map/0, t_map/1, t_is_singleton/2
+ ]).
+
+%%-define(DEBUG, true).
+%%-define(DEBUG_PP, true).
+%%-define(DEBUG_TIME, true).
+
+-ifdef(DEBUG).
+-import(erl_types, [t_to_string/1]).
+-define(debug(S_, L_), io:format(S_, L_)).
+-else.
+-define(debug(S_, L_), ok).
+-endif.
+
+%%--------------------------------------------------------------------
+
+-type type() :: erl_types:erl_type().
+-type types() :: erl_types:type_table().
+
+-type curr_fun() :: 'undefined' | 'top' | mfa_or_funlbl().
+
+-define(no_arg, no_arg).
+
+-define(TYPE_LIMIT, 3).
+
+-define(BITS, 128).
+
+%% Types with comment 'race' are due to dialyzer_races.erl.
+-record(state, {callgraph :: dialyzer_callgraph:callgraph()
+ | 'undefined', % race
+ codeserver :: dialyzer_codeserver:codeserver()
+ | 'undefined', % race
+ envs :: env_tab()
+ | 'undefined', % race
+ fun_tab :: fun_tab()
+ | 'undefined', % race
+ fun_homes :: dict:dict(label(), mfa())
+ | 'undefined', % race
+ plt :: dialyzer_plt:plt()
+ | 'undefined', % race
+ opaques :: [type()]
+ | 'undefined', % race
+ races = dialyzer_races:new() :: dialyzer_races:races(),
+ records = dict:new() :: types(),
+ tree_map :: dict:dict(label(), cerl:cerl())
+ | 'undefined', % race
+ warning_mode = false :: boolean(),
+ warnings = [] :: [raw_warning()],
+ work :: {[_], [_], sets:set()}
+ | 'undefined', % race
+ module :: module(),
+ curr_fun :: curr_fun()
+ }).
+
+-record(map, {map = maps:new() :: type_tab(),
+ subst = maps:new() :: subst_tab(),
+ modified = [] :: [Key :: term()],
+ modified_stack = [] :: [{[Key :: term()],reference()}],
+ ref = undefined :: reference() | undefined}).
+
+-type env_tab() :: dict:dict(label(), #map{}).
+-type fun_entry() :: {Args :: [type()], RetType :: type()}.
+-type fun_tab() :: dict:dict('top' | label(),
+ {'not_handled', fun_entry()} | fun_entry()).
+-type key() :: label() | cerl:cerl().
+-type type_tab() :: #{key() => type()}.
+-type subst_tab() :: #{key() => cerl:cerl()}.
+
+%% Exported Types
+
+-opaque state() :: #state{}.
+
+%%--------------------------------------------------------------------
+
+-type fun_types() :: dict:dict(label(), type()).
+
+-spec get_warnings(cerl:c_module(), dialyzer_plt:plt(),
+ dialyzer_callgraph:callgraph(),
+ dialyzer_codeserver:codeserver(),
+ types()) ->
+ {[raw_warning()], fun_types()}.
+
+get_warnings(Tree, Plt, Callgraph, Codeserver, Records) ->
+ State1 = analyze_module(Tree, Plt, Callgraph, Codeserver, Records, true),
+ State2 = state__renew_warnings(state__get_warnings(State1), State1),
+ State3 = state__get_race_warnings(State2),
+ {State3#state.warnings, state__all_fun_types(State3)}.
+
+-spec get_fun_types(cerl:c_module(), dialyzer_plt:plt(),
+ dialyzer_callgraph:callgraph(),
+ dialyzer_codeserver:codeserver(),
+ types()) -> fun_types().
+
+get_fun_types(Tree, Plt, Callgraph, Codeserver, Records) ->
+ State = analyze_module(Tree, Plt, Callgraph, Codeserver, Records, false),
+ state__all_fun_types(State).
+
+%%% ===========================================================================
+%%%
+%%% The analysis.
+%%%
+%%% ===========================================================================
+
+analyze_module(Tree, Plt, Callgraph, Codeserver, Records, GetWarnings) ->
+ debug_pp(Tree, false),
+ Module = cerl:atom_val(cerl:module_name(Tree)),
+ TopFun = cerl:ann_c_fun([{label, top}], [], Tree),
+ State = state__new(Callgraph, Codeserver, TopFun, Plt, Module, Records),
+ State1 = state__race_analysis(not GetWarnings, State),
+ State2 = analyze_loop(State1),
+ case GetWarnings of
+ true ->
+ State3 = state__set_warning_mode(State2),
+ State4 = analyze_loop(State3),
+ dialyzer_races:race(State4);
+ false ->
+ State2
+ end.
+
+analyze_loop(State) ->
+ case state__get_work(State) of
+ none -> state__set_curr_fun(undefined, State);
+ {Fun, NewState0} ->
+ NewState1 = state__set_curr_fun(get_label(Fun), NewState0),
+ {ArgTypes, IsCalled} = state__get_args_and_status(Fun, NewState1),
+ case not IsCalled of
+ true ->
+ ?debug("Not handling (not called) ~w: ~s\n",
+ [NewState1#state.curr_fun,
+ t_to_string(t_product(ArgTypes))]),
+ analyze_loop(NewState1);
+ false ->
+ case state__fun_env(Fun, NewState1) of
+ none ->
+ ?debug("Not handling (no env) ~w: ~s\n",
+ [NewState1#state.curr_fun,
+ t_to_string(t_product(ArgTypes))]),
+ analyze_loop(NewState1);
+ Map ->
+ ?debug("Handling fun ~p: ~s\n",
+ [NewState1#state.curr_fun,
+ t_to_string(state__fun_type(Fun, NewState1))]),
+ Vars = cerl:fun_vars(Fun),
+ Map1 = enter_type_lists(Vars, ArgTypes, Map),
+ Body = cerl:fun_body(Fun),
+ FunLabel = get_label(Fun),
+ IsRaceAnalysisEnabled = is_race_analysis_enabled(State),
+ NewState3 =
+ case IsRaceAnalysisEnabled of
+ true ->
+ NewState2 = state__renew_curr_fun(
+ state__lookup_name(FunLabel, NewState1), FunLabel,
+ NewState1),
+ state__renew_race_list([], 0, NewState2);
+ false -> NewState1
+ end,
+ {NewState4, _Map2, BodyType} =
+ traverse(Body, Map1, NewState3),
+ ?debug("Done analyzing: ~w:~s\n",
+ [NewState1#state.curr_fun,
+ t_to_string(t_fun(ArgTypes, BodyType))]),
+ NewState5 =
+ case IsRaceAnalysisEnabled of
+ true -> renew_race_code(NewState4);
+ false -> NewState4
+ end,
+ NewState6 =
+ state__update_fun_entry(Fun, ArgTypes, BodyType, NewState5),
+ ?debug("done adding stuff for ~w\n",
+ [state__lookup_name(get_label(Fun), State)]),
+ analyze_loop(NewState6)
+ end
+ end
+ end.
+
+traverse(Tree, Map, State) ->
+ ?debug("Handling ~p\n", [cerl:type(Tree)]),
+ %% debug_pp_map(Map),
+ case cerl:type(Tree) of
+ alias ->
+ %% This only happens when checking for illegal record patterns
+ %% so the handling is a bit rudimentary.
+ traverse(cerl:alias_pat(Tree), Map, State);
+ apply ->
+ handle_apply(Tree, Map, State);
+ binary ->
+ Segs = cerl:binary_segments(Tree),
+ {State1, Map1, SegTypes} = traverse_list(Segs, Map, State),
+ {State1, Map1, t_bitstr_concat(SegTypes)};
+ bitstr ->
+ handle_bitstr(Tree, Map, State);
+ call ->
+ handle_call(Tree, Map, State);
+ 'case' ->
+ handle_case(Tree, Map, State);
+ 'catch' ->
+ {State1, _Map1, _} = traverse(cerl:catch_body(Tree), Map, State),
+ {State1, Map, t_any()};
+ cons ->
+ handle_cons(Tree, Map, State);
+ 'fun' ->
+ Type = state__fun_type(Tree, State),
+ case state__warning_mode(State) of
+ true -> {State, Map, Type};
+ false ->
+ State2 = state__add_work(get_label(Tree), State),
+ State3 = state__update_fun_env(Tree, Map, State2),
+ {State3, Map, Type}
+ end;
+ 'let' ->
+ handle_let(Tree, Map, State);
+ letrec ->
+ Defs = cerl:letrec_defs(Tree),
+ Body = cerl:letrec_body(Tree),
+ %% By not including the variables in scope we can assure that we
+ %% will get the current function type when using the variables.
+ FoldFun = fun({Var, Fun}, {AccState, AccMap}) ->
+ {NewAccState, NewAccMap0, FunType} =
+ traverse(Fun, AccMap, AccState),
+ NewAccMap = enter_type(Var, FunType, NewAccMap0),
+ {NewAccState, NewAccMap}
+ end,
+ {State1, Map1} = lists:foldl(FoldFun, {State, Map}, Defs),
+ traverse(Body, Map1, State1);
+ literal ->
+ Type = literal_type(Tree),
+ {State, Map, Type};
+ module ->
+ handle_module(Tree, Map, State);
+ primop ->
+ Type =
+ case cerl:atom_val(cerl:primop_name(Tree)) of
+ match_fail -> t_none();
+ raise -> t_none();
+ bs_init_writable -> t_from_term(<<>>);
+ Other -> erlang:error({'Unsupported primop', Other})
+ end,
+ {State, Map, Type};
+ 'receive' ->
+ handle_receive(Tree, Map, State);
+ seq ->
+ Arg = cerl:seq_arg(Tree),
+ Body = cerl:seq_body(Tree),
+ {State1, Map1, ArgType} = SMA = traverse(Arg, Map, State),
+ case t_is_none_or_unit(ArgType) of
+ true ->
+ SMA;
+ false ->
+ State2 =
+ case
+ t_is_any(ArgType)
+ orelse t_is_simple(ArgType, State)
+ orelse is_call_to_send(Arg)
+ orelse is_lc_simple_list(Arg, ArgType, State)
+ of
+ true -> % do not warn in these cases
+ State1;
+ false ->
+ state__add_warning(State1, ?WARN_UNMATCHED_RETURN, Arg,
+ {unmatched_return,
+ [format_type(ArgType, State1)]})
+ end,
+ traverse(Body, Map1, State2)
+ end;
+ 'try' ->
+ handle_try(Tree, Map, State);
+ tuple ->
+ handle_tuple(Tree, Map, State);
+ map ->
+ handle_map(Tree, Map, State);
+ values ->
+ Elements = cerl:values_es(Tree),
+ {State1, Map1, EsType} = traverse_list(Elements, Map, State),
+ Type = t_product(EsType),
+ {State1, Map1, Type};
+ var ->
+ ?debug("Looking up unknown variable: ~p\n", [Tree]),
+ case state__lookup_type_for_letrec(Tree, State) of
+ error ->
+ LType = lookup_type(Tree, Map),
+ {State, Map, LType};
+ {ok, Type} -> {State, Map, Type}
+ end;
+ Other ->
+ erlang:error({'Unsupported type', Other})
+ end.
+
+traverse_list(Trees, Map, State) ->
+ traverse_list(Trees, Map, State, []).
+
+traverse_list([Tree|Tail], Map, State, Acc) ->
+ {State1, Map1, Type} = traverse(Tree, Map, State),
+ traverse_list(Tail, Map1, State1, [Type|Acc]);
+traverse_list([], Map, State, Acc) ->
+ {State, Map, lists:reverse(Acc)}.
+
+%%________________________________________
+%%
+%% Special instructions
+%%
+
+handle_apply(Tree, Map, State) ->
+ Args = cerl:apply_args(Tree),
+ Op = cerl:apply_op(Tree),
+ {State0, Map1, ArgTypes} = traverse_list(Args, Map, State),
+ {State1, Map2, OpType} = traverse(Op, Map1, State0),
+ case any_none(ArgTypes) of
+ true ->
+ {State1, Map2, t_none()};
+ false ->
+ FunList =
+ case state__lookup_call_site(Tree, State) of
+ error -> [external]; %% so that we go directly in the fallback
+ {ok, List} -> List
+ end,
+ FunInfoList = [{local, state__fun_info(Fun, State)} || Fun <- FunList],
+ case
+ handle_apply_or_call(FunInfoList, Args, ArgTypes, Map2, Tree, State1)
+ of
+ {had_external, State2} ->
+ %% Fallback: use whatever info we collected from traversing the op
+ %% instead of the result that has been generalized to t_any().
+ Arity = length(Args),
+ OpType1 = t_inf(OpType, t_fun(Arity, t_any())),
+ case t_is_none(OpType1) of
+ true ->
+ Msg = {fun_app_no_fun,
+ [format_cerl(Op), format_type(OpType, State2), Arity]},
+ State3 = state__add_warning(State2, ?WARN_FAILING_CALL,
+ Tree, Msg),
+ {State3, Map2, t_none()};
+ false ->
+ NewArgs = t_inf_lists(ArgTypes,
+ t_fun_args(OpType1, 'universe')),
+ case any_none(NewArgs) of
+ true ->
+ Msg = {fun_app_args,
+ [format_args(Args, ArgTypes, State),
+ format_type(OpType, State)]},
+ State3 = state__add_warning(State2, ?WARN_FAILING_CALL,
+ Tree, Msg),
+ {State3, enter_type(Op, OpType1, Map2), t_none()};
+ false ->
+ Map3 = enter_type_lists(Args, NewArgs, Map2),
+ Range0 = t_fun_range(OpType1, 'universe'),
+ Range =
+ case t_is_unit(Range0) of
+ true -> t_none();
+ false -> Range0
+ end,
+ {State2, enter_type(Op, OpType1, Map3), Range}
+ end
+ end;
+ Normal -> Normal
+ end
+ end.
+
+handle_apply_or_call(FunInfoList, Args, ArgTypes, Map, Tree, State) ->
+ None = t_none(),
+ %% Call-site analysis may be inaccurate and consider more funs than those that
+ %% are actually possible. If all of them are incorrect, then warnings can be
+ %% emitted. If at least one fun is ok, however, then no warning is emitted,
+ %% just in case the bad ones are not really possible. The last argument is
+ %% used for this, with the following encoding:
+ %% Initial value: {none, []}
+ %% First fun checked: {one, <List of warns>}
+ %% More funs checked: {many, <List of warns>}
+ %% A '{one, []}' can only become '{many, []}'.
+ %% If at any point an fun does not add warnings, then the list is also
+ %% replaced with an empty list.
+ handle_apply_or_call(FunInfoList, Args, ArgTypes, Map, Tree, State,
+ [None || _ <- ArgTypes], None, false, {none, []}).
+
+handle_apply_or_call([{local, external}|Left], Args, ArgTypes, Map, Tree, State,
+ _AccArgTypes, _AccRet, _HadExternal, Warns) ->
+ {HowMany, _} = Warns,
+ NewHowMany =
+ case HowMany of
+ none -> one;
+ _ -> many
+ end,
+ NewWarns = {NewHowMany, []},
+ handle_apply_or_call(Left, Args, ArgTypes, Map, Tree, State,
+ ArgTypes, t_any(), true, NewWarns);
+handle_apply_or_call([{TypeOfApply, {Fun, Sig, Contr, LocalRet}}|Left],
+ Args, ArgTypes, Map, Tree,
+ #state{opaques = Opaques} = State,
+ AccArgTypes, AccRet, HadExternal, Warns) ->
+ Any = t_any(),
+ AnyArgs = [Any || _ <- Args],
+ GenSig = {AnyArgs, fun(_) -> t_any() end},
+ {CArgs, CRange} =
+ case Contr of
+ {value, #contract{args = As} = C} ->
+ {As, fun(FunArgs) ->
+ dialyzer_contracts:get_contract_return(C, FunArgs)
+ end};
+ none -> GenSig
+ end,
+ {BifArgs, BifRange} =
+ case TypeOfApply of
+ remote ->
+ {M, F, A} = Fun,
+ case erl_bif_types:is_known(M, F, A) of
+ true ->
+ BArgs = erl_bif_types:arg_types(M, F, A),
+ BRange =
+ fun(FunArgs) ->
+ erl_bif_types:type(M, F, A, FunArgs, Opaques)
+ end,
+ {BArgs, BRange};
+ false ->
+ GenSig
+ end;
+ local -> GenSig
+ end,
+ {SigArgs, SigRange} =
+ case Sig of
+ {value, {SR, SA}} -> {SA, SR};
+ none -> {AnyArgs, t_any()}
+ end,
+
+ ?debug("--------------------------------------------------------\n", []),
+ ?debug("Fun: ~p\n", [state__lookup_name(Fun, State)]),
+ ?debug("Module ~p\n", [State#state.module]),
+ ?debug("CArgs ~s\n", [erl_types:t_to_string(t_product(CArgs))]),
+ ?debug("ArgTypes ~s\n", [erl_types:t_to_string(t_product(ArgTypes))]),
+ ?debug("BifArgs ~p\n", [erl_types:t_to_string(t_product(BifArgs))]),
+
+ NewArgsSig = t_inf_lists(SigArgs, ArgTypes, Opaques),
+ ?debug("SigArgs ~s\n", [erl_types:t_to_string(t_product(SigArgs))]),
+ ?debug("NewArgsSig: ~s\n", [erl_types:t_to_string(t_product(NewArgsSig))]),
+ NewArgsContract = t_inf_lists(CArgs, ArgTypes, Opaques),
+ ?debug("NewArgsContract: ~s\n",
+ [erl_types:t_to_string(t_product(NewArgsContract))]),
+ NewArgsBif = t_inf_lists(BifArgs, ArgTypes, Opaques),
+ ?debug("NewArgsBif: ~s\n", [erl_types:t_to_string(t_product(NewArgsBif))]),
+ NewArgTypes0 = t_inf_lists(NewArgsSig, NewArgsContract),
+ NewArgTypes = t_inf_lists(NewArgTypes0, NewArgsBif, Opaques),
+ ?debug("NewArgTypes ~s\n", [erl_types:t_to_string(t_product(NewArgTypes))]),
+ ?debug("\n", []),
+
+ BifRet = BifRange(NewArgTypes),
+ ContrRet = CRange(NewArgTypes),
+ RetWithoutContr = t_inf(SigRange, BifRet),
+ RetWithoutLocal = t_inf(ContrRet, RetWithoutContr),
+
+ ?debug("RetWithoutContr: ~s\n",[erl_types:t_to_string(RetWithoutContr)]),
+ ?debug("RetWithoutLocal: ~s\n", [erl_types:t_to_string(RetWithoutLocal)]),
+ ?debug("BifRet: ~s\n", [erl_types:t_to_string(BifRange(NewArgTypes))]),
+ ?debug("SigRange: ~s\n", [erl_types:t_to_string(SigRange)]),
+ ?debug("ContrRet: ~s\n", [erl_types:t_to_string(ContrRet)]),
+ ?debug("LocalRet: ~s\n", [erl_types:t_to_string(LocalRet)]),
+
+ State1 =
+ case is_race_analysis_enabled(State) of
+ true ->
+ Ann = cerl:get_ann(Tree),
+ File = get_file(Ann),
+ Line = abs(get_line(Ann)),
+ dialyzer_races:store_race_call(Fun, ArgTypes, Args,
+ {File, Line}, State);
+ false -> State
+ end,
+ FailedConj = any_none([RetWithoutLocal|NewArgTypes]),
+ IsFailBif = t_is_none(BifRange(BifArgs)),
+ IsFailSig = t_is_none(SigRange),
+ ?debug("FailedConj: ~p~n", [FailedConj]),
+ ?debug("IsFailBif: ~p~n", [IsFailBif]),
+ ?debug("IsFailSig: ~p~n", [IsFailSig]),
+ State2 =
+ case FailedConj andalso not (IsFailBif orelse IsFailSig) of
+ true ->
+ case t_is_none(RetWithoutLocal) andalso
+ not t_is_none(RetWithoutContr) andalso
+ not any_none(NewArgTypes) of
+ true ->
+ {value, C1} = Contr,
+ Contract = dialyzer_contracts:contract_to_string(C1),
+ {M1, F1, A1} = state__lookup_name(Fun, State),
+ ArgStrings = format_args(Args, ArgTypes, State),
+ CRet = erl_types:t_to_string(RetWithoutContr),
+ %% This Msg will be post_processed by dialyzer_succ_typings
+ Msg =
+ {contract_range, [Contract, M1, F1, A1, ArgStrings, CRet]},
+ state__add_warning(State1, ?WARN_CONTRACT_RANGE, Tree, Msg);
+ false ->
+ FailedSig = any_none(NewArgsSig),
+ FailedContract =
+ any_none([CRange(NewArgsContract)|NewArgsContract]),
+ FailedBif = any_none([BifRange(NewArgsBif)|NewArgsBif]),
+ InfSig = t_inf(t_fun(SigArgs, SigRange),
+ t_fun(BifArgs, BifRange(BifArgs))),
+ FailReason =
+ apply_fail_reason(FailedSig, FailedBif, FailedContract),
+ Msg = get_apply_fail_msg(Fun, Args, ArgTypes, NewArgTypes, InfSig,
+ Contr, CArgs, State1, FailReason, Opaques),
+ WarnType = case Msg of
+ {call, _} -> ?WARN_FAILING_CALL;
+ {apply, _} -> ?WARN_FAILING_CALL;
+ {call_with_opaque, _} -> ?WARN_OPAQUE;
+ {call_without_opaque, _} -> ?WARN_OPAQUE;
+ {opaque_type_test, _} -> ?WARN_OPAQUE
+ end,
+ Frc = {erlang, is_record, 3} =:= state__lookup_name(Fun, State),
+ state__add_warning(State1, WarnType, Tree, Msg, Frc)
+ end;
+ false -> State1
+ end,
+ State3 =
+ case TypeOfApply of
+ local ->
+ case state__is_escaping(Fun, State2) of
+ true -> State2;
+ false ->
+ ForwardArgs = [t_limit(X, ?TYPE_LIMIT) || X <- ArgTypes],
+ forward_args(Fun, ForwardArgs, State2)
+ end;
+ remote ->
+ add_bif_warnings(Fun, NewArgTypes, Tree, State2)
+ end,
+ NewAccArgTypes =
+ case FailedConj of
+ true -> AccArgTypes;
+ false -> [t_sup(X, Y) || {X, Y} <- lists:zip(NewArgTypes, AccArgTypes)]
+ end,
+ TotalRet =
+ case t_is_none(LocalRet) andalso t_is_unit(RetWithoutLocal) of
+ true -> RetWithoutLocal;
+ false -> t_inf(RetWithoutLocal, LocalRet)
+ end,
+ NewAccRet = t_sup(AccRet, TotalRet),
+ ?debug("NewAccRet: ~s\n", [t_to_string(NewAccRet)]),
+ {NewWarnings, State4} = state__remove_added_warnings(State, State3),
+ {HowMany, OldWarnings} = Warns,
+ NewWarns =
+ case HowMany of
+ none -> {one, NewWarnings};
+ _ ->
+ case OldWarnings =:= [] of
+ true -> {many, []};
+ false ->
+ case NewWarnings =:= [] of
+ true -> {many, []};
+ false -> {many, NewWarnings ++ OldWarnings}
+ end
+ end
+ end,
+ handle_apply_or_call(Left, Args, ArgTypes, Map, Tree,
+ State4, NewAccArgTypes, NewAccRet, HadExternal, NewWarns);
+handle_apply_or_call([], Args, _ArgTypes, Map, _Tree, State,
+ AccArgTypes, AccRet, HadExternal, {_, Warnings}) ->
+ State1 = state__add_warnings(Warnings, State),
+ case HadExternal of
+ false ->
+ NewMap = enter_type_lists(Args, AccArgTypes, Map),
+ {State1, NewMap, AccRet};
+ true ->
+ {had_external, State1}
+ end.
+
+apply_fail_reason(FailedSig, FailedBif, FailedContract) ->
+ if
+ (FailedSig orelse FailedBif) andalso (not FailedContract) -> only_sig;
+ FailedContract andalso (not (FailedSig orelse FailedBif)) -> only_contract;
+ true -> both
+ end.
+
+get_apply_fail_msg(Fun, Args, ArgTypes, NewArgTypes,
+ Sig, Contract, ContrArgs, State, FailReason, Opaques) ->
+ ArgStrings = format_args(Args, ArgTypes, State),
+ ContractInfo =
+ case Contract of
+ {value, #contract{} = C} ->
+ {dialyzer_contracts:is_overloaded(C),
+ dialyzer_contracts:contract_to_string(C)};
+ none -> {false, none}
+ end,
+ EnumArgTypes = lists:zip(lists:seq(1, length(NewArgTypes)), NewArgTypes),
+ ArgNs = [Arg || {Arg, Type} <- EnumArgTypes, t_is_none(Type)],
+ case state__lookup_name(Fun, State) of
+ {M, F, A} ->
+ case is_opaque_type_test_problem(Fun, Args, NewArgTypes, State) of
+ {yes, Arg, ArgType} ->
+ {opaque_type_test, [atom_to_list(F), ArgStrings,
+ format_arg(Arg), format_type(ArgType, State)]};
+ no ->
+ SigArgs = t_fun_args(Sig),
+ BadOpaque =
+ opaque_problems([SigArgs, ContrArgs], ArgTypes, Opaques, ArgNs),
+ %% In fact *both* 'call_with_opaque' and
+ %% 'call_without_opaque' are possible.
+ case lists:keyfind(decl, 1, BadOpaque) of
+ {decl, BadArgs} ->
+ %% a structured term is used where an opaque is expected
+ ExpectedTriples =
+ case FailReason of
+ only_sig -> expected_arg_triples(BadArgs, SigArgs, State);
+ _ -> expected_arg_triples(BadArgs, ContrArgs, State)
+ end,
+ {call_without_opaque, [M, F, ArgStrings, ExpectedTriples]};
+ false ->
+ case lists:keyfind(use, 1, BadOpaque) of
+ {use, BadArgs} ->
+ %% an opaque term is used where a structured term is expected
+ ExpectedArgs =
+ case FailReason of
+ only_sig -> SigArgs;
+ _ -> ContrArgs
+ end,
+ {call_with_opaque, [M, F, ArgStrings, BadArgs, ExpectedArgs]};
+ false ->
+ case
+ erl_bif_types:opaque_args(M, F, A, ArgTypes, Opaques)
+ of
+ [] -> %% there is a structured term clash in some argument
+ {call, [M, F, ArgStrings,
+ ArgNs, FailReason,
+ format_sig_args(Sig, State),
+ format_type(t_fun_range(Sig), State),
+ ContractInfo]};
+ Ns ->
+ {call_with_opaque, [M, F, ArgStrings, Ns, ContrArgs]}
+ end
+ end
+ end
+ end;
+ Label when is_integer(Label) ->
+ {apply, [ArgStrings,
+ ArgNs, FailReason,
+ format_sig_args(Sig, State),
+ format_type(t_fun_range(Sig), State),
+ ContractInfo]}
+ end.
+
+%% -> [{ElementI, [ArgN]}] where [ArgN] is a non-empty list of
+%% arguments containing unknown opaque types and Element is 1 or 2.
+opaque_problems(ContractOrSigList, ArgTypes, Opaques, ArgNs) ->
+ ArgElementList = find_unknown(ContractOrSigList, ArgTypes, Opaques, ArgNs),
+ F = fun(1) -> decl; (2) -> use end,
+ [{F(ElementI), lists:usort([ArgN || {ArgN, EI} <- ArgElementList,
+ EI =:= ElementI])} ||
+ ElementI <- lists:usort([EI || {_, EI} <- ArgElementList])].
+
+%% -> [{ArgN, ElementI}] where ElementI = 1 means there is an unknown
+%% opaque type in argument ArgN of the the contract/signature,
+%% and ElementI = 2 means that there is an unknown opaque type in
+%% argument ArgN of the the (current) argument types.
+find_unknown(ContractOrSigList, ArgTypes, Opaques, NoneArgNs) ->
+ ArgNs = lists:seq(1, length(ArgTypes)),
+ [{ArgN, ElementI} ||
+ ContractOrSig <- ContractOrSigList,
+ {E1, E2, ArgN} <- lists:zip3(ContractOrSig, ArgTypes, ArgNs),
+ lists:member(ArgN, NoneArgNs),
+ ElementI <- erl_types:t_find_unknown_opaque(E1, E2, Opaques)].
+
+is_opaque_type_test_problem(Fun, Args, ArgTypes, State) ->
+ case Fun of
+ {erlang, FN, 1} when FN =:= is_atom; FN =:= is_boolean;
+ FN =:= is_binary; FN =:= is_bitstring;
+ FN =:= is_float; FN =:= is_function;
+ FN =:= is_integer; FN =:= is_list;
+ FN =:= is_number; FN =:= is_pid; FN =:= is_port;
+ FN =:= is_reference; FN =:= is_tuple;
+ FN =:= is_map ->
+ type_test_opaque_arg(Args, ArgTypes, State#state.opaques);
+ {erlang, FN, 2} when FN =:= is_function ->
+ type_test_opaque_arg(Args, ArgTypes, State#state.opaques);
+ _ -> no
+ end.
+
+type_test_opaque_arg([], [], _Opaques) ->
+ no;
+type_test_opaque_arg([Arg|Args], [ArgType|ArgTypes], Opaques) ->
+ case erl_types:t_has_opaque_subtype(ArgType, Opaques) of
+ true -> {yes, Arg, ArgType};
+ false -> type_test_opaque_arg(Args, ArgTypes, Opaques)
+ end.
+
+expected_arg_triples(ArgNs, ArgTypes, State) ->
+ [begin
+ Arg = lists:nth(N, ArgTypes),
+ {N, Arg, format_type(Arg, State)}
+ end || N <- ArgNs].
+
+add_bif_warnings({erlang, Op, 2}, [T1, T2] = Ts, Tree, State)
+ when Op =:= '=:='; Op =:= '==' ->
+ Opaques = State#state.opaques,
+ Inf = t_inf(T1, T2, Opaques),
+ case
+ t_is_none(Inf) andalso (not any_none(Ts))
+ andalso (not is_int_float_eq_comp(T1, Op, T2, Opaques))
+ of
+ true ->
+ %% Give priority to opaque warning (as usual).
+ case erl_types:t_find_unknown_opaque(T1, T2, Opaques) of
+ [] ->
+ Args = comp_format_args([], T1, Op, T2, State),
+ state__add_warning(State, ?WARN_MATCHING, Tree, {exact_eq, Args});
+ Ns ->
+ Args = comp_format_args(Ns, T1, Op, T2, State),
+ state__add_warning(State, ?WARN_OPAQUE, Tree, {opaque_eq, Args})
+ end;
+ false ->
+ State
+ end;
+add_bif_warnings({erlang, Op, 2}, [T1, T2] = Ts, Tree, State)
+ when Op =:= '=/='; Op =:= '/=' ->
+ Opaques = State#state.opaques,
+ case
+ (not any_none(Ts))
+ andalso (not is_int_float_eq_comp(T1, Op, T2, Opaques))
+ of
+ true ->
+ case erl_types:t_find_unknown_opaque(T1, T2, Opaques) of
+ [] -> State;
+ Ns ->
+ Args = comp_format_args(Ns, T1, Op, T2, State),
+ state__add_warning(State, ?WARN_OPAQUE, Tree, {opaque_neq, Args})
+ end;
+ false ->
+ State
+ end;
+add_bif_warnings(_, _, _, State) ->
+ State.
+
+is_int_float_eq_comp(T1, Op, T2, Opaques) ->
+ (Op =:= '==' orelse Op =:= '/=') andalso
+ ((erl_types:t_is_float(T1, Opaques)
+ andalso t_is_integer(T2, Opaques)) orelse
+ (t_is_integer(T1, Opaques)
+ andalso erl_types:t_is_float(T2, Opaques))).
+
+comp_format_args([1|_], T1, Op, T2, State) ->
+ [format_type(T2, State), Op, format_type(T1, State)];
+comp_format_args(_, T1, Op, T2, State) ->
+ [format_type(T1, State), Op, format_type(T2, State)].
+
+%%----------------------------------------
+
+handle_bitstr(Tree, Map, State) ->
+ %% Construction of binaries.
+ Size = cerl:bitstr_size(Tree),
+ Val = cerl:bitstr_val(Tree),
+ BitstrType = cerl:concrete(cerl:bitstr_type(Tree)),
+ {State1, Map1, SizeType0} = traverse(Size, Map, State),
+ {State2, Map2, ValType0} = traverse(Val, Map1, State1),
+ case cerl:bitstr_bitsize(Tree) of
+ BitSz when BitSz =:= all orelse BitSz =:= utf ->
+ ValType =
+ case BitSz of
+ all ->
+ true = (BitstrType =:= binary),
+ t_inf(ValType0, t_bitstr());
+ utf ->
+ true = lists:member(BitstrType, [utf8, utf16, utf32]),
+ t_inf(ValType0, t_integer())
+ end,
+ Map3 = enter_type(Val, ValType, Map2),
+ case t_is_none(ValType) of
+ true ->
+ Msg = {bin_construction, ["value",
+ format_cerl(Val), format_cerl(Tree),
+ format_type(ValType0, State2)]},
+ State3 = state__add_warning(State2, ?WARN_BIN_CONSTRUCTION, Val, Msg),
+ {State3, Map3, t_none()};
+ false ->
+ {State2, Map3, t_bitstr()}
+ end;
+ BitSz when is_integer(BitSz) orelse BitSz =:= any ->
+ SizeType = t_inf(SizeType0, t_non_neg_integer()),
+ ValType =
+ case BitstrType of
+ binary -> t_inf(ValType0, t_bitstr());
+ float -> t_inf(ValType0, t_number());
+ integer -> t_inf(ValType0, t_integer())
+ end,
+ case any_none([SizeType, ValType]) of
+ true ->
+ {Msg, Offending} =
+ case t_is_none(SizeType) of
+ true ->
+ {{bin_construction,
+ ["size", format_cerl(Size), format_cerl(Tree),
+ format_type(SizeType0, State2)]},
+ Size};
+ false ->
+ {{bin_construction,
+ ["value", format_cerl(Val), format_cerl(Tree),
+ format_type(ValType0, State2)]},
+ Val}
+ end,
+ State3 = state__add_warning(State2, ?WARN_BIN_CONSTRUCTION,
+ Offending, Msg),
+ {State3, Map2, t_none()};
+ false ->
+ UnitVal = cerl:concrete(cerl:bitstr_unit(Tree)),
+ Opaques = State2#state.opaques,
+ NumberVals = t_number_vals(SizeType, Opaques),
+ {State3, Type} =
+ case t_contains_opaque(SizeType, Opaques) of
+ true ->
+ Msg = {opaque_size, [format_type(SizeType, State2),
+ format_cerl(Size)]},
+ {state__add_warning(State2, ?WARN_OPAQUE, Size, Msg),
+ t_none()};
+ false ->
+ case NumberVals of
+ [OneSize] -> {State2, t_bitstr(0, OneSize * UnitVal)};
+ unknown -> {State2, t_bitstr()};
+ _ ->
+ MinSize = erl_types:number_min(SizeType, Opaques),
+ {State2, t_bitstr(UnitVal, UnitVal * MinSize)}
+ end
+ end,
+ Map3 = enter_type_lists([Val, Size, Tree],
+ [ValType, SizeType, Type], Map2),
+ {State3, Map3, Type}
+ end
+ end.
+
+%%----------------------------------------
+
+handle_call(Tree, Map, State) ->
+ M = cerl:call_module(Tree),
+ F = cerl:call_name(Tree),
+ Args = cerl:call_args(Tree),
+ MFAList = [M, F|Args],
+ {State1, Map1, [MType0, FType0|As]} = traverse_list(MFAList, Map, State),
+ Opaques = State#state.opaques,
+ MType = t_inf(t_module(), MType0, Opaques),
+ FType = t_inf(t_atom(), FType0, Opaques),
+ Map2 = enter_type_lists([M, F], [MType, FType], Map1),
+ MOpaque = t_is_none(MType) andalso (not t_is_none(MType0)),
+ FOpaque = t_is_none(FType) andalso (not t_is_none(FType0)),
+ case any_none([MType, FType|As]) of
+ true ->
+ State2 =
+ if
+ MOpaque -> % This is a problem we just detected; not a known one
+ MS = format_cerl(M),
+ case t_is_none(t_inf(t_module(), MType0)) of
+ true ->
+ Msg = {app_call, [MS, format_cerl(F),
+ format_args(Args, As, State1),
+ MS, format_type(t_module(), State1),
+ format_type(MType0, State1)]},
+ state__add_warning(State1, ?WARN_FAILING_CALL, Tree, Msg);
+ false ->
+ Msg = {opaque_call, [MS, format_cerl(F),
+ format_args(Args, As, State1),
+ MS, format_type(MType0, State1)]},
+ state__add_warning(State1, ?WARN_FAILING_CALL, Tree, Msg)
+ end;
+ FOpaque ->
+ FS = format_cerl(F),
+ case t_is_none(t_inf(t_atom(), FType0)) of
+ true ->
+ Msg = {app_call, [format_cerl(M), FS,
+ format_args(Args, As, State1),
+ FS, format_type(t_atom(), State1),
+ format_type(FType0, State1)]},
+ state__add_warning(State1, ?WARN_FAILING_CALL, Tree, Msg);
+ false ->
+ Msg = {opaque_call, [format_cerl(M), FS,
+ format_args(Args, As, State1),
+ FS, format_type(FType0, State1)]},
+ state__add_warning(State1, ?WARN_FAILING_CALL, Tree, Msg)
+ end;
+ true -> State1
+ end,
+ {State2, Map2, t_none()};
+ false ->
+ case t_is_atom(MType) of
+ true ->
+ %% XXX: Consider doing this for all combinations of MF
+ case {t_atom_vals(MType), t_atom_vals(FType)} of
+ {[MAtom], [FAtom]} ->
+ FunInfo = [{remote, state__fun_info({MAtom, FAtom, length(Args)},
+ State1)}],
+ handle_apply_or_call(FunInfo, Args, As, Map2, Tree, State1);
+ {_MAtoms, _FAtoms} ->
+ {State1, Map2, t_any()}
+ end;
+ false ->
+ {State1, Map2, t_any()}
+ end
+ end.
+
+%%----------------------------------------
+
+handle_case(Tree, Map, State) ->
+ Arg = cerl:case_arg(Tree),
+ Clauses = filter_match_fail(cerl:case_clauses(Tree)),
+ {State1, Map1, ArgType} = SMA = traverse(Arg, Map, State),
+ case t_is_none_or_unit(ArgType) of
+ true -> SMA;
+ false ->
+ State2 =
+ case is_race_analysis_enabled(State) of
+ true ->
+ {RaceList, RaceListSize} = get_race_list_and_size(State1),
+ state__renew_race_list([beg_case|RaceList],
+ RaceListSize + 1, State1);
+ false -> State1
+ end,
+ Map2 = join_maps_begin(Map1),
+ {MapList, State3, Type} =
+ handle_clauses(Clauses, Arg, ArgType, ArgType, State2,
+ [], Map2, [], []),
+ Map3 = join_maps_end(MapList, Map2),
+ debug_pp_map(Map3),
+ {State3, Map3, Type}
+ end.
+
+%%----------------------------------------
+
+handle_cons(Tree, Map, State) ->
+ Hd = cerl:cons_hd(Tree),
+ Tl = cerl:cons_tl(Tree),
+ {State1, Map1, HdType} = traverse(Hd, Map, State),
+ {State2, Map2, TlType} = traverse(Tl, Map1, State1),
+ State3 =
+ case t_is_none(t_inf(TlType, t_list(), State2#state.opaques)) of
+ true ->
+ Msg = {improper_list_constr, [format_type(TlType, State2)]},
+ state__add_warning(State2, ?WARN_NON_PROPER_LIST, Tree, Msg);
+ false ->
+ State2
+ end,
+ Type = t_cons(HdType, TlType),
+ {State3, Map2, Type}.
+
+%%----------------------------------------
+
+handle_let(Tree, Map, State) ->
+ IsRaceAnalysisEnabled = is_race_analysis_enabled(State),
+ Arg = cerl:let_arg(Tree),
+ Vars = cerl:let_vars(Tree),
+ {Map0, State0} =
+ case cerl:is_c_var(Arg) of
+ true ->
+ [Var] = Vars,
+ {enter_subst(Var, Arg, Map),
+ case IsRaceAnalysisEnabled of
+ true ->
+ {RaceList, RaceListSize} = get_race_list_and_size(State),
+ state__renew_race_list(
+ [dialyzer_races:let_tag_new(Var, Arg)|RaceList],
+ RaceListSize + 1, State);
+ false -> State
+ end};
+ false -> {Map, State}
+ end,
+ Body = cerl:let_body(Tree),
+ {State1, Map1, ArgTypes} = SMA = traverse(Arg, Map0, State0),
+ State2 =
+ case IsRaceAnalysisEnabled andalso cerl:is_c_call(Arg) of
+ true ->
+ Mod = cerl:call_module(Arg),
+ Name = cerl:call_name(Arg),
+ case cerl:is_literal(Mod) andalso
+ cerl:concrete(Mod) =:= ets andalso
+ cerl:is_literal(Name) andalso
+ cerl:concrete(Name) =:= new of
+ true -> renew_race_public_tables(Vars, State1);
+ false -> State1
+ end;
+ false -> State1
+ end,
+ case t_is_none_or_unit(ArgTypes) of
+ true -> SMA;
+ false ->
+ Map2 = enter_type_lists(Vars, t_to_tlist(ArgTypes), Map1),
+ traverse(Body, Map2, State2)
+ end.
+
+%%----------------------------------------
+
+handle_module(Tree, Map, State) ->
+ %% By not including the variables in scope we can assure that we
+ %% will get the current function type when using the variables.
+ Defs = cerl:module_defs(Tree),
+ PartFun = fun({_Var, Fun}) ->
+ state__is_escaping(get_label(Fun), State)
+ end,
+ {Defs1, Defs2} = lists:partition(PartFun, Defs),
+ Letrec = cerl:c_letrec(Defs1, cerl:c_int(42)),
+ {State1, Map1, _FunTypes} = traverse(Letrec, Map, State),
+ %% Also add environments for the other top-level functions.
+ VarTypes = [{Var, state__fun_type(Fun, State1)} || {Var, Fun} <- Defs],
+ EnvMap = enter_type_list(VarTypes, Map),
+ FoldFun = fun({_Var, Fun}, AccState) ->
+ state__update_fun_env(Fun, EnvMap, AccState)
+ end,
+ State2 = lists:foldl(FoldFun, State1, Defs2),
+ {State2, Map1, t_any()}.
+
+%%----------------------------------------
+
+handle_receive(Tree, Map, State) ->
+ Clauses = filter_match_fail(cerl:receive_clauses(Tree)),
+ Timeout = cerl:receive_timeout(Tree),
+ State1 =
+ case is_race_analysis_enabled(State) of
+ true ->
+ {RaceList, RaceListSize} = get_race_list_and_size(State),
+ state__renew_race_list([beg_case|RaceList],
+ RaceListSize + 1, State);
+ false -> State
+ end,
+ {MapList, State2, ReceiveType} =
+ handle_clauses(Clauses, ?no_arg, t_any(), t_any(), State1, [], Map,
+ [], []),
+ Map1 = join_maps(MapList, Map),
+ {State3, Map2, TimeoutType} = traverse(Timeout, Map1, State2),
+ Opaques = State3#state.opaques,
+ case (t_is_atom(TimeoutType, Opaques) andalso
+ (t_atom_vals(TimeoutType, Opaques) =:= ['infinity'])) of
+ true ->
+ {State3, Map2, ReceiveType};
+ false ->
+ Action = cerl:receive_action(Tree),
+ {State4, Map3, ActionType} = traverse(Action, Map, State3),
+ Map4 = join_maps([Map3, Map1], Map),
+ Type = t_sup(ReceiveType, ActionType),
+ {State4, Map4, Type}
+ end.
+
+%%----------------------------------------
+
+handle_try(Tree, Map, State) ->
+ Arg = cerl:try_arg(Tree),
+ EVars = cerl:try_evars(Tree),
+ Vars = cerl:try_vars(Tree),
+ Body = cerl:try_body(Tree),
+ Handler = cerl:try_handler(Tree),
+ {State1, Map1, ArgType} = traverse(Arg, Map, State),
+ Map2 = mark_as_fresh(Vars, Map1),
+ {SuccState, SuccMap, SuccType} =
+ case bind_pat_vars(Vars, t_to_tlist(ArgType), [], Map2, State1) of
+ {error, _, _, _, _} ->
+ {State1, map__new(), t_none()};
+ {SuccMap1, VarTypes} ->
+ %% Try to bind the argument. Will only succeed if
+ %% it is a simple structured term.
+ SuccMap2 =
+ case bind_pat_vars_reverse([Arg], [t_product(VarTypes)], [],
+ SuccMap1, State1) of
+ {error, _, _, _, _} -> SuccMap1;
+ {SM, _} -> SM
+ end,
+ traverse(Body, SuccMap2, State1)
+ end,
+ ExcMap1 = mark_as_fresh(EVars, Map),
+ {State2, ExcMap2, HandlerType} = traverse(Handler, ExcMap1, SuccState),
+ TryType = t_sup(SuccType, HandlerType),
+ {State2, join_maps([ExcMap2, SuccMap], Map1), TryType}.
+
+%%----------------------------------------
+
+handle_map(Tree,Map,State) ->
+ Pairs = cerl:map_es(Tree),
+ Arg = cerl:map_arg(Tree),
+ {State1, Map1, ArgType} = traverse(Arg, Map, State),
+ ArgType1 = t_inf(t_map(), ArgType),
+ case t_is_none_or_unit(ArgType1) of
+ true ->
+ {State1, Map1, ArgType1};
+ false ->
+ {State2, Map2, TypePairs, ExactKeys} =
+ traverse_map_pairs(Pairs, Map1, State1, t_none(), [], []),
+ InsertPair = fun({KV,assoc,_},Acc) -> erl_types:t_map_put(KV,Acc);
+ ({KV,exact,KVTree},Acc) ->
+ case t_is_none(T=erl_types:t_map_update(KV,Acc)) of
+ true -> throw({none, Acc, KV, KVTree});
+ false -> T
+ end
+ end,
+ try lists:foldl(InsertPair, ArgType1, TypePairs)
+ of ResT ->
+ BindT = t_map([{K, t_any()} || K <- ExactKeys]),
+ case bind_pat_vars_reverse([Arg], [BindT], [], Map2, State2) of
+ {error, _, _, _, _} -> {State2, Map2, ResT};
+ {Map3, _} -> {State2, Map3, ResT}
+ end
+ catch {none, MapType, {K,_}, KVTree} ->
+ Msg2 = {map_update, [format_type(MapType, State2),
+ format_type(K, State2)]},
+ {state__add_warning(State2, ?WARN_MAP_CONSTRUCTION, KVTree, Msg2),
+ Map2, t_none()}
+ end
+ end.
+
+traverse_map_pairs([], Map, State, _ShadowKeys, PairAcc, KeyAcc) ->
+ {State, Map, lists:reverse(PairAcc), KeyAcc};
+traverse_map_pairs([Pair|Pairs], Map, State, ShadowKeys, PairAcc, KeyAcc) ->
+ Key = cerl:map_pair_key(Pair),
+ Val = cerl:map_pair_val(Pair),
+ Op = cerl:map_pair_op(Pair),
+ {State1, Map1, [K,V]} = traverse_list([Key,Val],Map,State),
+ KeyAcc1 =
+ case cerl:is_literal(Op) andalso cerl:concrete(Op) =:= exact andalso
+ t_is_singleton(K, State#state.opaques) andalso
+ t_is_none(t_inf(ShadowKeys, K)) of
+ true -> [K|KeyAcc];
+ false -> KeyAcc
+ end,
+ traverse_map_pairs(Pairs, Map1, State1, t_sup(K, ShadowKeys),
+ [{{K,V},cerl:concrete(Op),Pair}|PairAcc], KeyAcc1).
+
+%%----------------------------------------
+
+handle_tuple(Tree, Map, State) ->
+ Elements = cerl:tuple_es(Tree),
+ {State1, Map1, EsType} = traverse_list(Elements, Map, State),
+ TupleType = t_tuple(EsType),
+ case t_is_none(TupleType) of
+ true ->
+ {State1, Map1, t_none()};
+ false ->
+ %% Let's find out if this is a record
+ case Elements of
+ [Tag|Left] ->
+ case cerl:is_c_atom(Tag) andalso is_literal_record(Tree) of
+ true ->
+ TagVal = cerl:atom_val(Tag),
+ case state__lookup_record(TagVal, length(Left), State1) of
+ error -> {State1, Map1, TupleType};
+ {ok, RecType} ->
+ InfTupleType = t_inf(RecType, TupleType),
+ case t_is_none(InfTupleType) of
+ true ->
+ RecC = format_type(TupleType, State1),
+ FieldDiffs = format_field_diffs(TupleType, State1),
+ Msg = {record_constr, [RecC, FieldDiffs]},
+ State2 = state__add_warning(State1, ?WARN_MATCHING,
+ Tree, Msg),
+ {State2, Map1, t_none()};
+ false ->
+ case bind_pat_vars(Elements, t_tuple_args(RecType),
+ [], Map1, State1) of
+ {error, bind, ErrorPat, ErrorType, _} ->
+ Msg = {record_constr,
+ [TagVal, format_patterns(ErrorPat),
+ format_type(ErrorType, State1)]},
+ State2 = state__add_warning(State1, ?WARN_MATCHING,
+ Tree, Msg),
+ {State2, Map1, t_none()};
+ {error, opaque, ErrorPat, ErrorType, OpaqueType} ->
+ Msg = {opaque_match,
+ [format_patterns(ErrorPat),
+ format_type(ErrorType, State1),
+ format_type(OpaqueType, State1)]},
+ State2 = state__add_warning(State1, ?WARN_OPAQUE,
+ Tree, Msg),
+ {State2, Map1, t_none()};
+ {Map2, ETypes} ->
+ {State1, Map2, t_tuple(ETypes)}
+ end
+ end
+ end;
+ false ->
+ {State1, Map1, t_tuple(EsType)}
+ end;
+ [] ->
+ {State1, Map1, t_tuple([])}
+ end
+ end.
+
+%%----------------------------------------
+%% Clauses
+%%
+handle_clauses([C|Left], Arg, ArgType, OrigArgType, State, CaseTypes, MapIn,
+ Acc, ClauseAcc) ->
+ IsRaceAnalysisEnabled = is_race_analysis_enabled(State),
+ State1 =
+ case IsRaceAnalysisEnabled of
+ true ->
+ {RaceList, RaceListSize} = get_race_list_and_size(State),
+ state__renew_race_list(
+ [dialyzer_races:beg_clause_new(Arg, cerl:clause_pats(C),
+ cerl:clause_guard(C))|
+ RaceList], RaceListSize + 1,
+ State);
+ false -> State
+ end,
+ {State2, ClauseMap, BodyType, NewArgType} =
+ do_clause(C, Arg, ArgType, OrigArgType, MapIn, State1),
+ {NewClauseAcc, State3} =
+ case IsRaceAnalysisEnabled of
+ true ->
+ {RaceList1, RaceListSize1} = get_race_list_and_size(State2),
+ EndClause = dialyzer_races:end_clause_new(Arg, cerl:clause_pats(C),
+ cerl:clause_guard(C)),
+ {[EndClause|ClauseAcc],
+ state__renew_race_list([EndClause|RaceList1],
+ RaceListSize1 + 1, State2)};
+ false -> {ClauseAcc, State2}
+ end,
+ {NewCaseTypes, NewAcc} =
+ case t_is_none(BodyType) of
+ true -> {CaseTypes, Acc};
+ false -> {[BodyType|CaseTypes], [ClauseMap|Acc]}
+ end,
+ handle_clauses(Left, Arg, NewArgType, OrigArgType, State3,
+ NewCaseTypes, MapIn, NewAcc, NewClauseAcc);
+handle_clauses([], _Arg, _ArgType, _OrigArgType, State, CaseTypes, _MapIn, Acc,
+ ClauseAcc) ->
+ State1 =
+ case is_race_analysis_enabled(State) of
+ true ->
+ {RaceList, RaceListSize} = get_race_list_and_size(State),
+ state__renew_race_list(
+ [dialyzer_races:end_case_new(ClauseAcc)|RaceList],
+ RaceListSize + 1, State);
+ false -> State
+ end,
+ {lists:reverse(Acc), State1, t_sup(CaseTypes)}.
+
+do_clause(C, Arg, ArgType0, OrigArgType, Map, State) ->
+ Pats = cerl:clause_pats(C),
+ Guard = cerl:clause_guard(C),
+ Body = cerl:clause_body(C),
+ State1 =
+ case is_race_analysis_enabled(State) of
+ true ->
+ state__renew_fun_args(Pats, State);
+ false -> State
+ end,
+ Map0 = mark_as_fresh(Pats, Map),
+ Map1 = if Arg =:= ?no_arg -> Map0;
+ true -> bind_subst(Arg, Pats, Map0)
+ end,
+ BindRes =
+ case t_is_none(ArgType0) of
+ true ->
+ {error, bind, Pats, ArgType0, ArgType0};
+ false ->
+ ArgTypes =
+ case t_is_any(ArgType0) of
+ true -> [ArgType0 || _ <- Pats];
+ false -> t_to_tlist(ArgType0)
+ end,
+ bind_pat_vars(Pats, ArgTypes, [], Map1, State1)
+ end,
+ case BindRes of
+ {error, ErrorType, NewPats, Type, OpaqueTerm} ->
+ ?debug("Failed binding pattern: ~s\nto ~s\n",
+ [cerl_prettypr:format(C), format_type(ArgType0, State1)]),
+ case state__warning_mode(State1) of
+ false ->
+ {State1, Map, t_none(), ArgType0};
+ true ->
+ {Msg, Force} =
+ case t_is_none(ArgType0) of
+ true ->
+ PatString = format_patterns(Pats),
+ PatTypes = [PatString, format_type(OrigArgType, State1)],
+ %% See if this is covered by an earlier clause or if it
+ %% simply cannot match
+ OrigArgTypes =
+ case t_is_any(OrigArgType) of
+ true -> Any = t_any(), [Any || _ <- Pats];
+ false -> t_to_tlist(OrigArgType)
+ end,
+ Tag =
+ case bind_pat_vars(Pats, OrigArgTypes, [], Map1, State1) of
+ {error, bind, _, _, _} -> pattern_match;
+ {error, record, _, _, _} -> record_match;
+ {error, opaque, _, _, _} -> opaque_match;
+ {_, _} -> pattern_match_cov
+ end,
+ {{Tag, PatTypes}, false};
+ false ->
+ %% Try to find out if this is a default clause in a list
+ %% comprehension and supress this. A real Hack(tm)
+ Force0 =
+ case is_compiler_generated(cerl:get_ann(C)) of
+ true ->
+ case Pats of
+ [Pat] ->
+ case cerl:is_c_cons(Pat) of
+ true ->
+ not (cerl:is_c_var(cerl:cons_hd(Pat)) andalso
+ cerl:is_c_var(cerl:cons_tl(Pat)) andalso
+ cerl:is_literal(Guard) andalso
+ (cerl:concrete(Guard) =:= true));
+ false ->
+ true
+ end;
+ [Pat0, Pat1] -> % binary comprehension
+ case cerl:is_c_cons(Pat0) of
+ true ->
+ not (cerl:is_c_var(cerl:cons_hd(Pat0)) andalso
+ cerl:is_c_var(cerl:cons_tl(Pat0)) andalso
+ cerl:is_c_var(Pat1) andalso
+ cerl:is_literal(Guard) andalso
+ (cerl:concrete(Guard) =:= true));
+ false ->
+ true
+ end;
+ _ -> true
+ end;
+ false ->
+ true
+ end,
+ PatString =
+ case ErrorType of
+ bind -> format_patterns(Pats);
+ record -> format_patterns(NewPats);
+ opaque -> format_patterns(NewPats)
+ end,
+ PatTypes = case ErrorType of
+ bind -> [PatString, format_type(ArgType0, State1)];
+ record -> [PatString, format_type(Type, State1)];
+ opaque -> [PatString, format_type(Type, State1),
+ format_type(OpaqueTerm, State1)]
+ end,
+ FailedTag = case ErrorType of
+ bind -> pattern_match;
+ record -> record_match;
+ opaque -> opaque_match
+ end,
+ {{FailedTag, PatTypes}, Force0}
+ end,
+ WarnType = case Msg of
+ {opaque_match, _} -> ?WARN_OPAQUE;
+ {pattern_match, _} -> ?WARN_MATCHING;
+ {record_match, _} -> ?WARN_MATCHING;
+ {pattern_match_cov, _} -> ?WARN_MATCHING
+ end,
+ {state__add_warning(State1, WarnType, C, Msg, Force),
+ Map, t_none(), ArgType0}
+ end;
+ {Map2, PatTypes} ->
+ Map3 =
+ case Arg =:= ?no_arg of
+ true -> Map2;
+ false ->
+ %% Try to bind the argument. Will only succeed if
+ %% it is a simple structured term.
+ case bind_pat_vars_reverse([Arg], [t_product(PatTypes)],
+ [], Map2, State1) of
+ {error, _, _, _, _} -> Map2;
+ {NewMap, _} -> NewMap
+ end
+ end,
+ NewArgType =
+ case Arg =:= ?no_arg of
+ true -> ArgType0;
+ false ->
+ GenType = dialyzer_typesig:get_safe_underapprox(Pats, Guard),
+ t_subtract(t_product(t_to_tlist(ArgType0)), GenType)
+ end,
+ case bind_guard(Guard, Map3, State1) of
+ {error, Reason} ->
+ ?debug("Failed guard: ~s\n",
+ [cerl_prettypr:format(C, [{hook, cerl_typean:pp_hook()}])]),
+ PatString = format_patterns(Pats),
+ DefaultMsg =
+ case Pats =:= [] of
+ true -> {guard_fail, []};
+ false ->
+ {guard_fail_pat, [PatString, format_type(ArgType0, State1)]}
+ end,
+ State2 =
+ case Reason of
+ none -> state__add_warning(State1, ?WARN_MATCHING, C, DefaultMsg);
+ {FailGuard, Msg} ->
+ case is_compiler_generated(cerl:get_ann(FailGuard)) of
+ false ->
+ WarnType = case Msg of
+ {guard_fail, _} -> ?WARN_MATCHING;
+ {neg_guard_fail, _} -> ?WARN_MATCHING;
+ {opaque_guard, _} -> ?WARN_OPAQUE
+ end,
+ state__add_warning(State1, WarnType, FailGuard, Msg);
+ true ->
+ state__add_warning(State1, ?WARN_MATCHING, C, Msg)
+ end
+ end,
+ {State2, Map, t_none(), NewArgType};
+ Map4 ->
+ {RetState, RetMap, BodyType} = traverse(Body, Map4, State1),
+ {RetState, RetMap, BodyType, NewArgType}
+ end
+ end.
+
+bind_subst(Arg, Pats, Map) ->
+ case cerl:type(Arg) of
+ values ->
+ bind_subst_list(cerl:values_es(Arg), Pats, Map);
+ var ->
+ [Pat] = Pats,
+ enter_subst(Arg, Pat, Map);
+ _ ->
+ Map
+ end.
+
+bind_subst_list([Arg|ArgLeft], [Pat|PatLeft], Map) ->
+ NewMap =
+ case {cerl:type(Arg), cerl:type(Pat)} of
+ {var, var} -> enter_subst(Arg, Pat, Map);
+ {var, alias} -> enter_subst(Arg, cerl:alias_pat(Pat), Map);
+ {literal, literal} -> Map;
+ {T, T} -> bind_subst_list(lists:flatten(cerl:subtrees(Arg)),
+ lists:flatten(cerl:subtrees(Pat)),
+ Map);
+ _ -> Map
+ end,
+ bind_subst_list(ArgLeft, PatLeft, NewMap);
+bind_subst_list([], [], Map) ->
+ Map.
+
+%%----------------------------------------
+%% Patterns
+%%
+
+bind_pat_vars(Pats, Types, Acc, Map, State) ->
+ try
+ bind_pat_vars(Pats, Types, Acc, Map, State, false)
+ catch
+ throw:Error ->
+ %% Error = {error, bind | opaque | record, ErrorPats, ErrorType}
+ Error
+ end.
+
+bind_pat_vars_reverse(Pats, Types, Acc, Map, State) ->
+ try
+ bind_pat_vars(Pats, Types, Acc, Map, State, true)
+ catch
+ throw:Error ->
+ %% Error = {error, bind | opaque | record, ErrorPats, ErrorType}
+ Error
+ end.
+
+bind_pat_vars([Pat|PatLeft], [Type|TypeLeft], Acc, Map, State, Rev) ->
+ ?debug("Binding pat: ~w to ~s\n", [cerl:type(Pat), format_type(Type, State)]
+),
+ Opaques = State#state.opaques,
+ {NewMap, TypeOut} =
+ case cerl:type(Pat) of
+ alias ->
+ %% Map patterns are more allowing than the type of their literal. We
+ %% must unfold AliasPat if it is a literal.
+ AliasPat = dialyzer_utils:refold_pattern(cerl:alias_pat(Pat)),
+ Var = cerl:alias_var(Pat),
+ Map1 = enter_subst(Var, AliasPat, Map),
+ {Map2, [PatType]} = bind_pat_vars([AliasPat], [Type], [],
+ Map1, State, Rev),
+ {enter_type(Var, PatType, Map2), PatType};
+ binary ->
+ %% Cannot bind the binary if we are in reverse match since
+ %% binary patterns and binary construction are not symmetric.
+ case Rev of
+ true -> {Map, t_bitstr()};
+ false ->
+ BinType = t_inf(t_bitstr(), Type, Opaques),
+ case t_is_none(BinType) of
+ true ->
+ case t_find_opaque_mismatch(t_bitstr(), Type, Opaques) of
+ {ok, T1, T2} ->
+ bind_error([Pat], T1, T2, opaque);
+ error ->
+ bind_error([Pat], Type, t_none(), bind)
+ end;
+ false ->
+ Segs = cerl:binary_segments(Pat),
+ {Map1, SegTypes} = bind_bin_segs(Segs, BinType, Map, State),
+ {Map1, t_bitstr_concat(SegTypes)}
+ end
+ end;
+ cons ->
+ Cons = t_inf(Type, t_cons(), Opaques),
+ case t_is_none(Cons) of
+ true ->
+ bind_opaque_pats(t_cons(), Type, Pat, State);
+ false ->
+ {Map1, [HdType, TlType]} =
+ bind_pat_vars([cerl:cons_hd(Pat), cerl:cons_tl(Pat)],
+ [t_cons_hd(Cons, Opaques),
+ t_cons_tl(Cons, Opaques)],
+ [], Map, State, Rev),
+ {Map1, t_cons(HdType, TlType)}
+ end;
+ literal ->
+ Pat0 = dialyzer_utils:refold_pattern(Pat),
+ case cerl:is_literal(Pat0) of
+ true ->
+ Literal = literal_type(Pat),
+ case t_is_none(t_inf(Literal, Type, Opaques)) of
+ true ->
+ bind_opaque_pats(Literal, Type, Pat, State);
+ false -> {Map, Literal}
+ end;
+ false ->
+ %% Retry with the unfolded pattern
+ {Map1, [PatType]}
+ = bind_pat_vars([Pat0], [Type], [], Map, State, Rev),
+ {Map1, PatType}
+ end;
+ map ->
+ MapT = t_inf(Type, t_map(), Opaques),
+ case t_is_none(MapT) of
+ true ->
+ bind_opaque_pats(t_map(), Type, Pat, State);
+ false ->
+ case Rev of
+ %% TODO: Reverse matching (propagating a matched subset back to a value)
+ true -> {Map, MapT};
+ false ->
+ FoldFun =
+ fun(Pair, {MapAcc, ListAcc}) ->
+ %% Only exact (:=) can appear in patterns
+ exact = cerl:concrete(cerl:map_pair_op(Pair)),
+ Key = cerl:map_pair_key(Pair),
+ KeyType =
+ case cerl:type(Key) of
+ var ->
+ case state__lookup_type_for_letrec(Key, State) of
+ error -> lookup_type(Key, MapAcc);
+ {ok, RecType} -> RecType
+ end;
+ literal ->
+ literal_type(Key)
+ end,
+ Bind = erl_types:t_map_get(KeyType, MapT),
+ {MapAcc1, [ValType]} =
+ bind_pat_vars([cerl:map_pair_val(Pair)],
+ [Bind], [], MapAcc, State, Rev),
+ case t_is_singleton(KeyType, Opaques) of
+ true -> {MapAcc1, [{KeyType, ValType}|ListAcc]};
+ false -> {MapAcc1, ListAcc}
+ end
+ end,
+ {Map1, Pairs} = lists:foldl(FoldFun, {Map, []}, cerl:map_es(Pat)),
+ {Map1, t_inf(MapT, t_map(Pairs))}
+ end
+ end;
+ tuple ->
+ Es = cerl:tuple_es(Pat),
+ {TypedRecord, Prototype} =
+ case Es of
+ [] -> {false, t_tuple([])};
+ [Tag|Left] ->
+ case cerl:is_c_atom(Tag) andalso is_literal_record(Pat) of
+ true ->
+ TagAtom = cerl:atom_val(Tag),
+ case state__lookup_record(TagAtom, length(Left), State) of
+ error -> {false, t_tuple(length(Es))};
+ {ok, Record} ->
+ [_Head|AnyTail] = [t_any() || _ <- Es],
+ UntypedRecord = t_tuple([t_atom(TagAtom)|AnyTail]),
+ {not t_is_equal(Record, UntypedRecord), Record}
+ end;
+ false -> {false, t_tuple(length(Es))}
+ end
+ end,
+ Tuple = t_inf(Prototype, Type, Opaques),
+ case t_is_none(Tuple) of
+ true ->
+ bind_opaque_pats(Prototype, Type, Pat, State);
+ false ->
+ SubTuples = t_tuple_subtypes(Tuple, Opaques),
+ %% Need to call the top function to get the try-catch wrapper
+ MapJ = join_maps_begin(Map),
+ Results =
+ case Rev of
+ true ->
+ [bind_pat_vars_reverse(Es, t_tuple_args(SubTuple, Opaques),
+ [], MapJ, State)
+ || SubTuple <- SubTuples];
+ false ->
+ [bind_pat_vars(Es, t_tuple_args(SubTuple, Opaques), [],
+ MapJ, State)
+ || SubTuple <- SubTuples]
+ end,
+ case lists:keyfind(opaque, 2, Results) of
+ {error, opaque, _PatList, _Type, Opaque} ->
+ bind_error([Pat], Tuple, Opaque, opaque);
+ false ->
+ case [M || {M, _} <- Results, M =/= error] of
+ [] ->
+ case TypedRecord of
+ true -> bind_error([Pat], Tuple, Prototype, record);
+ false -> bind_error([Pat], Tuple, t_none(), bind)
+ end;
+ Maps ->
+ Map1 = join_maps_end(Maps, MapJ),
+ TupleType = t_sup([t_tuple(EsTypes)
+ || {M, EsTypes} <- Results, M =/= error]),
+ {Map1, TupleType}
+ end
+ end
+ end;
+ values ->
+ Es = cerl:values_es(Pat),
+ {Map1, EsTypes} =
+ bind_pat_vars(Es, t_to_tlist(Type), [], Map, State, Rev),
+ {Map1, t_product(EsTypes)};
+ var ->
+ VarType1 =
+ case state__lookup_type_for_letrec(Pat, State) of
+ error -> lookup_type(Pat, Map);
+ {ok, RecType} -> RecType
+ end,
+ %% Must do inf when binding args to pats. Vars in pats are fresh.
+ VarType2 = t_inf(VarType1, Type, Opaques),
+ case t_is_none(VarType2) of
+ true ->
+ case t_find_opaque_mismatch(VarType1, Type, Opaques) of
+ {ok, T1, T2} ->
+ bind_error([Pat], T1, T2, opaque);
+ error ->
+ bind_error([Pat], Type, t_none(), bind)
+ end;
+ false ->
+ Map1 = enter_type(Pat, VarType2, Map),
+ {Map1, VarType2}
+ end;
+ _Other ->
+ %% Catch all is needed when binding args to pats
+ ?debug("Failed match for ~p\n", [_Other]),
+ bind_error([Pat], Type, t_none(), bind)
+ end,
+ bind_pat_vars(PatLeft, TypeLeft, [TypeOut|Acc], NewMap, State, Rev);
+bind_pat_vars([], [], Acc, Map, _State, _Rev) ->
+ {Map, lists:reverse(Acc)}.
+
+bind_bin_segs(BinSegs, BinType, Map, State) ->
+ bind_bin_segs(BinSegs, BinType, [], Map, State).
+
+bind_bin_segs([Seg|Segs], BinType, Acc, Map, State) ->
+ Val = cerl:bitstr_val(Seg),
+ SegType = cerl:concrete(cerl:bitstr_type(Seg)),
+ UnitVal = cerl:concrete(cerl:bitstr_unit(Seg)),
+ case cerl:bitstr_bitsize(Seg) of
+ all ->
+ binary = SegType, [] = Segs, %% just an assert
+ T = t_inf(t_bitstr(UnitVal, 0), BinType),
+ {Map1, [Type]} = bind_pat_vars([Val], [T], [], Map, State, false),
+ Type1 = remove_local_opaque_types(Type, State#state.opaques),
+ bind_bin_segs(Segs, t_bitstr(0, 0), [Type1|Acc], Map1, State);
+ utf -> % XXX: possibly can be strengthened
+ true = lists:member(SegType, [utf8, utf16, utf32]),
+ {Map1, [_]} = bind_pat_vars([Val], [t_integer()], [], Map, State, false),
+ Type = t_binary(),
+ bind_bin_segs(Segs, BinType, [Type|Acc], Map1, State);
+ BitSz when is_integer(BitSz) orelse BitSz =:= any ->
+ Size = cerl:bitstr_size(Seg),
+ {Map1, [SizeType]} =
+ bind_pat_vars([Size], [t_non_neg_integer()], [], Map, State, false),
+ Opaques = State#state.opaques,
+ NumberVals = t_number_vals(SizeType, Opaques),
+ case t_contains_opaque(SizeType, Opaques) of
+ true -> bind_error([Seg], SizeType, t_none(), opaque);
+ false -> ok
+ end,
+ Type =
+ case NumberVals of
+ [OneSize] -> t_bitstr(0, UnitVal * OneSize);
+ _ -> % 'unknown' too
+ MinSize = erl_types:number_min(SizeType, Opaques),
+ t_bitstr(UnitVal, UnitVal * MinSize)
+ end,
+ ValConstr =
+ case SegType of
+ binary -> Type; %% The same constraints as for the whole bitstr
+ float -> t_float();
+ integer ->
+ case NumberVals of
+ unknown -> t_integer();
+ List ->
+ SizeVal = lists:max(List),
+ Flags = cerl:concrete(cerl:bitstr_flags(Seg)),
+ N = SizeVal * UnitVal,
+ case N >= ?BITS of
+ true ->
+ case lists:member(signed, Flags) of
+ true -> t_from_range(neg_inf, pos_inf);
+ false -> t_from_range(0, pos_inf)
+ end;
+ false ->
+ case lists:member(signed, Flags) of
+ true -> t_from_range(-(1 bsl (N - 1)), 1 bsl (N - 1) - 1);
+ false -> t_from_range(0, 1 bsl N - 1)
+ end
+ end
+ end
+ end,
+ {Map2, [_]} = bind_pat_vars([Val], [ValConstr], [], Map1, State, false),
+ NewBinType = t_bitstr_match(Type, BinType),
+ case t_is_none(NewBinType) of
+ true -> bind_error([Seg], BinType, t_none(), bind);
+ false -> bind_bin_segs(Segs, NewBinType, [Type|Acc], Map2, State)
+ end
+ end;
+bind_bin_segs([], _BinType, Acc, Map, _State) ->
+ {Map, lists:reverse(Acc)}.
+
+bind_error(Pats, Type, OpaqueType, Error0) ->
+ Error = case {Error0, Pats} of
+ {bind, [Pat]} ->
+ case is_literal_record(Pat) of
+ true -> record;
+ false -> Error0
+ end;
+ _ -> Error0
+ end,
+ throw({error, Error, Pats, Type, OpaqueType}).
+
+-spec bind_opaque_pats(type(), type(), cerl:c_literal(), state()) ->
+ no_return().
+
+bind_opaque_pats(GenType, Type, Pat, State) ->
+ case t_find_opaque_mismatch(GenType, Type, State#state.opaques) of
+ {ok, T1, T2} ->
+ bind_error([Pat], T1, T2, opaque);
+ error ->
+ bind_error([Pat], Type, t_none(), bind)
+ end.
+
+%%----------------------------------------
+%% Guards
+%%
+
+bind_guard(Guard, Map, State) ->
+ try bind_guard(Guard, Map, maps:new(), pos, State) of
+ {Map1, _Type} -> Map1
+ catch
+ throw:{fail, Warning} -> {error, Warning};
+ throw:{fatal_fail, Warning} -> {error, Warning}
+ end.
+
+bind_guard(Guard, Map, Env, Eval, State) ->
+ ?debug("Handling ~w guard: ~s\n",
+ [Eval, cerl_prettypr:format(Guard, [{noann, true}])]),
+ case cerl:type(Guard) of
+ binary ->
+ {Map, t_binary()};
+ 'case' ->
+ Arg = cerl:case_arg(Guard),
+ Clauses = cerl:case_clauses(Guard),
+ bind_guard_case_clauses(Arg, Clauses, Map, Env, Eval, State);
+ cons ->
+ Hd = cerl:cons_hd(Guard),
+ Tl = cerl:cons_tl(Guard),
+ {Map1, HdType} = bind_guard(Hd, Map, Env, dont_know, State),
+ {Map2, TlType} = bind_guard(Tl, Map1, Env, dont_know, State),
+ {Map2, t_cons(HdType, TlType)};
+ literal ->
+ {Map, literal_type(Guard)};
+ 'try' ->
+ Arg = cerl:try_arg(Guard),
+ [Var] = cerl:try_vars(Guard),
+ EVars = cerl:try_evars(Guard),
+ %%?debug("Storing: ~w\n", [Var]),
+ Map1 = join_maps_begin(Map),
+ Map2 = mark_as_fresh(EVars, Map1),
+ %% Visit handler first so we know if it should be ignored
+ {{HandlerMap, HandlerType}, HandlerE} =
+ try {bind_guard(cerl:try_handler(Guard), Map2, Env, Eval, State), none}
+ catch throw:HE ->
+ {{Map2, t_none()}, HE}
+ end,
+ BodyEnv = maps:put(get_label(Var), Arg, Env),
+ Wanted = case Eval of pos -> t_atom(true); neg -> t_atom(false);
+ dont_know -> t_any() end,
+ case t_is_none(t_inf(HandlerType, Wanted)) of
+ %% Handler won't save us; pretend it does not exist
+ true -> bind_guard(cerl:try_body(Guard), Map, BodyEnv, Eval, State);
+ false ->
+ {{BodyMap, BodyType}, BodyE} =
+ try {bind_guard(cerl:try_body(Guard), Map1, BodyEnv,
+ Eval, State), none}
+ catch throw:BE ->
+ {{Map1, t_none()}, BE}
+ end,
+ Map3 = join_maps_end([BodyMap, HandlerMap], Map1),
+ case t_is_none(Sup = t_sup(BodyType, HandlerType)) of
+ true ->
+ %% Pick a reason. N.B. We assume that the handler is always
+ %% compiler-generated if the body is; that way, we won't need to
+ %% check.
+ Fatality = case {BodyE, HandlerE} of
+ {{fatal_fail, _}, _} -> fatal_fail;
+ {_, {fatal_fail, _}} -> fatal_fail;
+ _ -> fail
+ end,
+ throw({Fatality,
+ case {BodyE, HandlerE} of
+ {{_, Rsn}, _} when Rsn =/= none -> Rsn;
+ {_, {_,Rsn}} -> Rsn;
+ _ -> none
+ end});
+ false -> {Map3, Sup}
+ end
+ end;
+ tuple ->
+ Es0 = cerl:tuple_es(Guard),
+ {Map1, Es} = bind_guard_list(Es0, Map, Env, dont_know, State),
+ {Map1, t_tuple(Es)};
+ map ->
+ case Eval of
+ dont_know -> handle_guard_map(Guard, Map, Env, State);
+ _PosOrNeg -> {Map, t_none()} %% Map exprs do not produce bools
+ end;
+ 'let' ->
+ Arg = cerl:let_arg(Guard),
+ [Var] = cerl:let_vars(Guard),
+ %%?debug("Storing: ~w\n", [Var]),
+ NewEnv = maps:put(get_label(Var), Arg, Env),
+ bind_guard(cerl:let_body(Guard), Map, NewEnv, Eval, State);
+ values ->
+ Es = cerl:values_es(Guard),
+ List = [bind_guard(V, Map, Env, dont_know, State) || V <- Es],
+ Type = t_product([T || {_, T} <- List]),
+ {Map, Type};
+ var ->
+ ?debug("Looking for var(~w)...", [cerl_trees:get_label(Guard)]),
+ case maps:find(get_label(Guard), Env) of
+ error ->
+ ?debug("Did not find it\n", []),
+ Type = lookup_type(Guard, Map),
+ Constr =
+ case Eval of
+ pos -> t_atom(true);
+ neg -> t_atom(false);
+ dont_know -> Type
+ end,
+ Inf = t_inf(Constr, Type),
+ {enter_type(Guard, Inf, Map), Inf};
+ {ok, Tree} ->
+ ?debug("Found it\n", []),
+ {Map1, Type} = bind_guard(Tree, Map, Env, Eval, State),
+ {enter_type(Guard, Type, Map1), Type}
+ end;
+ call ->
+ handle_guard_call(Guard, Map, Env, Eval, State)
+ end.
+
+handle_guard_call(Guard, Map, Env, Eval, State) ->
+ MFA = {cerl:atom_val(cerl:call_module(Guard)),
+ cerl:atom_val(cerl:call_name(Guard)),
+ cerl:call_arity(Guard)},
+ case MFA of
+ {erlang, F, 1} when F =:= is_atom; F =:= is_boolean;
+ F =:= is_binary; F =:= is_bitstring;
+ F =:= is_float; F =:= is_function;
+ F =:= is_integer; F =:= is_list; F =:= is_map;
+ F =:= is_number; F =:= is_pid; F =:= is_port;
+ F =:= is_reference; F =:= is_tuple ->
+ handle_guard_type_test(Guard, F, Map, Env, Eval, State);
+ {erlang, is_function, 2} ->
+ handle_guard_is_function(Guard, Map, Env, Eval, State);
+ MFA when (MFA =:= {erlang, internal_is_record, 3}) or
+ (MFA =:= {erlang, is_record, 3}) ->
+ handle_guard_is_record(Guard, Map, Env, Eval, State);
+ {erlang, '=:=', 2} ->
+ handle_guard_eqeq(Guard, Map, Env, Eval, State);
+ {erlang, '==', 2} ->
+ handle_guard_eq(Guard, Map, Env, Eval, State);
+ {erlang, 'and', 2} ->
+ handle_guard_and(Guard, Map, Env, Eval, State);
+ {erlang, 'or', 2} ->
+ handle_guard_or(Guard, Map, Env, Eval, State);
+ {erlang, 'not', 1} ->
+ handle_guard_not(Guard, Map, Env, Eval, State);
+ {erlang, Comp, 2} when Comp =:= '<'; Comp =:= '=<';
+ Comp =:= '>'; Comp =:= '>=' ->
+ handle_guard_comp(Guard, Comp, Map, Env, Eval, State);
+ _ ->
+ handle_guard_gen_fun(MFA, Guard, Map, Env, Eval, State)
+ end.
+
+handle_guard_gen_fun({M, F, A}, Guard, Map, Env, Eval, State) ->
+ Args = cerl:call_args(Guard),
+ {Map1, As} = bind_guard_list(Args, Map, Env, dont_know, State),
+ Opaques = State#state.opaques,
+ BifRet = erl_bif_types:type(M, F, A, As, Opaques),
+ case t_is_none(BifRet) of
+ true ->
+ %% Is this an error-bif?
+ case t_is_none(erl_bif_types:type(M, F, A)) of
+ true -> signal_guard_fail(Eval, Guard, As, State);
+ false -> signal_guard_fatal_fail(Eval, Guard, As, State)
+ end;
+ false ->
+ BifArgs = bif_args(M, F, A),
+ Map2 = enter_type_lists(Args, t_inf_lists(BifArgs, As, Opaques), Map1),
+ Ret =
+ case Eval of
+ pos -> t_inf(t_atom(true), BifRet);
+ neg -> t_inf(t_atom(false), BifRet);
+ dont_know -> BifRet
+ end,
+ case t_is_none(Ret) of
+ true ->
+ case Eval =:= pos of
+ true -> signal_guard_fail(Eval, Guard, As, State);
+ false -> throw({fail, none})
+ end;
+ false -> {Map2, Ret}
+ end
+ end.
+
+handle_guard_type_test(Guard, F, Map, Env, Eval, State) ->
+ [Arg] = cerl:call_args(Guard),
+ {Map1, ArgType} = bind_guard(Arg, Map, Env, dont_know, State),
+ case bind_type_test(Eval, F, ArgType, State) of
+ error ->
+ ?debug("Type test: ~w failed\n", [F]),
+ signal_guard_fail(Eval, Guard, [ArgType], State);
+ {ok, NewArgType, Ret} ->
+ ?debug("Type test: ~w succeeded, NewType: ~s, Ret: ~s\n",
+ [F, t_to_string(NewArgType), t_to_string(Ret)]),
+ {enter_type(Arg, NewArgType, Map1), Ret}
+ end.
+
+bind_type_test(Eval, TypeTest, ArgType, State) ->
+ Type = case TypeTest of
+ is_atom -> t_atom();
+ is_boolean -> t_boolean();
+ is_binary -> t_binary();
+ is_bitstring -> t_bitstr();
+ is_float -> t_float();
+ is_function -> t_fun();
+ is_integer -> t_integer();
+ is_list -> t_maybe_improper_list();
+ is_map -> t_map();
+ is_number -> t_number();
+ is_pid -> t_pid();
+ is_port -> t_port();
+ is_reference -> t_reference();
+ is_tuple -> t_tuple()
+ end,
+ case Eval of
+ pos ->
+ Inf = t_inf(Type, ArgType, State#state.opaques),
+ case t_is_none(Inf) of
+ true -> error;
+ false -> {ok, Inf, t_atom(true)}
+ end;
+ neg ->
+ Sub = t_subtract(ArgType, Type),
+ case t_is_none(Sub) of
+ true -> error;
+ false -> {ok, Sub, t_atom(false)}
+ end;
+ dont_know ->
+ {ok, ArgType, t_boolean()}
+ end.
+
+handle_guard_comp(Guard, Comp, Map, Env, Eval, State) ->
+ Args = cerl:call_args(Guard),
+ [Arg1, Arg2] = Args,
+ {Map1, ArgTypes} = bind_guard_list(Args, Map, Env, dont_know, State),
+ Opaques = State#state.opaques,
+ [Type1, Type2] = ArgTypes,
+ IsInt1 = t_is_integer(Type1, Opaques),
+ IsInt2 = t_is_integer(Type2, Opaques),
+ case {type(Arg1), type(Arg2)} of
+ {{literal, Lit1}, {literal, Lit2}} ->
+ case erlang:Comp(cerl:concrete(Lit1), cerl:concrete(Lit2)) of
+ true when Eval =:= pos -> {Map, t_atom(true)};
+ true when Eval =:= dont_know -> {Map, t_atom(true)};
+ true when Eval =:= neg -> {Map, t_atom(true)};
+ false when Eval =:= pos ->
+ signal_guard_fail(Eval, Guard, ArgTypes, State);
+ false when Eval =:= dont_know -> {Map, t_atom(false)};
+ false when Eval =:= neg -> {Map, t_atom(false)}
+ end;
+ {{literal, Lit1}, var} when IsInt1 andalso IsInt2 andalso (Eval =:= pos) ->
+ case bind_comp_literal_var(Lit1, Arg2, Type2, Comp, Map1, Opaques) of
+ error -> signal_guard_fail(Eval, Guard, ArgTypes, State);
+ {ok, NewMap} -> {NewMap, t_atom(true)}
+ end;
+ {var, {literal, Lit2}} when IsInt1 andalso IsInt2 andalso (Eval =:= pos) ->
+ case bind_comp_literal_var(Lit2, Arg1, Type1, invert_comp(Comp),
+ Map1, Opaques) of
+ error -> signal_guard_fail(Eval, Guard, ArgTypes, State);
+ {ok, NewMap} -> {NewMap, t_atom(true)}
+ end;
+ {_, _} ->
+ handle_guard_gen_fun({erlang, Comp, 2}, Guard, Map, Env, Eval, State)
+ end.
+
+invert_comp('=<') -> '>=';
+invert_comp('<') -> '>';
+invert_comp('>=') -> '=<';
+invert_comp('>') -> '<'.
+
+bind_comp_literal_var(Lit, Var, VarType, CompOp, Map, Opaques) ->
+ LitVal = cerl:concrete(Lit),
+ NewVarType =
+ case t_number_vals(VarType, Opaques) of
+ unknown ->
+ Range =
+ case CompOp of
+ '=<' -> t_from_range(LitVal, pos_inf);
+ '<' -> t_from_range(LitVal + 1, pos_inf);
+ '>=' -> t_from_range(neg_inf, LitVal);
+ '>' -> t_from_range(neg_inf, LitVal - 1)
+ end,
+ t_inf(Range, VarType, Opaques);
+ NumberVals ->
+ NewNumberVals = [X || X <- NumberVals, erlang:CompOp(LitVal, X)],
+ t_integers(NewNumberVals)
+ end,
+ case t_is_none(NewVarType) of
+ true -> error;
+ false -> {ok, enter_type(Var, NewVarType, Map)}
+ end.
+
+handle_guard_is_function(Guard, Map, Env, Eval, State) ->
+ Args = cerl:call_args(Guard),
+ {Map1, ArgTypes0} = bind_guard_list(Args, Map, Env, dont_know, State),
+ [FunType0, ArityType0] = ArgTypes0,
+ Opaques = State#state.opaques,
+ ArityType = t_inf(ArityType0, t_integer(), Opaques),
+ case t_is_none(ArityType) of
+ true -> signal_guard_fail(Eval, Guard, ArgTypes0, State);
+ false ->
+ FunTypeConstr =
+ case t_number_vals(ArityType, State#state.opaques) of
+ unknown -> t_fun();
+ Vals ->
+ t_sup([t_fun(lists:duplicate(X, t_any()), t_any()) || X <- Vals])
+ end,
+ FunType = t_inf(FunType0, FunTypeConstr, Opaques),
+ case t_is_none(FunType) of
+ true ->
+ case Eval of
+ pos -> signal_guard_fail(Eval, Guard, ArgTypes0, State);
+ neg -> {Map1, t_atom(false)};
+ dont_know -> {Map1, t_atom(false)}
+ end;
+ false ->
+ case Eval of
+ pos -> {enter_type_lists(Args, [FunType, ArityType], Map1),
+ t_atom(true)};
+ neg -> {Map1, t_atom(false)};
+ dont_know -> {Map1, t_boolean()}
+ end
+ end
+ end.
+
+handle_guard_is_record(Guard, Map, Env, Eval, State) ->
+ Args = cerl:call_args(Guard),
+ [Rec, Tag0, Arity0] = Args,
+ Tag = cerl:atom_val(Tag0),
+ Arity = cerl:int_val(Arity0),
+ {Map1, RecType} = bind_guard(Rec, Map, Env, dont_know, State),
+ ArityMin1 = Arity - 1,
+ Opaques = State#state.opaques,
+ Tuple = t_tuple([t_atom(Tag)|lists:duplicate(ArityMin1, t_any())]),
+ case t_is_none(t_inf(Tuple, RecType, Opaques)) of
+ true ->
+ case erl_types:t_has_opaque_subtype(RecType, Opaques) of
+ true ->
+ signal_guard_fail(Eval, Guard,
+ [RecType, t_from_term(Tag),
+ t_from_term(Arity)],
+ State);
+ false ->
+ case Eval of
+ pos -> signal_guard_fail(Eval, Guard,
+ [RecType, t_from_term(Tag),
+ t_from_term(Arity)],
+ State);
+ neg -> {Map1, t_atom(false)};
+ dont_know -> {Map1, t_atom(false)}
+ end
+ end;
+ false ->
+ TupleType =
+ case state__lookup_record(Tag, ArityMin1, State) of
+ error -> Tuple;
+ {ok, Prototype} -> Prototype
+ end,
+ Type = t_inf(TupleType, RecType, State#state.opaques),
+ case t_is_none(Type) of
+ true ->
+ %% No special handling of opaque errors.
+ FArgs = "record " ++ format_type(RecType, State),
+ Msg = {record_matching, [FArgs, Tag]},
+ throw({fail, {Guard, Msg}});
+ false ->
+ case Eval of
+ pos -> {enter_type(Rec, Type, Map1), t_atom(true)};
+ neg -> {Map1, t_atom(false)};
+ dont_know -> {Map1, t_boolean()}
+ end
+ end
+ end.
+
+handle_guard_eq(Guard, Map, Env, Eval, State) ->
+ [Arg1, Arg2] = cerl:call_args(Guard),
+ case {type(Arg1), type(Arg2)} of
+ {{literal, Lit1}, {literal, Lit2}} ->
+ case cerl:concrete(Lit1) =:= cerl:concrete(Lit2) of
+ true ->
+ if
+ Eval =:= pos -> {Map, t_atom(true)};
+ Eval =:= neg ->
+ ArgTypes = [t_from_term(cerl:concrete(Lit1)),
+ t_from_term(cerl:concrete(Lit2))],
+ signal_guard_fail(Eval, Guard, ArgTypes, State);
+ Eval =:= dont_know -> {Map, t_atom(true)}
+ end;
+ false ->
+ if
+ Eval =:= neg -> {Map, t_atom(false)};
+ Eval =:= dont_know -> {Map, t_atom(false)};
+ Eval =:= pos ->
+ ArgTypes = [t_from_term(cerl:concrete(Lit1)),
+ t_from_term(cerl:concrete(Lit2))],
+ signal_guard_fail(Eval, Guard, ArgTypes, State)
+ end
+ end;
+ {{literal, Lit1}, _} when Eval =:= pos ->
+ case cerl:concrete(Lit1) of
+ Atom when is_atom(Atom) ->
+ bind_eqeq_guard_lit_other(Guard, Lit1, Arg2, Map, Env, State);
+ [] ->
+ bind_eqeq_guard_lit_other(Guard, Lit1, Arg2, Map, Env, State);
+ _ ->
+ bind_eq_guard(Guard, Lit1, Arg2, Map, Env, Eval, State)
+ end;
+ {_, {literal, Lit2}} when Eval =:= pos ->
+ case cerl:concrete(Lit2) of
+ Atom when is_atom(Atom) ->
+ bind_eqeq_guard_lit_other(Guard, Lit2, Arg1, Map, Env, State);
+ [] ->
+ bind_eqeq_guard_lit_other(Guard, Lit2, Arg1, Map, Env, State);
+ _ ->
+ bind_eq_guard(Guard, Arg1, Lit2, Map, Env, Eval, State)
+ end;
+ {_, _} ->
+ bind_eq_guard(Guard, Arg1, Arg2, Map, Env, Eval, State)
+ end.
+
+bind_eq_guard(Guard, Arg1, Arg2, Map, Env, Eval, State) ->
+ {Map1, Type1} = bind_guard(Arg1, Map, Env, dont_know, State),
+ {Map2, Type2} = bind_guard(Arg2, Map1, Env, dont_know, State),
+ Opaques = State#state.opaques,
+ case
+ t_is_nil(Type1, Opaques) orelse t_is_nil(Type2, Opaques)
+ orelse t_is_atom(Type1, Opaques) orelse t_is_atom(Type2, Opaques)
+ of
+ true -> bind_eqeq_guard(Guard, Arg1, Arg2, Map, Env, Eval, State);
+ false ->
+ %% XXX. Is this test OK?
+ OpArgs = erl_types:t_find_unknown_opaque(Type1, Type2, Opaques),
+ case OpArgs =:= [] of
+ true ->
+ case Eval of
+ pos -> {Map2, t_atom(true)};
+ neg -> {Map2, t_atom(false)};
+ dont_know -> {Map2, t_boolean()}
+ end;
+ false ->
+ signal_guard_fail(Eval, Guard, [Type1, Type2], State)
+ end
+ end.
+
+handle_guard_eqeq(Guard, Map, Env, Eval, State) ->
+ [Arg1, Arg2] = cerl:call_args(Guard),
+ case {type(Arg1), type(Arg2)} of
+ {{literal, Lit1}, {literal, Lit2}} ->
+
+ case cerl:concrete(Lit1) =:= cerl:concrete(Lit2) of
+ true ->
+ if Eval =:= neg ->
+ ArgTypes = [t_from_term(cerl:concrete(Lit1)),
+ t_from_term(cerl:concrete(Lit2))],
+ signal_guard_fail(Eval, Guard, ArgTypes, State);
+ Eval =:= pos -> {Map, t_atom(true)};
+ Eval =:= dont_know -> {Map, t_atom(true)}
+ end;
+ false ->
+ if Eval =:= neg -> {Map, t_atom(false)};
+ Eval =:= dont_know -> {Map, t_atom(false)};
+ Eval =:= pos ->
+ ArgTypes = [t_from_term(cerl:concrete(Lit1)),
+ t_from_term(cerl:concrete(Lit2))],
+ signal_guard_fail(Eval, Guard, ArgTypes, State)
+ end
+ end;
+ {{literal, Lit1}, _} when Eval =:= pos ->
+ bind_eqeq_guard_lit_other(Guard, Lit1, Arg2, Map, Env, State);
+ {_, {literal, Lit2}} when Eval =:= pos ->
+ bind_eqeq_guard_lit_other(Guard, Lit2, Arg1, Map, Env, State);
+ {_, _} ->
+ bind_eqeq_guard(Guard, Arg1, Arg2, Map, Env, Eval, State)
+ end.
+
+bind_eqeq_guard(Guard, Arg1, Arg2, Map, Env, Eval, State) ->
+ {Map1, Type1} = bind_guard(Arg1, Map, Env, dont_know, State),
+ {Map2, Type2} = bind_guard(Arg2, Map1, Env, dont_know, State),
+ ?debug("Types are:~s =:= ~s\n", [t_to_string(Type1),
+ t_to_string(Type2)]),
+ Opaques = State#state.opaques,
+ Inf = t_inf(Type1, Type2, Opaques),
+ case t_is_none(Inf) of
+ true ->
+ OpArgs = erl_types:t_find_unknown_opaque(Type1, Type2, Opaques),
+ case OpArgs =:= [] of
+ true ->
+ case Eval of
+ neg -> {Map2, t_atom(false)};
+ dont_know -> {Map2, t_atom(false)};
+ pos -> signal_guard_fail(Eval, Guard, [Type1, Type2], State)
+ end;
+ false ->
+ signal_guard_fail(Eval, Guard, [Type1, Type2], State)
+ end;
+ false ->
+ case Eval of
+ pos ->
+ case {cerl:type(Arg1), cerl:type(Arg2)} of
+ {var, var} ->
+ Map3 = enter_subst(Arg1, Arg2, Map2),
+ Map4 = enter_type(Arg2, Inf, Map3),
+ {Map4, t_atom(true)};
+ {var, _} ->
+ Map3 = enter_type(Arg1, Inf, Map2),
+ {Map3, t_atom(true)};
+ {_, var} ->
+ Map3 = enter_type(Arg2, Inf, Map2),
+ {Map3, t_atom(true)};
+ {_, _} ->
+ {Map2, t_atom(true)}
+ end;
+ neg ->
+ {Map2, t_atom(false)};
+ dont_know ->
+ {Map2, t_boolean()}
+ end
+ end.
+
+bind_eqeq_guard_lit_other(Guard, Arg1, Arg2, Map, Env, State) ->
+ Eval = dont_know,
+ Opaques = State#state.opaques,
+ case cerl:concrete(Arg1) of
+ true ->
+ {_, Type} = MT = bind_guard(Arg2, Map, Env, pos, State),
+ case t_is_any_atom(true, Type, Opaques) of
+ true -> MT;
+ false ->
+ {_, Type0} = bind_guard(Arg2, Map, Env, Eval, State),
+ signal_guard_fail(Eval, Guard, [Type0, t_atom(true)], State)
+ end;
+ false ->
+ {Map1, Type} = bind_guard(Arg2, Map, Env, neg, State),
+ case t_is_any_atom(false, Type, Opaques) of
+ true -> {Map1, t_atom(true)};
+ false ->
+ {_, Type0} = bind_guard(Arg2, Map, Env, Eval, State),
+ signal_guard_fail(Eval, Guard, [Type0, t_atom(false)], State)
+ end;
+ Term ->
+ LitType = t_from_term(Term),
+ {Map1, Type} = bind_guard(Arg2, Map, Env, Eval, State),
+ case t_is_subtype(LitType, Type) of
+ false -> signal_guard_fail(Eval, Guard, [Type, LitType], State);
+ true ->
+ case cerl:is_c_var(Arg2) of
+ true -> {enter_type(Arg2, LitType, Map1), t_atom(true)};
+ false -> {Map1, t_atom(true)}
+ end
+ end
+ end.
+
+handle_guard_and(Guard, Map, Env, Eval, State) ->
+ [Arg1, Arg2] = cerl:call_args(Guard),
+ Opaques = State#state.opaques,
+ case Eval of
+ pos ->
+ {Map1, Type1} = bind_guard(Arg1, Map, Env, Eval, State),
+ case t_is_any_atom(true, Type1, Opaques) of
+ false -> signal_guard_fail(Eval, Guard, [Type1, t_any()], State);
+ true ->
+ {Map2, Type2} = bind_guard(Arg2, Map1, Env, Eval, State),
+ case t_is_any_atom(true, Type2, Opaques) of
+ false -> signal_guard_fail(Eval, Guard, [Type1, Type2], State);
+ true -> {Map2, t_atom(true)}
+ end
+ end;
+ neg ->
+ MapJ = join_maps_begin(Map),
+ {Map1, Type1} =
+ try bind_guard(Arg1, MapJ, Env, neg, State)
+ catch throw:{fail, _} -> bind_guard(Arg2, MapJ, Env, pos, State)
+ end,
+ {Map2, Type2} =
+ try bind_guard(Arg2, MapJ, Env, neg, State)
+ catch throw:{fail, _} -> bind_guard(Arg1, MapJ, Env, pos, State)
+ end,
+ case
+ t_is_any_atom(false, Type1, Opaques)
+ orelse t_is_any_atom(false, Type2, Opaques)
+ of
+ true -> {join_maps_end([Map1, Map2], MapJ), t_atom(false)};
+ false -> signal_guard_fail(Eval, Guard, [Type1, Type2], State)
+ end;
+ dont_know ->
+ MapJ = join_maps_begin(Map),
+ {Map1, Type1} = bind_guard(Arg1, MapJ, Env, dont_know, State),
+ {Map2, Type2} = bind_guard(Arg2, MapJ, Env, dont_know, State),
+ Bool1 = t_inf(Type1, t_boolean()),
+ Bool2 = t_inf(Type2, t_boolean()),
+ case t_is_none(Bool1) orelse t_is_none(Bool2) of
+ true -> throw({fatal_fail, none});
+ false ->
+ NewMap = join_maps_end([Map1, Map2], MapJ),
+ NewType =
+ case {t_atom_vals(Bool1, Opaques), t_atom_vals(Bool2, Opaques)} of
+ {['true'] , ['true'] } -> t_atom(true);
+ {['false'], _ } -> t_atom(false);
+ {_ , ['false']} -> t_atom(false);
+ {unknown , _ } ->
+ signal_guard_fail(Eval, Guard, [Type1, Type2], State);
+ {_ , unknown } ->
+ signal_guard_fail(Eval, Guard, [Type1, Type2], State);
+ {_ , _ } -> t_boolean()
+
+ end,
+ {NewMap, NewType}
+ end
+ end.
+
+handle_guard_or(Guard, Map, Env, Eval, State) ->
+ [Arg1, Arg2] = cerl:call_args(Guard),
+ Opaques = State#state.opaques,
+ case Eval of
+ pos ->
+ MapJ = join_maps_begin(Map),
+ {Map1, Bool1} =
+ try bind_guard(Arg1, MapJ, Env, pos, State)
+ catch
+ throw:{fail,_} -> bind_guard(Arg1, MapJ, Env, dont_know, State)
+ end,
+ {Map2, Bool2} =
+ try bind_guard(Arg2, MapJ, Env, pos, State)
+ catch
+ throw:{fail,_} -> bind_guard(Arg2, MapJ, Env, dont_know, State)
+ end,
+ case
+ ((t_is_any_atom(true, Bool1, Opaques)
+ andalso t_is_boolean(Bool2, Opaques))
+ orelse
+ (t_is_any_atom(true, Bool2, Opaques)
+ andalso t_is_boolean(Bool1, Opaques)))
+ of
+ true -> {join_maps_end([Map1, Map2], MapJ), t_atom(true)};
+ false -> signal_guard_fail(Eval, Guard, [Bool1, Bool2], State)
+ end;
+ neg ->
+ {Map1, Type1} = bind_guard(Arg1, Map, Env, neg, State),
+ case t_is_any_atom(false, Type1, Opaques) of
+ false -> signal_guard_fail(Eval, Guard, [Type1, t_any()], State);
+ true ->
+ {Map2, Type2} = bind_guard(Arg2, Map1, Env, neg, State),
+ case t_is_any_atom(false, Type2, Opaques) of
+ false -> signal_guard_fail(Eval, Guard, [Type1, Type2], State);
+ true -> {Map2, t_atom(false)}
+ end
+ end;
+ dont_know ->
+ MapJ = join_maps_begin(Map),
+ {Map1, Type1} = bind_guard(Arg1, MapJ, Env, dont_know, State),
+ {Map2, Type2} = bind_guard(Arg2, MapJ, Env, dont_know, State),
+ Bool1 = t_inf(Type1, t_boolean()),
+ Bool2 = t_inf(Type2, t_boolean()),
+ case t_is_none(Bool1) orelse t_is_none(Bool2) of
+ true -> throw({fatal_fail, none});
+ false ->
+ NewMap = join_maps_end([Map1, Map2], MapJ),
+ NewType =
+ case {t_atom_vals(Bool1, Opaques), t_atom_vals(Bool2, Opaques)} of
+ {['false'], ['false']} -> t_atom(false);
+ {['true'] , _ } -> t_atom(true);
+ {_ , ['true'] } -> t_atom(true);
+ {unknown , _ } ->
+ signal_guard_fail(Eval, Guard, [Type1, Type2], State);
+ {_ , unknown } ->
+ signal_guard_fail(Eval, Guard, [Type1, Type2], State);
+ {_ , _ } -> t_boolean()
+ end,
+ {NewMap, NewType}
+ end
+ end.
+
+handle_guard_not(Guard, Map, Env, Eval, State) ->
+ [Arg] = cerl:call_args(Guard),
+ Opaques = State#state.opaques,
+ case Eval of
+ neg ->
+ {Map1, Type} = bind_guard(Arg, Map, Env, pos, State),
+ case t_is_any_atom(true, Type, Opaques) of
+ true -> {Map1, t_atom(false)};
+ false ->
+ {_, Type0} = bind_guard(Arg, Map, Env, Eval, State),
+ signal_guard_fail(Eval, Guard, [Type0], State)
+ end;
+ pos ->
+ {Map1, Type} = bind_guard(Arg, Map, Env, neg, State),
+ case t_is_any_atom(false, Type, Opaques) of
+ true -> {Map1, t_atom(true)};
+ false ->
+ {_, Type0} = bind_guard(Arg, Map, Env, Eval, State),
+ signal_guard_fail(Eval, Guard, [Type0], State)
+ end;
+ dont_know ->
+ {Map1, Type} = bind_guard(Arg, Map, Env, dont_know, State),
+ Bool = t_inf(Type, t_boolean()),
+ case t_is_none(Bool) of
+ true -> throw({fatal_fail, none});
+ false ->
+ case t_atom_vals(Bool, Opaques) of
+ ['true'] -> {Map1, t_atom(false)};
+ ['false'] -> {Map1, t_atom(true)};
+ [_, _] -> {Map1, Bool};
+ unknown -> signal_guard_fail(Eval, Guard, [Type], State)
+ end
+ end
+ end.
+
+bind_guard_list(Guards, Map, Env, Eval, State) ->
+ bind_guard_list(Guards, Map, Env, Eval, State, []).
+
+bind_guard_list([G|Gs], Map, Env, Eval, State, Acc) ->
+ {Map1, T} = bind_guard(G, Map, Env, Eval, State),
+ bind_guard_list(Gs, Map1, Env, Eval, State, [T|Acc]);
+bind_guard_list([], Map, _Env, _Eval, _State, Acc) ->
+ {Map, lists:reverse(Acc)}.
+
+handle_guard_map(Guard, Map, Env, State) ->
+ Pairs = cerl:map_es(Guard),
+ Arg = cerl:map_arg(Guard),
+ {Map1, ArgType0} = bind_guard(Arg, Map, Env, dont_know, State),
+ ArgType1 = t_inf(t_map(), ArgType0),
+ case t_is_none_or_unit(ArgType1) of
+ true -> {Map1, t_none()};
+ false ->
+ {Map2, TypePairs} = bind_guard_map_pairs(Pairs, Map1, Env, State, []),
+ {Map2, lists:foldl(fun({KV,assoc},Acc) -> erl_types:t_map_put(KV,Acc);
+ ({KV,exact},Acc) -> erl_types:t_map_update(KV,Acc)
+ end, ArgType1, TypePairs)}
+ end.
+
+bind_guard_map_pairs([], Map, _Env, _State, PairAcc) ->
+ {Map, lists:reverse(PairAcc)};
+bind_guard_map_pairs([Pair|Pairs], Map, Env, State, PairAcc) ->
+ Key = cerl:map_pair_key(Pair),
+ Val = cerl:map_pair_val(Pair),
+ Op = cerl:map_pair_op(Pair),
+ {Map1, [K,V]} = bind_guard_list([Key,Val],Map,Env,dont_know,State),
+ bind_guard_map_pairs(Pairs, Map1, Env, State,
+ [{{K,V},cerl:concrete(Op)}|PairAcc]).
+
+-type eval() :: 'pos' | 'neg' | 'dont_know'.
+
+-spec signal_guard_fail(eval(), cerl:c_call(), [type()],
+ state()) -> no_return().
+
+signal_guard_fail(Eval, Guard, ArgTypes, State) ->
+ signal_guard_failure(Eval, Guard, ArgTypes, fail, State).
+
+-spec signal_guard_fatal_fail(eval(), cerl:c_call(), [erl_types:erl_type()],
+ state()) -> no_return().
+
+signal_guard_fatal_fail(Eval, Guard, ArgTypes, State) ->
+ signal_guard_failure(Eval, Guard, ArgTypes, fatal_fail, State).
+
+signal_guard_failure(Eval, Guard, ArgTypes, Tag, State) ->
+ Args = cerl:call_args(Guard),
+ F = cerl:atom_val(cerl:call_name(Guard)),
+ {M, F, A} = MFA = {cerl:atom_val(cerl:call_module(Guard)), F, length(Args)},
+ Opaques = State#state.opaques,
+ {Kind, XInfo} =
+ case erl_bif_types:opaque_args(M, F, A, ArgTypes, Opaques) of
+ [] ->
+ {case Eval of
+ neg -> neg_guard_fail;
+ pos -> guard_fail;
+ dont_know -> guard_fail
+ end,
+ []};
+ Ns -> {opaque_guard, [Ns]}
+ end,
+ FArgs =
+ case is_infix_op(MFA) of
+ true ->
+ [ArgType1, ArgType2] = ArgTypes,
+ [Arg1, Arg2] = Args,
+ [format_args_1([Arg1], [ArgType1], State),
+ atom_to_list(F),
+ format_args_1([Arg2], [ArgType2], State)] ++ XInfo;
+ false ->
+ [F, format_args(Args, ArgTypes, State)]
+ end,
+ Msg = {Kind, FArgs},
+ throw({Tag, {Guard, Msg}}).
+
+is_infix_op({erlang, '=:=', 2}) -> true;
+is_infix_op({erlang, '==', 2}) -> true;
+is_infix_op({erlang, '=/=', 2}) -> true;
+is_infix_op({erlang, '=/', 2}) -> true;
+is_infix_op({erlang, '<', 2}) -> true;
+is_infix_op({erlang, '=<', 2}) -> true;
+is_infix_op({erlang, '>', 2}) -> true;
+is_infix_op({erlang, '>=', 2}) -> true;
+is_infix_op({M, F, A}) when is_atom(M), is_atom(F),
+ is_integer(A), 0 =< A, A =< 255 -> false.
+
+bif_args(M, F, A) ->
+ case erl_bif_types:arg_types(M, F, A) of
+ unknown -> lists:duplicate(A, t_any());
+ List -> List
+ end.
+
+bind_guard_case_clauses(Arg, Clauses, Map0, Env, Eval, State) ->
+ Clauses1 = filter_fail_clauses(Clauses),
+ Map = join_maps_begin(Map0),
+ {GenMap, GenArgType} = bind_guard(Arg, Map, Env, dont_know, State),
+ bind_guard_case_clauses(GenArgType, GenMap, Arg, Clauses1, Map, Env, Eval,
+ t_none(), [], State).
+
+filter_fail_clauses([Clause|Left]) ->
+ case (cerl:clause_pats(Clause) =:= []) of
+ true ->
+ Body = cerl:clause_body(Clause),
+ case cerl:is_literal(Body) andalso (cerl:concrete(Body) =:= fail) orelse
+ cerl:is_c_primop(Body) andalso
+ (cerl:atom_val(cerl:primop_name(Body)) =:= match_fail) of
+ true -> filter_fail_clauses(Left);
+ false -> [Clause|filter_fail_clauses(Left)]
+ end;
+ false ->
+ [Clause|filter_fail_clauses(Left)]
+ end;
+filter_fail_clauses([]) ->
+ [].
+
+bind_guard_case_clauses(GenArgType, GenMap, ArgExpr, [Clause|Left],
+ Map, Env, Eval, AccType, AccMaps, State) ->
+ Pats = cerl:clause_pats(Clause),
+ {NewMap0, ArgType} =
+ case Pats of
+ [Pat] ->
+ case cerl:is_literal(Pat) of
+ true ->
+ try
+ case cerl:concrete(Pat) of
+ true -> bind_guard(ArgExpr, Map, Env, pos, State);
+ false -> bind_guard(ArgExpr, Map, Env, neg, State);
+ _ -> {GenMap, GenArgType}
+ end
+ catch
+ throw:{fail, _} -> {none, GenArgType}
+ end;
+ false ->
+ {GenMap, GenArgType}
+ end;
+ _ -> {GenMap, GenArgType}
+ end,
+ NewMap1 =
+ case Pats =:= [] of
+ true -> NewMap0;
+ false ->
+ case t_is_none(ArgType) of
+ true -> none;
+ false ->
+ ArgTypes = case t_is_any(ArgType) of
+ true -> Any = t_any(), [Any || _ <- Pats];
+ false -> t_to_tlist(ArgType)
+ end,
+ case bind_pat_vars(Pats, ArgTypes, [], NewMap0, State) of
+ {error, _, _, _, _} -> none;
+ {PatMap, _PatTypes} -> PatMap
+ end
+ end
+ end,
+ Guard = cerl:clause_guard(Clause),
+ GenPatType = dialyzer_typesig:get_safe_underapprox(Pats, Guard),
+ NewGenArgType = t_subtract(GenArgType, GenPatType),
+ case (NewMap1 =:= none) orelse t_is_none(GenArgType) of
+ true ->
+ bind_guard_case_clauses(NewGenArgType, GenMap, ArgExpr, Left, Map, Env,
+ Eval, AccType, AccMaps, State);
+ false ->
+ {NewAccType, NewAccMaps} =
+ try
+ {NewMap2, GuardType} = bind_guard(Guard, NewMap1, Env, pos, State),
+ case t_is_none(t_inf(t_atom(true), GuardType)) of
+ true -> throw({fail, none});
+ false -> ok
+ end,
+ {NewMap3, CType} = bind_guard(cerl:clause_body(Clause), NewMap2,
+ Env, Eval, State),
+ Opaques = State#state.opaques,
+ case Eval of
+ pos ->
+ case t_is_any_atom(true, CType, Opaques) of
+ true -> ok;
+ false -> throw({fail, none})
+ end;
+ neg ->
+ case t_is_any_atom(false, CType, Opaques) of
+ true -> ok;
+ false -> throw({fail, none})
+ end;
+ dont_know ->
+ ok
+ end,
+ {t_sup(AccType, CType), [NewMap3|AccMaps]}
+ catch
+ throw:{fail, _What} -> {AccType, AccMaps}
+ end,
+ bind_guard_case_clauses(NewGenArgType, GenMap, ArgExpr, Left, Map, Env,
+ Eval, NewAccType, NewAccMaps, State)
+ end;
+bind_guard_case_clauses(_GenArgType, _GenMap, _ArgExpr, [], Map, _Env, _Eval,
+ AccType, AccMaps, _State) ->
+ case t_is_none(AccType) of
+ true -> throw({fail, none});
+ false -> {join_maps_end(AccMaps, Map), AccType}
+ end.
+
+%%% ===========================================================================
+%%%
+%%% Maps and types.
+%%%
+%%% ===========================================================================
+
+map__new() ->
+ #map{}.
+
+%% join_maps_begin pushes 'modified' to the stack; join_maps pops
+%% 'modified' from the stack.
+
+join_maps_begin(#map{modified = M, modified_stack = S, ref = Ref} = Map) ->
+ Map#map{ref = make_ref(), modified = [], modified_stack = [{M,Ref} | S]}.
+
+join_maps_end(Maps, MapOut) ->
+ #map{ref = Ref, modified_stack = [{M1,R1} | S]} = MapOut,
+ true = lists:all(fun(M) -> M#map.ref =:= Ref end, Maps), % sanity
+ Keys0 = lists:usort(lists:append([M#map.modified || M <- Maps])),
+ #map{map = Map, subst = Subst} = MapOut,
+ Keys = [Key ||
+ Key <- Keys0,
+ maps:is_key(Key, Map) orelse maps:is_key(Key, Subst)],
+ Out = case Maps of
+ [] -> join_maps(Maps, MapOut);
+ _ -> join_maps(Keys, Maps, MapOut)
+ end,
+ debug_join_check(Maps, MapOut, Out),
+ Out#map{ref = R1,
+ modified = Out#map.modified ++ M1, % duplicates possible
+ modified_stack = S}.
+
+join_maps(Maps, MapOut) ->
+ #map{map = Map, subst = Subst} = MapOut,
+ Keys = ordsets:from_list(maps:keys(Map) ++ maps:keys(Subst)),
+ join_maps(Keys, Maps, MapOut).
+
+join_maps(Keys, Maps, MapOut) ->
+ KTs = join_maps_collect(Keys, Maps, MapOut),
+ lists:foldl(fun({K, T}, M) -> enter_type(K, T, M) end, MapOut, KTs).
+
+join_maps_collect([Key|Left], Maps, MapOut) ->
+ Type = join_maps_one_key(Maps, Key, t_none()),
+ case t_is_equal(lookup_type(Key, MapOut), Type) of
+ true -> join_maps_collect(Left, Maps, MapOut);
+ false -> [{Key, Type} | join_maps_collect(Left, Maps, MapOut)]
+ end;
+join_maps_collect([], _Maps, _MapOut) ->
+ [].
+
+join_maps_one_key([Map|Left], Key, AccType) ->
+ case t_is_any(AccType) of
+ true ->
+ %% We can stop here
+ AccType;
+ false ->
+ join_maps_one_key(Left, Key, t_sup(lookup_type(Key, Map), AccType))
+ end;
+join_maps_one_key([], _Key, AccType) ->
+ AccType.
+
+-ifdef(DEBUG).
+debug_join_check(Maps, MapOut, Out) ->
+ #map{map = Map, subst = Subst} = Out,
+ #map{map = Map2, subst = Subst2} = join_maps(Maps, MapOut),
+ F = fun(D) -> lists:keysort(1, maps:to_list(D)) end,
+ [throw({bug, join_maps}) ||
+ F(Map) =/= F(Map2) orelse F(Subst) =/= F(Subst2)].
+-else.
+debug_join_check(_Maps, _MapOut, _Out) -> ok.
+-endif.
+
+enter_type_lists([Key|KeyTail], [Val|ValTail], Map) ->
+ Map1 = enter_type(Key, Val, Map),
+ enter_type_lists(KeyTail, ValTail, Map1);
+enter_type_lists([], [], Map) ->
+ Map.
+
+enter_type_list([{Key, Val}|Left], Map) ->
+ Map1 = enter_type(Key, Val, Map),
+ enter_type_list(Left, Map1);
+enter_type_list([], Map) ->
+ Map.
+
+enter_type(Key, Val, MS) ->
+ case cerl:is_literal(Key) of
+ true -> MS;
+ false ->
+ case cerl:is_c_values(Key) of
+ true ->
+ Keys = cerl:values_es(Key),
+ case t_is_any(Val) orelse t_is_none(Val) of
+ true ->
+ enter_type_lists(Keys, [Val || _ <- Keys], MS);
+ false ->
+ enter_type_lists(Keys, t_to_tlist(Val), MS)
+ end;
+ false ->
+ #map{map = Map, subst = Subst} = MS,
+ KeyLabel = get_label(Key),
+ case maps:find(KeyLabel, Subst) of
+ {ok, NewKey} ->
+ ?debug("Binding ~p to ~p\n", [KeyLabel, NewKey]),
+ enter_type(NewKey, Val, MS);
+ error ->
+ ?debug("Entering ~p :: ~s\n", [KeyLabel, t_to_string(Val)]),
+ case maps:find(KeyLabel, Map) of
+ {ok, Value} ->
+ case erl_types:t_is_equal(Val, Value) of
+ true -> MS;
+ false -> store_map(KeyLabel, Val, MS)
+ end;
+ error -> store_map(KeyLabel, Val, MS)
+ end
+ end
+ end
+ end.
+
+store_map(Key, Val, #map{map = Map, ref = undefined} = MapRec) ->
+ MapRec#map{map = maps:put(Key, Val, Map)};
+store_map(Key, Val, #map{map = Map, modified = Mod} = MapRec) ->
+ MapRec#map{map = maps:put(Key, Val, Map), modified = [Key | Mod]}.
+
+enter_subst(Key, Val0, #map{subst = Subst} = MS) ->
+ KeyLabel = get_label(Key),
+ Val = dialyzer_utils:refold_pattern(Val0),
+ case cerl:is_literal(Val) of
+ true ->
+ store_map(KeyLabel, literal_type(Val), MS);
+ false ->
+ case cerl:is_c_var(Val) of
+ false -> MS;
+ true ->
+ ValLabel = get_label(Val),
+ case maps:find(ValLabel, Subst) of
+ {ok, NewVal} ->
+ enter_subst(Key, NewVal, MS);
+ error ->
+ if KeyLabel =:= ValLabel -> MS;
+ true ->
+ ?debug("Subst: storing ~p = ~p\n", [KeyLabel, ValLabel]),
+ store_subst(KeyLabel, ValLabel, MS)
+ end
+ end
+ end
+ end.
+
+store_subst(Key, Val, #map{subst = S, ref = undefined} = Map) ->
+ Map#map{subst = maps:put(Key, Val, S)};
+store_subst(Key, Val, #map{subst = S, modified = Mod} = Map) ->
+ Map#map{subst = maps:put(Key, Val, S), modified = [Key | Mod]}.
+
+lookup_type(Key, #map{map = Map, subst = Subst}) ->
+ lookup(Key, Map, Subst, t_none()).
+
+lookup(Key, Map, Subst, AnyNone) ->
+ case cerl:is_literal(Key) of
+ true -> literal_type(Key);
+ false ->
+ Label = get_label(Key),
+ case maps:find(Label, Subst) of
+ {ok, NewKey} -> lookup(NewKey, Map, Subst, AnyNone);
+ error ->
+ case maps:find(Label, Map) of
+ {ok, Val} -> Val;
+ error -> AnyNone
+ end
+ end
+ end.
+
+lookup_fun_sig(Fun, Callgraph, Plt) ->
+ MFAorLabel =
+ case dialyzer_callgraph:lookup_name(Fun, Callgraph) of
+ error -> Fun;
+ {ok, MFA} -> MFA
+ end,
+ dialyzer_plt:lookup(Plt, MFAorLabel).
+
+literal_type(Lit) ->
+ t_from_term(cerl:concrete(Lit)).
+
+mark_as_fresh([Tree|Left], Map) ->
+ SubTrees1 = lists:append(cerl:subtrees(Tree)),
+ {SubTrees2, Map1} =
+ case cerl:type(Tree) of
+ bitstr ->
+ %% The Size field is not fresh.
+ {SubTrees1 -- [cerl:bitstr_size(Tree)], Map};
+ map_pair ->
+ %% The keys are not fresh
+ {SubTrees1 -- [cerl:map_pair_key(Tree)], Map};
+ var ->
+ {SubTrees1, enter_type(Tree, t_any(), Map)};
+ _ ->
+ {SubTrees1, Map}
+ end,
+ mark_as_fresh(SubTrees2 ++ Left, Map1);
+mark_as_fresh([], Map) ->
+ Map.
+
+-ifdef(DEBUG).
+debug_pp_map(#map{map = Map}=MapRec) ->
+ Keys = maps:keys(Map),
+ io:format("Map:\n", []),
+ lists:foreach(fun (Key) ->
+ io:format("\t~w :: ~s\n",
+ [Key, t_to_string(lookup_type(Key, MapRec))])
+ end, Keys),
+ ok.
+-else.
+debug_pp_map(_Map) -> ok.
+-endif.
+
+%%% ===========================================================================
+%%%
+%%% Utilities
+%%%
+%%% ===========================================================================
+
+get_label(L) when is_integer(L) ->
+ L;
+get_label(T) ->
+ cerl_trees:get_label(T).
+
+t_is_simple(ArgType, State) ->
+ Opaques = State#state.opaques,
+ t_is_atom(ArgType, Opaques) orelse t_is_number(ArgType, Opaques)
+ orelse t_is_port(ArgType, Opaques)
+ orelse t_is_pid(ArgType, Opaques) orelse t_is_reference(ArgType, Opaques)
+ orelse t_is_nil(ArgType, Opaques).
+
+remove_local_opaque_types(Type, Opaques) ->
+ t_unopaque(Type, Opaques).
+
+%% t_is_structured(ArgType) ->
+%% case t_is_nil(ArgType) of
+%% true -> false;
+%% false ->
+%% SType = t_inf(t_sup([t_list(), t_tuple(), t_binary()]), ArgType),
+%% t_is_equal(ArgType, SType)
+%% end.
+
+is_call_to_send(Tree) ->
+ case cerl:is_c_call(Tree) of
+ false -> false;
+ true ->
+ Mod = cerl:call_module(Tree),
+ Name = cerl:call_name(Tree),
+ Arity = cerl:call_arity(Tree),
+ cerl:is_c_atom(Mod)
+ andalso cerl:is_c_atom(Name)
+ andalso is_send(cerl:atom_val(Name))
+ andalso (cerl:atom_val(Mod) =:= erlang)
+ andalso (Arity =:= 2)
+ end.
+
+is_send('!') -> true;
+is_send(send) -> true;
+is_send(_) -> false.
+
+is_lc_simple_list(Tree, TreeType, State) ->
+ Opaques = State#state.opaques,
+ Ann = cerl:get_ann(Tree),
+ lists:member(list_comprehension, Ann)
+ andalso t_is_list(TreeType)
+ andalso t_is_simple(t_list_elements(TreeType, Opaques), State).
+
+filter_match_fail([Clause] = Cls) ->
+ Body = cerl:clause_body(Clause),
+ case cerl:type(Body) of
+ primop ->
+ case cerl:atom_val(cerl:primop_name(Body)) of
+ match_fail -> [];
+ raise -> [];
+ _ -> Cls
+ end;
+ _ -> Cls
+ end;
+filter_match_fail([H|T]) ->
+ [H|filter_match_fail(T)];
+filter_match_fail([]) ->
+ %% This can actually happen, for example in
+ %% receive after 1 -> ok end
+ [].
+
+%%% ===========================================================================
+%%%
+%%% The State.
+%%%
+%%% ===========================================================================
+
+state__new(Callgraph, Codeserver, Tree, Plt, Module, Records) ->
+ Opaques = erl_types:t_opaque_from_records(Records),
+ {TreeMap, FunHomes} = build_tree_map(Tree, Callgraph),
+ Funs = dict:fetch_keys(TreeMap),
+ FunTab = init_fun_tab(Funs, dict:new(), TreeMap, Callgraph, Plt),
+ ExportedFuns =
+ [Fun || Fun <- Funs--[top], dialyzer_callgraph:is_escaping(Fun, Callgraph)],
+ Work = init_work(ExportedFuns),
+ Env = lists:foldl(fun(Fun, Env) -> dict:store(Fun, map__new(), Env) end,
+ dict:new(), Funs),
+ #state{callgraph = Callgraph, codeserver = Codeserver,
+ envs = Env, fun_tab = FunTab, fun_homes = FunHomes, opaques = Opaques,
+ plt = Plt, races = dialyzer_races:new(), records = Records,
+ warning_mode = false, warnings = [], work = Work, tree_map = TreeMap,
+ module = Module}.
+
+state__warning_mode(#state{warning_mode = WM}) ->
+ WM.
+
+state__set_warning_mode(#state{tree_map = TreeMap, fun_tab = FunTab,
+ races = Races} = State) ->
+ ?debug("==========\nStarting warning pass\n==========\n", []),
+ Funs = dict:fetch_keys(TreeMap),
+ State#state{work = init_work([top|Funs--[top]]),
+ fun_tab = FunTab, warning_mode = true,
+ races = dialyzer_races:put_race_analysis(true, Races)}.
+
+state__race_analysis(Analysis, #state{races = Races} = State) ->
+ State#state{races = dialyzer_races:put_race_analysis(Analysis, Races)}.
+
+state__renew_curr_fun(CurrFun, CurrFunLabel,
+ #state{races = Races} = State) ->
+ State#state{races = dialyzer_races:put_curr_fun(CurrFun, CurrFunLabel,
+ Races)}.
+
+state__renew_fun_args(Args, #state{races = Races} = State) ->
+ case state__warning_mode(State) of
+ true -> State;
+ false ->
+ State#state{races = dialyzer_races:put_fun_args(Args, Races)}
+ end.
+
+state__renew_race_list(RaceList, RaceListSize,
+ #state{races = Races} = State) ->
+ State#state{races = dialyzer_races:put_race_list(RaceList, RaceListSize,
+ Races)}.
+
+state__renew_warnings(Warnings, State) ->
+ State#state{warnings = Warnings}.
+
+-spec state__add_warning(raw_warning(), state()) -> state().
+
+state__add_warning(Warn, #state{warnings = Warnings} = State) ->
+ State#state{warnings = [Warn|Warnings]}.
+
+state__add_warning(State, Tag, Tree, Msg) ->
+ state__add_warning(State, Tag, Tree, Msg, false).
+
+state__add_warning(#state{warning_mode = false} = State, _, _, _, _) ->
+ State;
+state__add_warning(#state{warnings = Warnings, warning_mode = true} = State,
+ Tag, Tree, Msg, Force) ->
+ Ann = cerl:get_ann(Tree),
+ case Force of
+ true ->
+ WarningInfo = {get_file(Ann),
+ abs(get_line(Ann)),
+ State#state.curr_fun},
+ Warn = {Tag, WarningInfo, Msg},
+ ?debug("MSG ~s\n", [dialyzer:format_warning(Warn)]),
+ State#state{warnings = [Warn|Warnings]};
+ false ->
+ case is_compiler_generated(Ann) of
+ true -> State;
+ false ->
+ WarningInfo = {get_file(Ann), get_line(Ann), State#state.curr_fun},
+ Warn = {Tag, WarningInfo, Msg},
+ case Tag of
+ ?WARN_CONTRACT_RANGE -> ok;
+ _ -> ?debug("MSG ~s\n", [dialyzer:format_warning(Warn)])
+ end,
+ State#state{warnings = [Warn|Warnings]}
+ end
+ end.
+
+state__remove_added_warnings(OldState, NewState) ->
+ #state{warnings = OldWarnings} = OldState,
+ #state{warnings = NewWarnings} = NewState,
+ {NewWarnings -- OldWarnings, NewState#state{warnings = OldWarnings}}.
+
+state__add_warnings(Warns, #state{warnings = Warnings} = State) ->
+ State#state{warnings = Warns ++ Warnings}.
+
+-spec state__set_curr_fun(curr_fun(), state()) -> state().
+
+state__set_curr_fun(undefined, State) ->
+ State#state{curr_fun = undefined};
+state__set_curr_fun(FunLbl, State) ->
+ State#state{curr_fun = find_function(FunLbl, State)}.
+
+-spec state__find_function(mfa_or_funlbl(), state()) -> mfa_or_funlbl().
+
+state__find_function(FunLbl, State) ->
+ find_function(FunLbl, State).
+
+state__get_race_warnings(#state{races = Races} = State) ->
+ {Races1, State1} = dialyzer_races:get_race_warnings(Races, State),
+ State1#state{races = Races1}.
+
+state__get_warnings(#state{tree_map = TreeMap, fun_tab = FunTab,
+ callgraph = Callgraph, plt = Plt} = State) ->
+ FoldFun =
+ fun({top, _}, AccState) -> AccState;
+ ({FunLbl, Fun}, AccState) ->
+ AccState1 = state__set_curr_fun(FunLbl, AccState),
+ {NotCalled, Ret} =
+ case dict:fetch(get_label(Fun), FunTab) of
+ {not_handled, {_Args0, Ret0}} -> {true, Ret0};
+ {_Args0, Ret0} -> {false, Ret0}
+ end,
+ case NotCalled of
+ true ->
+ case dialyzer_callgraph:lookup_name(FunLbl, Callgraph) of
+ error -> AccState1;
+ {ok, {_M, F, A}} ->
+ Msg = {unused_fun, [F, A]},
+ state__add_warning(AccState1, ?WARN_NOT_CALLED, Fun, Msg)
+ end;
+ false ->
+ {Name, Contract} =
+ case dialyzer_callgraph:lookup_name(FunLbl, Callgraph) of
+ error -> {[], none};
+ {ok, {_M, F, A} = MFA} ->
+ {[F, A], dialyzer_plt:lookup_contract(Plt, MFA)}
+ end,
+ case t_is_none(Ret) of
+ true ->
+ %% Check if the function has a contract that allows this.
+ Warn =
+ case Contract of
+ none -> not parent_allows_this(FunLbl, AccState1);
+ {value, C} ->
+ GenRet = dialyzer_contracts:get_contract_return(C),
+ not t_is_unit(GenRet)
+ end,
+ case Warn of
+ true ->
+ case classify_returns(Fun) of
+ no_match ->
+ Msg = {no_return, [no_match|Name]},
+ state__add_warning(AccState1, ?WARN_RETURN_NO_RETURN,
+ Fun, Msg);
+ only_explicit ->
+ Msg = {no_return, [only_explicit|Name]},
+ state__add_warning(AccState1, ?WARN_RETURN_ONLY_EXIT,
+ Fun, Msg);
+ only_normal ->
+ Msg = {no_return, [only_normal|Name]},
+ state__add_warning(AccState1, ?WARN_RETURN_NO_RETURN,
+ Fun, Msg);
+ both ->
+ Msg = {no_return, [both|Name]},
+ state__add_warning(AccState1, ?WARN_RETURN_NO_RETURN,
+ Fun, Msg)
+ end;
+ false ->
+ AccState
+ end;
+ false ->
+ AccState
+ end
+ end
+ end,
+ #state{warnings = Warn} = lists:foldl(FoldFun, State, dict:to_list(TreeMap)),
+ Warn.
+
+state__is_escaping(Fun, #state{callgraph = Callgraph}) ->
+ dialyzer_callgraph:is_escaping(Fun, Callgraph).
+
+state__lookup_type_for_letrec(Var, #state{callgraph = Callgraph} = State) ->
+ Label = get_label(Var),
+ case dialyzer_callgraph:lookup_letrec(Label, Callgraph) of
+ error -> error;
+ {ok, FunLabel} ->
+ {ok, state__fun_type(FunLabel, State)}
+ end.
+
+state__lookup_name({_, _, _} = MFA, #state{}) ->
+ MFA;
+state__lookup_name(top, #state{}) ->
+ top;
+state__lookup_name(Fun, #state{callgraph = Callgraph}) ->
+ case dialyzer_callgraph:lookup_name(Fun, Callgraph) of
+ {ok, MFA} -> MFA;
+ error -> Fun
+ end.
+
+state__lookup_record(Tag, Arity, #state{records = Records}) ->
+ case erl_types:lookup_record(Tag, Arity, Records) of
+ {ok, Fields} ->
+ RecType =
+ t_tuple([t_atom(Tag)|
+ [FieldType || {_FieldName, _Abstr, FieldType} <- Fields]]),
+ {ok, RecType};
+ error ->
+ error
+ end.
+
+state__get_args_and_status(Tree, #state{fun_tab = FunTab}) ->
+ Fun = get_label(Tree),
+ case dict:find(Fun, FunTab) of
+ {ok, {not_handled, {ArgTypes, _}}} -> {ArgTypes, false};
+ {ok, {ArgTypes, _}} -> {ArgTypes, true}
+ end.
+
+build_tree_map(Tree, Callgraph) ->
+ Fun =
+ fun(T, {Dict, Homes, FunLbls} = Acc) ->
+ case cerl:is_c_fun(T) of
+ true ->
+ FunLbl = get_label(T),
+ Dict1 = dict:store(FunLbl, T, Dict),
+ case catch dialyzer_callgraph:lookup_name(FunLbl, Callgraph) of
+ {ok, MFA} ->
+ F2 =
+ fun(Lbl, Dict0) ->
+ dict:store(Lbl, MFA, Dict0)
+ end,
+ Homes1 = lists:foldl(F2, Homes, [FunLbl|FunLbls]),
+ {Dict1, Homes1, []};
+ _ ->
+ {Dict1, Homes, [FunLbl|FunLbls]}
+ end;
+ false ->
+ Acc
+ end
+ end,
+ Dict0 = dict:new(),
+ {Dict, Homes, _} = cerl_trees:fold(Fun, {Dict0, Dict0, []}, Tree),
+ {Dict, Homes}.
+
+init_fun_tab([top|Left], Dict, TreeMap, Callgraph, Plt) ->
+ NewDict = dict:store(top, {[], t_none()}, Dict),
+ init_fun_tab(Left, NewDict, TreeMap, Callgraph, Plt);
+init_fun_tab([Fun|Left], Dict, TreeMap, Callgraph, Plt) ->
+ Arity = cerl:fun_arity(dict:fetch(Fun, TreeMap)),
+ FunEntry =
+ case dialyzer_callgraph:is_escaping(Fun, Callgraph) of
+ true ->
+ Args = lists:duplicate(Arity, t_any()),
+ case lookup_fun_sig(Fun, Callgraph, Plt) of
+ none -> {Args, t_unit()};
+ {value, {RetType, _}} ->
+ case t_is_none(RetType) of
+ true -> {Args, t_none()};
+ false -> {Args, t_unit()}
+ end
+ end;
+ false -> {not_handled, {lists:duplicate(Arity, t_none()), t_unit()}}
+ end,
+ NewDict = dict:store(Fun, FunEntry, Dict),
+ init_fun_tab(Left, NewDict, TreeMap, Callgraph, Plt);
+init_fun_tab([], Dict, _TreeMap, _Callgraph, _Plt) ->
+ ?debug("DICT:~p\n",[dict:to_list(Dict)]),
+ Dict.
+
+state__update_fun_env(Tree, Map, #state{envs = Envs} = State) ->
+ NewEnvs = dict:store(get_label(Tree), Map, Envs),
+ State#state{envs = NewEnvs}.
+
+state__fun_env(Tree, #state{envs = Envs}) ->
+ Fun = get_label(Tree),
+ case dict:find(Fun, Envs) of
+ error -> none;
+ {ok, Map} -> Map
+ end.
+
+state__clean_not_called(#state{fun_tab = FunTab} = State) ->
+ NewFunTab =
+ dict:map(fun(top, Entry) -> Entry;
+ (_Fun, {not_handled, {Args, _}}) -> {Args, t_none()};
+ (_Fun, Entry) -> Entry
+ end, FunTab),
+ State#state{fun_tab = NewFunTab}.
+
+state__all_fun_types(State) ->
+ #state{fun_tab = FunTab} = state__clean_not_called(State),
+ Tab1 = dict:erase(top, FunTab),
+ dict:map(fun(_Fun, {Args, Ret}) -> t_fun(Args, Ret)end, Tab1).
+
+state__fun_type(Fun, #state{fun_tab = FunTab}) ->
+ Label =
+ if is_integer(Fun) -> Fun;
+ true -> get_label(Fun)
+ end,
+ Entry = dict:find(Label, FunTab),
+ ?debug("FunType ~p:~p\n",[Label, Entry]),
+ case Entry of
+ {ok, {not_handled, {A, R}}} ->
+ t_fun(A, R);
+ {ok, {A, R}} ->
+ t_fun(A, R)
+ end.
+
+state__update_fun_entry(Tree, ArgTypes, Out0,
+ #state{fun_tab=FunTab, callgraph=CG, plt=Plt} = State)->
+ Fun = get_label(Tree),
+ Out1 =
+ if Fun =:= top -> Out0;
+ true ->
+ case lookup_fun_sig(Fun, CG, Plt) of
+ {value, {SigRet, _}} -> t_inf(SigRet, Out0);
+ none -> Out0
+ end
+ end,
+ Out = t_limit(Out1, ?TYPE_LIMIT),
+ {ok, {OldArgTypes, OldOut}} = dict:find(Fun, FunTab),
+ SameArgs = lists:all(fun({A, B}) -> erl_types:t_is_equal(A, B)
+ end, lists:zip(OldArgTypes, ArgTypes)),
+ SameOut = t_is_equal(OldOut, Out),
+ if
+ SameArgs, SameOut ->
+ ?debug("Fixpoint for ~w: ~s\n",
+ [state__lookup_name(Fun, State),
+ t_to_string(t_fun(ArgTypes, Out))]),
+ State;
+ true ->
+ %% Can only happen in self-recursive functions.
+ NewEntry = {OldArgTypes, Out},
+ ?debug("New Entry for ~w: ~s\n",
+ [state__lookup_name(Fun, State),
+ t_to_string(t_fun(OldArgTypes, Out))]),
+ NewFunTab = dict:store(Fun, NewEntry, FunTab),
+ State1 = State#state{fun_tab = NewFunTab},
+ state__add_work_from_fun(Tree, State1)
+ end.
+
+state__add_work_from_fun(_Tree, #state{warning_mode = true} = State) ->
+ State;
+state__add_work_from_fun(Tree, #state{callgraph = Callgraph,
+ tree_map = TreeMap} = State) ->
+ case get_label(Tree) of
+ top -> State;
+ Label when is_integer(Label) ->
+ case dialyzer_callgraph:in_neighbours(Label, Callgraph) of
+ none -> State;
+ MFAList ->
+ LabelList = [dialyzer_callgraph:lookup_label(MFA, Callgraph)
+ || MFA <- MFAList],
+ %% Must filter the result for results in this module.
+ FilteredList = [L || {ok, L} <- LabelList, dict:is_key(L, TreeMap)],
+ ?debug("~w: Will try to add:~w\n",
+ [state__lookup_name(Label, State), MFAList]),
+ lists:foldl(fun(L, AccState) ->
+ state__add_work(L, AccState)
+ end, State, FilteredList)
+ end
+ end.
+
+state__add_work(external, State) ->
+ State;
+state__add_work(top, State) ->
+ State;
+state__add_work(Fun, #state{work = Work} = State) ->
+ NewWork = add_work(Fun, Work),
+ State#state{work = NewWork}.
+
+state__get_work(#state{work = Work, tree_map = TreeMap} = State) ->
+ case get_work(Work) of
+ none -> none;
+ {Fun, NewWork} ->
+ {dict:fetch(Fun, TreeMap), State#state{work = NewWork}}
+ end.
+
+state__lookup_call_site(Tree, #state{callgraph = Callgraph}) ->
+ Label = get_label(Tree),
+ dialyzer_callgraph:lookup_call_site(Label, Callgraph).
+
+state__fun_info(external, #state{}) ->
+ external;
+state__fun_info({_, _, _} = MFA, #state{plt = PLT}) ->
+ {MFA,
+ dialyzer_plt:lookup(PLT, MFA),
+ dialyzer_plt:lookup_contract(PLT, MFA),
+ t_any()};
+state__fun_info(Fun, #state{callgraph = CG, fun_tab = FunTab, plt = PLT}) ->
+ {Sig, Contract} =
+ case dialyzer_callgraph:lookup_name(Fun, CG) of
+ error ->
+ {dialyzer_plt:lookup(PLT, Fun), none};
+ {ok, MFA} ->
+ {dialyzer_plt:lookup(PLT, MFA), dialyzer_plt:lookup_contract(PLT, MFA)}
+ end,
+ LocalRet =
+ case dict:fetch(Fun, FunTab) of
+ {not_handled, {_Args, Ret}} -> Ret;
+ {_Args, Ret} -> Ret
+ end,
+ ?debug("LocalRet: ~s\n", [t_to_string(LocalRet)]),
+ {Fun, Sig, Contract, LocalRet}.
+
+forward_args(Fun, ArgTypes, #state{work = Work, fun_tab = FunTab} = State) ->
+ {OldArgTypes, OldOut, Fixpoint} =
+ case dict:find(Fun, FunTab) of
+ {ok, {not_handled, {OldArgTypes0, OldOut0}}} ->
+ {OldArgTypes0, OldOut0, false};
+ {ok, {OldArgTypes0, OldOut0}} ->
+ {OldArgTypes0, OldOut0,
+ t_is_subtype(t_product(ArgTypes), t_product(OldArgTypes0))}
+ end,
+ case Fixpoint of
+ true -> State;
+ false ->
+ NewArgTypes = [t_sup(X, Y) ||
+ {X, Y} <- lists:zip(ArgTypes, OldArgTypes)],
+ NewWork = add_work(Fun, Work),
+ ?debug("~w: forwarding args ~s\n",
+ [state__lookup_name(Fun, State),
+ t_to_string(t_product(NewArgTypes))]),
+ NewFunTab = dict:store(Fun, {NewArgTypes, OldOut}, FunTab),
+ State#state{work = NewWork, fun_tab = NewFunTab}
+ end.
+
+-spec state__cleanup(state()) -> state().
+
+state__cleanup(#state{callgraph = Callgraph,
+ races = Races,
+ records = Records}) ->
+ #state{callgraph = dialyzer_callgraph:cleanup(Callgraph),
+ races = dialyzer_races:cleanup(Races),
+ records = Records}.
+
+-spec state__duplicate(state()) -> state().
+
+state__duplicate(#state{callgraph = Callgraph} = State) ->
+ State#state{callgraph = dialyzer_callgraph:duplicate(Callgraph)}.
+
+-spec dispose_state(state()) -> ok.
+
+dispose_state(#state{callgraph = Callgraph}) ->
+ dialyzer_callgraph:dispose_race_server(Callgraph).
+
+-spec state__get_callgraph(state()) -> dialyzer_callgraph:callgraph().
+
+state__get_callgraph(#state{callgraph = Callgraph}) ->
+ Callgraph.
+
+-spec state__get_races(state()) -> dialyzer_races:races().
+
+state__get_races(#state{races = Races}) ->
+ Races.
+
+-spec state__get_records(state()) -> types().
+
+state__get_records(#state{records = Records}) ->
+ Records.
+
+-spec state__put_callgraph(dialyzer_callgraph:callgraph(), state()) ->
+ state().
+
+state__put_callgraph(Callgraph, State) ->
+ State#state{callgraph = Callgraph}.
+
+-spec state__put_races(dialyzer_races:races(), state()) -> state().
+
+state__put_races(Races, State) ->
+ State#state{races = Races}.
+
+-spec state__records_only(state()) -> state().
+
+state__records_only(#state{records = Records}) ->
+ #state{records = Records}.
+
+%%% ===========================================================================
+%%%
+%%% Races
+%%%
+%%% ===========================================================================
+
+is_race_analysis_enabled(#state{races = Races, callgraph = Callgraph}) ->
+ RaceDetection = dialyzer_callgraph:get_race_detection(Callgraph),
+ RaceAnalysis = dialyzer_races:get_race_analysis(Races),
+ RaceDetection andalso RaceAnalysis.
+
+get_race_list_and_size(#state{races = Races}) ->
+ dialyzer_races:get_race_list_and_size(Races).
+
+renew_race_code(#state{races = Races, callgraph = Callgraph,
+ warning_mode = WarningMode} = State) ->
+ case WarningMode of
+ true -> State;
+ false ->
+ NewCallgraph = dialyzer_callgraph:renew_race_code(Races, Callgraph),
+ State#state{callgraph = NewCallgraph}
+ end.
+
+renew_race_public_tables([Var], #state{races = Races, callgraph = Callgraph,
+ warning_mode = WarningMode} = State) ->
+ case WarningMode of
+ true -> State;
+ false ->
+ Table = dialyzer_races:get_new_table(Races),
+ case Table of
+ no_t -> State;
+ _Other ->
+ VarLabel = get_label(Var),
+ NewCallgraph =
+ dialyzer_callgraph:renew_race_public_tables(VarLabel, Callgraph),
+ State#state{callgraph = NewCallgraph}
+ end
+ end.
+
+%%% ===========================================================================
+%%%
+%%% Worklist
+%%%
+%%% ===========================================================================
+
+init_work(List) ->
+ {List, [], sets:from_list(List)}.
+
+get_work({[], [], _Set}) ->
+ none;
+get_work({[H|T], Rev, Set}) ->
+ {H, {T, Rev, sets:del_element(H, Set)}};
+get_work({[], Rev, Set}) ->
+ get_work({lists:reverse(Rev), [], Set}).
+
+add_work(New, {List, Rev, Set} = Work) ->
+ case sets:is_element(New, Set) of
+ true -> Work;
+ false -> {List, [New|Rev], sets:add_element(New, Set)}
+ end.
+
+%%% ===========================================================================
+%%%
+%%% Utilities.
+%%%
+%%% ===========================================================================
+
+get_line([Line|_]) when is_integer(Line) -> Line;
+get_line([_|Tail]) -> get_line(Tail);
+get_line([]) -> -1.
+
+get_file([]) -> [];
+get_file([{file, File}|_]) -> File;
+get_file([_|Tail]) -> get_file(Tail).
+
+is_compiler_generated(Ann) ->
+ lists:member(compiler_generated, Ann) orelse (get_line(Ann) < 1).
+
+is_literal_record(Tree) ->
+ Ann = cerl:get_ann(Tree),
+ lists:member(record, Ann).
+
+-spec format_args([cerl:cerl()], [type()], state()) ->
+ nonempty_string().
+
+format_args([], [], _State) ->
+ "()";
+format_args(ArgList0, TypeList, State) ->
+ ArgList = fold_literals(ArgList0),
+ "(" ++ format_args_1(ArgList, TypeList, State) ++ ")".
+
+format_args_1([Arg], [Type], State) ->
+ format_arg(Arg) ++ format_type(Type, State);
+format_args_1([Arg|Args], [Type|Types], State) ->
+ String =
+ case cerl:is_literal(Arg) of
+ true -> format_cerl(Arg);
+ false -> format_arg(Arg) ++ format_type(Type, State)
+ end,
+ String ++ "," ++ format_args_1(Args, Types, State).
+
+format_arg(Arg) ->
+ Default = "",
+ case cerl:is_c_var(Arg) of
+ true ->
+ case cerl:var_name(Arg) of
+ Atom when is_atom(Atom) ->
+ case atom_to_list(Atom) of
+ "cor"++_ -> Default;
+ "rec"++_ -> Default;
+ Name -> Name ++ "::"
+ end;
+ _What -> Default
+ end;
+ false ->
+ Default
+ end.
+
+-spec format_type(type(), state()) -> string().
+
+format_type(Type, #state{records = R}) ->
+ t_to_string(Type, R).
+
+-spec format_field_diffs(type(), state()) -> string().
+
+format_field_diffs(RecConstruction, #state{records = R}) ->
+ erl_types:record_field_diffs_to_string(RecConstruction, R).
+
+-spec format_sig_args(type(), state()) -> string().
+
+format_sig_args(Type, #state{opaques = Opaques} = State) ->
+ SigArgs = t_fun_args(Type, Opaques),
+ case SigArgs of
+ [] -> "()";
+ [SArg|SArgs] ->
+ lists:flatten("(" ++ format_type(SArg, State)
+ ++ ["," ++ format_type(T, State) || T <- SArgs] ++ ")")
+ end.
+
+format_cerl(Tree) ->
+ cerl_prettypr:format(cerl:set_ann(Tree, []),
+ [{hook, dialyzer_utils:pp_hook()},
+ {noann, true},
+ {paper, 100000}, %% These guys strip
+ {ribbon, 100000} %% newlines.
+ ]).
+
+format_patterns(Pats0) ->
+ Pats = fold_literals(Pats0),
+ NewPats = map_pats(cerl:c_values(Pats)),
+ String = format_cerl(NewPats),
+ case Pats of
+ [PosVar] ->
+ case cerl:is_c_var(PosVar) andalso (cerl:var_name(PosVar) =/= '') of
+ true -> "variable "++String;
+ false -> "pattern "++String
+ end;
+ _ ->
+ "pattern "++String
+ end.
+
+map_pats(Pats) ->
+ Fun = fun(Tree) ->
+ case cerl:is_c_var(Tree) of
+ true ->
+ case cerl:var_name(Tree) of
+ Atom when is_atom(Atom) ->
+ case atom_to_list(Atom) of
+ "cor"++_ -> cerl:c_var('');
+ "rec"++_ -> cerl:c_var('');
+ _ -> cerl:set_ann(Tree, [])
+ end;
+ _What -> cerl:c_var('')
+ end;
+ false ->
+ cerl:set_ann(Tree, [])
+ end
+ end,
+ cerl_trees:map(Fun, Pats).
+
+fold_literals(TreeList) ->
+ [cerl:fold_literal(Tree) || Tree <- TreeList].
+
+type(Tree) ->
+ Folded = cerl:fold_literal(Tree),
+ case cerl:type(Folded) of
+ literal -> {literal, Folded};
+ Type -> Type
+ end.
+
+is_literal(Tree) ->
+ Folded = cerl:fold_literal(Tree),
+ case cerl:is_literal(Folded) of
+ true -> {yes, Folded};
+ false -> no
+ end.
+
+parent_allows_this(FunLbl, #state{callgraph = Callgraph, plt = Plt} =State) ->
+ case state__is_escaping(FunLbl, State) of
+ false -> false; % if it isn't escaping it can't be a return value
+ true ->
+ case state__lookup_name(FunLbl, State) of
+ {_M, _F, _A} -> false; % if it has a name it is not a fun
+ _ ->
+ case dialyzer_callgraph:in_neighbours(FunLbl, Callgraph) of
+ [Parent] ->
+ case state__lookup_name(Parent, State) of
+ {_M, _F, _A} = PMFA ->
+ case dialyzer_plt:lookup_contract(Plt, PMFA) of
+ none -> false;
+ {value, C} ->
+ GenRet = dialyzer_contracts:get_contract_return(C),
+ case erl_types:t_is_fun(GenRet) of
+ false -> false; % element of structure? far-fetched...
+ true -> t_is_unit(t_fun_range(GenRet))
+ end
+ end;
+ _ -> false % parent should have a name to have a contract
+ end;
+ _ -> false % called in other funs? far-fetched...
+ end
+ end
+ end.
+
+find_function({_, _, _} = MFA, _State) ->
+ MFA;
+find_function(top, _State) ->
+ top;
+find_function(FunLbl, #state{fun_homes = Homes}) ->
+ dict:fetch(FunLbl, Homes).
+
+classify_returns(Tree) ->
+ case find_terminals(cerl:fun_body(Tree)) of
+ {false, false} -> no_match;
+ {true, false} -> only_explicit;
+ {false, true} -> only_normal;
+ {true, true} -> both
+ end.
+
+find_terminals(Tree) ->
+ case cerl:type(Tree) of
+ apply -> {false, true};
+ binary -> {false, true};
+ bitstr -> {false, true};
+ call ->
+ M0 = cerl:call_module(Tree),
+ F0 = cerl:call_name(Tree),
+ A = length(cerl:call_args(Tree)),
+ case {is_literal(M0), is_literal(F0)} of
+ {{yes, LitM}, {yes, LitF}} ->
+ M = cerl:concrete(LitM),
+ F = cerl:concrete(LitF),
+ case (erl_bif_types:is_known(M, F, A)
+ andalso t_is_none(erl_bif_types:type(M, F, A))) of
+ true -> {true, false};
+ false -> {false, true}
+ end;
+ _ ->
+ %% We cannot make assumptions. Say that both are true.
+ {true, true}
+ end;
+ 'case' -> find_terminals_list(cerl:case_clauses(Tree));
+ 'catch' -> find_terminals(cerl:catch_body(Tree));
+ clause -> find_terminals(cerl:clause_body(Tree));
+ cons -> {false, true};
+ 'fun' -> {false, true};
+ 'let' -> find_terminals(cerl:let_body(Tree));
+ letrec -> find_terminals(cerl:letrec_body(Tree));
+ literal -> {false, true};
+ map -> {false, true};
+ primop -> {false, false}; %% match_fail, etc. are not explicit exits.
+ 'receive' ->
+ Timeout = cerl:receive_timeout(Tree),
+ Clauses = cerl:receive_clauses(Tree),
+ case (cerl:is_literal(Timeout) andalso
+ (cerl:concrete(Timeout) =:= infinity)) of
+ true ->
+ if Clauses =:= [] -> {false, true}; %% A never ending receive.
+ true -> find_terminals_list(Clauses)
+ end;
+ false -> find_terminals_list([cerl:receive_action(Tree)|Clauses])
+ end;
+ seq -> find_terminals(cerl:seq_body(Tree));
+ 'try' ->
+ find_terminals_list([cerl:try_handler(Tree), cerl:try_body(Tree)]);
+ tuple -> {false, true};
+ values -> {false, true};
+ var -> {false, true}
+ end.
+
+find_terminals_list(List) ->
+ find_terminals_list(List, false, false).
+
+find_terminals_list([Tree|Left], Explicit1, Normal1) ->
+ {Explicit2, Normal2} = find_terminals(Tree),
+ case {Explicit1 or Explicit2, Normal1 or Normal2} of
+ {true, true} = Ans -> Ans;
+ {NewExplicit, NewNormal} ->
+ find_terminals_list(Left, NewExplicit, NewNormal)
+ end;
+find_terminals_list([], Explicit, Normal) ->
+ {Explicit, Normal}.
+
+%%----------------------------------------------------------------------------
+
+-ifdef(DEBUG_PP).
+debug_pp(Tree, true) ->
+ io:put_chars(cerl_prettypr:format(Tree, [{hook, cerl_typean:pp_hook()}])),
+ io:nl(),
+ ok;
+debug_pp(Tree, false) ->
+ io:put_chars(cerl_prettypr:format(strip_annotations(Tree))),
+ io:nl(),
+ ok.
+
+strip_annotations(Tree) ->
+ Fun = fun(T) ->
+ case cerl:type(T) of
+ var ->
+ cerl:set_ann(T, [{label, cerl_trees:get_label(T)}]);
+ 'fun' ->
+ cerl:set_ann(T, [{label, cerl_trees:get_label(T)}]);
+ _ ->
+ cerl:set_ann(T, [])
+ end
+ end,
+ cerl_trees:map(Fun, Tree).
+
+-else.
+
+debug_pp(_Tree, _UseHook) ->
+ ok.
+-endif.
diff --git a/lib/dialyzer/test/opaque_SUITE_data/src/recrec/dialyzer_races.erl b/lib/dialyzer/test/opaque_SUITE_data/src/recrec/dialyzer_races.erl
new file mode 100644
index 0000000000..bb43d1dcb8
--- /dev/null
+++ b/lib/dialyzer/test/opaque_SUITE_data/src/recrec/dialyzer_races.erl
@@ -0,0 +1,2494 @@
+%% -*- erlang-indent-level: 2 -*-
+%%-----------------------------------------------------------------------
+%% %CopyrightBegin%
+%%
+%% Copyright Ericsson AB 2008-2015. All Rights Reserved.
+%%
+%% Licensed under the Apache License, Version 2.0 (the "License");
+%% you may not use this file except in compliance with the License.
+%% You may obtain a copy of the License at
+%%
+%% http://www.apache.org/licenses/LICENSE-2.0
+%%
+%% Unless required by applicable law or agreed to in writing, software
+%% distributed under the License is distributed on an "AS IS" BASIS,
+%% WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+%% See the License for the specific language governing permissions and
+%% limitations under the License.
+%%
+%% %CopyrightEnd%
+%%
+
+%%%----------------------------------------------------------------------
+%%% File : dialyzer_races.erl
+%%% Author : Maria Christakis <[email protected]>
+%%% Description : Utility functions for race condition detection
+%%%
+%%% Created : 21 Nov 2008 by Maria Christakis <[email protected]>
+%%%----------------------------------------------------------------------
+-module(dialyzer_races).
+
+%% Race Analysis
+
+-export([store_race_call/5, race/1, get_race_warnings/2, format_args/4]).
+
+%% Record Interfaces
+
+-export([beg_clause_new/3, cleanup/1, end_case_new/1, end_clause_new/3,
+ get_curr_fun/1, get_curr_fun_args/1, get_new_table/1,
+ get_race_analysis/1, get_race_list/1, get_race_list_size/1,
+ get_race_list_and_size/1,
+ let_tag_new/2, new/0, put_curr_fun/3, put_fun_args/2,
+ put_race_analysis/2, put_race_list/3]).
+
+-export_type([races/0, core_vars/0]).
+
+-include("dialyzer.hrl").
+
+%%% ===========================================================================
+%%%
+%%% Definitions
+%%%
+%%% ===========================================================================
+
+-define(local, 5).
+-define(no_arg, no_arg).
+-define(no_label, no_label).
+-define(bypassed, bypassed).
+
+-define(WARN_WHEREIS_REGISTER, warn_whereis_register).
+-define(WARN_WHEREIS_UNREGISTER, warn_whereis_unregister).
+-define(WARN_ETS_LOOKUP_INSERT, warn_ets_lookup_insert).
+-define(WARN_MNESIA_DIRTY_READ_WRITE, warn_mnesia_dirty_read_write).
+-define(WARN_NO_WARN, warn_no_warn).
+
+%%% ===========================================================================
+%%%
+%%% Local Types
+%%%
+%%% ===========================================================================
+
+-type label_type() :: label() | [label()] | {label()} | ?no_label.
+-type args() :: [label_type() | [string()]].
+-type core_vars() :: cerl:cerl() | ?no_arg | ?bypassed.
+-type var_to_map1() :: core_vars() | [cerl:cerl()].
+-type var_to_map2() :: cerl:cerl() | [cerl:cerl()] | ?bypassed.
+-type core_args() :: [core_vars()] | 'empty'.
+-type op() :: 'bind' | 'unbind'.
+
+-type dep_calls() :: 'whereis' | 'ets_lookup' | 'mnesia_dirty_read'.
+-type warn_calls() :: 'register' | 'unregister' | 'ets_insert'
+ | 'mnesia_dirty_write'.
+-type call() :: 'whereis' | 'register' | 'unregister' | 'ets_new'
+ | 'ets_lookup' | 'ets_insert' | 'mnesia_dirty_read1'
+ | 'mnesia_dirty_read2' | 'mnesia_dirty_write1'
+ | 'mnesia_dirty_write2' | 'function_call'.
+-type race_tag() :: 'whereis_register' | 'whereis_unregister'
+ | 'ets_lookup_insert' | 'mnesia_dirty_read_write'.
+
+%% The following type is similar to the raw_warning() type but has a
+%% tag which is local to this module and is not propagated to outside
+-type dial_race_warning() :: {race_warn_tag(), warning_info(), {atom(), [term()]}}.
+-type race_warn_tag() :: ?WARN_WHEREIS_REGISTER | ?WARN_WHEREIS_UNREGISTER
+ | ?WARN_ETS_LOOKUP_INSERT | ?WARN_MNESIA_DIRTY_READ_WRITE.
+
+-record(beg_clause, {arg :: var_to_map1() | 'undefined',
+ pats :: var_to_map1() | 'undefined',
+ guard :: cerl:cerl() | 'undefined'}).
+-record(end_clause, {arg :: var_to_map1() | 'undefined',
+ pats :: var_to_map1() | 'undefined',
+ guard :: cerl:cerl() | 'undefined'}).
+-record(end_case, {clauses :: [#end_clause{}]}).
+-record(curr_fun, {status :: 'in' | 'out' | 'undefined',
+ mfa :: dialyzer_callgraph:mfa_or_funlbl()
+ | 'undefined',
+ label :: label() | 'undefined',
+ def_vars :: [core_vars()] | 'undefined',
+ arg_types :: [erl_types:erl_type()] | 'undefined',
+ call_vars :: [core_vars()] | 'undefined',
+ var_map :: dict:dict() | 'undefined'}).
+-record(dep_call, {call_name :: dep_calls(),
+ args :: args() | 'undefined',
+ arg_types :: [erl_types:erl_type()],
+ vars :: [core_vars()],
+ state :: dialyzer_dataflow:state(),
+ file_line :: file_line(),
+ var_map :: dict:dict() | 'undefined'}).
+-record(fun_call, {caller :: dialyzer_callgraph:mfa_or_funlbl(),
+ callee :: dialyzer_callgraph:mfa_or_funlbl(),
+ arg_types :: [erl_types:erl_type()],
+ vars :: [core_vars()]}).
+-record(let_tag, {var :: var_to_map1(),
+ arg :: var_to_map1()}).
+-record(warn_call, {call_name :: warn_calls(),
+ args :: args(),
+ var_map :: dict:dict() | 'undefined'}).
+
+-type case_tags() :: 'beg_case' | #beg_clause{} | #end_clause{} | #end_case{}.
+-type code() :: [#dep_call{} | #fun_call{} | #warn_call{} |
+ #curr_fun{} | #let_tag{} | case_tags() | race_tag()].
+
+-type table_var() :: label() | ?no_label.
+-type table() :: {'named', table_var(), [string()]} | 'other' | 'no_t'.
+
+-record(race_fun, {mfa :: mfa(),
+ args :: args(),
+ arg_types :: [erl_types:erl_type()],
+ vars :: [core_vars()],
+ file_line :: file_line(),
+ index :: non_neg_integer(),
+ fun_mfa :: dialyzer_callgraph:mfa_or_funlbl(),
+ fun_label :: label()}).
+
+-record(races, {curr_fun :: dialyzer_callgraph:mfa_or_funlbl()
+ | 'undefined',
+ curr_fun_label :: label() | 'undefined',
+ curr_fun_args = 'empty' :: core_args(),
+ new_table = 'no_t' :: table(),
+ race_list = [] :: code(),
+ race_list_size = 0 :: non_neg_integer(),
+ race_tags = [] :: [#race_fun{}],
+ %% true for fun types and warning mode
+ race_analysis = false :: boolean(),
+ race_warnings = [] :: [dial_race_warning()]}).
+
+%%% ===========================================================================
+%%%
+%%% Exported Types
+%%%
+%%% ===========================================================================
+
+-opaque races() :: #races{}.
+
+%%% ===========================================================================
+%%%
+%%% Race Analysis
+%%%
+%%% ===========================================================================
+
+-spec store_race_call(dialyzer_callgraph:mfa_or_funlbl(),
+ [erl_types:erl_type()], [core_vars()],
+ file_line(), dialyzer_dataflow:state()) ->
+ dialyzer_dataflow:state().
+
+store_race_call(Fun, ArgTypes, Args, FileLine, State) ->
+ Races = dialyzer_dataflow:state__get_races(State),
+ CurrFun = Races#races.curr_fun,
+ CurrFunLabel = Races#races.curr_fun_label,
+ RaceTags = Races#races.race_tags,
+ CleanState = dialyzer_dataflow:state__records_only(State),
+ {NewRaceList, NewRaceListSize, NewRaceTags, NewTable} =
+ case CurrFun of
+ {_Module, module_info, A} when A =:= 0 orelse A =:= 1 ->
+ {[], 0, RaceTags, no_t};
+ _Thing ->
+ RaceList = Races#races.race_list,
+ RaceListSize = Races#races.race_list_size,
+ case Fun of
+ {erlang, get_module_info, A} when A =:= 1 orelse A =:= 2 ->
+ {[], 0, RaceTags, no_t};
+ {erlang, register, 2} ->
+ VarArgs = format_args(Args, ArgTypes, CleanState, register),
+ RaceFun = #race_fun{mfa = Fun, args = VarArgs,
+ arg_types = ArgTypes, vars = Args,
+ file_line = FileLine, index = RaceListSize,
+ fun_mfa = CurrFun, fun_label = CurrFunLabel},
+ {[#warn_call{call_name = register, args = VarArgs}|
+ RaceList], RaceListSize + 1, [RaceFun|RaceTags], no_t};
+ {erlang, unregister, 1} ->
+ VarArgs = format_args(Args, ArgTypes, CleanState, unregister),
+ RaceFun = #race_fun{mfa = Fun, args = VarArgs,
+ arg_types = ArgTypes, vars = Args,
+ file_line = FileLine, index = RaceListSize,
+ fun_mfa = CurrFun, fun_label = CurrFunLabel},
+ {[#warn_call{call_name = unregister, args = VarArgs}|
+ RaceList], RaceListSize + 1, [RaceFun|RaceTags], no_t};
+ {erlang, whereis, 1} ->
+ VarArgs = format_args(Args, ArgTypes, CleanState, whereis),
+ {[#dep_call{call_name = whereis, args = VarArgs,
+ arg_types = ArgTypes, vars = Args,
+ state = CleanState, file_line = FileLine}|
+ RaceList], RaceListSize + 1, RaceTags, no_t};
+ {ets, insert, 2} ->
+ VarArgs = format_args(Args, ArgTypes, CleanState, ets_insert),
+ RaceFun = #race_fun{mfa = Fun, args = VarArgs,
+ arg_types = ArgTypes, vars = Args,
+ file_line = FileLine, index = RaceListSize,
+ fun_mfa = CurrFun, fun_label = CurrFunLabel},
+ {[#warn_call{call_name = ets_insert, args = VarArgs}|
+ RaceList], RaceListSize + 1, [RaceFun|RaceTags], no_t};
+ {ets, lookup, 2} ->
+ VarArgs = format_args(Args, ArgTypes, CleanState, ets_lookup),
+ {[#dep_call{call_name = ets_lookup, args = VarArgs,
+ arg_types = ArgTypes, vars = Args,
+ state = CleanState, file_line = FileLine}|
+ RaceList], RaceListSize + 1, RaceTags, no_t};
+ {ets, new, 2} ->
+ VarArgs = format_args(Args, ArgTypes, CleanState, ets_new),
+ [VarArgs1, VarArgs2, _, Options] = VarArgs,
+ NewTable1 =
+ case lists:member("'public'", Options) of
+ true ->
+ case lists:member("'named_table'", Options) of
+ true ->
+ {named, VarArgs1, VarArgs2};
+ false -> other
+ end;
+ false -> no_t
+ end,
+ {RaceList, RaceListSize, RaceTags, NewTable1};
+ {mnesia, dirty_read, A} when A =:= 1 orelse A =:= 2 ->
+ VarArgs =
+ case A of
+ 1 ->
+ format_args(Args, ArgTypes, CleanState, mnesia_dirty_read1);
+ 2 ->
+ format_args(Args, ArgTypes, CleanState, mnesia_dirty_read2)
+ end,
+ {[#dep_call{call_name = mnesia_dirty_read, args = VarArgs,
+ arg_types = ArgTypes, vars = Args,
+ state = CleanState, file_line = FileLine}|RaceList],
+ RaceListSize + 1, RaceTags, no_t};
+ {mnesia, dirty_write, A} when A =:= 1 orelse A =:= 2 ->
+ VarArgs =
+ case A of
+ 1 ->
+ format_args(Args, ArgTypes, CleanState, mnesia_dirty_write1);
+ 2 ->
+ format_args(Args, ArgTypes, CleanState, mnesia_dirty_write2)
+ end,
+ RaceFun = #race_fun{mfa = Fun, args = VarArgs,
+ arg_types = ArgTypes, vars = Args,
+ file_line = FileLine, index = RaceListSize,
+ fun_mfa = CurrFun, fun_label = CurrFunLabel},
+ {[#warn_call{call_name = mnesia_dirty_write,
+ args = VarArgs}|RaceList],
+ RaceListSize + 1, [RaceFun|RaceTags], no_t};
+ Int when is_integer(Int) ->
+ {[#fun_call{caller = CurrFun, callee = Int, arg_types = ArgTypes,
+ vars = Args}|RaceList],
+ RaceListSize + 1, RaceTags, no_t};
+ _Other ->
+ Callgraph = dialyzer_dataflow:state__get_callgraph(State),
+ case digraph:vertex(dialyzer_callgraph:get_digraph(Callgraph),
+ Fun) of
+ {Fun, confirmed} ->
+ {[#fun_call{caller = CurrFun, callee = Fun,
+ arg_types = ArgTypes, vars = Args}|RaceList],
+ RaceListSize + 1, RaceTags, no_t};
+ false ->
+ {RaceList, RaceListSize, RaceTags, no_t}
+ end
+ end
+ end,
+ state__renew_info(NewRaceList, NewRaceListSize, NewRaceTags, NewTable, State).
+
+-spec race(dialyzer_dataflow:state()) -> dialyzer_dataflow:state().
+
+race(State) ->
+ Races = dialyzer_dataflow:state__get_races(State),
+ RaceTags = Races#races.race_tags,
+ RetState =
+ case RaceTags of
+ [] -> State;
+ [#race_fun{mfa = Fun,
+ args = VarArgs, arg_types = ArgTypes,
+ vars = Args, file_line = FileLine,
+ index = Index, fun_mfa = CurrFun,
+ fun_label = CurrFunLabel}|T] ->
+ Callgraph = dialyzer_dataflow:state__get_callgraph(State),
+ {ok, [_Args, Code]} =
+ dict:find(CurrFun, dialyzer_callgraph:get_race_code(Callgraph)),
+ RaceList = lists:reverse(Code),
+ RaceWarnTag =
+ case Fun of
+ {erlang, register, 2} -> ?WARN_WHEREIS_REGISTER;
+ {erlang, unregister, 1} -> ?WARN_WHEREIS_UNREGISTER;
+ {ets, insert, 2} -> ?WARN_ETS_LOOKUP_INSERT;
+ {mnesia, dirty_write, _A} -> ?WARN_MNESIA_DIRTY_READ_WRITE
+ end,
+ State1 =
+ state__renew_curr_fun(CurrFun,
+ state__renew_curr_fun_label(CurrFunLabel,
+ state__renew_race_list(lists:nthtail(length(RaceList) - Index,
+ RaceList), State))),
+ DepList = fixup_race_list(RaceWarnTag, VarArgs, State1),
+ {State2, RaceWarn} =
+ get_race_warn(Fun, Args, ArgTypes, DepList, State),
+ {File, Line} = FileLine,
+ CurrMFA = dialyzer_dataflow:state__find_function(CurrFun, State),
+ WarningInfo = {File, Line, CurrMFA},
+ race(
+ state__add_race_warning(
+ state__renew_race_tags(T, State2), RaceWarn, RaceWarnTag,
+ WarningInfo))
+ end,
+ state__renew_race_tags([], RetState).
+
+fixup_race_list(RaceWarnTag, WarnVarArgs, State) ->
+ Races = dialyzer_dataflow:state__get_races(State),
+ CurrFun = Races#races.curr_fun,
+ CurrFunLabel = Races#races.curr_fun_label,
+ RaceList = Races#races.race_list,
+ Callgraph = dialyzer_dataflow:state__get_callgraph(State),
+ Digraph = dialyzer_callgraph:get_digraph(Callgraph),
+ Calls = digraph:edges(Digraph),
+ RaceTag =
+ case RaceWarnTag of
+ ?WARN_WHEREIS_REGISTER -> whereis_register;
+ ?WARN_WHEREIS_UNREGISTER -> whereis_unregister;
+ ?WARN_ETS_LOOKUP_INSERT -> ets_lookup_insert;
+ ?WARN_MNESIA_DIRTY_READ_WRITE -> mnesia_dirty_read_write
+ end,
+ NewRaceList = [RaceTag|RaceList],
+ CleanState = dialyzer_dataflow:state__cleanup(State),
+ NewState = state__renew_race_list(NewRaceList, CleanState),
+ DepList1 =
+ fixup_race_forward_pullout(CurrFun, CurrFunLabel, Calls,
+ lists:reverse(NewRaceList), [], CurrFun,
+ WarnVarArgs, RaceWarnTag, dict:new(),
+ [], [], [], 2 * ?local, NewState),
+ Parents = fixup_race_backward(CurrFun, Calls, Calls, [], ?local),
+ UParents = lists:usort(Parents),
+ Filtered = filter_parents(UParents, UParents, Digraph),
+ NewParents =
+ case lists:member(CurrFun, Filtered) of
+ true -> Filtered;
+ false -> [CurrFun|Filtered]
+ end,
+ DepList2 =
+ fixup_race_list_helper(NewParents, Calls, CurrFun, WarnVarArgs,
+ RaceWarnTag, NewState),
+ dialyzer_dataflow:dispose_state(CleanState),
+ lists:usort(cleanup_dep_calls(DepList1 ++ DepList2)).
+
+fixup_race_list_helper(Parents, Calls, CurrFun, WarnVarArgs, RaceWarnTag,
+ State) ->
+ case Parents of
+ [] -> [];
+ [Head|Tail] ->
+ Callgraph = dialyzer_dataflow:state__get_callgraph(State),
+ Code =
+ case dict:find(Head, dialyzer_callgraph:get_race_code(Callgraph)) of
+ error -> [];
+ {ok, [_A, C]} -> C
+ end,
+ {ok, FunLabel} = dialyzer_callgraph:lookup_label(Head, Callgraph),
+ DepList1 =
+ fixup_race_forward_pullout(Head, FunLabel, Calls, Code, [], CurrFun,
+ WarnVarArgs, RaceWarnTag, dict:new(),
+ [], [], [], 2 * ?local, State),
+ DepList2 =
+ fixup_race_list_helper(Tail, Calls, CurrFun, WarnVarArgs,
+ RaceWarnTag, State),
+ DepList1 ++ DepList2
+ end.
+
+%%% ===========================================================================
+%%%
+%%% Forward Analysis
+%%%
+%%% ===========================================================================
+
+fixup_race_forward_pullout(CurrFun, CurrFunLabel, Calls, Code, RaceList,
+ InitFun, WarnVarArgs, RaceWarnTag, RaceVarMap,
+ FunDefVars, FunCallVars, FunArgTypes, NestingLevel,
+ State) ->
+ TState = dialyzer_dataflow:state__duplicate(State),
+ {DepList, NewCurrFun, NewCurrFunLabel, NewCalls,
+ NewCode, NewRaceList, NewRaceVarMap, NewFunDefVars,
+ NewFunCallVars, NewFunArgTypes, NewNestingLevel} =
+ fixup_race_forward(CurrFun, CurrFunLabel, Calls, Code, RaceList,
+ InitFun, WarnVarArgs, RaceWarnTag, RaceVarMap,
+ FunDefVars, FunCallVars, FunArgTypes, NestingLevel,
+ cleanup_race_code(TState)),
+ dialyzer_dataflow:dispose_state(TState),
+ case NewCode of
+ [] -> DepList;
+ [#fun_call{caller = NewCurrFun, callee = Call, arg_types = FunTypes,
+ vars = FunArgs}|Tail] ->
+ Callgraph = dialyzer_dataflow:state__get_callgraph(State),
+ OkCall = {ok, Call},
+ {Name, Label} =
+ case is_integer(Call) of
+ true ->
+ case dialyzer_callgraph:lookup_name(Call, Callgraph) of
+ error -> {OkCall, OkCall};
+ N -> {N, OkCall}
+ end;
+ false ->
+ {OkCall, dialyzer_callgraph:lookup_label(Call, Callgraph)}
+ end,
+ {NewCurrFun1, NewCurrFunLabel1, NewCalls1, NewCode1, NewRaceList1,
+ NewRaceVarMap1, NewFunDefVars1, NewFunCallVars1, NewFunArgTypes1,
+ NewNestingLevel1} =
+ case Label =:= error of
+ true ->
+ {NewCurrFun, NewCurrFunLabel, NewCalls, Tail, NewRaceList,
+ NewRaceVarMap, NewFunDefVars, NewFunCallVars, NewFunArgTypes,
+ NewNestingLevel};
+ false ->
+ {ok, Fun} = Name,
+ {ok, Int} = Label,
+ case dict:find(Fun, dialyzer_callgraph:get_race_code(Callgraph)) of
+ error ->
+ {NewCurrFun, NewCurrFunLabel, NewCalls, Tail, NewRaceList,
+ NewRaceVarMap, NewFunDefVars, NewFunCallVars, NewFunArgTypes,
+ NewNestingLevel};
+ {ok, [Args, CodeB]} ->
+ Races = dialyzer_dataflow:state__get_races(State),
+ {RetCurrFun, RetCurrFunLabel, RetCalls, RetCode,
+ RetRaceList, RetRaceVarMap, RetFunDefVars, RetFunCallVars,
+ RetFunArgTypes, RetNestingLevel} =
+ fixup_race_forward_helper(NewCurrFun,
+ NewCurrFunLabel, Fun, Int, NewCalls, NewCalls,
+ [#curr_fun{status = out, mfa = NewCurrFun,
+ label = NewCurrFunLabel,
+ var_map = NewRaceVarMap,
+ def_vars = NewFunDefVars,
+ call_vars = NewFunCallVars,
+ arg_types = NewFunArgTypes}|
+ Tail],
+ NewRaceList, InitFun, FunArgs, FunTypes, RaceWarnTag,
+ NewRaceVarMap, NewFunDefVars, NewFunCallVars,
+ NewFunArgTypes, NewNestingLevel, Args, CodeB,
+ Races#races.race_list),
+ case RetCode of
+ [#curr_fun{}|_CodeTail] ->
+ {NewCurrFun, NewCurrFunLabel, RetCalls, RetCode,
+ RetRaceList, NewRaceVarMap, NewFunDefVars,
+ NewFunCallVars, NewFunArgTypes, RetNestingLevel};
+ _Else ->
+ {RetCurrFun, RetCurrFunLabel, RetCalls, RetCode,
+ RetRaceList, RetRaceVarMap, RetFunDefVars,
+ RetFunCallVars, RetFunArgTypes, RetNestingLevel}
+ end
+ end
+ end,
+ DepList ++
+ fixup_race_forward_pullout(NewCurrFun1, NewCurrFunLabel1, NewCalls1,
+ NewCode1, NewRaceList1, InitFun, WarnVarArgs,
+ RaceWarnTag, NewRaceVarMap1, NewFunDefVars1,
+ NewFunCallVars1, NewFunArgTypes1,
+ NewNestingLevel1, State)
+ end.
+
+fixup_race_forward(CurrFun, CurrFunLabel, Calls, Code, RaceList,
+ InitFun, WarnVarArgs, RaceWarnTag, RaceVarMap,
+ FunDefVars, FunCallVars, FunArgTypes, NestingLevel,
+ State) ->
+ case Code of
+ [] ->
+ {[], CurrFun, CurrFunLabel, Calls, Code, RaceList, RaceVarMap,
+ FunDefVars, FunCallVars, FunArgTypes, NestingLevel};
+ [Head|Tail] ->
+ Callgraph = dialyzer_dataflow:state__get_callgraph(State),
+ {NewRL, DepList, NewNL, Return} =
+ case Head of
+ #dep_call{call_name = whereis} ->
+ case RaceWarnTag of
+ WarnWhereis when WarnWhereis =:= ?WARN_WHEREIS_REGISTER orelse
+ WarnWhereis =:= ?WARN_WHEREIS_UNREGISTER ->
+ {[Head#dep_call{var_map = RaceVarMap}|RaceList],
+ [], NestingLevel, false};
+ _Other ->
+ {RaceList, [], NestingLevel, false}
+ end;
+ #dep_call{call_name = ets_lookup} ->
+ case RaceWarnTag of
+ ?WARN_ETS_LOOKUP_INSERT ->
+ {[Head#dep_call{var_map = RaceVarMap}|RaceList],
+ [], NestingLevel, false};
+ _Other ->
+ {RaceList, [], NestingLevel, false}
+ end;
+ #dep_call{call_name = mnesia_dirty_read} ->
+ case RaceWarnTag of
+ ?WARN_MNESIA_DIRTY_READ_WRITE ->
+ {[Head#dep_call{var_map = RaceVarMap}|RaceList],
+ [], NestingLevel, false};
+ _Other ->
+ {RaceList, [], NestingLevel, false}
+ end;
+ #warn_call{call_name = RegCall} when RegCall =:= register orelse
+ RegCall =:= unregister ->
+ case RaceWarnTag of
+ WarnWhereis when WarnWhereis =:= ?WARN_WHEREIS_REGISTER orelse
+ WarnWhereis =:= ?WARN_WHEREIS_UNREGISTER ->
+ {[Head#warn_call{var_map = RaceVarMap}|RaceList],
+ [], NestingLevel, false};
+ _Other ->
+ {RaceList, [], NestingLevel, false}
+ end;
+ #warn_call{call_name = ets_insert} ->
+ case RaceWarnTag of
+ ?WARN_ETS_LOOKUP_INSERT ->
+ {[Head#warn_call{var_map = RaceVarMap}|RaceList],
+ [], NestingLevel, false};
+ _Other ->
+ {RaceList, [], NestingLevel, false}
+ end;
+ #warn_call{call_name = mnesia_dirty_write} ->
+ case RaceWarnTag of
+ ?WARN_MNESIA_DIRTY_READ_WRITE ->
+ {[Head#warn_call{var_map = RaceVarMap}|RaceList],
+ [], NestingLevel, false};
+ _Other ->
+ {RaceList, [], NestingLevel, false}
+ end;
+ #fun_call{caller = CurrFun, callee = InitFun} ->
+ {RaceList, [], NestingLevel, false};
+ #fun_call{caller = CurrFun} ->
+ {RaceList, [], NestingLevel - 1, false};
+ beg_case ->
+ {[Head|RaceList], [], NestingLevel, false};
+ #beg_clause{} ->
+ {[#beg_clause{}|RaceList], [], NestingLevel, false};
+ #end_clause{} ->
+ {[#end_clause{}|RaceList], [], NestingLevel, false};
+ #end_case{} ->
+ {[Head|RaceList], [], NestingLevel, false};
+ #let_tag{} ->
+ {RaceList, [], NestingLevel, false};
+ #curr_fun{status = in, mfa = InitFun,
+ label = _InitFunLabel, var_map = _NewRVM,
+ def_vars = NewFDV, call_vars = NewFCV,
+ arg_types = _NewFAT} ->
+ {[#curr_fun{status = out, var_map = RaceVarMap,
+ def_vars = NewFDV, call_vars = NewFCV}|
+ RaceList], [], NestingLevel - 1, false};
+ #curr_fun{status = in, def_vars = NewFDV,
+ call_vars = NewFCV} ->
+ {[#curr_fun{status = out, var_map = RaceVarMap,
+ def_vars = NewFDV, call_vars = NewFCV}|
+ RaceList],
+ [], NestingLevel - 1, false};
+ #curr_fun{status = out} ->
+ {[#curr_fun{status = in, var_map = RaceVarMap}|RaceList], [],
+ NestingLevel + 1, false};
+ RaceTag ->
+ PublicTables = dialyzer_callgraph:get_public_tables(Callgraph),
+ NamedTables = dialyzer_callgraph:get_named_tables(Callgraph),
+ WarnVarArgs1 =
+ var_type_analysis(FunDefVars, FunArgTypes, WarnVarArgs,
+ RaceWarnTag, RaceVarMap,
+ dialyzer_dataflow:state__records_only(State)),
+ {NewDepList, IsPublic, _Return} =
+ get_deplist_paths(RaceList, WarnVarArgs1, RaceWarnTag,
+ RaceVarMap, 0, PublicTables, NamedTables),
+ {NewHead, NewDepList1} =
+ case RaceTag of
+ whereis_register ->
+ {[#warn_call{call_name = register, args = WarnVarArgs,
+ var_map = RaceVarMap}],
+ NewDepList};
+ whereis_unregister ->
+ {[#warn_call{call_name = unregister, args = WarnVarArgs,
+ var_map = RaceVarMap}],
+ NewDepList};
+ ets_lookup_insert ->
+ NewWarnCall =
+ [#warn_call{call_name = ets_insert, args = WarnVarArgs,
+ var_map = RaceVarMap}],
+ [Tab, Names, _, _] = WarnVarArgs,
+ case IsPublic orelse
+ compare_var_list(Tab, PublicTables, RaceVarMap)
+ orelse
+ length(Names -- NamedTables) < length(Names) of
+ true ->
+ {NewWarnCall, NewDepList};
+ false -> {NewWarnCall, []}
+ end;
+ mnesia_dirty_read_write ->
+ {[#warn_call{call_name = mnesia_dirty_write,
+ args = WarnVarArgs, var_map = RaceVarMap}],
+ NewDepList}
+ end,
+ {NewHead ++ RaceList, NewDepList1, NestingLevel,
+ is_last_race(RaceTag, InitFun, Tail, Callgraph)}
+ end,
+ {NewCurrFun, NewCurrFunLabel, NewCode, NewRaceList, NewRaceVarMap,
+ NewFunDefVars, NewFunCallVars, NewFunArgTypes, NewNestingLevel,
+ PullOut} =
+ case Head of
+ #fun_call{caller = CurrFun} ->
+ case NewNL =:= 0 of
+ true ->
+ {CurrFun, CurrFunLabel, Tail, NewRL, RaceVarMap,
+ FunDefVars, FunCallVars, FunArgTypes, NewNL, false};
+ false ->
+ {CurrFun, CurrFunLabel, Code, NewRL, RaceVarMap,
+ FunDefVars, FunCallVars, FunArgTypes, NewNL, true}
+ end;
+ #beg_clause{arg = Arg, pats = Pats, guard = Guard} ->
+ {RaceVarMap1, RemoveClause} =
+ race_var_map_guard(Arg, Pats, Guard, RaceVarMap, bind),
+ case RemoveClause of
+ true ->
+ {RaceList2,
+ #curr_fun{mfa = CurrFun2, label = CurrFunLabel2,
+ var_map = RaceVarMap2, def_vars = FunDefVars2,
+ call_vars = FunCallVars2, arg_types = FunArgTypes2},
+ Code2, NestingLevel2} =
+ remove_clause(NewRL,
+ #curr_fun{mfa = CurrFun, label = CurrFunLabel,
+ var_map = RaceVarMap1,
+ def_vars = FunDefVars,
+ call_vars = FunCallVars,
+ arg_types = FunArgTypes},
+ Tail, NewNL),
+ {CurrFun2, CurrFunLabel2, Code2, RaceList2,
+ RaceVarMap2, FunDefVars2, FunCallVars2, FunArgTypes2,
+ NestingLevel2, false};
+ false ->
+ {CurrFun, CurrFunLabel, Tail, NewRL, RaceVarMap1,
+ FunDefVars, FunCallVars, FunArgTypes, NewNL, false}
+ end;
+ #end_clause{arg = Arg, pats = Pats, guard = Guard} ->
+ {RaceVarMap1, _RemoveClause} =
+ race_var_map_guard(Arg, Pats, Guard, RaceVarMap, unbind),
+ {CurrFun, CurrFunLabel, Tail, NewRL, RaceVarMap1,
+ FunDefVars, FunCallVars, FunArgTypes, NewNL,
+ false};
+ #end_case{clauses = Clauses} ->
+ RaceVarMap1 =
+ race_var_map_clauses(Clauses, RaceVarMap),
+ {CurrFun, CurrFunLabel, Tail, NewRL, RaceVarMap1,
+ FunDefVars, FunCallVars, FunArgTypes, NewNL,
+ false};
+ #let_tag{var = Var, arg = Arg} ->
+ {CurrFun, CurrFunLabel, Tail, NewRL,
+ race_var_map(Var, Arg, RaceVarMap, bind), FunDefVars,
+ FunCallVars, FunArgTypes, NewNL, false};
+ #curr_fun{mfa = CurrFun1, label = CurrFunLabel1,
+ var_map = RaceVarMap1, def_vars = FunDefVars1,
+ call_vars = FunCallVars1, arg_types = FunArgTypes1} ->
+ case NewNL =:= 0 of
+ true ->
+ {CurrFun, CurrFunLabel,
+ remove_nonlocal_functions(Tail, 1), NewRL, RaceVarMap,
+ FunDefVars, FunCallVars, FunArgTypes, NewNL, false};
+ false ->
+ {CurrFun1, CurrFunLabel1, Tail, NewRL, RaceVarMap1,
+ FunDefVars1, FunCallVars1, FunArgTypes1, NewNL, false}
+ end;
+ _Thing ->
+ {CurrFun, CurrFunLabel, Tail, NewRL, RaceVarMap,
+ FunDefVars, FunCallVars, FunArgTypes, NewNL, false}
+ end,
+ case Return of
+ true ->
+ {DepList, NewCurrFun, NewCurrFunLabel, Calls,
+ [], NewRaceList, NewRaceVarMap, NewFunDefVars,
+ NewFunCallVars, NewFunArgTypes, NewNestingLevel};
+ false ->
+ NewNestingLevel1 =
+ case NewNestingLevel =:= 0 of
+ true -> NewNestingLevel + 1;
+ false -> NewNestingLevel
+ end,
+ case PullOut of
+ true ->
+ {DepList, NewCurrFun, NewCurrFunLabel, Calls,
+ NewCode, NewRaceList, NewRaceVarMap, NewFunDefVars,
+ NewFunCallVars, NewFunArgTypes, NewNestingLevel1};
+ false ->
+ {RetDepList, NewCurrFun1, NewCurrFunLabel1, NewCalls1,
+ NewCode1, NewRaceList1, NewRaceVarMap1, NewFunDefVars1,
+ NewFunCallVars1, NewFunArgTypes1, NewNestingLevel2} =
+ fixup_race_forward(NewCurrFun, NewCurrFunLabel, Calls,
+ NewCode, NewRaceList, InitFun, WarnVarArgs,
+ RaceWarnTag, NewRaceVarMap, NewFunDefVars,
+ NewFunCallVars, NewFunArgTypes,
+ NewNestingLevel1, State),
+ {DepList ++ RetDepList, NewCurrFun1, NewCurrFunLabel1,
+ NewCalls1, NewCode1, NewRaceList1, NewRaceVarMap1,
+ NewFunDefVars1, NewFunCallVars1, NewFunArgTypes1,
+ NewNestingLevel2}
+ end
+ end
+ end.
+
+get_deplist_paths(RaceList, WarnVarArgs, RaceWarnTag, RaceVarMap, CurrLevel,
+ PublicTables, NamedTables) ->
+ case RaceList of
+ [] -> {[], false, true};
+ [Head|Tail] ->
+ case Head of
+ #end_case{} ->
+ {RaceList1, DepList1, IsPublic1, Continue1} =
+ handle_case(Tail, WarnVarArgs, RaceWarnTag, RaceVarMap, CurrLevel,
+ PublicTables, NamedTables),
+ case Continue1 of
+ true ->
+ {DepList2, IsPublic2, Continue2} =
+ get_deplist_paths(RaceList1, WarnVarArgs, RaceWarnTag,
+ RaceVarMap, CurrLevel, PublicTables,
+ NamedTables),
+ {DepList1 ++ DepList2, IsPublic1 orelse IsPublic2, Continue2};
+ false -> {DepList1, IsPublic1, false}
+ end;
+ #beg_clause{} ->
+ get_deplist_paths(fixup_before_case_path(Tail), WarnVarArgs,
+ RaceWarnTag, RaceVarMap, CurrLevel, PublicTables,
+ NamedTables);
+ #curr_fun{status = in, var_map = RaceVarMap1} ->
+ {DepList, IsPublic, Continue} =
+ get_deplist_paths(Tail, WarnVarArgs, RaceWarnTag, RaceVarMap,
+ CurrLevel + 1, PublicTables, NamedTables),
+ IsPublic1 =
+ case RaceWarnTag of
+ ?WARN_ETS_LOOKUP_INSERT ->
+ [Tabs, Names, _, _] = WarnVarArgs,
+ IsPublic orelse
+ lists:any(
+ fun (T) ->
+ compare_var_list(T, PublicTables, RaceVarMap1)
+ end, Tabs)
+ orelse
+ length(Names -- NamedTables) < length(Names);
+ _ -> true
+ end,
+ {DepList, IsPublic1, Continue};
+ #curr_fun{status = out, var_map = RaceVarMap1, def_vars = FunDefVars,
+ call_vars = FunCallVars} ->
+ WarnVarArgs1 =
+ var_analysis([format_arg(DefVar) || DefVar <- FunDefVars],
+ [format_arg(CallVar) || CallVar <- FunCallVars],
+ WarnVarArgs, RaceWarnTag),
+ {WarnVarArgs2, Stop} =
+ case RaceWarnTag of
+ ?WARN_WHEREIS_REGISTER ->
+ [WVA1, WVA2, WVA3, WVA4] = WarnVarArgs1,
+ Vars =
+ lists:flatten(
+ [find_all_bound_vars(V, RaceVarMap1) || V <- WVA1]),
+ case {Vars, CurrLevel} of
+ {[], 0} ->
+ {WarnVarArgs, true};
+ {[], _} ->
+ {WarnVarArgs, false};
+ _ ->
+ {[Vars, WVA2, WVA3, WVA4], false}
+ end;
+ ?WARN_WHEREIS_UNREGISTER ->
+ [WVA1, WVA2] = WarnVarArgs1,
+ Vars =
+ lists:flatten(
+ [find_all_bound_vars(V, RaceVarMap1) || V <- WVA1]),
+ case {Vars, CurrLevel} of
+ {[], 0} ->
+ {WarnVarArgs, true};
+ {[], _} ->
+ {WarnVarArgs, false};
+ _ ->
+ {[Vars, WVA2], false}
+ end;
+ ?WARN_ETS_LOOKUP_INSERT ->
+ [WVA1, WVA2, WVA3, WVA4] = WarnVarArgs1,
+ Vars1 =
+ lists:flatten(
+ [find_all_bound_vars(V1, RaceVarMap1) || V1 <- WVA1]),
+ Vars2 =
+ lists:flatten(
+ [find_all_bound_vars(V2, RaceVarMap1) || V2 <- WVA3]),
+ case {Vars1, Vars2, CurrLevel} of
+ {[], _, 0} ->
+ {WarnVarArgs, true};
+ {[], _, _} ->
+ {WarnVarArgs, false};
+ {_, [], 0} ->
+ {WarnVarArgs, true};
+ {_, [], _} ->
+ {WarnVarArgs, false};
+ _ ->
+ {[Vars1, WVA2, Vars2, WVA4], false}
+ end;
+ ?WARN_MNESIA_DIRTY_READ_WRITE ->
+ [WVA1, WVA2|T] = WarnVarArgs1,
+ Vars =
+ lists:flatten(
+ [find_all_bound_vars(V, RaceVarMap1) || V <- WVA1]),
+ case {Vars, CurrLevel} of
+ {[], 0} ->
+ {WarnVarArgs, true};
+ {[], _} ->
+ {WarnVarArgs, false};
+ _ ->
+ {[Vars, WVA2|T], false}
+ end
+ end,
+ case Stop of
+ true -> {[], false, false};
+ false ->
+ CurrLevel1 =
+ case CurrLevel of
+ 0 -> CurrLevel;
+ _ -> CurrLevel - 1
+ end,
+ get_deplist_paths(Tail, WarnVarArgs2, RaceWarnTag, RaceVarMap1,
+ CurrLevel1, PublicTables, NamedTables)
+ end;
+ #warn_call{call_name = RegCall, args = WarnVarArgs1,
+ var_map = RaceVarMap1} when RegCall =:= register orelse
+ RegCall =:= unregister ->
+ case compare_first_arg(WarnVarArgs, WarnVarArgs1, RaceVarMap1) of
+ true -> {[], false, false};
+ NewWarnVarArgs ->
+ get_deplist_paths(Tail, NewWarnVarArgs, RaceWarnTag, RaceVarMap,
+ CurrLevel, PublicTables, NamedTables)
+ end;
+ #warn_call{call_name = ets_insert, args = WarnVarArgs1,
+ var_map = RaceVarMap1} ->
+ case compare_ets_insert(WarnVarArgs, WarnVarArgs1, RaceVarMap1) of
+ true -> {[], false, false};
+ NewWarnVarArgs ->
+ get_deplist_paths(Tail, NewWarnVarArgs, RaceWarnTag, RaceVarMap,
+ CurrLevel, PublicTables, NamedTables)
+ end;
+ #warn_call{call_name = mnesia_dirty_write, args = WarnVarArgs1,
+ var_map = RaceVarMap1} ->
+ case compare_first_arg(WarnVarArgs, WarnVarArgs1, RaceVarMap1) of
+ true -> {[], false, false};
+ NewWarnVarArgs ->
+ get_deplist_paths(Tail, NewWarnVarArgs, RaceWarnTag, RaceVarMap,
+ CurrLevel, PublicTables, NamedTables)
+ end;
+ #dep_call{var_map = RaceVarMap1} ->
+ {DepList, IsPublic, Continue} =
+ get_deplist_paths(Tail, WarnVarArgs, RaceWarnTag, RaceVarMap,
+ CurrLevel, PublicTables, NamedTables),
+ {refine_race(Head, WarnVarArgs, RaceWarnTag, DepList, RaceVarMap1),
+ IsPublic, Continue}
+ end
+ end.
+
+handle_case(RaceList, WarnVarArgs, RaceWarnTag, RaceVarMap, CurrLevel,
+ PublicTables, NamedTables) ->
+ case RaceList of
+ [] -> {[], [], false, true};
+ [Head|Tail] ->
+ case Head of
+ #end_clause{} ->
+ {RestRaceList, DepList1, IsPublic1, Continue1} =
+ do_clause(Tail, WarnVarArgs, RaceWarnTag, RaceVarMap, CurrLevel,
+ PublicTables, NamedTables),
+ {RetRaceList, DepList2, IsPublic2, Continue2} =
+ handle_case(RestRaceList, WarnVarArgs, RaceWarnTag, RaceVarMap,
+ CurrLevel, PublicTables, NamedTables),
+ {RetRaceList, DepList1 ++ DepList2, IsPublic1 orelse IsPublic2,
+ Continue1 orelse Continue2};
+ beg_case -> {Tail, [], false, false}
+ end
+ end.
+
+do_clause(RaceList, WarnVarArgs, RaceWarnTag, RaceVarMap, CurrLevel,
+ PublicTables, NamedTables) ->
+ {DepList, IsPublic, Continue} =
+ get_deplist_paths(fixup_case_path(RaceList, 0), WarnVarArgs,
+ RaceWarnTag, RaceVarMap, CurrLevel,
+ PublicTables, NamedTables),
+ {fixup_case_rest_paths(RaceList, 0), DepList, IsPublic, Continue}.
+
+fixup_case_path(RaceList, NestingLevel) ->
+ case RaceList of
+ [] -> [];
+ [Head|Tail] ->
+ {NewNestingLevel, Return} =
+ case Head of
+ beg_case -> {NestingLevel - 1, false};
+ #end_case{} -> {NestingLevel + 1, false};
+ #beg_clause{} ->
+ case NestingLevel =:= 0 of
+ true -> {NestingLevel, true};
+ false -> {NestingLevel, false}
+ end;
+ _Other -> {NestingLevel, false}
+ end,
+ case Return of
+ true -> [];
+ false -> [Head|fixup_case_path(Tail, NewNestingLevel)]
+ end
+ end.
+
+%% Gets the race list before a case clause.
+fixup_before_case_path(RaceList) ->
+ case RaceList of
+ [] -> [];
+ [Head|Tail] ->
+ case Head of
+ #end_clause{} ->
+ fixup_before_case_path(fixup_case_rest_paths(Tail, 0));
+ beg_case -> Tail
+ end
+ end.
+
+fixup_case_rest_paths(RaceList, NestingLevel) ->
+ case RaceList of
+ [] -> [];
+ [Head|Tail] ->
+ {NewNestingLevel, Return} =
+ case Head of
+ beg_case -> {NestingLevel - 1, false};
+ #end_case{} -> {NestingLevel + 1, false};
+ #beg_clause{} ->
+ case NestingLevel =:= 0 of
+ true -> {NestingLevel, true};
+ false -> {NestingLevel, false}
+ end;
+ _Other -> {NestingLevel, false}
+ end,
+ case Return of
+ true -> Tail;
+ false -> fixup_case_rest_paths(Tail, NewNestingLevel)
+ end
+ end.
+
+fixup_race_forward_helper(CurrFun, CurrFunLabel, Fun, FunLabel,
+ Calls, CallsToAnalyze, Code, RaceList,
+ InitFun, NewFunArgs, NewFunTypes,
+ RaceWarnTag, RaceVarMap, FunDefVars,
+ FunCallVars, FunArgTypes, NestingLevel,
+ Args, CodeB, StateRaceList) ->
+ case Calls of
+ [] ->
+ {NewRaceList,
+ #curr_fun{mfa = NewCurrFun, label = NewCurrFunLabel,
+ var_map = NewRaceVarMap, def_vars = NewFunDefVars,
+ call_vars = NewFunCallVars, arg_types = NewFunArgTypes},
+ NewCode, NewNestingLevel} =
+ remove_clause(RaceList,
+ #curr_fun{mfa = CurrFun, label = CurrFunLabel, var_map = RaceVarMap,
+ def_vars = FunDefVars, call_vars = FunCallVars,
+ arg_types = FunArgTypes},
+ Code, NestingLevel),
+ {NewCurrFun, NewCurrFunLabel, CallsToAnalyze, NewCode, NewRaceList,
+ NewRaceVarMap, NewFunDefVars, NewFunCallVars, NewFunArgTypes,
+ NewNestingLevel};
+ [Head|Tail] ->
+ case Head of
+ {InitFun, InitFun} when CurrFun =:= InitFun, Fun =:= InitFun ->
+ NewCallsToAnalyze = lists:delete(Head, CallsToAnalyze),
+ NewRaceVarMap =
+ race_var_map(Args, NewFunArgs, RaceVarMap, bind),
+ RetC =
+ fixup_all_calls(InitFun, InitFun, FunLabel, Args,
+ CodeB ++
+ [#curr_fun{status = out, mfa = InitFun,
+ label = CurrFunLabel, var_map = RaceVarMap,
+ def_vars = FunDefVars, call_vars = FunCallVars,
+ arg_types = FunArgTypes}],
+ Code, RaceVarMap),
+ NewCode =
+ fixup_all_calls(InitFun, InitFun, FunLabel, Args,
+ CodeB ++
+ [#curr_fun{status = out, mfa = InitFun,
+ label = CurrFunLabel, var_map = NewRaceVarMap,
+ def_vars = Args, call_vars = NewFunArgs,
+ arg_types = NewFunTypes}],
+ [#curr_fun{status = in, mfa = Fun,
+ label = FunLabel, var_map = NewRaceVarMap,
+ def_vars = Args, call_vars = NewFunArgs,
+ arg_types = NewFunTypes}|
+ lists:reverse(StateRaceList)] ++
+ RetC, NewRaceVarMap),
+ {InitFun, FunLabel, NewCallsToAnalyze, NewCode, RaceList,
+ NewRaceVarMap, Args, NewFunArgs, NewFunTypes, NestingLevel};
+ {CurrFun, Fun} ->
+ NewCallsToAnalyze = lists:delete(Head, CallsToAnalyze),
+ NewRaceVarMap = race_var_map(Args, NewFunArgs, RaceVarMap, bind),
+ RetC =
+ case Fun of
+ InitFun ->
+ fixup_all_calls(CurrFun, Fun, FunLabel, Args,
+ lists:reverse(StateRaceList) ++
+ [#curr_fun{status = out, mfa = CurrFun,
+ label = CurrFunLabel, var_map = RaceVarMap,
+ def_vars = FunDefVars, call_vars = FunCallVars,
+ arg_types = FunArgTypes}],
+ Code, RaceVarMap);
+ _Other1 ->
+ fixup_all_calls(CurrFun, Fun, FunLabel, Args,
+ CodeB ++
+ [#curr_fun{status = out, mfa = CurrFun,
+ label = CurrFunLabel, var_map = RaceVarMap,
+ def_vars = FunDefVars, call_vars = FunCallVars,
+ arg_types = FunArgTypes}],
+ Code, RaceVarMap)
+ end,
+ NewCode =
+ case Fun of
+ InitFun ->
+ [#curr_fun{status = in, mfa = Fun,
+ label = FunLabel, var_map = NewRaceVarMap,
+ def_vars = Args, call_vars = NewFunArgs,
+ arg_types = NewFunTypes}|
+ lists:reverse(StateRaceList)] ++ RetC;
+ _ ->
+ [#curr_fun{status = in, mfa = Fun,
+ label = FunLabel, var_map = NewRaceVarMap,
+ def_vars = Args, call_vars = NewFunArgs,
+ arg_types = NewFunTypes}|CodeB] ++
+ RetC
+ end,
+ {Fun, FunLabel, NewCallsToAnalyze, NewCode, RaceList, NewRaceVarMap,
+ Args, NewFunArgs, NewFunTypes, NestingLevel};
+ {_TupleA, _TupleB} ->
+ fixup_race_forward_helper(CurrFun, CurrFunLabel, Fun, FunLabel,
+ Tail, CallsToAnalyze, Code, RaceList, InitFun, NewFunArgs,
+ NewFunTypes, RaceWarnTag, RaceVarMap, FunDefVars, FunCallVars,
+ FunArgTypes, NestingLevel, Args, CodeB, StateRaceList)
+ end
+ end.
+
+%%% ===========================================================================
+%%%
+%%% Backward Analysis
+%%%
+%%% ===========================================================================
+
+fixup_race_backward(CurrFun, Calls, CallsToAnalyze, Parents, Height) ->
+ case Height =:= 0 of
+ true -> Parents;
+ false ->
+ case Calls of
+ [] ->
+ case is_integer(CurrFun) orelse lists:member(CurrFun, Parents) of
+ true -> Parents;
+ false -> [CurrFun|Parents]
+ end;
+ [Head|Tail] ->
+ {Parent, TupleB} = Head,
+ case TupleB =:= CurrFun of
+ true -> % more paths are needed
+ NewCallsToAnalyze = lists:delete(Head, CallsToAnalyze),
+ NewParents =
+ fixup_race_backward(Parent, NewCallsToAnalyze,
+ NewCallsToAnalyze, Parents, Height - 1),
+ fixup_race_backward(CurrFun, Tail, NewCallsToAnalyze, NewParents,
+ Height);
+ false ->
+ fixup_race_backward(CurrFun, Tail, CallsToAnalyze, Parents,
+ Height)
+ end
+ end
+ end.
+
+%%% ===========================================================================
+%%%
+%%% Utilities
+%%%
+%%% ===========================================================================
+
+are_bound_labels(Label1, Label2, RaceVarMap) ->
+ case dict:find(Label1, RaceVarMap) of
+ error -> false;
+ {ok, Labels} ->
+ lists:member(Label2, Labels) orelse
+ are_bound_labels_helper(Labels, Label1, Label2, RaceVarMap)
+ end.
+
+are_bound_labels_helper(Labels, OldLabel, CompLabel, RaceVarMap) ->
+ case dict:size(RaceVarMap) of
+ 0 -> false;
+ _ ->
+ case Labels of
+ [] -> false;
+ [Head|Tail] ->
+ NewRaceVarMap = dict:erase(OldLabel, RaceVarMap),
+ are_bound_labels(Head, CompLabel, NewRaceVarMap) orelse
+ are_bound_labels_helper(Tail, Head, CompLabel, NewRaceVarMap)
+ end
+ end.
+
+are_bound_vars(Vars1, Vars2, RaceVarMap) ->
+ case is_list(Vars1) andalso is_list(Vars2) of
+ true ->
+ case Vars1 of
+ [] -> false;
+ [AHead|ATail] ->
+ case Vars2 of
+ [] -> false;
+ [PHead|PTail] ->
+ are_bound_vars(AHead, PHead, RaceVarMap) andalso
+ are_bound_vars(ATail, PTail, RaceVarMap)
+ end
+ end;
+ false ->
+ {NewVars1, NewVars2, IsList} =
+ case is_list(Vars1) of
+ true ->
+ case Vars1 of
+ [Var1] -> {Var1, Vars2, true};
+ _Thing -> {Vars1, Vars2, false}
+ end;
+ false ->
+ case is_list(Vars2) of
+ true ->
+ case Vars2 of
+ [Var2] -> {Vars1, Var2, true};
+ _Thing -> {Vars1, Vars2, false}
+ end;
+ false -> {Vars1, Vars2, true}
+ end
+ end,
+ case IsList of
+ true ->
+ case cerl:type(NewVars1) of
+ var ->
+ case cerl:type(NewVars2) of
+ var ->
+ ALabel = cerl_trees:get_label(NewVars1),
+ PLabel = cerl_trees:get_label(NewVars2),
+ are_bound_labels(ALabel, PLabel, RaceVarMap) orelse
+ are_bound_labels(PLabel, ALabel, RaceVarMap);
+ alias ->
+ are_bound_vars(NewVars1, cerl:alias_var(NewVars2),
+ RaceVarMap);
+ values ->
+ are_bound_vars(NewVars1, cerl:values_es(NewVars2),
+ RaceVarMap);
+ _Other -> false
+ end;
+ tuple ->
+ case cerl:type(NewVars2) of
+ tuple ->
+ are_bound_vars(cerl:tuple_es(NewVars1),
+ cerl:tuple_es(NewVars2), RaceVarMap);
+ alias ->
+ are_bound_vars(NewVars1, cerl:alias_var(NewVars2),
+ RaceVarMap);
+ values ->
+ are_bound_vars(NewVars1, cerl:values_es(NewVars2),
+ RaceVarMap);
+ _Other -> false
+ end;
+ cons ->
+ case cerl:type(NewVars2) of
+ cons ->
+ are_bound_vars(cerl:cons_hd(NewVars1),
+ cerl:cons_hd(NewVars2), RaceVarMap)
+ andalso
+ are_bound_vars(cerl:cons_tl(NewVars1),
+ cerl:cons_tl(NewVars2), RaceVarMap);
+ alias ->
+ are_bound_vars(NewVars1, cerl:alias_var(NewVars2),
+ RaceVarMap);
+ values ->
+ are_bound_vars(NewVars1, cerl:values_es(NewVars2),
+ RaceVarMap);
+ _Other -> false
+ end;
+ alias ->
+ case cerl:type(NewVars2) of
+ alias ->
+ are_bound_vars(cerl:alias_var(NewVars1),
+ cerl:alias_var(NewVars2), RaceVarMap);
+ _Other ->
+ are_bound_vars(cerl:alias_var(NewVars1),
+ NewVars2, RaceVarMap)
+ end;
+ values ->
+ case cerl:type(NewVars2) of
+ values ->
+ are_bound_vars(cerl:values_es(NewVars1),
+ cerl:values_es(NewVars2), RaceVarMap);
+ _Other ->
+ are_bound_vars(cerl:values_es(NewVars1),
+ NewVars2, RaceVarMap)
+ end;
+ _Other -> false
+ end;
+ false -> false
+ end
+ end.
+
+callgraph__renew_tables(Table, Callgraph) ->
+ case Table of
+ {named, NameLabel, Names} ->
+ PTablesToAdd =
+ case NameLabel of
+ ?no_label -> [];
+ _Other -> [NameLabel]
+ end,
+ NamesToAdd = filter_named_tables(Names),
+ PTables = dialyzer_callgraph:get_public_tables(Callgraph),
+ NTables = dialyzer_callgraph:get_named_tables(Callgraph),
+ dialyzer_callgraph:put_public_tables(
+ lists:usort(PTablesToAdd ++ PTables),
+ dialyzer_callgraph:put_named_tables(
+ NamesToAdd ++ NTables, Callgraph));
+ _Other ->
+ Callgraph
+ end.
+
+cleanup_clause_code(#curr_fun{mfa = CurrFun} = CurrTuple, Code,
+ NestingLevel, LocalNestingLevel) ->
+ case Code of
+ [] -> {CurrTuple, []};
+ [Head|Tail] ->
+ {NewLocalNestingLevel, NewNestingLevel, NewCurrTuple, Return} =
+ case Head of
+ beg_case ->
+ {LocalNestingLevel, NestingLevel + 1, CurrTuple, false};
+ #end_case{} ->
+ {LocalNestingLevel, NestingLevel - 1, CurrTuple, false};
+ #end_clause{} ->
+ case NestingLevel =:= 0 of
+ true ->
+ {LocalNestingLevel, NestingLevel, CurrTuple, true};
+ false ->
+ {LocalNestingLevel, NestingLevel, CurrTuple, false}
+ end;
+ #fun_call{caller = CurrFun} ->
+ {LocalNestingLevel - 1, NestingLevel, CurrTuple, false};
+ #curr_fun{status = in} ->
+ {LocalNestingLevel - 1, NestingLevel, Head, false};
+ #curr_fun{status = out} ->
+ {LocalNestingLevel + 1, NestingLevel, Head, false};
+ Other when Other =/= #fun_call{} ->
+ {LocalNestingLevel, NestingLevel, CurrTuple, false}
+ end,
+ case Return of
+ true -> {NewCurrTuple, Tail};
+ false ->
+ cleanup_clause_code(NewCurrTuple, Tail, NewNestingLevel,
+ NewLocalNestingLevel)
+ end
+ end.
+
+cleanup_dep_calls(DepList) ->
+ case DepList of
+ [] -> [];
+ [#dep_call{call_name = CallName, arg_types = ArgTypes,
+ vars = Vars, state = State, file_line = FileLine}|T] ->
+ [#dep_call{call_name = CallName, arg_types = ArgTypes,
+ vars = Vars, state = State, file_line = FileLine}|
+ cleanup_dep_calls(T)]
+ end.
+
+cleanup_race_code(State) ->
+ Callgraph = dialyzer_dataflow:state__get_callgraph(State),
+ dialyzer_dataflow:state__put_callgraph(
+ dialyzer_callgraph:race_code_new(Callgraph), State).
+
+filter_named_tables(NamesList) ->
+ case NamesList of
+ [] -> [];
+ [Head|Tail] ->
+ NewHead =
+ case string:rstr(Head, "()") of
+ 0 -> [Head];
+ _Other -> []
+ end,
+ NewHead ++ filter_named_tables(Tail)
+ end.
+
+filter_parents(Parents, NewParents, Digraph) ->
+ case Parents of
+ [] -> NewParents;
+ [Head|Tail] ->
+ NewParents1 = filter_parents_helper1(Head, Tail, NewParents, Digraph),
+ filter_parents(Tail, NewParents1, Digraph)
+ end.
+
+filter_parents_helper1(First, Rest, NewParents, Digraph) ->
+ case Rest of
+ [] -> NewParents;
+ [Head|Tail] ->
+ NewParents1 = filter_parents_helper2(First, Head, NewParents, Digraph),
+ filter_parents_helper1(First, Tail, NewParents1, Digraph)
+ end.
+
+filter_parents_helper2(Parent1, Parent2, NewParents, Digraph) ->
+ case digraph:get_path(Digraph, Parent1, Parent2) of
+ false ->
+ case digraph:get_path(Digraph, Parent2, Parent1) of
+ false -> NewParents;
+ _Vertices -> NewParents -- [Parent1]
+ end;
+ _Vertices -> NewParents -- [Parent2]
+ end.
+
+find_all_bound_vars(Label, RaceVarMap) ->
+ case dict:find(Label, RaceVarMap) of
+ error -> [Label];
+ {ok, Labels} ->
+ lists:usort(Labels ++
+ find_all_bound_vars_helper(Labels, Label, RaceVarMap))
+ end.
+
+find_all_bound_vars_helper(Labels, Label, RaceVarMap) ->
+ case dict:size(RaceVarMap) of
+ 0 -> [];
+ _ ->
+ case Labels of
+ [] -> [];
+ [Head|Tail] ->
+ NewRaceVarMap = dict:erase(Label, RaceVarMap),
+ find_all_bound_vars(Head, NewRaceVarMap) ++
+ find_all_bound_vars_helper(Tail, Head, NewRaceVarMap)
+ end
+ end.
+
+fixup_all_calls(CurrFun, NextFun, NextFunLabel, Args, CodeToReplace,
+ Code, RaceVarMap) ->
+ case Code of
+ [] -> [];
+ [Head|Tail] ->
+ NewCode =
+ case Head of
+ #fun_call{caller = CurrFun, callee = Callee,
+ arg_types = FunArgTypes, vars = FunArgs}
+ when Callee =:= NextFun orelse Callee =:= NextFunLabel ->
+ RaceVarMap1 = race_var_map(Args, FunArgs, RaceVarMap, bind),
+ [#curr_fun{status = in, mfa = NextFun, label = NextFunLabel,
+ var_map = RaceVarMap1, def_vars = Args,
+ call_vars = FunArgs, arg_types = FunArgTypes}|
+ CodeToReplace];
+ _Other -> [Head]
+ end,
+ RetCode =
+ fixup_all_calls(CurrFun, NextFun, NextFunLabel, Args, CodeToReplace,
+ Tail, RaceVarMap),
+ NewCode ++ RetCode
+ end.
+
+is_last_race(RaceTag, InitFun, Code, Callgraph) ->
+ case Code of
+ [] -> true;
+ [Head|Tail] ->
+ case Head of
+ RaceTag -> false;
+ #fun_call{callee = Fun} ->
+ FunName =
+ case is_integer(Fun) of
+ true ->
+ case dialyzer_callgraph:lookup_name(Fun, Callgraph) of
+ error -> Fun;
+ {ok, Name} -> Name
+ end;
+ false -> Fun
+ end,
+ Digraph = dialyzer_callgraph:get_digraph(Callgraph),
+ case FunName =:= InitFun orelse
+ digraph:get_path(Digraph, FunName, InitFun) of
+ false -> is_last_race(RaceTag, InitFun, Tail, Callgraph);
+ _Vertices -> false
+ end;
+ _Other -> is_last_race(RaceTag, InitFun, Tail, Callgraph)
+ end
+ end.
+
+lists_key_member(Member, List, N) when is_integer(Member) ->
+ case List of
+ [] -> 0;
+ [Head|Tail] ->
+ NewN = N + 1,
+ case Head of
+ Member -> NewN;
+ _Other -> lists_key_member(Member, Tail, NewN)
+ end
+ end;
+lists_key_member(_M, _L, _N) ->
+ 0.
+
+lists_key_member_lists(MemberList, List) ->
+ case MemberList of
+ [] -> 0;
+ [Head|Tail] ->
+ case lists_key_member(Head, List, 0) of
+ 0 -> lists_key_member_lists(Tail, List);
+ Other -> Other
+ end
+ end.
+
+lists_key_members_lists(MemberList, List) ->
+ case MemberList of
+ [] -> [];
+ [Head|Tail] ->
+ lists:usort(
+ lists_key_members_lists_helper(Head, List, 1) ++
+ lists_key_members_lists(Tail, List))
+ end.
+
+lists_key_members_lists_helper(Elem, List, N) when is_integer(Elem) ->
+ case List of
+ [] -> [];
+ [Head|Tail] ->
+ NewHead =
+ case Head =:= Elem of
+ true -> [N];
+ false -> []
+ end,
+ NewHead ++ lists_key_members_lists_helper(Elem, Tail, N + 1)
+ end;
+lists_key_members_lists_helper(_Elem, _List, _N) ->
+ [0].
+
+lists_key_replace(N, List, NewMember) ->
+ {Before, [_|After]} = lists:split(N - 1, List),
+ Before ++ [NewMember|After].
+
+lists_get(0, _List) -> ?no_label;
+lists_get(N, List) -> lists:nth(N, List).
+
+refine_race(RaceCall, WarnVarArgs, RaceWarnTag, DependencyList, RaceVarMap) ->
+ case RaceWarnTag of
+ WarnWhereis when WarnWhereis =:= ?WARN_WHEREIS_REGISTER orelse
+ WarnWhereis =:= ?WARN_WHEREIS_UNREGISTER ->
+ case RaceCall of
+ #dep_call{call_name = ets_lookup} ->
+ DependencyList;
+ #dep_call{call_name = mnesia_dirty_read} ->
+ DependencyList;
+ #dep_call{call_name = whereis, args = VarArgs} ->
+ refine_race_helper(RaceCall, VarArgs, WarnVarArgs, RaceWarnTag,
+ DependencyList, RaceVarMap)
+ end;
+ ?WARN_ETS_LOOKUP_INSERT ->
+ case RaceCall of
+ #dep_call{call_name = whereis} ->
+ DependencyList;
+ #dep_call{call_name = mnesia_dirty_read} ->
+ DependencyList;
+ #dep_call{call_name = ets_lookup, args = VarArgs} ->
+ refine_race_helper(RaceCall, VarArgs, WarnVarArgs, RaceWarnTag,
+ DependencyList, RaceVarMap)
+ end;
+ ?WARN_MNESIA_DIRTY_READ_WRITE ->
+ case RaceCall of
+ #dep_call{call_name = whereis} ->
+ DependencyList;
+ #dep_call{call_name = ets_lookup} ->
+ DependencyList;
+ #dep_call{call_name = mnesia_dirty_read, args = VarArgs} ->
+ refine_race_helper(RaceCall, VarArgs, WarnVarArgs, RaceWarnTag,
+ DependencyList, RaceVarMap)
+ end
+ end.
+
+refine_race_helper(RaceCall, VarArgs, WarnVarArgs, RaceWarnTag, DependencyList,
+ RaceVarMap) ->
+ case compare_types(VarArgs, WarnVarArgs, RaceWarnTag, RaceVarMap) of
+ true -> [RaceCall|DependencyList];
+ false -> DependencyList
+ end.
+
+remove_clause(RaceList, CurrTuple, Code, NestingLevel) ->
+ NewRaceList = fixup_case_rest_paths(RaceList, 0),
+ {NewCurrTuple, NewCode} =
+ cleanup_clause_code(CurrTuple, Code, 0, NestingLevel),
+ ReturnTuple = {NewRaceList, NewCurrTuple, NewCode, NestingLevel},
+ case NewRaceList of
+ [beg_case|RTail] ->
+ case NewCode of
+ [#end_case{}|CTail] ->
+ remove_clause(RTail, NewCurrTuple, CTail, NestingLevel);
+ _Other -> ReturnTuple
+ end;
+ _Else -> ReturnTuple
+ end.
+
+remove_nonlocal_functions(Code, NestingLevel) ->
+ case Code of
+ [] -> [];
+ [H|T] ->
+ NewNL =
+ case H of
+ #curr_fun{status = in} ->
+ NestingLevel + 1;
+ #curr_fun{status = out} ->
+ NestingLevel - 1;
+ _Other ->
+ NestingLevel
+ end,
+ case NewNL =:= 0 of
+ true -> T;
+ false -> remove_nonlocal_functions(T, NewNL)
+ end
+ end.
+
+renew_curr_fun(CurrFun, Races) ->
+ Races#races{curr_fun = CurrFun}.
+
+renew_curr_fun_label(CurrFunLabel, Races) ->
+ Races#races{curr_fun_label = CurrFunLabel}.
+
+renew_race_list(RaceList, Races) ->
+ Races#races{race_list = RaceList}.
+
+renew_race_list_size(RaceListSize, Races) ->
+ Races#races{race_list_size = RaceListSize}.
+
+renew_race_tags(RaceTags, Races) ->
+ Races#races{race_tags = RaceTags}.
+
+renew_table(Table, Races) ->
+ Races#races{new_table = Table}.
+
+state__renew_curr_fun(CurrFun, State) ->
+ Races = dialyzer_dataflow:state__get_races(State),
+ dialyzer_dataflow:state__put_races(renew_curr_fun(CurrFun, Races), State).
+
+state__renew_curr_fun_label(CurrFunLabel, State) ->
+ Races = dialyzer_dataflow:state__get_races(State),
+ dialyzer_dataflow:state__put_races(
+ renew_curr_fun_label(CurrFunLabel, Races), State).
+
+state__renew_race_list(RaceList, State) ->
+ Races = dialyzer_dataflow:state__get_races(State),
+ dialyzer_dataflow:state__put_races(renew_race_list(RaceList, Races), State).
+
+state__renew_race_tags(RaceTags, State) ->
+ Races = dialyzer_dataflow:state__get_races(State),
+ dialyzer_dataflow:state__put_races(renew_race_tags(RaceTags, Races), State).
+
+state__renew_info(RaceList, RaceListSize, RaceTags, Table, State) ->
+ Callgraph = dialyzer_dataflow:state__get_callgraph(State),
+ Races = dialyzer_dataflow:state__get_races(State),
+ dialyzer_dataflow:state__put_callgraph(
+ callgraph__renew_tables(Table, Callgraph),
+ dialyzer_dataflow:state__put_races(
+ renew_table(Table,
+ renew_race_list(RaceList,
+ renew_race_list_size(RaceListSize,
+ renew_race_tags(RaceTags, Races)))), State)).
+
+%%% ===========================================================================
+%%%
+%%% Variable and Type Utilities
+%%%
+%%% ===========================================================================
+
+any_args(StrList) ->
+ case StrList of
+ [] -> false;
+ [Head|Tail] ->
+ case string:rstr(Head, "()") of
+ 0 -> any_args(Tail);
+ _Other -> true
+ end
+ end.
+
+-spec bind_dict_vars(label(), label(), dict:dict()) -> dict:dict().
+
+bind_dict_vars(Key, Label, RaceVarMap) ->
+ case Key =:= Label of
+ true -> RaceVarMap;
+ false ->
+ case dict:find(Key, RaceVarMap) of
+ error -> dict:store(Key, [Label], RaceVarMap);
+ {ok, Labels} ->
+ case lists:member(Label, Labels) of
+ true -> RaceVarMap;
+ false -> dict:store(Key, [Label|Labels], RaceVarMap)
+ end
+ end
+ end.
+
+bind_dict_vars_list(Key, Labels, RaceVarMap) ->
+ case Labels of
+ [] -> RaceVarMap;
+ [Head|Tail] ->
+ bind_dict_vars_list(Key, Tail, bind_dict_vars(Key, Head, RaceVarMap))
+ end.
+
+compare_ets_insert(OldWarnVarArgs, NewWarnVarArgs, RaceVarMap) ->
+ [Old1, Old2, Old3, Old4] = OldWarnVarArgs,
+ [New1, New2, New3, New4] = NewWarnVarArgs,
+ Bool =
+ case any_args(Old2) of
+ true -> compare_var_list(New1, Old1, RaceVarMap);
+ false ->
+ case any_args(New2) of
+ true -> compare_var_list(New1, Old1, RaceVarMap);
+ false -> compare_var_list(New1, Old1, RaceVarMap)
+ orelse (Old2 =:= New2)
+ end
+ end,
+ case Bool of
+ true ->
+ case any_args(Old4) of
+ true ->
+ case compare_list_vars(Old3, ets_list_args(New3), [], RaceVarMap) of
+ true -> true;
+ Args3 -> lists_key_replace(3, OldWarnVarArgs, Args3)
+ end;
+ false ->
+ case any_args(New4) of
+ true ->
+ case compare_list_vars(Old3, ets_list_args(New3), [],
+ RaceVarMap) of
+ true -> true;
+ Args3 -> lists_key_replace(3, OldWarnVarArgs, Args3)
+ end;
+ false ->
+ case compare_list_vars(Old3, ets_list_args(New3), [],
+ RaceVarMap) of
+ true -> true;
+ Args3 ->
+ lists_key_replace(4,
+ lists_key_replace(3, OldWarnVarArgs, Args3), Old4 -- New4)
+ end
+ end
+ end;
+ false -> OldWarnVarArgs
+ end.
+
+compare_first_arg(OldWarnVarArgs, NewWarnVarArgs, RaceVarMap) ->
+ [Old1, Old2|_OldT] = OldWarnVarArgs,
+ [New1, New2|_NewT] = NewWarnVarArgs,
+ case any_args(Old2) of
+ true ->
+ case compare_var_list(New1, Old1, RaceVarMap) of
+ true -> true;
+ false -> OldWarnVarArgs
+ end;
+ false ->
+ case any_args(New2) of
+ true ->
+ case compare_var_list(New1, Old1, RaceVarMap) of
+ true -> true;
+ false -> OldWarnVarArgs
+ end;
+ false ->
+ case compare_var_list(New1, Old1, RaceVarMap) of
+ true -> true;
+ false -> lists_key_replace(2, OldWarnVarArgs, Old2 -- New2)
+ end
+ end
+ end.
+
+compare_argtypes(ArgTypes, WarnArgTypes) ->
+ lists:any(fun (X) -> lists:member(X, WarnArgTypes) end, ArgTypes).
+
+%% Compares the argument types of the two suspicious calls.
+compare_types(VarArgs, WarnVarArgs, RaceWarnTag, RaceVarMap) ->
+ case RaceWarnTag of
+ ?WARN_WHEREIS_REGISTER ->
+ [VA1, VA2] = VarArgs,
+ [WVA1, WVA2, _, _] = WarnVarArgs,
+ case any_args(VA2) of
+ true -> compare_var_list(VA1, WVA1, RaceVarMap);
+ false ->
+ case any_args(WVA2) of
+ true -> compare_var_list(VA1, WVA1, RaceVarMap);
+ false ->
+ compare_var_list(VA1, WVA1, RaceVarMap) orelse
+ compare_argtypes(VA2, WVA2)
+ end
+ end;
+ ?WARN_WHEREIS_UNREGISTER ->
+ [VA1, VA2] = VarArgs,
+ [WVA1, WVA2] = WarnVarArgs,
+ case any_args(VA2) of
+ true -> compare_var_list(VA1, WVA1, RaceVarMap);
+ false ->
+ case any_args(WVA2) of
+ true -> compare_var_list(VA1, WVA1, RaceVarMap);
+ false ->
+ compare_var_list(VA1, WVA1, RaceVarMap) orelse
+ compare_argtypes(VA2, WVA2)
+ end
+ end;
+ ?WARN_ETS_LOOKUP_INSERT ->
+ [VA1, VA2, VA3, VA4] = VarArgs,
+ [WVA1, WVA2, WVA3, WVA4] = WarnVarArgs,
+ Bool =
+ case any_args(VA2) of
+ true -> compare_var_list(VA1, WVA1, RaceVarMap);
+ false ->
+ case any_args(WVA2) of
+ true -> compare_var_list(VA1, WVA1, RaceVarMap);
+ false ->
+ compare_var_list(VA1, WVA1, RaceVarMap) orelse
+ compare_argtypes(VA2, WVA2)
+ end
+ end,
+ Bool andalso
+ (case any_args(VA4) of
+ true ->
+ compare_var_list(VA3, WVA3, RaceVarMap);
+ false ->
+ case any_args(WVA4) of
+ true ->
+ compare_var_list(VA3, WVA3, RaceVarMap);
+ false ->
+ compare_var_list(VA3, WVA3, RaceVarMap) orelse
+ compare_argtypes(VA4, WVA4)
+ end
+ end);
+ ?WARN_MNESIA_DIRTY_READ_WRITE ->
+ [VA1, VA2|_] = VarArgs, %% Two or four elements
+ [WVA1, WVA2|_] = WarnVarArgs,
+ case any_args(VA2) of
+ true -> compare_var_list(VA1, WVA1, RaceVarMap);
+ false ->
+ case any_args(WVA2) of
+ true -> compare_var_list(VA1, WVA1, RaceVarMap);
+ false ->
+ compare_var_list(VA1, WVA1, RaceVarMap) orelse
+ compare_argtypes(VA2, WVA2)
+ end
+ end
+ end.
+
+compare_list_vars(VarList1, VarList2, NewVarList1, RaceVarMap) ->
+ case VarList1 of
+ [] ->
+ case NewVarList1 of
+ [] -> true;
+ _Other -> NewVarList1
+ end;
+ [Head|Tail] ->
+ NewHead =
+ case compare_var_list(Head, VarList2, RaceVarMap) of
+ true -> [];
+ false -> [Head]
+ end,
+ compare_list_vars(Tail, VarList2, NewHead ++ NewVarList1, RaceVarMap)
+ end.
+
+compare_vars(Var1, Var2, RaceVarMap) when is_integer(Var1), is_integer(Var2) ->
+ Var1 =:= Var2 orelse
+ are_bound_labels(Var1, Var2, RaceVarMap) orelse
+ are_bound_labels(Var2, Var1, RaceVarMap);
+compare_vars(_Var1, _Var2, _RaceVarMap) ->
+ false.
+
+-spec compare_var_list(label_type(), [label_type()], dict:dict()) -> boolean().
+
+compare_var_list(Var, VarList, RaceVarMap) ->
+ lists:any(fun (V) -> compare_vars(Var, V, RaceVarMap) end, VarList).
+
+ets_list_args(MaybeList) ->
+ case is_list(MaybeList) of
+ true ->
+ try [ets_tuple_args(T) || T <- MaybeList]
+ catch _:_ -> [?no_label]
+ end;
+ false -> [ets_tuple_args(MaybeList)]
+ end.
+
+ets_list_argtypes(ListStr) ->
+ ListStr1 = string:strip(ListStr, left, $[),
+ ListStr2 = string:strip(ListStr1, right, $]),
+ ListStr3 = string:strip(ListStr2, right, $.),
+ string:strip(ListStr3, right, $,).
+
+ets_tuple_args(MaybeTuple) ->
+ case is_tuple(MaybeTuple) of
+ true -> element(1, MaybeTuple);
+ false -> ?no_label
+ end.
+
+ets_tuple_argtypes2(TupleList, ElemList) ->
+ case TupleList of
+ [] -> ElemList;
+ [H|T] ->
+ ets_tuple_argtypes2(T,
+ ets_tuple_argtypes2_helper(H, [], 0) ++ ElemList)
+ end.
+
+ets_tuple_argtypes2_helper(TupleStr, ElemStr, NestingLevel) ->
+ case TupleStr of
+ [] -> [];
+ [H|T] ->
+ {NewElemStr, NewNestingLevel, Return} =
+ case H of
+ ${ when NestingLevel =:= 0 ->
+ {ElemStr, NestingLevel + 1, false};
+ ${ ->
+ {[H|ElemStr], NestingLevel + 1, false};
+ $[ ->
+ {[H|ElemStr], NestingLevel + 1, false};
+ $( ->
+ {[H|ElemStr], NestingLevel + 1, false};
+ $} ->
+ {[H|ElemStr], NestingLevel - 1, false};
+ $] ->
+ {[H|ElemStr], NestingLevel - 1, false};
+ $) ->
+ {[H|ElemStr], NestingLevel - 1, false};
+ $, when NestingLevel =:= 1 ->
+ {lists:reverse(ElemStr), NestingLevel, true};
+ _Other ->
+ {[H|ElemStr], NestingLevel, false}
+ end,
+ case Return of
+ true -> string:tokens(NewElemStr, " |");
+ false ->
+ ets_tuple_argtypes2_helper(T, NewElemStr, NewNestingLevel)
+ end
+ end.
+
+ets_tuple_argtypes1(Str, Tuple, TupleList, NestingLevel) ->
+ case Str of
+ [] -> TupleList;
+ [H|T] ->
+ {NewTuple, NewNestingLevel, Add} =
+ case H of
+ ${ ->
+ {[H|Tuple], NestingLevel + 1, false};
+ $} ->
+ case NestingLevel of
+ 1 ->
+ {[H|Tuple], NestingLevel - 1, true};
+ _Else ->
+ {[H|Tuple], NestingLevel - 1, false}
+ end;
+ _Other1 when NestingLevel =:= 0 ->
+ {Tuple, NestingLevel, false};
+ _Other2 ->
+ {[H|Tuple], NestingLevel, false}
+ end,
+ case Add of
+ true ->
+ ets_tuple_argtypes1(T, [],
+ [lists:reverse(NewTuple)|TupleList],
+ NewNestingLevel);
+ false ->
+ ets_tuple_argtypes1(T, NewTuple, TupleList, NewNestingLevel)
+ end
+ end.
+
+format_arg(?bypassed) -> ?no_label;
+format_arg(Arg0) ->
+ Arg = cerl:fold_literal(Arg0),
+ case cerl:type(Arg) of
+ var -> cerl_trees:get_label(Arg);
+ tuple -> list_to_tuple([format_arg(A) || A <- cerl:tuple_es(Arg)]);
+ cons -> [format_arg(cerl:cons_hd(Arg))|format_arg(cerl:cons_tl(Arg))];
+ alias -> format_arg(cerl:alias_var(Arg));
+ literal ->
+ case cerl:is_c_nil(Arg) of
+ true -> [];
+ false -> ?no_label
+ end;
+ _Other -> ?no_label
+ end.
+
+-spec format_args([core_vars()], [erl_types:erl_type()],
+ dialyzer_dataflow:state(), call()) ->
+ args().
+
+format_args([], [], _State, _Call) ->
+ [];
+format_args(ArgList, TypeList, CleanState, Call) ->
+ format_args_2(format_args_1(ArgList, TypeList, CleanState), Call).
+
+format_args_1([Arg], [Type], CleanState) ->
+ [format_arg(Arg), format_type(Type, CleanState)];
+format_args_1([Arg|Args], [Type|Types], CleanState) ->
+ List =
+ case Arg =:= ?bypassed of
+ true -> [?no_label, format_type(Type, CleanState)];
+ false ->
+ case cerl:is_literal(cerl:fold_literal(Arg)) of
+ true -> [?no_label, format_cerl(Arg)];
+ false -> [format_arg(Arg), format_type(Type, CleanState)]
+ end
+ end,
+ List ++ format_args_1(Args, Types, CleanState).
+
+format_args_2(StrArgList, Call) ->
+ case Call of
+ whereis ->
+ lists_key_replace(2, StrArgList,
+ string:tokens(lists:nth(2, StrArgList), " |"));
+ register ->
+ lists_key_replace(2, StrArgList,
+ string:tokens(lists:nth(2, StrArgList), " |"));
+ unregister ->
+ lists_key_replace(2, StrArgList,
+ string:tokens(lists:nth(2, StrArgList), " |"));
+ ets_new ->
+ StrArgList1 = lists_key_replace(2, StrArgList,
+ string:tokens(lists:nth(2, StrArgList), " |")),
+ lists_key_replace(4, StrArgList1,
+ string:tokens(ets_list_argtypes(lists:nth(4, StrArgList1)), " |"));
+ ets_lookup ->
+ StrArgList1 = lists_key_replace(2, StrArgList,
+ string:tokens(lists:nth(2, StrArgList), " |")),
+ lists_key_replace(4, StrArgList1,
+ string:tokens(lists:nth(4, StrArgList1), " |"));
+ ets_insert ->
+ StrArgList1 = lists_key_replace(2, StrArgList,
+ string:tokens(lists:nth(2, StrArgList), " |")),
+ lists_key_replace(4, StrArgList1,
+ ets_tuple_argtypes2(
+ ets_tuple_argtypes1(lists:nth(4, StrArgList1), [], [], 0),
+ []));
+ mnesia_dirty_read1 ->
+ lists_key_replace(2, StrArgList,
+ [mnesia_tuple_argtypes(T) || T <- string:tokens(
+ lists:nth(2, StrArgList), " |")]);
+ mnesia_dirty_read2 ->
+ lists_key_replace(2, StrArgList,
+ string:tokens(lists:nth(2, StrArgList), " |"));
+ mnesia_dirty_write1 ->
+ lists_key_replace(2, StrArgList,
+ [mnesia_record_tab(R) || R <- string:tokens(
+ lists:nth(2, StrArgList), " |")]);
+ mnesia_dirty_write2 ->
+ lists_key_replace(2, StrArgList,
+ string:tokens(lists:nth(2, StrArgList), " |"));
+ function_call -> StrArgList
+ end.
+
+format_cerl(Tree) ->
+ cerl_prettypr:format(cerl:set_ann(Tree, []),
+ [{hook, dialyzer_utils:pp_hook()},
+ {noann, true},
+ {paper, 100000},
+ {ribbon, 100000}
+ ]).
+
+format_type(Type, State) ->
+ R = dialyzer_dataflow:state__get_records(State),
+ erl_types:t_to_string(Type, R).
+
+mnesia_record_tab(RecordStr) ->
+ case string:str(RecordStr, "#") =:= 1 of
+ true ->
+ "'" ++
+ string:sub_string(RecordStr, 2, string:str(RecordStr, "{") - 1) ++
+ "'";
+ false -> RecordStr
+ end.
+
+mnesia_tuple_argtypes(TupleStr) ->
+ TupleStr1 = string:strip(TupleStr, left, ${),
+ [TupleStr2|_T] = string:tokens(TupleStr1, " ,"),
+ lists:flatten(string:tokens(TupleStr2, " |")).
+
+-spec race_var_map(var_to_map1(), var_to_map2(), dict:dict(), op()) ->
+ dict:dict().
+
+race_var_map(Vars1, Vars2, RaceVarMap, Op) ->
+ case Vars1 =:= ?no_arg orelse Vars1 =:= ?bypassed
+ orelse Vars2 =:= ?bypassed of
+ true -> RaceVarMap;
+ false ->
+ case is_list(Vars1) andalso is_list(Vars2) of
+ true ->
+ case Vars1 of
+ [] -> RaceVarMap;
+ [AHead|ATail] ->
+ case Vars2 of
+ [] -> RaceVarMap;
+ [PHead|PTail] ->
+ NewRaceVarMap = race_var_map(AHead, PHead, RaceVarMap, Op),
+ race_var_map(ATail, PTail, NewRaceVarMap, Op)
+ end
+ end;
+ false ->
+ {NewVars1, NewVars2, Bool} =
+ case is_list(Vars1) of
+ true ->
+ case Vars1 of
+ [Var1] -> {Var1, Vars2, true};
+ _Thing -> {Vars1, Vars2, false}
+ end;
+ false ->
+ case is_list(Vars2) of
+ true ->
+ case Vars2 of
+ [Var2] -> {Vars1, Var2, true};
+ _Thing -> {Vars1, Vars2, false}
+ end;
+ false -> {Vars1, Vars2, true}
+ end
+ end,
+ case Bool of
+ true ->
+ case cerl:type(NewVars1) of
+ var ->
+ case cerl:type(NewVars2) of
+ var ->
+ ALabel = cerl_trees:get_label(NewVars1),
+ PLabel = cerl_trees:get_label(NewVars2),
+ case Op of
+ bind ->
+ TempRaceVarMap =
+ bind_dict_vars(ALabel, PLabel, RaceVarMap),
+ bind_dict_vars(PLabel, ALabel, TempRaceVarMap);
+ unbind ->
+ TempRaceVarMap =
+ unbind_dict_vars(ALabel, PLabel, RaceVarMap),
+ unbind_dict_vars(PLabel, ALabel, TempRaceVarMap)
+ end;
+ alias ->
+ race_var_map(NewVars1, cerl:alias_var(NewVars2),
+ RaceVarMap, Op);
+ values ->
+ race_var_map(NewVars1, cerl:values_es(NewVars2),
+ RaceVarMap, Op);
+ _Other -> RaceVarMap
+ end;
+ tuple ->
+ case cerl:type(NewVars2) of
+ tuple ->
+ race_var_map(cerl:tuple_es(NewVars1),
+ cerl:tuple_es(NewVars2), RaceVarMap, Op);
+ alias ->
+ race_var_map(NewVars1, cerl:alias_var(NewVars2),
+ RaceVarMap, Op);
+ values ->
+ race_var_map(NewVars1, cerl:values_es(NewVars2),
+ RaceVarMap, Op);
+ _Other -> RaceVarMap
+ end;
+ cons ->
+ case cerl:type(NewVars2) of
+ cons ->
+ NewRaceVarMap = race_var_map(cerl:cons_hd(NewVars1),
+ cerl:cons_hd(NewVars2), RaceVarMap, Op),
+ race_var_map(cerl:cons_tl(NewVars1),
+ cerl:cons_tl(NewVars2), NewRaceVarMap, Op);
+ alias ->
+ race_var_map(NewVars1, cerl:alias_var(NewVars2),
+ RaceVarMap, Op);
+ values ->
+ race_var_map(NewVars1, cerl:values_es(NewVars2),
+ RaceVarMap, Op);
+ _Other -> RaceVarMap
+ end;
+ alias ->
+ case cerl:type(NewVars2) of
+ alias ->
+ race_var_map(cerl:alias_var(NewVars1),
+ cerl:alias_var(NewVars2), RaceVarMap, Op);
+ _Other ->
+ race_var_map(cerl:alias_var(NewVars1),
+ NewVars2, RaceVarMap, Op)
+ end;
+ values ->
+ case cerl:type(NewVars2) of
+ values ->
+ race_var_map(cerl:values_es(NewVars1),
+ cerl:values_es(NewVars2), RaceVarMap, Op);
+ _Other ->
+ race_var_map(cerl:values_es(NewVars1),
+ NewVars2, RaceVarMap, Op)
+ end;
+ _Other -> RaceVarMap
+ end;
+ false -> RaceVarMap
+ end
+ end
+ end.
+
+race_var_map_clauses(Clauses, RaceVarMap) ->
+ case Clauses of
+ [] -> RaceVarMap;
+ [#end_clause{arg = Arg, pats = Pats, guard = Guard}|T] ->
+ {RaceVarMap1, _RemoveClause} =
+ race_var_map_guard(Arg, Pats, Guard, RaceVarMap, bind),
+ race_var_map_clauses(T, RaceVarMap1)
+ end.
+
+race_var_map_guard(Arg, Pats, Guard, RaceVarMap, Op) ->
+ {NewRaceVarMap, RemoveClause} =
+ case cerl:type(Guard) of
+ call ->
+ CallName = cerl:call_name(Guard),
+ case cerl:is_literal(CallName) of
+ true ->
+ case cerl:concrete(CallName) of
+ '=:=' ->
+ [Arg1, Arg2] = cerl:call_args(Guard),
+ {race_var_map(Arg1, Arg2, RaceVarMap, Op), false};
+ '==' ->
+ [Arg1, Arg2] = cerl:call_args(Guard),
+ {race_var_map(Arg1, Arg2, RaceVarMap, Op), false};
+ '=/=' ->
+ case Op of
+ bind ->
+ [Arg1, Arg2] = cerl:call_args(Guard),
+ {RaceVarMap, are_bound_vars(Arg1, Arg2, RaceVarMap)};
+ unbind -> {RaceVarMap, false}
+ end;
+ _Other -> {RaceVarMap, false}
+ end;
+ false -> {RaceVarMap, false}
+ end;
+ _Other -> {RaceVarMap, false}
+ end,
+ {RaceVarMap1, RemoveClause1} =
+ race_var_map_guard_helper1(Arg, Pats,
+ race_var_map(Arg, Pats, NewRaceVarMap, Op), Op),
+ {RaceVarMap1, RemoveClause orelse RemoveClause1}.
+
+race_var_map_guard_helper1(Arg, Pats, RaceVarMap, Op) ->
+ case Arg =:= ?no_arg orelse Arg =:= ?bypassed of
+ true -> {RaceVarMap, false};
+ false ->
+ case cerl:type(Arg) of
+ call ->
+ case Pats of
+ [NewPat] ->
+ ModName = cerl:call_module(Arg),
+ CallName = cerl:call_name(Arg),
+ case cerl:is_literal(ModName) andalso
+ cerl:is_literal(CallName) of
+ true ->
+ case {cerl:concrete(ModName),
+ cerl:concrete(CallName)} of
+ {erlang, '=:='} ->
+ race_var_map_guard_helper2(Arg, NewPat, true,
+ RaceVarMap, Op);
+ {erlang, '=='} ->
+ race_var_map_guard_helper2(Arg, NewPat, true,
+ RaceVarMap, Op);
+ {erlang, '=/='} ->
+ race_var_map_guard_helper2(Arg, NewPat, false,
+ RaceVarMap, Op);
+ _Else -> {RaceVarMap, false}
+ end;
+ false -> {RaceVarMap, false}
+ end;
+ _Other -> {RaceVarMap, false}
+ end;
+ _Other -> {RaceVarMap, false}
+ end
+ end.
+
+race_var_map_guard_helper2(Arg, Pat0, Bool, RaceVarMap, Op) ->
+ Pat = cerl:fold_literal(Pat0),
+ case cerl:type(Pat) of
+ literal ->
+ [Arg1, Arg2] = cerl:call_args(Arg),
+ case cerl:concrete(Pat) of
+ Bool ->
+ {race_var_map(Arg1, Arg2, RaceVarMap, Op), false};
+ _Else ->
+ case Op of
+ bind ->
+ {RaceVarMap, are_bound_vars(Arg1, Arg2, RaceVarMap)};
+ unbind -> {RaceVarMap, false}
+ end
+ end;
+ _Else -> {RaceVarMap, false}
+ end.
+
+unbind_dict_vars(Var, Var, RaceVarMap) ->
+ RaceVarMap;
+unbind_dict_vars(Var1, Var2, RaceVarMap) ->
+ case dict:find(Var1, RaceVarMap) of
+ error -> RaceVarMap;
+ {ok, Labels} ->
+ case Labels of
+ [] -> dict:erase(Var1, RaceVarMap);
+ _Else ->
+ case lists:member(Var2, Labels) of
+ true ->
+ unbind_dict_vars(Var1, Var2,
+ bind_dict_vars_list(Var1, Labels -- [Var2],
+ dict:erase(Var1, RaceVarMap)));
+ false ->
+ unbind_dict_vars_helper(Labels, Var1, Var2, RaceVarMap)
+ end
+ end
+ end.
+
+unbind_dict_vars_helper(Labels, Key, CompLabel, RaceVarMap) ->
+ case dict:size(RaceVarMap) of
+ 0 -> RaceVarMap;
+ _ ->
+ case Labels of
+ [] -> RaceVarMap;
+ [Head|Tail] ->
+ NewRaceVarMap =
+ case are_bound_labels(Head, CompLabel, RaceVarMap) orelse
+ are_bound_labels(CompLabel, Head, RaceVarMap) of
+ true ->
+ bind_dict_vars_list(Key, Labels -- [Head],
+ dict:erase(Key, RaceVarMap));
+ false -> RaceVarMap
+ end,
+ unbind_dict_vars_helper(Tail, Key, CompLabel, NewRaceVarMap)
+ end
+ end.
+
+var_analysis(FunDefArgs, FunCallArgs, WarnVarArgs, RaceWarnTag) ->
+ case RaceWarnTag of
+ ?WARN_WHEREIS_REGISTER ->
+ [WVA1, WVA2, WVA3, WVA4] = WarnVarArgs,
+ ArgNos = lists_key_members_lists(WVA1, FunDefArgs),
+ [[lists_get(N, FunCallArgs) || N <- ArgNos], WVA2, WVA3, WVA4];
+ ?WARN_WHEREIS_UNREGISTER ->
+ [WVA1, WVA2] = WarnVarArgs,
+ ArgNos = lists_key_members_lists(WVA1, FunDefArgs),
+ [[lists_get(N, FunCallArgs) || N <- ArgNos], WVA2];
+ ?WARN_ETS_LOOKUP_INSERT ->
+ [WVA1, WVA2, WVA3, WVA4] = WarnVarArgs,
+ ArgNos1 = lists_key_members_lists(WVA1, FunDefArgs),
+ ArgNos2 = lists_key_members_lists(WVA3, FunDefArgs),
+ [[lists_get(N1, FunCallArgs) || N1 <- ArgNos1], WVA2,
+ [lists_get(N2, FunCallArgs) || N2 <- ArgNos2], WVA4];
+ ?WARN_MNESIA_DIRTY_READ_WRITE ->
+ [WVA1, WVA2|T] = WarnVarArgs,
+ ArgNos = lists_key_members_lists(WVA1, FunDefArgs),
+ [[lists_get(N, FunCallArgs) || N <- ArgNos], WVA2|T]
+ end.
+
+var_type_analysis(FunDefArgs, FunCallTypes, WarnVarArgs, RaceWarnTag,
+ RaceVarMap, CleanState) ->
+ FunVarArgs = format_args(FunDefArgs, FunCallTypes, CleanState, function_call),
+ case RaceWarnTag of
+ ?WARN_WHEREIS_REGISTER ->
+ [WVA1, WVA2, WVA3, WVA4] = WarnVarArgs,
+ Vars = find_all_bound_vars(WVA1, RaceVarMap),
+ case lists_key_member_lists(Vars, FunVarArgs) of
+ 0 -> [Vars, WVA2, WVA3, WVA4];
+ N when is_integer(N) ->
+ NewWVA2 = string:tokens(lists:nth(N + 1, FunVarArgs), " |"),
+ [Vars, NewWVA2, WVA3, WVA4]
+ end;
+ ?WARN_WHEREIS_UNREGISTER ->
+ [WVA1, WVA2] = WarnVarArgs,
+ Vars = find_all_bound_vars(WVA1, RaceVarMap),
+ case lists_key_member_lists(Vars, FunVarArgs) of
+ 0 -> [Vars, WVA2];
+ N when is_integer(N) ->
+ NewWVA2 = string:tokens(lists:nth(N + 1, FunVarArgs), " |"),
+ [Vars, NewWVA2]
+ end;
+ ?WARN_ETS_LOOKUP_INSERT ->
+ [WVA1, WVA2, WVA3, WVA4] = WarnVarArgs,
+ Vars1 = find_all_bound_vars(WVA1, RaceVarMap),
+ FirstVarArg =
+ case lists_key_member_lists(Vars1, FunVarArgs) of
+ 0 -> [Vars1, WVA2];
+ N1 when is_integer(N1) ->
+ NewWVA2 = string:tokens(lists:nth(N1 + 1, FunVarArgs), " |"),
+ [Vars1, NewWVA2]
+ end,
+ Vars2 =
+ lists:flatten(
+ [find_all_bound_vars(A, RaceVarMap) || A <- ets_list_args(WVA3)]),
+ case lists_key_member_lists(Vars2, FunVarArgs) of
+ 0 -> FirstVarArg ++ [Vars2, WVA4];
+ N2 when is_integer(N2) ->
+ NewWVA4 =
+ ets_tuple_argtypes2(
+ ets_tuple_argtypes1(lists:nth(N2 + 1, FunVarArgs), [], [], 0),
+ []),
+ FirstVarArg ++ [Vars2, NewWVA4]
+
+ end;
+ ?WARN_MNESIA_DIRTY_READ_WRITE ->
+ [WVA1, WVA2|T] = WarnVarArgs,
+ Arity =
+ case T of
+ [] -> 1;
+ _Else -> 2
+ end,
+ Vars = find_all_bound_vars(WVA1, RaceVarMap),
+ case lists_key_member_lists(Vars, FunVarArgs) of
+ 0 -> [Vars, WVA2|T];
+ N when is_integer(N) ->
+ NewWVA2 =
+ case Arity of
+ 1 ->
+ [mnesia_record_tab(R) || R <- string:tokens(
+ lists:nth(2, FunVarArgs), " |")];
+ 2 ->
+ string:tokens(lists:nth(N + 1, FunVarArgs), " |")
+ end,
+ [Vars, NewWVA2|T]
+ end
+ end.
+
+%%% ===========================================================================
+%%%
+%%% Warning Format Utilities
+%%%
+%%% ===========================================================================
+
+add_race_warning(Warn, #races{race_warnings = Warns} = Races) ->
+ Races#races{race_warnings = [Warn|Warns]}.
+
+get_race_warn(Fun, Args, ArgTypes, DepList, State) ->
+ {M, F, _A} = Fun,
+ case DepList of
+ [] -> {State, no_race};
+ _Other ->
+ {State, {race_condition, [M, F, Args, ArgTypes, State, DepList]}}
+ end.
+
+-spec get_race_warnings(races(), dialyzer_dataflow:state()) ->
+ {races(), dialyzer_dataflow:state()}.
+
+get_race_warnings(#races{race_warnings = RaceWarnings}, State) ->
+ get_race_warnings_helper(RaceWarnings, State).
+
+get_race_warnings_helper(Warnings, State) ->
+ case Warnings of
+ [] ->
+ {dialyzer_dataflow:state__get_races(State), State};
+ [H|T] ->
+ {RaceWarnTag, WarningInfo, {race_condition, [M, F, A, AT, S, DepList]}} = H,
+ Reason =
+ case RaceWarnTag of
+ ?WARN_WHEREIS_REGISTER ->
+ get_reason(lists:keysort(7, DepList),
+ "might fail due to a possible race condition "
+ "caused by its combination with ");
+ ?WARN_WHEREIS_UNREGISTER ->
+ get_reason(lists:keysort(7, DepList),
+ "might fail due to a possible race condition "
+ "caused by its combination with ");
+ ?WARN_ETS_LOOKUP_INSERT ->
+ get_reason(lists:keysort(7, DepList),
+ "might have an unintended effect due to " ++
+ "a possible race condition " ++
+ "caused by its combination with ");
+ ?WARN_MNESIA_DIRTY_READ_WRITE ->
+ get_reason(lists:keysort(7, DepList),
+ "might have an unintended effect due to " ++
+ "a possible race condition " ++
+ "caused by its combination with ")
+ end,
+ W =
+ {?WARN_RACE_CONDITION, WarningInfo,
+ {race_condition,
+ [M, F, dialyzer_dataflow:format_args(A, AT, S), Reason]}},
+ get_race_warnings_helper(T,
+ dialyzer_dataflow:state__add_warning(W, State))
+ end.
+
+get_reason(DependencyList, Reason) ->
+ case DependencyList of
+ [] -> "";
+ [#dep_call{call_name = Call, arg_types = ArgTypes, vars = Args,
+ state = State, file_line = {File, Line}}|T] ->
+ R =
+ Reason ++
+ case Call of
+ whereis -> "the erlang:whereis";
+ ets_lookup -> "the ets:lookup";
+ mnesia_dirty_read -> "the mnesia:dirty_read"
+ end ++
+ dialyzer_dataflow:format_args(Args, ArgTypes, State) ++
+ " call in " ++
+ filename:basename(File) ++
+ " on line " ++
+ lists:flatten(io_lib:write(Line)),
+ case T of
+ [] -> R;
+ _ -> get_reason(T, R ++ ", ")
+ end
+ end.
+
+state__add_race_warning(State, RaceWarn, RaceWarnTag, WarningInfo) ->
+ case RaceWarn of
+ no_race -> State;
+ _Else ->
+ Races = dialyzer_dataflow:state__get_races(State),
+ Warn = {RaceWarnTag, WarningInfo, RaceWarn},
+ dialyzer_dataflow:state__put_races(add_race_warning(Warn, Races), State)
+ end.
+
+%%% ===========================================================================
+%%%
+%%% Record Interfaces
+%%%
+%%% ===========================================================================
+
+-spec beg_clause_new(var_to_map1(), var_to_map1(), cerl:cerl()) ->
+ #beg_clause{}.
+
+beg_clause_new(Arg, Pats, Guard) ->
+ #beg_clause{arg = Arg, pats = Pats, guard = Guard}.
+
+-spec cleanup(races()) -> races().
+
+cleanup(#races{race_list = RaceList}) ->
+ #races{race_list = RaceList}.
+
+-spec end_case_new([#end_clause{}]) -> #end_case{}.
+
+end_case_new(Clauses) ->
+ #end_case{clauses = Clauses}.
+
+-spec end_clause_new(var_to_map1(), var_to_map1(), cerl:cerl()) ->
+ #end_clause{}.
+
+end_clause_new(Arg, Pats, Guard) ->
+ #end_clause{arg = Arg, pats = Pats, guard = Guard}.
+
+-spec get_curr_fun(races()) -> dialyzer_callgraph:mfa_or_funlbl().
+
+get_curr_fun(#races{curr_fun = CurrFun}) ->
+ CurrFun.
+
+-spec get_curr_fun_args(races()) -> core_args().
+
+get_curr_fun_args(#races{curr_fun_args = CurrFunArgs}) ->
+ CurrFunArgs.
+
+-spec get_new_table(races()) -> table().
+
+get_new_table(#races{new_table = Table}) ->
+ Table.
+
+-spec get_race_analysis(races()) -> boolean().
+
+get_race_analysis(#races{race_analysis = RaceAnalysis}) ->
+ RaceAnalysis.
+
+-spec get_race_list(races()) -> code().
+
+get_race_list(#races{race_list = RaceList}) ->
+ RaceList.
+
+-spec get_race_list_size(races()) -> non_neg_integer().
+
+get_race_list_size(#races{race_list_size = RaceListSize}) ->
+ RaceListSize.
+
+-spec get_race_list_and_size(races()) -> {code(), non_neg_integer()}.
+
+get_race_list_and_size(#races{race_list = RaceList,
+ race_list_size = RaceListSize}) ->
+ {RaceList, RaceListSize}.
+
+-spec let_tag_new(var_to_map1(), var_to_map1()) -> #let_tag{}.
+
+let_tag_new(Var, Arg) ->
+ #let_tag{var = Var, arg = Arg}.
+
+-spec new() -> races().
+
+new() -> #races{}.
+
+-spec put_curr_fun(dialyzer_callgraph:mfa_or_funlbl(), label(), races()) ->
+ races().
+
+put_curr_fun(CurrFun, CurrFunLabel, Races) ->
+ Races#races{curr_fun = CurrFun,
+ curr_fun_label = CurrFunLabel,
+ curr_fun_args = empty}.
+
+-spec put_fun_args(core_args(), races()) -> races().
+
+put_fun_args(Args, #races{curr_fun_args = CurrFunArgs} = Races) ->
+ case CurrFunArgs of
+ empty -> Races#races{curr_fun_args = Args};
+ _Other -> Races
+ end.
+
+-spec put_race_analysis(boolean(), races()) ->
+ races().
+
+put_race_analysis(Analysis, Races) ->
+ Races#races{race_analysis = Analysis}.
+
+-spec put_race_list(code(), non_neg_integer(), races()) ->
+ races().
+
+put_race_list(RaceList, RaceListSize, Races) ->
+ Races#races{race_list = RaceList, race_list_size = RaceListSize}.
diff --git a/lib/dialyzer/test/opaque_SUITE_data/src/recrec/erl_types.erl b/lib/dialyzer/test/opaque_SUITE_data/src/recrec/erl_types.erl
new file mode 100644
index 0000000000..7826dada9d
--- /dev/null
+++ b/lib/dialyzer/test/opaque_SUITE_data/src/recrec/erl_types.erl
@@ -0,0 +1,5741 @@
+%% -*- erlang-indent-level: 2 -*-
+%%
+%% %CopyrightBegin%
+%%
+%% Copyright Ericsson AB 2003-2016. All Rights Reserved.
+%%
+%% Licensed under the Apache License, Version 2.0 (the "License");
+%% you may not use this file except in compliance with the License.
+%% You may obtain a copy of the License at
+%%
+%% http://www.apache.org/licenses/LICENSE-2.0
+%%
+%% Unless required by applicable law or agreed to in writing, software
+%% distributed under the License is distributed on an "AS IS" BASIS,
+%% WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+%% See the License for the specific language governing permissions and
+%% limitations under the License.
+%%
+%% %CopyrightEnd%
+%%
+%% ======================================================================
+%% Copyright (C) 2000-2003 Richard Carlsson
+%%
+%% ======================================================================
+%% Provides a representation of Erlang types.
+%%
+%% The initial author of this file is Richard Carlsson (2000-2004).
+%% In July 2006, the type representation was totally re-designed by
+%% Tobias Lindahl. This is the representation which is used currently.
+%% In late 2008, Manouk Manoukian and Kostis Sagonas added support for
+%% opaque types to the structure-based representation of types.
+%% During February and March 2009, Kostis Sagonas significantly
+%% cleaned up the type representation and added spec declarations.
+%%
+%% ======================================================================
+
+-module(erl_types).
+
+-export([any_none/1,
+ any_none_or_unit/1,
+ lookup_record/3,
+ max/2,
+ min/2,
+ number_max/1, number_max/2,
+ number_min/1, number_min/2,
+ t_abstract_records/2,
+ t_any/0,
+ t_arity/0,
+ t_atom/0,
+ t_atom/1,
+ t_atoms/1,
+ t_atom_vals/1, t_atom_vals/2,
+ t_binary/0,
+ t_bitstr/0,
+ t_bitstr/2,
+ t_bitstr_base/1,
+ t_bitstr_concat/1,
+ t_bitstr_concat/2,
+ t_bitstr_match/2,
+ t_bitstr_unit/1,
+ t_bitstrlist/0,
+ t_boolean/0,
+ t_byte/0,
+ t_char/0,
+ t_collect_vars/1,
+ t_cons/0,
+ t_cons/2,
+ t_cons_hd/1, t_cons_hd/2,
+ t_cons_tl/1, t_cons_tl/2,
+ t_contains_opaque/1, t_contains_opaque/2,
+ t_decorate_with_opaque/3,
+ t_elements/1,
+ t_find_opaque_mismatch/3,
+ t_find_unknown_opaque/3,
+ t_fixnum/0,
+ t_map/2,
+ t_non_neg_fixnum/0,
+ t_pos_fixnum/0,
+ t_float/0,
+ t_var_names/1,
+ t_form_to_string/1,
+ t_from_form/6,
+ t_from_form_without_remote/3,
+ t_check_record_fields/6,
+ t_from_range/2,
+ t_from_range_unsafe/2,
+ t_from_term/1,
+ t_fun/0,
+ t_fun/1,
+ t_fun/2,
+ t_fun_args/1, t_fun_args/2,
+ t_fun_arity/1, t_fun_arity/2,
+ t_fun_range/1, t_fun_range/2,
+ t_has_opaque_subtype/2,
+ t_has_var/1,
+ t_identifier/0,
+ %% t_improper_list/2,
+ t_inf/1,
+ t_inf/2,
+ t_inf/3,
+ t_inf_lists/2,
+ t_inf_lists/3,
+ t_integer/0,
+ t_integer/1,
+ t_non_neg_integer/0,
+ t_pos_integer/0,
+ t_integers/1,
+ t_iodata/0,
+ t_iolist/0,
+ t_is_any/1,
+ t_is_atom/1, t_is_atom/2,
+ t_is_any_atom/2, t_is_any_atom/3,
+ t_is_binary/1, t_is_binary/2,
+ t_is_bitstr/1, t_is_bitstr/2,
+ t_is_bitwidth/1,
+ t_is_boolean/1, t_is_boolean/2,
+ %% t_is_byte/1,
+ %% t_is_char/1,
+ t_is_cons/1, t_is_cons/2,
+ t_is_equal/2,
+ t_is_fixnum/1,
+ t_is_float/1, t_is_float/2,
+ t_is_fun/1, t_is_fun/2,
+ t_is_instance/2,
+ t_is_integer/1, t_is_integer/2,
+ t_is_list/1,
+ t_is_map/1,
+ t_is_map/2,
+ t_is_matchstate/1,
+ t_is_nil/1, t_is_nil/2,
+ t_is_non_neg_integer/1,
+ t_is_none/1,
+ t_is_none_or_unit/1,
+ t_is_number/1, t_is_number/2,
+ t_is_opaque/1, t_is_opaque/2,
+ t_is_pid/1, t_is_pid/2,
+ t_is_port/1, t_is_port/2,
+ t_is_maybe_improper_list/1, t_is_maybe_improper_list/2,
+ t_is_reference/1, t_is_reference/2,
+ t_is_singleton/1,
+ t_is_singleton/2,
+ t_is_string/1,
+ t_is_subtype/2,
+ t_is_tuple/1, t_is_tuple/2,
+ t_is_unit/1,
+ t_is_var/1,
+ t_limit/2,
+ t_list/0,
+ t_list/1,
+ t_list_elements/1, t_list_elements/2,
+ t_list_termination/1, t_list_termination/2,
+ t_map/0,
+ t_map/1,
+ t_map/3,
+ t_map_entries/2, t_map_entries/1,
+ t_map_def_key/2, t_map_def_key/1,
+ t_map_def_val/2, t_map_def_val/1,
+ t_map_get/2, t_map_get/3,
+ t_map_is_key/2, t_map_is_key/3,
+ t_map_update/2, t_map_update/3,
+ t_map_put/2, t_map_put/3,
+ t_matchstate/0,
+ t_matchstate/2,
+ t_matchstate_present/1,
+ t_matchstate_slot/2,
+ t_matchstate_slots/1,
+ t_matchstate_update_present/2,
+ t_matchstate_update_slot/3,
+ t_mfa/0,
+ t_module/0,
+ t_nil/0,
+ t_node/0,
+ t_none/0,
+ t_nonempty_list/0,
+ t_nonempty_list/1,
+ t_nonempty_string/0,
+ t_number/0,
+ t_number/1,
+ t_number_vals/1, t_number_vals/2,
+ t_opaque_from_records/1,
+ t_opaque_structure/1,
+ t_pid/0,
+ t_port/0,
+ t_maybe_improper_list/0,
+ %% t_maybe_improper_list/2,
+ t_product/1,
+ t_reference/0,
+ t_singleton_to_term/2,
+ t_string/0,
+ t_struct_from_opaque/2,
+ t_subst/2,
+ t_subtract/2,
+ t_subtract_list/2,
+ t_sup/1,
+ t_sup/2,
+ t_timeout/0,
+ t_to_string/1,
+ t_to_string/2,
+ t_to_tlist/1,
+ t_tuple/0,
+ t_tuple/1,
+ t_tuple_args/1, t_tuple_args/2,
+ t_tuple_size/1, t_tuple_size/2,
+ t_tuple_sizes/1,
+ t_tuple_subtypes/1,
+ t_tuple_subtypes/2,
+ t_unify/2,
+ t_unit/0,
+ t_unopaque/1, t_unopaque/2,
+ t_var/1,
+ t_var_name/1,
+ %% t_assign_variables_to_subtype/2,
+ type_is_defined/4,
+ record_field_diffs_to_string/2,
+ subst_all_vars_to_any/1,
+ lift_list_to_pos_empty/1, lift_list_to_pos_empty/2,
+ is_opaque_type/2,
+ is_erl_type/1,
+ atom_to_string/1,
+ var_table__new/0,
+ cache__new/0,
+ map_pairwise_merge/3
+ ]).
+
+%%-define(DO_ERL_TYPES_TEST, true).
+-compile({no_auto_import,[min/2,max/2]}).
+
+-ifdef(DO_ERL_TYPES_TEST).
+-export([test/0]).
+-else.
+-define(NO_UNUSED, true).
+-endif.
+
+-ifndef(NO_UNUSED).
+-export([t_is_identifier/1]).
+-endif.
+
+-export_type([erl_type/0, opaques/0, type_table/0, var_table/0, cache/0]).
+
+%%-define(DEBUG, true).
+
+-ifdef(DEBUG).
+-define(debug(__A), __A).
+-else.
+-define(debug(__A), ok).
+-endif.
+
+%%=============================================================================
+%%
+%% Definition of the type structure
+%%
+%%=============================================================================
+
+%%-----------------------------------------------------------------------------
+%% Limits
+%%
+
+-define(REC_TYPE_LIMIT, 2).
+-define(EXPAND_DEPTH, 16).
+-define(EXPAND_LIMIT, 10000).
+
+-define(TUPLE_TAG_LIMIT, 5).
+-define(TUPLE_ARITY_LIMIT, 8).
+-define(SET_LIMIT, 13).
+-define(MAX_BYTE, 255).
+-define(MAX_CHAR, 16#10ffff).
+
+-define(UNIT_MULTIPLIER, 8).
+
+-define(TAG_IMMED1_SIZE, 4).
+-define(BITS, (erlang:system_info(wordsize) * 8) - ?TAG_IMMED1_SIZE).
+
+-define(MAX_TUPLE_SIZE, (1 bsl 10)).
+
+%%-----------------------------------------------------------------------------
+%% Type tags and qualifiers
+%%
+
+-define(atom_tag, atom).
+-define(binary_tag, binary).
+-define(function_tag, function).
+-define(identifier_tag, identifier).
+-define(list_tag, list).
+-define(map_tag, map).
+-define(matchstate_tag, matchstate).
+-define(nil_tag, nil).
+-define(number_tag, number).
+-define(opaque_tag, opaque).
+-define(product_tag, product).
+-define(tuple_set_tag, tuple_set).
+-define(tuple_tag, tuple).
+-define(union_tag, union).
+-define(var_tag, var).
+
+-type tag() :: ?atom_tag | ?binary_tag | ?function_tag | ?identifier_tag
+ | ?list_tag | ?map_tag | ?matchstate_tag | ?nil_tag | ?number_tag
+ | ?opaque_tag | ?product_tag
+ | ?tuple_tag | ?tuple_set_tag | ?union_tag | ?var_tag.
+
+-define(float_qual, float).
+-define(integer_qual, integer).
+-define(nonempty_qual, nonempty).
+-define(pid_qual, pid).
+-define(port_qual, port).
+-define(reference_qual, reference).
+-define(unknown_qual, unknown).
+
+-type qual() :: ?float_qual | ?integer_qual | ?nonempty_qual | ?pid_qual
+ | ?port_qual | ?reference_qual | ?unknown_qual | {_, _}.
+
+%%-----------------------------------------------------------------------------
+%% The type representation
+%%
+
+-define(any, any).
+-define(none, none).
+-define(unit, unit).
+%% Generic constructor - elements can be many things depending on the tag.
+-record(c, {tag :: tag(),
+ elements = [] :: term(),
+ qualifier = ?unknown_qual :: qual()}).
+
+-opaque erl_type() :: ?any | ?none | ?unit | #c{}.
+
+%%-----------------------------------------------------------------------------
+%% Auxiliary types and convenient macros
+%%
+
+-type parse_form() :: erl_parse:abstract_type().
+-type rng_elem() :: 'pos_inf' | 'neg_inf' | integer().
+
+-record(int_set, {set :: [integer()]}).
+-record(int_rng, {from :: rng_elem(), to :: rng_elem()}).
+%% Note: the definition of #opaque{} was changed to 'mod' and 'name';
+%% it used to be an ordsets of {Mod, Name} pairs. The Dialyzer version
+%% was updated to 2.7 due to this change.
+-record(opaque, {mod :: module(), name :: atom(),
+ args = [] :: [erl_type()], struct :: erl_type()}).
+
+-define(atom(Set), #c{tag=?atom_tag, elements=Set}).
+-define(bitstr(Unit, Base), #c{tag=?binary_tag, elements=[Unit,Base]}).
+-define(float, ?number(?any, ?float_qual)).
+-define(function(Domain, Range), #c{tag=?function_tag,
+ elements=[Domain, Range]}).
+-define(identifier(Types), #c{tag=?identifier_tag, elements=Types}).
+-define(integer(Types), ?number(Types, ?integer_qual)).
+-define(int_range(From, To), ?integer(#int_rng{from=From, to=To})).
+-define(int_set(Set), ?integer(#int_set{set=Set})).
+-define(list(Types, Term, Size), #c{tag=?list_tag, elements=[Types,Term],
+ qualifier=Size}).
+-define(nil, #c{tag=?nil_tag}).
+-define(nonempty_list(Types, Term),?list(Types, Term, ?nonempty_qual)).
+-define(number(Set, Qualifier), #c{tag=?number_tag, elements=Set,
+ qualifier=Qualifier}).
+-define(map(Pairs,DefKey,DefVal),
+ #c{tag=?map_tag, elements={Pairs,DefKey,DefVal}}).
+-define(opaque(Optypes), #c{tag=?opaque_tag, elements=Optypes}).
+-define(product(Types), #c{tag=?product_tag, elements=Types}).
+-define(tuple(Types, Arity, Qual), #c{tag=?tuple_tag, elements=Types,
+ qualifier={Arity, Qual}}).
+-define(tuple_set(Tuples), #c{tag=?tuple_set_tag, elements=Tuples}).
+-define(var(Id), #c{tag=?var_tag, elements=Id}).
+
+-define(matchstate(P, Slots), #c{tag=?matchstate_tag, elements=[P,Slots]}).
+-define(any_matchstate, ?matchstate(t_bitstr(), ?any)).
+
+-define(byte, ?int_range(0, ?MAX_BYTE)).
+-define(char, ?int_range(0, ?MAX_CHAR)).
+-define(integer_pos, ?int_range(1, pos_inf)).
+-define(integer_non_neg, ?int_range(0, pos_inf)).
+-define(integer_neg, ?int_range(neg_inf, -1)).
+
+-type opaques() :: [erl_type()] | 'universe'.
+
+-type record_key() :: {'record', atom()}.
+-type type_key() :: {'type' | 'opaque', mfa()}.
+-type record_value() :: [{atom(), erl_parse:abstract_expr(), erl_type()}].
+-type type_value() :: {{module(), {file:name(), erl_anno:line()},
+ erl_parse:abstract_type(), ArgNames :: [atom()]},
+ erl_type()}.
+-type type_table() :: dict:dict(record_key() | type_key(),
+ record_value() | type_value()).
+
+-opaque var_table() :: #{atom() => erl_type()}.
+
+%%-----------------------------------------------------------------------------
+%% Unions
+%%
+
+-define(union(List), #c{tag=?union_tag, elements=[_,_,_,_,_,_,_,_,_,_]=List}).
+
+-define(atom_union(T), ?union([T,?none,?none,?none,?none,?none,?none,?none,?none,?none])).
+-define(bitstr_union(T), ?union([?none,T,?none,?none,?none,?none,?none,?none,?none,?none])).
+-define(function_union(T), ?union([?none,?none,T,?none,?none,?none,?none,?none,?none,?none])).
+-define(identifier_union(T), ?union([?none,?none,?none,T,?none,?none,?none,?none,?none,?none])).
+-define(list_union(T), ?union([?none,?none,?none,?none,T,?none,?none,?none,?none,?none])).
+-define(number_union(T), ?union([?none,?none,?none,?none,?none,T,?none,?none,?none,?none])).
+-define(tuple_union(T), ?union([?none,?none,?none,?none,?none,?none,T,?none,?none,?none])).
+-define(matchstate_union(T), ?union([?none,?none,?none,?none,?none,?none,?none,T,?none,?none])).
+-define(opaque_union(T), ?union([?none,?none,?none,?none,?none,?none,?none,?none,T,?none])).
+-define(map_union(T), ?union([?none,?none,?none,?none,?none,?none,?none,?none,?none,T])).
+-define(integer_union(T), ?number_union(T)).
+-define(float_union(T), ?number_union(T)).
+-define(nil_union(T), ?list_union(T)).
+
+
+%%=============================================================================
+%%
+%% Primitive operations such as type construction and type tests
+%%
+%%=============================================================================
+
+%%-----------------------------------------------------------------------------
+%% Top and bottom
+%%
+
+-spec t_any() -> erl_type().
+
+t_any() ->
+ ?any.
+
+-spec t_is_any(erl_type()) -> boolean().
+
+t_is_any(Type) ->
+ do_opaque(Type, 'universe', fun is_any/1).
+
+is_any(?any) -> true;
+is_any(_) -> false.
+
+-spec t_none() -> erl_type().
+
+t_none() ->
+ ?none.
+
+-spec t_is_none(erl_type()) -> boolean().
+
+t_is_none(?none) -> true;
+t_is_none(_) -> false.
+
+%%-----------------------------------------------------------------------------
+%% Opaque types
+%%
+
+-spec t_opaque(module(), atom(), [_], erl_type()) -> erl_type().
+
+t_opaque(Mod, Name, Args, Struct) ->
+ O = #opaque{mod = Mod, name = Name, args = Args, struct = Struct},
+ ?opaque(set_singleton(O)).
+
+-spec t_is_opaque(erl_type(), [erl_type()]) -> boolean().
+
+t_is_opaque(?opaque(_) = Type, Opaques) ->
+ not is_opaque_type(Type, Opaques);
+t_is_opaque(_Type, _Opaques) -> false.
+
+-spec t_is_opaque(erl_type()) -> boolean().
+
+t_is_opaque(?opaque(_)) -> true;
+t_is_opaque(_) -> false.
+
+-spec t_has_opaque_subtype(erl_type(), opaques()) -> boolean().
+
+t_has_opaque_subtype(Type, Opaques) ->
+ do_opaque(Type, Opaques, fun has_opaque_subtype/1).
+
+has_opaque_subtype(?union(Ts)) ->
+ lists:any(fun t_is_opaque/1, Ts);
+has_opaque_subtype(T) ->
+ t_is_opaque(T).
+
+-spec t_opaque_structure(erl_type()) -> erl_type().
+
+t_opaque_structure(?opaque(Elements)) ->
+ t_sup([Struct || #opaque{struct = Struct} <- ordsets:to_list(Elements)]).
+
+-spec t_contains_opaque(erl_type()) -> boolean().
+
+t_contains_opaque(Type) ->
+ t_contains_opaque(Type, []).
+
+%% Returns 'true' iff there is an opaque type that is *not* one of
+%% the types of the second argument.
+
+-spec t_contains_opaque(erl_type(), [erl_type()]) -> boolean().
+
+t_contains_opaque(?any, _Opaques) -> false;
+t_contains_opaque(?none, _Opaques) -> false;
+t_contains_opaque(?unit, _Opaques) -> false;
+t_contains_opaque(?atom(_Set), _Opaques) -> false;
+t_contains_opaque(?bitstr(_Unit, _Base), _Opaques) -> false;
+t_contains_opaque(?float, _Opaques) -> false;
+t_contains_opaque(?function(Domain, Range), Opaques) ->
+ t_contains_opaque(Domain, Opaques)
+ orelse t_contains_opaque(Range, Opaques);
+t_contains_opaque(?identifier(_Types), _Opaques) -> false;
+t_contains_opaque(?integer(_Types), _Opaques) -> false;
+t_contains_opaque(?int_range(_From, _To), _Opaques) -> false;
+t_contains_opaque(?int_set(_Set), _Opaques) -> false;
+t_contains_opaque(?list(Type, Tail, _), Opaques) ->
+ t_contains_opaque(Type, Opaques) orelse t_contains_opaque(Tail, Opaques);
+t_contains_opaque(?map(_, _, _) = Map, Opaques) ->
+ list_contains_opaque(map_all_types(Map), Opaques);
+t_contains_opaque(?matchstate(_P, _Slots), _Opaques) -> false;
+t_contains_opaque(?nil, _Opaques) -> false;
+t_contains_opaque(?number(_Set, _Tag), _Opaques) -> false;
+t_contains_opaque(?opaque(_)=T, Opaques) ->
+ not is_opaque_type(T, Opaques)
+ orelse t_contains_opaque(t_opaque_structure(T));
+t_contains_opaque(?product(Types), Opaques) ->
+ list_contains_opaque(Types, Opaques);
+t_contains_opaque(?tuple(?any, _, _), _Opaques) -> false;
+t_contains_opaque(?tuple(Types, _, _), Opaques) ->
+ list_contains_opaque(Types, Opaques);
+t_contains_opaque(?tuple_set(_Set) = T, Opaques) ->
+ list_contains_opaque(t_tuple_subtypes(T), Opaques);
+t_contains_opaque(?union(List), Opaques) ->
+ list_contains_opaque(List, Opaques);
+t_contains_opaque(?var(_Id), _Opaques) -> false.
+
+-spec list_contains_opaque([erl_type()], [erl_type()]) -> boolean().
+
+list_contains_opaque(List, Opaques) ->
+ lists:any(fun(E) -> t_contains_opaque(E, Opaques) end, List).
+
+%% t_find_opaque_mismatch/2 of two types should only be used if their
+%% t_inf is t_none() due to some opaque type violation.
+%%
+%% The first argument of the function is the pattern and its second
+%% argument the type we are matching against the pattern.
+
+-spec t_find_opaque_mismatch(erl_type(), erl_type(), [erl_type()]) ->
+ 'error' | {'ok', erl_type(), erl_type()}.
+
+t_find_opaque_mismatch(T1, T2, Opaques) ->
+ t_find_opaque_mismatch(T1, T2, T2, Opaques).
+
+t_find_opaque_mismatch(?any, _Type, _TopType, _Opaques) -> error;
+t_find_opaque_mismatch(?none, _Type, _TopType, _Opaques) -> error;
+t_find_opaque_mismatch(?list(T1, Tl1, _), ?list(T2, Tl2, _), TopType, Opaques) ->
+ t_find_opaque_mismatch_ordlists([T1, Tl1], [T2, Tl2], TopType, Opaques);
+t_find_opaque_mismatch(T1, ?opaque(_) = T2, TopType, Opaques) ->
+ case is_opaque_type(T2, Opaques) of
+ false -> {ok, TopType, T2};
+ true ->
+ t_find_opaque_mismatch(T1, t_opaque_structure(T2), TopType, Opaques)
+ end;
+t_find_opaque_mismatch(?opaque(_) = T1, T2, TopType, Opaques) ->
+ %% The generated message is somewhat misleading:
+ case is_opaque_type(T1, Opaques) of
+ false -> {ok, TopType, T1};
+ true ->
+ t_find_opaque_mismatch(t_opaque_structure(T1), T2, TopType, Opaques)
+ end;
+t_find_opaque_mismatch(?product(T1), ?product(T2), TopType, Opaques) ->
+ t_find_opaque_mismatch_ordlists(T1, T2, TopType, Opaques);
+t_find_opaque_mismatch(?tuple(T1, Arity, _), ?tuple(T2, Arity, _),
+ TopType, Opaques) ->
+ t_find_opaque_mismatch_ordlists(T1, T2, TopType, Opaques);
+t_find_opaque_mismatch(?tuple(_, _, _) = T1, ?tuple_set(_) = T2,
+ TopType, Opaques) ->
+ Tuples1 = t_tuple_subtypes(T1),
+ Tuples2 = t_tuple_subtypes(T2),
+ t_find_opaque_mismatch_lists(Tuples1, Tuples2, TopType, Opaques);
+t_find_opaque_mismatch(T1, ?union(U2), TopType, Opaques) ->
+ t_find_opaque_mismatch_lists([T1], U2, TopType, Opaques);
+t_find_opaque_mismatch(_T1, _T2, _TopType, _Opaques) -> error.
+
+t_find_opaque_mismatch_ordlists(L1, L2, TopType, Opaques) ->
+ List = lists:zipwith(fun(T1, T2) ->
+ t_find_opaque_mismatch(T1, T2, TopType, Opaques)
+ end, L1, L2),
+ t_find_opaque_mismatch_list(List).
+
+t_find_opaque_mismatch_lists(L1, L2, _TopType, Opaques) ->
+ List = [t_find_opaque_mismatch(T1, T2, T2, Opaques) || T1 <- L1, T2 <- L2],
+ t_find_opaque_mismatch_list(List).
+
+t_find_opaque_mismatch_list([]) -> error;
+t_find_opaque_mismatch_list([H|T]) ->
+ case H of
+ {ok, _T1, _T2} -> H;
+ error -> t_find_opaque_mismatch_list(T)
+ end.
+
+-spec t_find_unknown_opaque(erl_type(), erl_type(), opaques()) ->
+ [pos_integer()].
+
+%% The nice thing about using two types and t_inf() as compared to
+%% calling t_contains_opaque/2 is that the traversal stops when
+%% there is a mismatch which means that unknown opaque types "below"
+%% the mismatch are not found.
+t_find_unknown_opaque(_T1, _T2, 'universe') -> [];
+t_find_unknown_opaque(T1, T2, Opaques) ->
+ try t_inf(T1, T2, {match, Opaques}) of
+ _ -> []
+ catch throw:{pos, Ns} -> Ns
+ end.
+
+-spec t_decorate_with_opaque(erl_type(), erl_type(), [erl_type()]) -> erl_type().
+
+%% The first argument can contain opaque types. The second argument
+%% is assumed to be taken from the contract.
+
+t_decorate_with_opaque(T1, T2, Opaques) ->
+ case t_is_equal(T1, T2) orelse not t_contains_opaque(T2) of
+ true -> T1;
+ false ->
+ T = t_inf(T1, T2),
+ case t_contains_opaque(T) of
+ false -> T1;
+ true ->
+ R = decorate(T1, T, Opaques),
+ ?debug(case catch t_is_equal(t_unopaque(R), t_unopaque(T1)) of
+ true -> ok;
+ false ->
+ io:format("T1 = ~p,\n", [T1]),
+ io:format("T2 = ~p,\n", [T2]),
+ io:format("O = ~p,\n", [Opaques]),
+ io:format("erl_types:t_decorate_with_opaque(T1,T2,O).\n"),
+ throw({error, "Failed to handle opaque types"})
+ end),
+ R
+ end
+ end.
+
+decorate(Type, ?none, _Opaques) -> Type;
+decorate(?function(Domain, Range), ?function(D, R), Opaques) ->
+ ?function(decorate(Domain, D, Opaques), decorate(Range, R, Opaques));
+decorate(?list(Types, Tail, Size), ?list(Ts, Tl, _Sz), Opaques) ->
+ ?list(decorate(Types, Ts, Opaques), decorate(Tail, Tl, Opaques), Size);
+decorate(?product(Types), ?product(Ts), Opaques) ->
+ ?product(list_decorate(Types, Ts, Opaques));
+decorate(?tuple(_, _, _)=T, ?tuple(?any, _, _), _Opaques) -> T;
+decorate(?tuple(?any, _, _)=T, ?tuple(_, _, _), _Opaques) -> T;
+decorate(?tuple(Types, Arity, Tag), ?tuple(Ts, Arity, _), Opaques) ->
+ ?tuple(list_decorate(Types, Ts, Opaques), Arity, Tag);
+decorate(?tuple_set(List), ?tuple(_, Arity, _) = T, Opaques) ->
+ decorate_tuple_sets(List, [{Arity, [T]}], Opaques);
+decorate(?tuple_set(List), ?tuple_set(L), Opaques) ->
+ decorate_tuple_sets(List, L, Opaques);
+decorate(?union(List), T, Opaques) when T =/= ?any ->
+ ?union(L) = force_union(T),
+ union_decorate(List, L, Opaques);
+decorate(?opaque(_)=T, _, _Opaques) -> T;
+decorate(T, ?union(L), Opaques) when T =/= ?any ->
+ ?union(List) = force_union(T),
+ union_decorate(List, L, Opaques);
+decorate(Type, ?opaque(_)=T, Opaques) ->
+ decorate_with_opaque(Type, T, Opaques);
+decorate(Type, _T, _Opaques) -> Type.
+
+%% Note: it is important that #opaque.struct is a subtype of the
+%% opaque type.
+decorate_with_opaque(Type, ?opaque(Set2), Opaques) ->
+ case decoration(set_to_list(Set2), Type, Opaques, [], false) of
+ {[], false} -> Type;
+ {List, All} when List =/= [] ->
+ NewType = ?opaque(ordsets:from_list(List)),
+ case All of
+ true -> NewType;
+ false -> t_sup(NewType, Type)
+ end
+ end.
+
+decoration([#opaque{struct = S} = Opaque|OpaqueTypes], Type, Opaques,
+ NewOpaqueTypes0, All) ->
+ IsOpaque = is_opaque_type2(Opaque, Opaques),
+ I = t_inf(Type, S),
+ case not IsOpaque orelse t_is_none(I) of
+ true -> decoration(OpaqueTypes, Type, Opaques, NewOpaqueTypes0, All);
+ false ->
+ NewOpaque = Opaque#opaque{struct = decorate(I, S, Opaques)},
+ NewAll = All orelse t_is_equal(I, Type),
+ NewOpaqueTypes = [NewOpaque|NewOpaqueTypes0],
+ decoration(OpaqueTypes, Type, Opaques, NewOpaqueTypes, NewAll)
+ end;
+decoration([], _Type, _Opaques, NewOpaqueTypes, All) ->
+ {NewOpaqueTypes, All}.
+
+-spec list_decorate([erl_type()], [erl_type()], opaques()) -> [erl_type()].
+
+list_decorate(List, L, Opaques) ->
+ [decorate(Elem, E, Opaques) || {Elem, E} <- lists:zip(List, L)].
+
+union_decorate(U1, U2, Opaques) ->
+ Union = union_decorate(U1, U2, Opaques, 0, []),
+ [A,B,F,I,L,N,T,M,_,Map] = U1,
+ [_,_,_,_,_,_,_,_,Opaque,_] = U2,
+ List = [A,B,F,I,L,N,T,M,Map],
+ DecList = [Dec ||
+ E <- List,
+ not t_is_none(E),
+ not t_is_none(Dec = decorate(E, Opaque, Opaques))],
+ t_sup([Union|DecList]).
+
+union_decorate([?none|Left1], [_|Left2], Opaques, N, Acc) ->
+ union_decorate(Left1, Left2, Opaques, N, [?none|Acc]);
+union_decorate([T1|Left1], [?none|Left2], Opaques, N, Acc) ->
+ union_decorate(Left1, Left2, Opaques, N+1, [T1|Acc]);
+union_decorate([T1|Left1], [T2|Left2], Opaques, N, Acc) ->
+ union_decorate(Left1, Left2, Opaques, N+1, [decorate(T1, T2, Opaques)|Acc]);
+union_decorate([], [], _Opaques, N, Acc) ->
+ if N =:= 0 -> ?none;
+ N =:= 1 ->
+ [Type] = [T || T <- Acc, T =/= ?none],
+ Type;
+ N >= 2 -> ?union(lists:reverse(Acc))
+ end.
+
+decorate_tuple_sets(List, L, Opaques) ->
+ decorate_tuple_sets(List, L, Opaques, []).
+
+decorate_tuple_sets([{Arity, Tuples}|List], [{Arity, Ts}|L], Opaques, Acc) ->
+ DecTs = decorate_tuples_in_sets(Tuples, Ts, Opaques),
+ decorate_tuple_sets(List, L, Opaques, [{Arity, DecTs}|Acc]);
+decorate_tuple_sets([ArTup|List], L, Opaques, Acc) ->
+ decorate_tuple_sets(List, L, Opaques, [ArTup|Acc]);
+decorate_tuple_sets([], _L, _Opaques, Acc) ->
+ ?tuple_set(lists:reverse(Acc)).
+
+decorate_tuples_in_sets([?tuple(Elements, _, ?any)], Ts, Opaques) ->
+ NewList = [list_decorate(Elements, Es, Opaques) || ?tuple(Es, _, _) <- Ts],
+ case t_sup([t_tuple(Es) || Es <- NewList]) of
+ ?tuple_set([{_Arity, Tuples}]) -> Tuples;
+ ?tuple(_, _, _)=Tuple -> [Tuple]
+ end;
+decorate_tuples_in_sets(Tuples, Ts, Opaques) ->
+ decorate_tuples_in_sets(Tuples, Ts, Opaques, []).
+
+decorate_tuples_in_sets([?tuple(Elements, Arity, Tag1) = T1|Tuples] = L1,
+ [?tuple(Es, Arity, Tag2)|Ts] = L2, Opaques, Acc) ->
+ if
+ Tag1 < Tag2 -> decorate_tuples_in_sets(Tuples, L2, Opaques, [T1|Acc]);
+ Tag1 > Tag2 -> decorate_tuples_in_sets(L1, Ts, Opaques, Acc);
+ Tag1 =:= Tag2 ->
+ NewElements = list_decorate(Elements, Es, Opaques),
+ NewAcc = [?tuple(NewElements, Arity, Tag1)|Acc],
+ decorate_tuples_in_sets(Tuples, Ts, Opaques, NewAcc)
+ end;
+decorate_tuples_in_sets([T1|Tuples], L2, Opaques, Acc) ->
+ decorate_tuples_in_sets(Tuples, L2, Opaques, [T1|Acc]);
+decorate_tuples_in_sets([], _L, _Opaques, Acc) ->
+ lists:reverse(Acc).
+
+-spec t_opaque_from_records(type_table()) -> [erl_type()].
+
+t_opaque_from_records(RecDict) ->
+ OpaqueRecDict =
+ dict:filter(fun(Key, _Value) ->
+ case Key of
+ {opaque, _Name, _Arity} -> true;
+ _ -> false
+ end
+ end, RecDict),
+ OpaqueTypeDict =
+ dict:map(fun({opaque, Name, _Arity},
+ {{Module, _FileLine, _Form, ArgNames}, _Type}) ->
+ %% Args = args_to_types(ArgNames),
+ %% List = lists:zip(ArgNames, Args),
+ %% TmpVarTab = maps:to_list(List),
+ %% Rep = t_from_form(Type, RecDict, TmpVarTab),
+ Rep = t_any(), % not used for anything right now
+ Args = [t_any() || _ <- ArgNames],
+ t_opaque(Module, Name, Args, Rep)
+ end, OpaqueRecDict),
+ [OpaqueType || {_Key, OpaqueType} <- dict:to_list(OpaqueTypeDict)].
+
+%% Decompose opaque instances of type arg2 to structured types, in arg1
+%% XXX: Same as t_unopaque
+-spec t_struct_from_opaque(erl_type(), [erl_type()]) -> erl_type().
+
+t_struct_from_opaque(?function(Domain, Range), Opaques) ->
+ ?function(t_struct_from_opaque(Domain, Opaques),
+ t_struct_from_opaque(Range, Opaques));
+t_struct_from_opaque(?list(Types, Term, Size), Opaques) ->
+ ?list(t_struct_from_opaque(Types, Opaques),
+ t_struct_from_opaque(Term, Opaques), Size);
+t_struct_from_opaque(?opaque(_) = T, Opaques) ->
+ case is_opaque_type(T, Opaques) of
+ true -> t_opaque_structure(T);
+ false -> T
+ end;
+t_struct_from_opaque(?product(Types), Opaques) ->
+ ?product(list_struct_from_opaque(Types, Opaques));
+t_struct_from_opaque(?tuple(?any, _, _) = T, _Opaques) -> T;
+t_struct_from_opaque(?tuple(Types, Arity, Tag), Opaques) ->
+ ?tuple(list_struct_from_opaque(Types, Opaques), Arity, Tag);
+t_struct_from_opaque(?tuple_set(Set), Opaques) ->
+ NewSet = [{Sz, [t_struct_from_opaque(T, Opaques) || T <- Tuples]}
+ || {Sz, Tuples} <- Set],
+ ?tuple_set(NewSet);
+t_struct_from_opaque(?union(List), Opaques) ->
+ t_sup(list_struct_from_opaque(List, Opaques));
+t_struct_from_opaque(Type, _Opaques) -> Type.
+
+list_struct_from_opaque(Types, Opaques) ->
+ [t_struct_from_opaque(Type, Opaques) || Type <- Types].
+
+%%-----------------------------------------------------------------------------
+
+-type mod_records() :: dict:dict(module(), type_table()).
+
+%%-----------------------------------------------------------------------------
+%% Unit type. Signals non termination.
+%%
+
+-spec t_unit() -> erl_type().
+
+t_unit() ->
+ ?unit.
+
+-spec t_is_unit(erl_type()) -> boolean().
+
+t_is_unit(?unit) -> true;
+t_is_unit(_) -> false.
+
+-spec t_is_none_or_unit(erl_type()) -> boolean().
+
+t_is_none_or_unit(?none) -> true;
+t_is_none_or_unit(?unit) -> true;
+t_is_none_or_unit(_) -> false.
+
+%%-----------------------------------------------------------------------------
+%% Atoms and the derived type boolean
+%%
+
+-spec t_atom() -> erl_type().
+
+t_atom() ->
+ ?atom(?any).
+
+-spec t_atom(atom()) -> erl_type().
+
+t_atom(A) when is_atom(A) ->
+ ?atom(set_singleton(A)).
+
+-spec t_atoms([atom()]) -> erl_type().
+
+t_atoms(List) when is_list(List) ->
+ t_sup([t_atom(A) || A <- List]).
+
+-spec t_atom_vals(erl_type()) -> 'unknown' | [atom(),...].
+
+t_atom_vals(Type) ->
+ t_atom_vals(Type, 'universe').
+
+-spec t_atom_vals(erl_type(), opaques()) -> 'unknown' | [atom(),...].
+
+t_atom_vals(Type, Opaques) ->
+ do_opaque(Type, Opaques, fun atom_vals/1).
+
+atom_vals(?atom(?any)) -> unknown;
+atom_vals(?atom(Set)) -> set_to_list(Set);
+atom_vals(?opaque(_)) -> unknown;
+atom_vals(Other) ->
+ ?atom(_) = Atm = t_inf(t_atom(), Other),
+ atom_vals(Atm).
+
+-spec t_is_atom(erl_type()) -> boolean().
+
+t_is_atom(Type) ->
+ t_is_atom(Type, 'universe').
+
+-spec t_is_atom(erl_type(), opaques()) -> boolean().
+
+t_is_atom(Type, Opaques) ->
+ do_opaque(Type, Opaques, fun is_atom1/1).
+
+is_atom1(?atom(_)) -> true;
+is_atom1(_) -> false.
+
+-spec t_is_any_atom(atom(), erl_type()) -> boolean().
+
+t_is_any_atom(Atom, SomeAtomsType) ->
+ t_is_any_atom(Atom, SomeAtomsType, 'universe').
+
+-spec t_is_any_atom(atom(), erl_type(), opaques()) -> boolean().
+
+t_is_any_atom(Atom, SomeAtomsType, Opaques) ->
+ do_opaque(SomeAtomsType, Opaques,
+ fun(AtomsType) -> is_any_atom(Atom, AtomsType) end).
+
+is_any_atom(Atom, ?atom(?any)) when is_atom(Atom) -> false;
+is_any_atom(Atom, ?atom(Set)) when is_atom(Atom) ->
+ set_is_singleton(Atom, Set);
+is_any_atom(Atom, _) when is_atom(Atom) -> false.
+
+%%------------------------------------
+
+-spec t_is_boolean(erl_type()) -> boolean().
+
+t_is_boolean(Type) ->
+ t_is_boolean(Type, 'universe').
+
+-spec t_is_boolean(erl_type(), opaques()) -> boolean().
+
+t_is_boolean(Type, Opaques) ->
+ do_opaque(Type, Opaques, fun is_boolean/1).
+
+-spec t_boolean() -> erl_type().
+
+t_boolean() ->
+ ?atom(set_from_list([false, true])).
+
+is_boolean(?atom(?any)) -> false;
+is_boolean(?atom(Set)) ->
+ case set_size(Set) of
+ 1 -> set_is_element(true, Set) orelse set_is_element(false, Set);
+ 2 -> set_is_element(true, Set) andalso set_is_element(false, Set);
+ N when is_integer(N), N > 2 -> false
+ end;
+is_boolean(_) -> false.
+
+%%-----------------------------------------------------------------------------
+%% Binaries
+%%
+
+-spec t_binary() -> erl_type().
+
+t_binary() ->
+ ?bitstr(8, 0).
+
+-spec t_is_binary(erl_type()) -> boolean().
+
+t_is_binary(Type) ->
+ t_is_binary(Type, 'universe').
+
+-spec t_is_binary(erl_type(), opaques()) -> boolean().
+
+t_is_binary(Type, Opaques) ->
+ do_opaque(Type, Opaques, fun is_binary/1).
+
+is_binary(?bitstr(U, B)) ->
+ ((U rem 8) =:= 0) andalso ((B rem 8) =:= 0);
+is_binary(_) -> false.
+
+%%-----------------------------------------------------------------------------
+%% Bitstrings
+%%
+
+-spec t_bitstr() -> erl_type().
+
+t_bitstr() ->
+ ?bitstr(1, 0).
+
+-spec t_bitstr(non_neg_integer(), non_neg_integer()) -> erl_type().
+
+t_bitstr(U, B) ->
+ NewB =
+ if
+ U =:= 0 -> B;
+ B >= (U * (?UNIT_MULTIPLIER + 1)) ->
+ (B rem U) + U * ?UNIT_MULTIPLIER;
+ true ->
+ B
+ end,
+ ?bitstr(U, NewB).
+
+-spec t_bitstr_unit(erl_type()) -> non_neg_integer().
+
+t_bitstr_unit(?bitstr(U, _)) -> U.
+
+-spec t_bitstr_base(erl_type()) -> non_neg_integer().
+
+t_bitstr_base(?bitstr(_, B)) -> B.
+
+-spec t_bitstr_concat([erl_type()]) -> erl_type().
+
+t_bitstr_concat(List) ->
+ t_bitstr_concat_1(List, t_bitstr(0, 0)).
+
+t_bitstr_concat_1([T|Left], Acc) ->
+ t_bitstr_concat_1(Left, t_bitstr_concat(Acc, T));
+t_bitstr_concat_1([], Acc) ->
+ Acc.
+
+-spec t_bitstr_concat(erl_type(), erl_type()) -> erl_type().
+
+t_bitstr_concat(T1, T2) ->
+ T1p = t_inf(t_bitstr(), T1),
+ T2p = t_inf(t_bitstr(), T2),
+ bitstr_concat(t_unopaque(T1p), t_unopaque(T2p)).
+
+-spec t_bitstr_match(erl_type(), erl_type()) -> erl_type().
+
+t_bitstr_match(T1, T2) ->
+ T1p = t_inf(t_bitstr(), T1),
+ T2p = t_inf(t_bitstr(), T2),
+ bitstr_match(t_unopaque(T1p), t_unopaque(T2p)).
+
+-spec t_is_bitstr(erl_type()) -> boolean().
+
+t_is_bitstr(Type) ->
+ t_is_bitstr(Type, 'universe').
+
+-spec t_is_bitstr(erl_type(), opaques()) -> boolean().
+
+t_is_bitstr(Type, Opaques) ->
+ do_opaque(Type, Opaques, fun is_bitstr/1).
+
+is_bitstr(?bitstr(_, _)) -> true;
+is_bitstr(_) -> false.
+
+%%-----------------------------------------------------------------------------
+%% Matchstates
+%%
+
+-spec t_matchstate() -> erl_type().
+
+t_matchstate() ->
+ ?any_matchstate.
+
+-spec t_matchstate(erl_type(), non_neg_integer()) -> erl_type().
+
+t_matchstate(Init, 0) ->
+ ?matchstate(Init, Init);
+t_matchstate(Init, Max) when is_integer(Max) ->
+ Slots = [Init|[?none || _ <- lists:seq(1, Max)]],
+ ?matchstate(Init, t_product(Slots)).
+
+-spec t_is_matchstate(erl_type()) -> boolean().
+
+t_is_matchstate(?matchstate(_, _)) -> true;
+t_is_matchstate(_) -> false.
+
+-spec t_matchstate_present(erl_type()) -> erl_type().
+
+t_matchstate_present(Type) ->
+ case t_inf(t_matchstate(), Type) of
+ ?matchstate(P, _) -> P;
+ _ -> ?none
+ end.
+
+-spec t_matchstate_slot(erl_type(), non_neg_integer()) -> erl_type().
+
+t_matchstate_slot(Type, Slot) ->
+ RealSlot = Slot + 1,
+ case t_inf(t_matchstate(), Type) of
+ ?matchstate(_, ?any) -> ?any;
+ ?matchstate(_, ?product(Vals)) when length(Vals) >= RealSlot ->
+ lists:nth(RealSlot, Vals);
+ ?matchstate(_, ?product(_)) ->
+ ?none;
+ ?matchstate(_, SlotType) when RealSlot =:= 1 ->
+ SlotType;
+ _ ->
+ ?none
+ end.
+
+-spec t_matchstate_slots(erl_type()) -> erl_type().
+
+t_matchstate_slots(?matchstate(_, Slots)) ->
+ Slots.
+
+-spec t_matchstate_update_present(erl_type(), erl_type()) -> erl_type().
+
+t_matchstate_update_present(New, Type) ->
+ case t_inf(t_matchstate(), Type) of
+ ?matchstate(_, Slots) ->
+ ?matchstate(New, Slots);
+ _ -> ?none
+ end.
+
+-spec t_matchstate_update_slot(erl_type(), erl_type(), non_neg_integer()) -> erl_type().
+
+t_matchstate_update_slot(New, Type, Slot) ->
+ RealSlot = Slot + 1,
+ case t_inf(t_matchstate(), Type) of
+ ?matchstate(Pres, Slots) ->
+ NewSlots =
+ case Slots of
+ ?any ->
+ ?any;
+ ?product(Vals) when length(Vals) >= RealSlot ->
+ NewTuple = setelement(RealSlot, list_to_tuple(Vals), New),
+ NewVals = tuple_to_list(NewTuple),
+ ?product(NewVals);
+ ?product(_) ->
+ ?none;
+ _ when RealSlot =:= 1 ->
+ New;
+ _ ->
+ ?none
+ end,
+ ?matchstate(Pres, NewSlots);
+ _ ->
+ ?none
+ end.
+
+%%-----------------------------------------------------------------------------
+%% Functions
+%%
+
+-spec t_fun() -> erl_type().
+
+t_fun() ->
+ ?function(?any, ?any).
+
+-spec t_fun(erl_type()) -> erl_type().
+
+t_fun(Range) ->
+ ?function(?any, Range).
+
+-spec t_fun([erl_type()] | arity(), erl_type()) -> erl_type().
+
+t_fun(Domain, Range) when is_list(Domain) ->
+ ?function(?product(Domain), Range);
+t_fun(Arity, Range) when is_integer(Arity), 0 =< Arity, Arity =< 255 ->
+ ?function(?product(lists:duplicate(Arity, ?any)), Range).
+
+-spec t_fun_args(erl_type()) -> 'unknown' | [erl_type()].
+
+t_fun_args(Type) ->
+ t_fun_args(Type, 'universe').
+
+-spec t_fun_args(erl_type(), opaques()) -> 'unknown' | [erl_type()].
+
+t_fun_args(Type, Opaques) ->
+ do_opaque(Type, Opaques, fun fun_args/1).
+
+fun_args(?function(?any, _)) ->
+ unknown;
+fun_args(?function(?product(Domain), _)) when is_list(Domain) ->
+ Domain.
+
+-spec t_fun_arity(erl_type()) -> 'unknown' | non_neg_integer().
+
+t_fun_arity(Type) ->
+ t_fun_arity(Type, 'universe').
+
+-spec t_fun_arity(erl_type(), opaques()) -> 'unknown' | non_neg_integer().
+
+t_fun_arity(Type, Opaques) ->
+ do_opaque(Type, Opaques, fun fun_arity/1).
+
+fun_arity(?function(?any, _)) ->
+ unknown;
+fun_arity(?function(?product(Domain), _)) ->
+ length(Domain).
+
+-spec t_fun_range(erl_type()) -> erl_type().
+
+t_fun_range(Type) ->
+ t_fun_range(Type, 'universe').
+
+-spec t_fun_range(erl_type(), opaques()) -> erl_type().
+
+t_fun_range(Type, Opaques) ->
+ do_opaque(Type, Opaques, fun fun_range/1).
+
+fun_range(?function(_, Range)) ->
+ Range.
+
+-spec t_is_fun(erl_type()) -> boolean().
+
+t_is_fun(Type) ->
+ t_is_fun(Type, 'universe').
+
+-spec t_is_fun(erl_type(), opaques()) -> boolean().
+
+t_is_fun(Type, Opaques) ->
+ do_opaque(Type, Opaques, fun is_fun/1).
+
+is_fun(?function(_, _)) -> true;
+is_fun(_) -> false.
+
+%%-----------------------------------------------------------------------------
+%% Identifiers. Includes ports, pids and refs.
+%%
+
+-spec t_identifier() -> erl_type().
+
+t_identifier() ->
+ ?identifier(?any).
+
+-ifdef(DO_ERL_TYPES_TEST).
+-spec t_is_identifier(erl_type()) -> erl_type().
+
+t_is_identifier(?identifier(_)) -> true;
+t_is_identifier(_) -> false.
+-endif.
+
+%%------------------------------------
+
+-spec t_port() -> erl_type().
+
+t_port() ->
+ ?identifier(set_singleton(?port_qual)).
+
+-spec t_is_port(erl_type()) -> boolean().
+
+t_is_port(Type) ->
+ t_is_port(Type, 'universe').
+
+-spec t_is_port(erl_type(), opaques()) -> boolean().
+
+t_is_port(Type, Opaques) ->
+ do_opaque(Type, Opaques, fun is_port1/1).
+
+is_port1(?identifier(?any)) -> false;
+is_port1(?identifier(Set)) -> set_is_singleton(?port_qual, Set);
+is_port1(_) -> false.
+
+%%------------------------------------
+
+-spec t_pid() -> erl_type().
+
+t_pid() ->
+ ?identifier(set_singleton(?pid_qual)).
+
+-spec t_is_pid(erl_type()) -> boolean().
+
+t_is_pid(Type) ->
+ t_is_pid(Type, 'universe').
+
+-spec t_is_pid(erl_type(), opaques()) -> boolean().
+
+t_is_pid(Type, Opaques) ->
+ do_opaque(Type, Opaques, fun is_pid1/1).
+
+is_pid1(?identifier(?any)) -> false;
+is_pid1(?identifier(Set)) -> set_is_singleton(?pid_qual, Set);
+is_pid1(_) -> false.
+
+%%------------------------------------
+
+-spec t_reference() -> erl_type().
+
+t_reference() ->
+ ?identifier(set_singleton(?reference_qual)).
+
+-spec t_is_reference(erl_type()) -> boolean().
+
+t_is_reference(Type) ->
+ t_is_reference(Type, 'universe').
+
+-spec t_is_reference(erl_type(), opaques()) -> boolean().
+
+t_is_reference(Type, Opaques) ->
+ do_opaque(Type, Opaques, fun is_reference1/1).
+
+is_reference1(?identifier(?any)) -> false;
+is_reference1(?identifier(Set)) -> set_is_singleton(?reference_qual, Set);
+is_reference1(_) -> false.
+
+%%-----------------------------------------------------------------------------
+%% Numbers are divided into floats, integers, chars and bytes.
+%%
+
+-spec t_number() -> erl_type().
+
+t_number() ->
+ ?number(?any, ?unknown_qual).
+
+-spec t_number(integer()) -> erl_type().
+
+t_number(X) when is_integer(X) ->
+ t_integer(X).
+
+-spec t_is_number(erl_type()) -> boolean().
+
+t_is_number(Type) ->
+ t_is_number(Type, 'universe').
+
+-spec t_is_number(erl_type(), opaques()) -> boolean().
+
+t_is_number(Type, Opaques) ->
+ do_opaque(Type, Opaques, fun is_number/1).
+
+is_number(?number(_, _)) -> true;
+is_number(_) -> false.
+
+%% Currently, the type system collapses all floats to ?float and does
+%% not keep any information about their values. As a result, the list
+%% that this function returns contains only integers.
+
+-spec t_number_vals(erl_type()) -> 'unknown' | [integer(),...].
+
+t_number_vals(Type) ->
+ t_number_vals(Type, 'universe').
+
+-spec t_number_vals(erl_type(), opaques()) -> 'unknown' | [integer(),...].
+
+t_number_vals(Type, Opaques) ->
+ do_opaque(Type, Opaques, fun number_vals/1).
+
+number_vals(?int_set(Set)) -> set_to_list(Set);
+number_vals(?number(_, _)) -> unknown;
+number_vals(?opaque(_)) -> unknown;
+number_vals(Other) ->
+ Inf = t_inf(Other, t_number()),
+ false = t_is_none(Inf), % sanity check
+ number_vals(Inf).
+
+%%------------------------------------
+
+-spec t_float() -> erl_type().
+
+t_float() ->
+ ?float.
+
+-spec t_is_float(erl_type()) -> boolean().
+
+t_is_float(Type) ->
+ t_is_float(Type, 'universe').
+
+-spec t_is_float(erl_type(), opaques()) -> boolean().
+
+t_is_float(Type, Opaques) ->
+ do_opaque(Type, Opaques, fun is_float1/1).
+
+is_float1(?float) -> true;
+is_float1(_) -> false.
+
+%%------------------------------------
+
+-spec t_integer() -> erl_type().
+
+t_integer() ->
+ ?integer(?any).
+
+-spec t_integer(integer()) -> erl_type().
+
+t_integer(I) when is_integer(I) ->
+ ?int_set(set_singleton(I)).
+
+-spec t_integers([integer()]) -> erl_type().
+
+t_integers(List) when is_list(List) ->
+ t_sup([t_integer(I) || I <- List]).
+
+-spec t_is_integer(erl_type()) -> boolean().
+
+t_is_integer(Type) ->
+ t_is_integer(Type, 'universe').
+
+-spec t_is_integer(erl_type(), opaques()) -> boolean().
+
+t_is_integer(Type, Opaques) ->
+ do_opaque(Type, Opaques, fun is_integer1/1).
+
+is_integer1(?integer(_)) -> true;
+is_integer1(_) -> false.
+
+%%------------------------------------
+
+-spec t_byte() -> erl_type().
+
+t_byte() ->
+ ?byte.
+
+-ifdef(DO_ERL_TYPES_TEST).
+-spec t_is_byte(erl_type()) -> boolean().
+
+t_is_byte(?int_range(neg_inf, _)) -> false;
+t_is_byte(?int_range(_, pos_inf)) -> false;
+t_is_byte(?int_range(From, To))
+ when is_integer(From), From >= 0, is_integer(To), To =< ?MAX_BYTE -> true;
+t_is_byte(?int_set(Set)) ->
+ (set_min(Set) >= 0) andalso (set_max(Set) =< ?MAX_BYTE);
+t_is_byte(_) -> false.
+-endif.
+
+%%------------------------------------
+
+-spec t_char() -> erl_type().
+
+t_char() ->
+ ?char.
+
+-spec t_is_char(erl_type()) -> boolean().
+
+t_is_char(?int_range(neg_inf, _)) -> false;
+t_is_char(?int_range(_, pos_inf)) -> false;
+t_is_char(?int_range(From, To))
+ when is_integer(From), From >= 0, is_integer(To), To =< ?MAX_CHAR -> true;
+t_is_char(?int_set(Set)) ->
+ (set_min(Set) >= 0) andalso (set_max(Set) =< ?MAX_CHAR);
+t_is_char(_) -> false.
+
+%%-----------------------------------------------------------------------------
+%% Lists
+%%
+
+-spec t_cons() -> erl_type().
+
+t_cons() ->
+ ?nonempty_list(?any, ?any).
+
+%% Note that if the tail argument can be a list, we must collapse the
+%% content of the list to include both the content of the tail list
+%% and the head of the cons. If for example the tail argument is any()
+%% then there can be any list in the tail and the content of the
+%% returned list must be any().
+
+-spec t_cons(erl_type(), erl_type()) -> erl_type().
+
+t_cons(?none, _) -> ?none;
+t_cons(_, ?none) -> ?none;
+t_cons(?unit, _) -> ?none;
+t_cons(_, ?unit) -> ?none;
+t_cons(Hd, ?nil) ->
+ ?nonempty_list(Hd, ?nil);
+t_cons(Hd, ?list(Contents, Termination, _)) ->
+ ?nonempty_list(t_sup(Contents, Hd), Termination);
+t_cons(Hd, Tail) ->
+ case cons_tail(t_inf(Tail, t_maybe_improper_list())) of
+ ?list(Contents, Termination, _Size) ->
+ %% Collapse the list part of the termination but keep the
+ %% non-list part intact.
+ NewTermination = t_sup(t_subtract(Tail, t_maybe_improper_list()),
+ Termination),
+ ?nonempty_list(t_sup(Hd, Contents), NewTermination);
+ ?nil -> ?nonempty_list(Hd, Tail);
+ ?none -> ?nonempty_list(Hd, Tail);
+ ?unit -> ?none
+ end.
+
+cons_tail(Type) ->
+ do_opaque(Type, 'universe', fun(T) -> T end).
+
+-spec t_is_cons(erl_type()) -> boolean().
+
+t_is_cons(Type) ->
+ t_is_cons(Type, 'universe').
+
+-spec t_is_cons(erl_type(), opaques()) -> boolean().
+
+t_is_cons(Type, Opaques) ->
+ do_opaque(Type, Opaques, fun is_cons/1).
+
+is_cons(?nonempty_list(_, _)) -> true;
+is_cons(_) -> false.
+
+-spec t_cons_hd(erl_type()) -> erl_type().
+
+t_cons_hd(Type) ->
+ t_cons_hd(Type, 'universe').
+
+-spec t_cons_hd(erl_type(), opaques()) -> erl_type().
+
+t_cons_hd(Type, Opaques) ->
+ do_opaque(Type, Opaques, fun cons_hd/1).
+
+cons_hd(?nonempty_list(Contents, _Termination)) -> Contents.
+
+-spec t_cons_tl(erl_type()) -> erl_type().
+
+t_cons_tl(Type) ->
+ t_cons_tl(Type, 'universe').
+
+-spec t_cons_tl(erl_type(), opaques()) -> erl_type().
+
+t_cons_tl(Type, Opaques) ->
+ do_opaque(Type, Opaques, fun cons_tl/1).
+
+cons_tl(?nonempty_list(_Contents, Termination) = T) ->
+ t_sup(Termination, T).
+
+-spec t_nil() -> erl_type().
+
+t_nil() ->
+ ?nil.
+
+-spec t_is_nil(erl_type()) -> boolean().
+
+t_is_nil(Type) ->
+ t_is_nil(Type, 'universe').
+
+-spec t_is_nil(erl_type(), opaques()) -> boolean().
+
+t_is_nil(Type, Opaques) ->
+ do_opaque(Type, Opaques, fun is_nil/1).
+
+is_nil(?nil) -> true;
+is_nil(_) -> false.
+
+-spec t_list() -> erl_type().
+
+t_list() ->
+ ?list(?any, ?nil, ?unknown_qual).
+
+-spec t_list(erl_type()) -> erl_type().
+
+t_list(?none) -> ?none;
+t_list(?unit) -> ?none;
+t_list(Contents) ->
+ ?list(Contents, ?nil, ?unknown_qual).
+
+-spec t_list_elements(erl_type()) -> erl_type().
+
+t_list_elements(Type) ->
+ t_list_elements(Type, 'universe').
+
+-spec t_list_elements(erl_type(), opaques()) -> erl_type().
+
+t_list_elements(Type, Opaques) ->
+ do_opaque(Type, Opaques, fun list_elements/1).
+
+list_elements(?list(Contents, _, _)) -> Contents;
+list_elements(?nil) -> ?none.
+
+-spec t_list_termination(erl_type(), opaques()) -> erl_type().
+
+t_list_termination(Type, Opaques) ->
+ do_opaque(Type, Opaques, fun t_list_termination/1).
+
+-spec t_list_termination(erl_type()) -> erl_type().
+
+t_list_termination(?nil) -> ?nil;
+t_list_termination(?list(_, Term, _)) -> Term.
+
+-spec t_is_list(erl_type()) -> boolean().
+
+t_is_list(?list(_Contents, ?nil, _)) -> true;
+t_is_list(?nil) -> true;
+t_is_list(_) -> false.
+
+-spec t_nonempty_list() -> erl_type().
+
+t_nonempty_list() ->
+ t_cons(?any, ?nil).
+
+-spec t_nonempty_list(erl_type()) -> erl_type().
+
+t_nonempty_list(Type) ->
+ t_cons(Type, ?nil).
+
+-spec t_nonempty_string() -> erl_type().
+
+t_nonempty_string() ->
+ t_nonempty_list(t_char()).
+
+-spec t_string() -> erl_type().
+
+t_string() ->
+ t_list(t_char()).
+
+-spec t_is_string(erl_type()) -> boolean().
+
+t_is_string(X) ->
+ t_is_list(X) andalso t_is_char(t_list_elements(X)).
+
+-spec t_maybe_improper_list() -> erl_type().
+
+t_maybe_improper_list() ->
+ ?list(?any, ?any, ?unknown_qual).
+
+%% Should only be used if you know what you are doing. See t_cons/2
+-spec t_maybe_improper_list(erl_type(), erl_type()) -> erl_type().
+
+t_maybe_improper_list(_Content, ?unit) -> ?none;
+t_maybe_improper_list(?unit, _Termination) -> ?none;
+t_maybe_improper_list(Content, Termination) ->
+ %% Safety check: would be nice to have but does not work with remote types
+ %% true = t_is_subtype(t_nil(), Termination),
+ ?list(Content, Termination, ?unknown_qual).
+
+-spec t_is_maybe_improper_list(erl_type()) -> boolean().
+
+t_is_maybe_improper_list(Type) ->
+ t_is_maybe_improper_list(Type, 'universe').
+
+-spec t_is_maybe_improper_list(erl_type(), opaques()) -> boolean().
+
+t_is_maybe_improper_list(Type, Opaques) ->
+ do_opaque(Type, Opaques, fun is_maybe_improper_list/1).
+
+is_maybe_improper_list(?list(_, _, _)) -> true;
+is_maybe_improper_list(?nil) -> true;
+is_maybe_improper_list(_) -> false.
+
+%% %% Should only be used if you know what you are doing. See t_cons/2
+%% -spec t_improper_list(erl_type(), erl_type()) -> erl_type().
+%%
+%% t_improper_list(?unit, _Termination) -> ?none;
+%% t_improper_list(_Content, ?unit) -> ?none;
+%% t_improper_list(Content, Termination) ->
+%% %% Safety check: would be nice to have but does not work with remote types
+%% %% false = t_is_subtype(t_nil(), Termination),
+%% ?list(Content, Termination, ?any).
+
+-spec lift_list_to_pos_empty(erl_type(), opaques()) -> erl_type().
+
+lift_list_to_pos_empty(Type, Opaques) ->
+ do_opaque(Type, Opaques, fun lift_list_to_pos_empty/1).
+
+-spec lift_list_to_pos_empty(erl_type()) -> erl_type().
+
+lift_list_to_pos_empty(?nil) -> ?nil;
+lift_list_to_pos_empty(?list(Content, Termination, _)) ->
+ ?list(Content, Termination, ?unknown_qual).
+
+%%-----------------------------------------------------------------------------
+%% Maps
+%%
+%% Representation:
+%% ?map(Pairs, DefaultKey, DefaultValue)
+%%
+%% Pairs is a sorted dictionary of types with a mandatoriness tag on each pair
+%% (t_map_dict()). DefaultKey and DefaultValue are plain types.
+%%
+%% A map M belongs to this type iff
+%% For each pair {KT, mandatory, VT} in Pairs, there exists a pair {K, V} in M
+%% such that K \in KT and V \in VT.
+%% For each pair {KT, optional, VT} in Pairs, either there exists no key K in
+%% M s.t. K in KT, or there exists a pair {K, V} in M such that K \in KT and
+%% V \in VT.
+%% For each remaining pair {K, V} in M (where remaining means that there is no
+%% key KT in Pairs s.t. K \in KT), K \in DefaultKey and V \in DefaultValue.
+%%
+%% Invariants:
+%% * The keys in Pairs are singleton types.
+%% * The values of Pairs must not be unit, and may only be none if the
+%% mandatoriness tag is 'optional'.
+%% * Optional must contain no pair {K,V} s.t. K is a subtype of DefaultKey and
+%% V is equal to DefaultKey.
+%% * DefaultKey must be the empty type iff DefaultValue is the empty type.
+%% * DefaultKey must not be a singleton type.
+%% * For every key K in Pairs, DefaultKey - K must not be representable; i.e.
+%% t_subtract(DefaultKey, K) must return DefaultKey.
+%% * For every pair {K, 'optional', ?none} in Pairs, K must be a subtype of
+%% DefaultKey.
+%% * Pairs must be sorted and not contain any duplicate keys.
+%%
+%% These invariants ensure that equal map types are represented by equal terms.
+
+-define(mand, mandatory).
+-define(opt, optional).
+
+-type t_map_mandatoriness() :: ?mand | ?opt.
+-type t_map_pair() :: {erl_type(), t_map_mandatoriness(), erl_type()}.
+-type t_map_dict() :: [t_map_pair()].
+
+-spec t_map() -> erl_type().
+
+t_map() ->
+ t_map([], t_any(), t_any()).
+
+-spec t_map([{erl_type(), erl_type()}]) -> erl_type().
+
+t_map(L) ->
+ lists:foldl(fun t_map_put/2, t_map(), L).
+
+-spec t_map(t_map_dict(), erl_type(), erl_type()) -> erl_type().
+
+t_map(Pairs0, DefK0, DefV0) ->
+ DefK1 = lists:foldl(fun({K,_,_},Acc)->t_subtract(Acc,K)end, DefK0, Pairs0),
+ {DefK2, DefV1} =
+ case t_is_none_or_unit(DefK1) orelse t_is_none_or_unit(DefV0) of
+ true -> {?none, ?none};
+ false -> {DefK1, DefV0}
+ end,
+ {Pairs1, DefK, DefV}
+ = case is_singleton_type(DefK2) of
+ true -> {mapdict_insert({DefK2, ?opt, DefV1}, Pairs0), ?none, ?none};
+ false -> {Pairs0, DefK2, DefV1}
+ end,
+ Pairs = normalise_map_optionals(Pairs1, DefK, DefV),
+ %% Validate invariants of the map representation.
+ %% Since we needed to iterate over the arguments in order to normalise anyway,
+ %% we might as well save us some future pain and do this even without
+ %% define(DEBUG, true).
+ try
+ validate_map_elements(Pairs)
+ catch error:badarg -> error(badarg, [Pairs0,DefK0,DefV0]);
+ error:{badarg, E} -> error({badarg, E}, [Pairs0,DefK0,DefV0])
+ end,
+ ?map(Pairs, DefK, DefV).
+
+normalise_map_optionals([], _, _) -> [];
+normalise_map_optionals([E={K,?opt,?none}|T], DefK, DefV) ->
+ Diff = t_subtract(DefK, K),
+ case t_is_subtype(K, DefK) andalso DefK =:= Diff of
+ true -> [E|normalise_map_optionals(T, DefK, DefV)];
+ false -> normalise_map_optionals(T, Diff, DefV)
+ end;
+normalise_map_optionals([E={K,?opt,V}|T], DefK, DefV) ->
+ case t_is_equal(V, DefV) andalso t_is_subtype(K, DefK) of
+ true -> normalise_map_optionals(T, DefK, DefV);
+ false -> [E|normalise_map_optionals(T, DefK, DefV)]
+ end;
+normalise_map_optionals([E|T], DefK, DefV) ->
+ [E|normalise_map_optionals(T, DefK, DefV)].
+
+validate_map_elements([{_,?mand,?none}|_]) -> error({badarg, none_in_mand});
+validate_map_elements([{K1,_,_}|Rest=[{K2,_,_}|_]]) ->
+ case is_singleton_type(K1) andalso K1 < K2 of
+ false -> error(badarg);
+ true -> validate_map_elements(Rest)
+ end;
+validate_map_elements([{K,_,_}]) ->
+ case is_singleton_type(K) of
+ false -> error(badarg);
+ true -> true
+ end;
+validate_map_elements([]) -> true.
+
+-spec t_is_map(erl_type()) -> boolean().
+
+t_is_map(Type) ->
+ t_is_map(Type, 'universe').
+
+-spec t_is_map(erl_type(), opaques()) -> boolean().
+
+t_is_map(Type, Opaques) ->
+ do_opaque(Type, Opaques, fun is_map1/1).
+
+is_map1(?map(_, _, _)) -> true;
+is_map1(_) -> false.
+
+-spec t_map_entries(erl_type()) -> t_map_dict().
+
+t_map_entries(M) ->
+ t_map_entries(M, 'universe').
+
+-spec t_map_entries(erl_type(), opaques()) -> t_map_dict().
+
+t_map_entries(M, Opaques) ->
+ do_opaque(M, Opaques, fun map_entries/1).
+
+map_entries(?map(Pairs,_,_)) ->
+ Pairs.
+
+-spec t_map_def_key(erl_type()) -> erl_type().
+
+t_map_def_key(M) ->
+ t_map_def_key(M, 'universe').
+
+-spec t_map_def_key(erl_type(), opaques()) -> erl_type().
+
+t_map_def_key(M, Opaques) ->
+ do_opaque(M, Opaques, fun map_def_key/1).
+
+map_def_key(?map(_,DefK,_)) ->
+ DefK.
+
+-spec t_map_def_val(erl_type()) -> erl_type().
+
+t_map_def_val(M) ->
+ t_map_def_val(M, 'universe').
+
+-spec t_map_def_val(erl_type(), opaques()) -> erl_type().
+
+t_map_def_val(M, Opaques) ->
+ do_opaque(M, Opaques, fun map_def_val/1).
+
+map_def_val(?map(_,_,DefV)) ->
+ DefV.
+
+-spec mapdict_store(t_map_pair(), t_map_dict()) -> t_map_dict().
+
+mapdict_store(E={K,_,_}, [{K,_,_}|T]) -> [E|T];
+mapdict_store(E1={K1,_,_}, [E2={K2,_,_}|T]) when K1 > K2 ->
+ [E2|mapdict_store(E1, T)];
+mapdict_store(E={_,_,_}, T) -> [E|T].
+
+-spec mapdict_insert(t_map_pair(), t_map_dict()) -> t_map_dict().
+
+mapdict_insert(E={K,_,_}, D=[{K,_,_}|_]) -> error(badarg, [E, D]);
+mapdict_insert(E1={K1,_,_}, [E2={K2,_,_}|T]) when K1 > K2 ->
+ [E2|mapdict_insert(E1, T)];
+mapdict_insert(E={_,_,_}, T) -> [E|T].
+
+%% Merges the pairs of two maps together. Missing pairs become (?opt, DefV) or
+%% (?opt, ?none), depending on whether K \in DefK.
+-spec map_pairwise_merge(fun((erl_type(),
+ t_map_mandatoriness(), erl_type(),
+ t_map_mandatoriness(), erl_type())
+ -> t_map_pair() | false),
+ erl_type(), erl_type()) -> t_map_dict().
+map_pairwise_merge(F, ?map(APairs, ADefK, ADefV),
+ ?map(BPairs, BDefK, BDefV)) ->
+ map_pairwise_merge(F, APairs, ADefK, ADefV, BPairs, BDefK, BDefV).
+
+map_pairwise_merge(_, [], _, _, [], _, _) -> [];
+map_pairwise_merge(F, As0, ADefK, ADefV, Bs0, BDefK, BDefV) ->
+ {K1, AMNess1, AV1, As1, BMNess1, BV1, Bs1} =
+ case {As0, Bs0} of
+ {[{K,AMNess,AV}|As], [{K, BMNess,BV}|Bs]} ->
+ {K, AMNess, AV, As, BMNess, BV, Bs};
+ {[{K,AMNess,AV}|As], [{BK,_, _ }|_]=Bs} when K < BK ->
+ {K, AMNess, AV, As, ?opt, mapmerge_otherv(K, BDefK, BDefV), Bs};
+ {As, [{K, BMNess,BV}|Bs]} ->
+ {K, ?opt, mapmerge_otherv(K, ADefK, ADefV), As, BMNess, BV, Bs};
+ {[{K,AMNess,AV}|As], []=Bs} ->
+ {K, AMNess, AV, As, ?opt, mapmerge_otherv(K, BDefK, BDefV), Bs}
+ end,
+ MK = K1, %% Rename to make clear that we are matching below
+ case F(K1, AMNess1, AV1, BMNess1, BV1) of
+ false -> map_pairwise_merge(F,As1,ADefK,ADefV,Bs1,BDefK,BDefV);
+ {MK,_,_}=M -> [M|map_pairwise_merge(F,As1,ADefK,ADefV,Bs1,BDefK,BDefV)]
+ end.
+
+%% Folds over the pairs in two maps simultaneously in reverse key order. Missing
+%% pairs become (?opt, DefV) or (?opt, ?none), depending on whether K \in DefK.
+-spec map_pairwise_merge_foldr(fun((erl_type(),
+ t_map_mandatoriness(), erl_type(),
+ t_map_mandatoriness(), erl_type(),
+ Acc) -> Acc),
+ Acc, erl_type(), erl_type()) -> Acc.
+
+map_pairwise_merge_foldr(F, AccIn, ?map(APairs, ADefK, ADefV),
+ ?map(BPairs, BDefK, BDefV)) ->
+ map_pairwise_merge_foldr(F, AccIn, APairs, ADefK, ADefV, BPairs, BDefK, BDefV).
+
+map_pairwise_merge_foldr(_, Acc, [], _, _, [], _, _) -> Acc;
+map_pairwise_merge_foldr(F, AccIn, As0, ADefK, ADefV, Bs0, BDefK, BDefV) ->
+ {K1, AMNess1, AV1, As1, BMNess1, BV1, Bs1} =
+ case {As0, Bs0} of
+ {[{K,AMNess,AV}|As], [{K,BMNess,BV}|Bs]} ->
+ {K, AMNess, AV, As, BMNess, BV, Bs};
+ {[{K,AMNess,AV}|As], [{BK,_, _ }|_]=Bs} when K < BK ->
+ {K, AMNess, AV, As, ?opt, mapmerge_otherv(K, BDefK, BDefV), Bs};
+ {As, [{K,BMNess,BV}|Bs]} ->
+ {K, ?opt, mapmerge_otherv(K, ADefK, ADefV), As, BMNess, BV, Bs};
+ {[{K,AMNess,AV}|As], []=Bs} ->
+ {K, AMNess, AV, As, ?opt, mapmerge_otherv(K, BDefK, BDefV), Bs}
+ end,
+ F(K1, AMNess1, AV1, BMNess1, BV1,
+ map_pairwise_merge_foldr(F,AccIn,As1,ADefK,ADefV,Bs1,BDefK,BDefV)).
+
+%% By observing that a missing pair in a map is equivalent to an optional pair,
+%% with ?none or DefV value, depending on whether K \in DefK, we can simplify
+%% merging by denormalising the map pairs temporarily, removing all 'false'
+%% cases, at the cost of the creation of more tuples:
+mapmerge_otherv(K, ODefK, ODefV) ->
+ case t_inf(K, ODefK) of
+ ?none -> ?none;
+ _KOrOpaque -> ODefV
+ end.
+
+-spec t_map_put({erl_type(), erl_type()}, erl_type()) -> erl_type().
+
+t_map_put(KV, Map) ->
+ t_map_put(KV, Map, 'universe').
+
+-spec t_map_put({erl_type(), erl_type()}, erl_type(), opaques()) -> erl_type().
+
+t_map_put(KV, Map, Opaques) ->
+ do_opaque(Map, Opaques, fun(UM) -> map_put(KV, UM, Opaques) end).
+
+%% Key and Value are *not* unopaqued, but the map is
+map_put(_, ?none, _) -> ?none;
+map_put({Key, Value}, ?map(Pairs,DefK,DefV), Opaques) ->
+ case t_is_none_or_unit(Key) orelse t_is_none_or_unit(Value) of
+ true -> ?none;
+ false ->
+ case is_singleton_type(Key) of
+ true ->
+ t_map(mapdict_store({Key, ?mand, Value}, Pairs), DefK, DefV);
+ false ->
+ t_map([{K, MNess, case t_is_none(t_inf(K, Key, Opaques)) of
+ true -> V;
+ false -> t_sup(V, Value)
+ end} || {K, MNess, V} <- Pairs],
+ t_sup(DefK, Key),
+ t_sup(DefV, Value))
+ end
+ end.
+
+-spec t_map_update({erl_type(), erl_type()}, erl_type()) -> erl_type().
+
+t_map_update(KV, Map) ->
+ t_map_update(KV, Map, 'universe').
+
+-spec t_map_update({erl_type(), erl_type()}, erl_type(), opaques()) -> erl_type().
+
+t_map_update(_, ?none, _) -> ?none;
+t_map_update(KV={Key, _}, M, Opaques) ->
+ case t_is_subtype(t_atom('true'), t_map_is_key(Key, M, Opaques)) of
+ false -> ?none;
+ true -> t_map_put(KV, M, Opaques)
+ end.
+
+-spec t_map_get(erl_type(), erl_type()) -> erl_type().
+
+t_map_get(Key, Map) ->
+ t_map_get(Key, Map, 'universe').
+
+-spec t_map_get(erl_type(), erl_type(), opaques()) -> erl_type().
+
+t_map_get(Key, Map, Opaques) ->
+ do_opaque(Map, Opaques,
+ fun(UM) ->
+ do_opaque(Key, Opaques, fun(UK) -> map_get(UK, UM) end)
+ end).
+
+map_get(_, ?none) -> ?none;
+map_get(Key, ?map(Pairs, DefK, DefV)) ->
+ DefRes =
+ case t_do_overlap(DefK, Key) of
+ false -> t_none();
+ true -> DefV
+ end,
+ case is_singleton_type(Key) of
+ false ->
+ lists:foldl(fun({K, _, V}, Res) ->
+ case t_do_overlap(K, Key) of
+ false -> Res;
+ true -> t_sup(Res, V)
+ end
+ end, DefRes, Pairs);
+ true ->
+ case lists:keyfind(Key, 1, Pairs) of
+ false -> DefRes;
+ {_, _, ValType} -> ValType
+ end
+ end.
+
+-spec t_map_is_key(erl_type(), erl_type()) -> erl_type().
+
+t_map_is_key(Key, Map) ->
+ t_map_is_key(Key, Map, 'universe').
+
+-spec t_map_is_key(erl_type(), erl_type(), opaques()) -> erl_type().
+
+t_map_is_key(Key, Map, Opaques) ->
+ do_opaque(Map, Opaques,
+ fun(UM) ->
+ do_opaque(Key, Opaques, fun(UK) -> map_is_key(UK, UM) end)
+ end).
+
+map_is_key(_, ?none) -> ?none;
+map_is_key(Key, ?map(Pairs, DefK, _DefV)) ->
+ case is_singleton_type(Key) of
+ true ->
+ case lists:keyfind(Key, 1, Pairs) of
+ {Key, ?mand, _} -> t_atom(true);
+ {Key, ?opt, ?none} -> t_atom(false);
+ {Key, ?opt, _} -> t_boolean();
+ false ->
+ case t_do_overlap(DefK, Key) of
+ false -> t_atom(false);
+ true -> t_boolean()
+ end
+ end;
+ false ->
+ case t_do_overlap(DefK, Key)
+ orelse lists:any(fun({_,_,?none}) -> false;
+ ({K,_,_}) -> t_do_overlap(K, Key)
+ end, Pairs)
+ of
+ true -> t_boolean();
+ false -> t_atom(false)
+ end
+ end.
+
+%%-----------------------------------------------------------------------------
+%% Tuples
+%%
+
+-spec t_tuple() -> erl_type().
+
+t_tuple() ->
+ ?tuple(?any, ?any, ?any).
+
+-spec t_tuple(non_neg_integer() | [erl_type()]) -> erl_type().
+
+t_tuple(N) when is_integer(N), N > ?MAX_TUPLE_SIZE ->
+ t_tuple();
+t_tuple(N) when is_integer(N) ->
+ ?tuple(lists:duplicate(N, ?any), N, ?any);
+t_tuple(List) ->
+ case any_none_or_unit(List) of
+ true -> t_none();
+ false ->
+ Arity = length(List),
+ case get_tuple_tags(List) of
+ [Tag] -> ?tuple(List, Arity, Tag); %% Tag can also be ?any here
+ TagList ->
+ SortedTagList = lists:sort(TagList),
+ Tuples = [?tuple([T|tl(List)], Arity, T) || T <- SortedTagList],
+ ?tuple_set([{Arity, Tuples}])
+ end
+ end.
+
+-spec get_tuple_tags([erl_type()]) -> [erl_type(),...].
+
+get_tuple_tags([Tag|_]) ->
+ do_opaque(Tag, 'universe', fun tuple_tags/1);
+get_tuple_tags(_) -> [?any].
+
+tuple_tags(?atom(?any)) -> [?any];
+tuple_tags(?atom(Set)) ->
+ case set_size(Set) > ?TUPLE_TAG_LIMIT of
+ true -> [?any];
+ false -> [t_atom(A) || A <- set_to_list(Set)]
+ end;
+tuple_tags(_) -> [?any].
+
+%% to be used for a tuple with known types for its arguments (not ?any)
+-spec t_tuple_args(erl_type()) -> [erl_type()].
+
+t_tuple_args(Type) ->
+ t_tuple_args(Type, 'universe').
+
+%% to be used for a tuple with known types for its arguments (not ?any)
+-spec t_tuple_args(erl_type(), opaques()) -> [erl_type()].
+
+t_tuple_args(Type, Opaques) ->
+ do_opaque(Type, Opaques, fun tuple_args/1).
+
+tuple_args(?tuple(Args, _, _)) when is_list(Args) -> Args.
+
+%% to be used for a tuple with a known size (not ?any)
+-spec t_tuple_size(erl_type()) -> non_neg_integer().
+
+t_tuple_size(Type) ->
+ t_tuple_size(Type, 'universe').
+
+%% to be used for a tuple with a known size (not ?any)
+-spec t_tuple_size(erl_type(), opaques()) -> non_neg_integer().
+
+t_tuple_size(Type, Opaques) ->
+ do_opaque(Type, Opaques, fun tuple_size1/1).
+
+tuple_size1(?tuple(_, Size, _)) when is_integer(Size) -> Size.
+
+-spec t_tuple_sizes(erl_type()) -> 'unknown' | [non_neg_integer(),...].
+
+t_tuple_sizes(Type) ->
+ do_opaque(Type, 'universe', fun tuple_sizes/1).
+
+tuple_sizes(?tuple(?any, ?any, ?any)) -> unknown;
+tuple_sizes(?tuple(_, Size, _)) when is_integer(Size) -> [Size];
+tuple_sizes(?tuple_set(List)) -> [Size || {Size, _} <- List].
+
+-spec t_tuple_subtypes(erl_type(), opaques()) ->
+ 'unknown' | [erl_type(),...].
+
+t_tuple_subtypes(Type, Opaques) ->
+ Fun = fun(?tuple_set(List)) ->
+ t_tuple_subtypes_tuple_list(List, Opaques);
+ (?opaque(_)) -> unknown;
+ (T) -> t_tuple_subtypes(T)
+ end,
+ do_opaque(Type, Opaques, Fun).
+
+t_tuple_subtypes_tuple_list(List, Opaques) ->
+ lists:append([t_tuple_subtypes_list(Tuples, Opaques) ||
+ {_Size, Tuples} <- List]).
+
+t_tuple_subtypes_list(List, Opaques) ->
+ ListOfLists = [t_tuple_subtypes(E, Opaques) || E <- List, E =/= ?none],
+ lists:append([L || L <- ListOfLists, L =/= 'unknown']).
+
+-spec t_tuple_subtypes(erl_type()) -> 'unknown' | [erl_type(),...].
+
+%% XXX. Not the same as t_tuple_subtypes(T, 'universe')...
+t_tuple_subtypes(?tuple(?any, ?any, ?any)) -> unknown;
+t_tuple_subtypes(?tuple(_, _, _) = T) -> [T];
+t_tuple_subtypes(?tuple_set(List)) ->
+ lists:append([Tuples || {_Size, Tuples} <- List]).
+
+-spec t_is_tuple(erl_type()) -> boolean().
+
+t_is_tuple(Type) ->
+ t_is_tuple(Type, 'universe').
+
+-spec t_is_tuple(erl_type(), opaques()) -> boolean().
+
+t_is_tuple(Type, Opaques) ->
+ do_opaque(Type, Opaques, fun is_tuple1/1).
+
+is_tuple1(?tuple(_, _, _)) -> true;
+is_tuple1(?tuple_set(_)) -> true;
+is_tuple1(_) -> false.
+
+%%-----------------------------------------------------------------------------
+%% Non-primitive types, including some handy syntactic sugar types
+%%
+
+-spec t_bitstrlist() -> erl_type().
+
+t_bitstrlist() ->
+ t_iolist(1, t_bitstr()).
+
+-spec t_arity() -> erl_type().
+
+t_arity() ->
+ t_from_range(0, 255). % was t_byte().
+
+-spec t_pos_integer() -> erl_type().
+
+t_pos_integer() ->
+ t_from_range(1, pos_inf).
+
+-spec t_non_neg_integer() -> erl_type().
+
+t_non_neg_integer() ->
+ t_from_range(0, pos_inf).
+
+-spec t_is_non_neg_integer(erl_type()) -> boolean().
+
+t_is_non_neg_integer(?integer(_) = T) ->
+ t_is_subtype(T, t_non_neg_integer());
+t_is_non_neg_integer(_) -> false.
+
+-spec t_neg_integer() -> erl_type().
+
+t_neg_integer() ->
+ t_from_range(neg_inf, -1).
+
+-spec t_fixnum() -> erl_type().
+
+t_fixnum() ->
+ t_integer(). % Gross over-approximation
+
+-spec t_pos_fixnum() -> erl_type().
+
+t_pos_fixnum() ->
+ t_pos_integer(). % Gross over-approximation
+
+-spec t_non_neg_fixnum() -> erl_type().
+
+t_non_neg_fixnum() ->
+ t_non_neg_integer(). % Gross over-approximation
+
+-spec t_mfa() -> erl_type().
+
+t_mfa() ->
+ t_tuple([t_atom(), t_atom(), t_arity()]).
+
+-spec t_module() -> erl_type().
+
+t_module() ->
+ t_atom().
+
+-spec t_node() -> erl_type().
+
+t_node() ->
+ t_atom().
+
+-spec t_iodata() -> erl_type().
+
+t_iodata() ->
+ t_sup(t_iolist(), t_binary()).
+
+-spec t_iolist() -> erl_type().
+
+t_iolist() ->
+ t_iolist(1, t_binary()).
+
+%% Added a second argument which currently is t_binary() | t_bitstr()
+-spec t_iolist(non_neg_integer(), erl_type()) -> erl_type().
+
+t_iolist(N, T) when N > 0 ->
+ t_maybe_improper_list(t_sup([t_iolist(N-1, T), T, t_byte()]),
+ t_sup(T, t_nil()));
+t_iolist(0, T) ->
+ t_maybe_improper_list(t_any(), t_sup(T, t_nil())).
+
+-spec t_timeout() -> erl_type().
+
+t_timeout() ->
+ t_sup(t_non_neg_integer(), t_atom('infinity')).
+
+%%------------------------------------
+
+%% ?none is allowed in products. A product of size 1 is not a product.
+
+-spec t_product([erl_type()]) -> erl_type().
+
+t_product([T]) -> T;
+t_product(Types) when is_list(Types) ->
+ ?product(Types).
+
+%% This function is intended to be the inverse of the one above.
+%% It should NOT be used with ?any, ?none or ?unit as input argument.
+
+-spec t_to_tlist(erl_type()) -> [erl_type()].
+
+t_to_tlist(?product(Types)) -> Types;
+t_to_tlist(T) when T =/= ?any orelse T =/= ?none orelse T =/= ?unit -> [T].
+
+%%------------------------------------
+
+-spec t_var(atom() | integer()) -> erl_type().
+
+t_var(Atom) when is_atom(Atom) -> ?var(Atom);
+t_var(Int) when is_integer(Int) -> ?var(Int).
+
+-spec t_is_var(erl_type()) -> boolean().
+
+t_is_var(?var(_)) -> true;
+t_is_var(_) -> false.
+
+-spec t_var_name(erl_type()) -> atom() | integer().
+
+t_var_name(?var(Id)) -> Id.
+
+-spec t_has_var(erl_type()) -> boolean().
+
+t_has_var(?var(_)) -> true;
+t_has_var(?function(Domain, Range)) ->
+ t_has_var(Domain) orelse t_has_var(Range);
+t_has_var(?list(Contents, Termination, _)) ->
+ t_has_var(Contents) orelse t_has_var(Termination);
+t_has_var(?product(Types)) -> t_has_var_list(Types);
+t_has_var(?tuple(?any, ?any, ?any)) -> false;
+t_has_var(?tuple(Elements, _, _)) ->
+ t_has_var_list(Elements);
+t_has_var(?tuple_set(_) = T) ->
+ t_has_var_list(t_tuple_subtypes(T));
+t_has_var(?map(_, DefK, _)= Map) ->
+ t_has_var_list(map_all_values(Map)) orelse
+ t_has_var(DefK);
+t_has_var(?opaque(Set)) ->
+ %% Assume variables in 'args' are also present i 'struct'
+ t_has_var_list([O#opaque.struct || O <- set_to_list(Set)]);
+t_has_var(?union(List)) ->
+ t_has_var_list(List);
+t_has_var(_) -> false.
+
+-spec t_has_var_list([erl_type()]) -> boolean().
+
+t_has_var_list([T|Ts]) ->
+ t_has_var(T) orelse t_has_var_list(Ts);
+t_has_var_list([]) -> false.
+
+-spec t_collect_vars(erl_type()) -> [erl_type()].
+
+t_collect_vars(T) ->
+ t_collect_vars(T, []).
+
+-spec t_collect_vars(erl_type(), [erl_type()]) -> [erl_type()].
+
+t_collect_vars(?var(_) = Var, Acc) ->
+ ordsets:add_element(Var, Acc);
+t_collect_vars(?function(Domain, Range), Acc) ->
+ ordsets:union(t_collect_vars(Domain, Acc), t_collect_vars(Range, []));
+t_collect_vars(?list(Contents, Termination, _), Acc) ->
+ ordsets:union(t_collect_vars(Contents, Acc), t_collect_vars(Termination, []));
+t_collect_vars(?product(Types), Acc) ->
+ t_collect_vars_list(Types, Acc);
+t_collect_vars(?tuple(?any, ?any, ?any), Acc) ->
+ Acc;
+t_collect_vars(?tuple(Types, _, _), Acc) ->
+ t_collect_vars_list(Types, Acc);
+t_collect_vars(?tuple_set(_) = TS, Acc) ->
+ t_collect_vars_list(t_tuple_subtypes(TS), Acc);
+t_collect_vars(?map(_, DefK, _) = Map, Acc0) ->
+ Acc = t_collect_vars_list(map_all_values(Map), Acc0),
+ t_collect_vars(DefK, Acc);
+t_collect_vars(?opaque(Set), Acc) ->
+ %% Assume variables in 'args' are also present i 'struct'
+ t_collect_vars_list([O#opaque.struct || O <- set_to_list(Set)], Acc);
+t_collect_vars(?union(List), Acc) ->
+ t_collect_vars_list(List, Acc);
+t_collect_vars(_, Acc) ->
+ Acc.
+
+t_collect_vars_list([T|Ts], Acc0) ->
+ Acc = t_collect_vars(T, Acc0),
+ t_collect_vars_list(Ts, Acc);
+t_collect_vars_list([], Acc) -> Acc.
+
+%%=============================================================================
+%%
+%% Type construction from Erlang terms.
+%%
+%%=============================================================================
+
+%%-----------------------------------------------------------------------------
+%% Make a type from a term. No type depth is enforced.
+%%
+
+-spec t_from_term(term()) -> erl_type().
+
+t_from_term([H|T]) -> t_cons(t_from_term(H), t_from_term(T));
+t_from_term([]) -> t_nil();
+t_from_term(T) when is_atom(T) -> t_atom(T);
+t_from_term(T) when is_bitstring(T) -> t_bitstr(0, erlang:bit_size(T));
+t_from_term(T) when is_float(T) -> t_float();
+t_from_term(T) when is_function(T) ->
+ {arity, Arity} = erlang:fun_info(T, arity),
+ t_fun(Arity, t_any());
+t_from_term(T) when is_integer(T) -> t_integer(T);
+t_from_term(T) when is_map(T) ->
+ Pairs = [{t_from_term(K), ?mand, t_from_term(V)}
+ || {K, V} <- maps:to_list(T)],
+ {Stons, Rest} = lists:partition(fun({K,_,_}) -> is_singleton_type(K) end,
+ Pairs),
+ {DefK, DefV}
+ = lists:foldl(fun({K,_,V},{AK,AV}) -> {t_sup(K,AK), t_sup(V,AV)} end,
+ {t_none(), t_none()}, Rest),
+ t_map(lists:keysort(1, Stons), DefK, DefV);
+t_from_term(T) when is_pid(T) -> t_pid();
+t_from_term(T) when is_port(T) -> t_port();
+t_from_term(T) when is_reference(T) -> t_reference();
+t_from_term(T) when is_tuple(T) ->
+ t_tuple([t_from_term(E) || E <- tuple_to_list(T)]).
+
+%%-----------------------------------------------------------------------------
+%% Integer types from a range.
+%%-----------------------------------------------------------------------------
+
+%%-define(USE_UNSAFE_RANGES, true).
+
+-spec t_from_range(rng_elem(), rng_elem()) -> erl_type().
+
+-ifdef(USE_UNSAFE_RANGES).
+
+t_from_range(X, Y) ->
+ t_from_range_unsafe(X, Y).
+
+-else.
+
+t_from_range(neg_inf, pos_inf) -> t_integer();
+t_from_range(neg_inf, Y) when is_integer(Y), Y < 0 -> ?integer_neg;
+t_from_range(neg_inf, Y) when is_integer(Y), Y >= 0 -> t_integer();
+t_from_range(X, pos_inf) when is_integer(X), X >= 1 -> ?integer_pos;
+t_from_range(X, pos_inf) when is_integer(X), X >= 0 -> ?integer_non_neg;
+t_from_range(X, pos_inf) when is_integer(X), X < 0 -> t_integer();
+t_from_range(X, Y) when is_integer(X), is_integer(Y), X > Y -> t_none();
+t_from_range(X, Y) when is_integer(X), is_integer(Y) ->
+ case ((Y - X) < ?SET_LIMIT) of
+ true -> t_integers(lists:seq(X, Y));
+ false ->
+ case X >= 0 of
+ false ->
+ if Y < 0 -> ?integer_neg;
+ true -> t_integer()
+ end;
+ true ->
+ if Y =< ?MAX_BYTE, X >= 1 -> ?int_range(1, ?MAX_BYTE);
+ Y =< ?MAX_BYTE -> t_byte();
+ Y =< ?MAX_CHAR, X >= 1 -> ?int_range(1, ?MAX_CHAR);
+ Y =< ?MAX_CHAR -> t_char();
+ X >= 1 -> ?integer_pos;
+ X >= 0 -> ?integer_non_neg
+ end
+ end
+ end;
+t_from_range(pos_inf, neg_inf) -> t_none().
+
+-endif.
+
+-spec t_from_range_unsafe(rng_elem(), rng_elem()) -> erl_type().
+
+t_from_range_unsafe(neg_inf, pos_inf) -> t_integer();
+t_from_range_unsafe(neg_inf, Y) -> ?int_range(neg_inf, Y);
+t_from_range_unsafe(X, pos_inf) -> ?int_range(X, pos_inf);
+t_from_range_unsafe(X, Y) when is_integer(X), is_integer(Y), X =< Y ->
+ if (Y - X) < ?SET_LIMIT -> t_integers(lists:seq(X, Y));
+ true -> ?int_range(X, Y)
+ end;
+t_from_range_unsafe(X, Y) when is_integer(X), is_integer(Y) -> t_none();
+t_from_range_unsafe(pos_inf, neg_inf) -> t_none().
+
+-spec t_is_fixnum(erl_type()) -> boolean().
+
+t_is_fixnum(?int_range(neg_inf, _)) -> false;
+t_is_fixnum(?int_range(_, pos_inf)) -> false;
+t_is_fixnum(?int_range(From, To)) ->
+ is_fixnum(From) andalso is_fixnum(To);
+t_is_fixnum(?int_set(Set)) ->
+ is_fixnum(set_min(Set)) andalso is_fixnum(set_max(Set));
+t_is_fixnum(_) -> false.
+
+-spec is_fixnum(integer()) -> boolean().
+
+is_fixnum(N) when is_integer(N) ->
+ Bits = ?BITS,
+ (N =< ((1 bsl (Bits - 1)) - 1)) andalso (N >= -(1 bsl (Bits - 1))).
+
+infinity_geq(pos_inf, _) -> true;
+infinity_geq(_, pos_inf) -> false;
+infinity_geq(_, neg_inf) -> true;
+infinity_geq(neg_inf, _) -> false;
+infinity_geq(A, B) -> A >= B.
+
+-spec t_is_bitwidth(erl_type()) -> boolean().
+
+t_is_bitwidth(?int_range(neg_inf, _)) -> false;
+t_is_bitwidth(?int_range(_, pos_inf)) -> false;
+t_is_bitwidth(?int_range(From, To)) ->
+ infinity_geq(From, 0) andalso infinity_geq(?BITS, To);
+t_is_bitwidth(?int_set(Set)) ->
+ infinity_geq(set_min(Set), 0) andalso infinity_geq(?BITS, set_max(Set));
+t_is_bitwidth(_) -> false.
+
+-spec number_min(erl_type()) -> rng_elem().
+
+number_min(Type) ->
+ number_min(Type, 'universe').
+
+-spec number_min(erl_type(), opaques()) -> rng_elem().
+
+number_min(Type, Opaques) ->
+ do_opaque(Type, Opaques, fun number_min2/1).
+
+number_min2(?int_range(From, _)) -> From;
+number_min2(?int_set(Set)) -> set_min(Set);
+number_min2(?number(?any, _Tag)) -> neg_inf.
+
+-spec number_max(erl_type()) -> rng_elem().
+
+number_max(Type) ->
+ number_max(Type, 'universe').
+
+-spec number_max(erl_type(), opaques()) -> rng_elem().
+
+number_max(Type, Opaques) ->
+ do_opaque(Type, Opaques, fun number_max2/1).
+
+number_max2(?int_range(_, To)) -> To;
+number_max2(?int_set(Set)) -> set_max(Set);
+number_max2(?number(?any, _Tag)) -> pos_inf.
+
+%% -spec int_range(rgn_elem(), rng_elem()) -> erl_type().
+%%
+%% int_range(neg_inf, pos_inf) -> t_integer();
+%% int_range(neg_inf, To) -> ?int_range(neg_inf, To);
+%% int_range(From, pos_inf) -> ?int_range(From, pos_inf);
+%% int_range(From, To) when From =< To -> t_from_range(From, To);
+%% int_range(From, To) when To < From -> ?none.
+
+in_range(_, ?int_range(neg_inf, pos_inf)) -> true;
+in_range(X, ?int_range(From, pos_inf)) -> X >= From;
+in_range(X, ?int_range(neg_inf, To)) -> X =< To;
+in_range(X, ?int_range(From, To)) -> (X >= From) andalso (X =< To).
+
+-spec min(rng_elem(), rng_elem()) -> rng_elem().
+
+min(neg_inf, _) -> neg_inf;
+min(_, neg_inf) -> neg_inf;
+min(pos_inf, Y) -> Y;
+min(X, pos_inf) -> X;
+min(X, Y) when X =< Y -> X;
+min(_, Y) -> Y.
+
+-spec max(rng_elem(), rng_elem()) -> rng_elem().
+
+max(neg_inf, Y) -> Y;
+max(X, neg_inf) -> X;
+max(pos_inf, _) -> pos_inf;
+max(_, pos_inf) -> pos_inf;
+max(X, Y) when X =< Y -> Y;
+max(X, _) -> X.
+
+expand_range_from_set(Range = ?int_range(From, To), Set) ->
+ Min = min(set_min(Set), From),
+ Max = max(set_max(Set), To),
+ if From =:= Min, To =:= Max -> Range;
+ true -> t_from_range(Min, Max)
+ end.
+
+%%=============================================================================
+%%
+%% Lattice operations
+%%
+%%=============================================================================
+
+%%-----------------------------------------------------------------------------
+%% Supremum
+%%
+
+-spec t_sup([erl_type()]) -> erl_type().
+
+t_sup([]) -> ?none;
+t_sup(Ts) ->
+ case lists:any(fun is_any/1, Ts) of
+ true -> ?any;
+ false ->
+ t_sup1(Ts, [])
+ end.
+
+t_sup1([H1, H2|T], L) ->
+ t_sup1(T, [t_sup(H1, H2)|L]);
+t_sup1([T], []) -> subst_all_vars_to_any(T);
+t_sup1(Ts, L) ->
+ t_sup1(Ts++L, []).
+
+-spec t_sup(erl_type(), erl_type()) -> erl_type().
+
+t_sup(?any, _) -> ?any;
+t_sup(_, ?any) -> ?any;
+t_sup(?none, T) -> T;
+t_sup(T, ?none) -> T;
+t_sup(?unit, T) -> T;
+t_sup(T, ?unit) -> T;
+t_sup(T, T) -> subst_all_vars_to_any(T);
+t_sup(?var(_), _) -> ?any;
+t_sup(_, ?var(_)) -> ?any;
+t_sup(?atom(Set1), ?atom(Set2)) ->
+ ?atom(set_union(Set1, Set2));
+t_sup(?bitstr(U1, B1), ?bitstr(U2, B2)) ->
+ t_bitstr(gcd(gcd(U1, U2), abs(B1-B2)), lists:min([B1, B2]));
+t_sup(?function(Domain1, Range1), ?function(Domain2, Range2)) ->
+ %% The domain is either a product or any.
+ ?function(t_sup(Domain1, Domain2), t_sup(Range1, Range2));
+t_sup(?identifier(Set1), ?identifier(Set2)) ->
+ ?identifier(set_union(Set1, Set2));
+t_sup(?opaque(Set1), ?opaque(Set2)) ->
+ sup_opaque(set_to_list(ordsets:union(Set1, Set2)));
+%%Disallow unions with opaque types
+%%t_sup(T1=?opaque(_,_,_), T2) ->
+%% io:format("Debug: t_sup executed with args ~w and ~w~n",[T1, T2]), ?none;
+%%t_sup(T1, T2=?opaque(_,_,_)) ->
+%% io:format("Debug: t_sup executed with args ~w and ~w~n",[T1, T2]), ?none;
+t_sup(?matchstate(Pres1, Slots1), ?matchstate(Pres2, Slots2)) ->
+ ?matchstate(t_sup(Pres1, Pres2), t_sup(Slots1, Slots2));
+t_sup(?nil, ?nil) -> ?nil;
+t_sup(?nil, ?list(Contents, Termination, _)) ->
+ ?list(Contents, t_sup(?nil, Termination), ?unknown_qual);
+t_sup(?list(Contents, Termination, _), ?nil) ->
+ ?list(Contents, t_sup(?nil, Termination), ?unknown_qual);
+t_sup(?list(Contents1, Termination1, Size1),
+ ?list(Contents2, Termination2, Size2)) ->
+ NewSize =
+ case {Size1, Size2} of
+ {?unknown_qual, ?unknown_qual} -> ?unknown_qual;
+ {?unknown_qual, ?nonempty_qual} -> ?unknown_qual;
+ {?nonempty_qual, ?unknown_qual} -> ?unknown_qual;
+ {?nonempty_qual, ?nonempty_qual} -> ?nonempty_qual
+ end,
+ NewContents = t_sup(Contents1, Contents2),
+ NewTermination = t_sup(Termination1, Termination2),
+ TmpList = t_cons(NewContents, NewTermination),
+ case NewSize of
+ ?nonempty_qual -> TmpList;
+ ?unknown_qual ->
+ ?list(FinalContents, FinalTermination, _) = TmpList,
+ ?list(FinalContents, FinalTermination, ?unknown_qual)
+ end;
+t_sup(?number(_, _), ?number(?any, ?unknown_qual) = T) -> T;
+t_sup(?number(?any, ?unknown_qual) = T, ?number(_, _)) -> T;
+t_sup(?float, ?float) -> ?float;
+t_sup(?float, ?integer(_)) -> t_number();
+t_sup(?integer(_), ?float) -> t_number();
+t_sup(?integer(?any) = T, ?integer(_)) -> T;
+t_sup(?integer(_), ?integer(?any) = T) -> T;
+t_sup(?int_set(Set1), ?int_set(Set2)) ->
+ case set_union(Set1, Set2) of
+ ?any ->
+ t_from_range(min(set_min(Set1), set_min(Set2)),
+ max(set_max(Set1), set_max(Set2)));
+ Set -> ?int_set(Set)
+ end;
+t_sup(?int_range(From1, To1), ?int_range(From2, To2)) ->
+ t_from_range(min(From1, From2), max(To1, To2));
+t_sup(Range = ?int_range(_, _), ?int_set(Set)) ->
+ expand_range_from_set(Range, Set);
+t_sup(?int_set(Set), Range = ?int_range(_, _)) ->
+ expand_range_from_set(Range, Set);
+t_sup(?product(Types1), ?product(Types2)) ->
+ L1 = length(Types1),
+ L2 = length(Types2),
+ if L1 =:= L2 -> ?product(t_sup_lists(Types1, Types2));
+ true -> ?any
+ end;
+t_sup(?product(_), _) ->
+ ?any;
+t_sup(_, ?product(_)) ->
+ ?any;
+t_sup(?tuple(?any, ?any, ?any) = T, ?tuple(_, _, _)) -> T;
+t_sup(?tuple(_, _, _), ?tuple(?any, ?any, ?any) = T) -> T;
+t_sup(?tuple(?any, ?any, ?any) = T, ?tuple_set(_)) -> T;
+t_sup(?tuple_set(_), ?tuple(?any, ?any, ?any) = T) -> T;
+t_sup(?tuple(Elements1, Arity, Tag1) = T1,
+ ?tuple(Elements2, Arity, Tag2) = T2) ->
+ if Tag1 =:= Tag2 -> t_tuple(t_sup_lists(Elements1, Elements2));
+ Tag1 =:= ?any -> t_tuple(t_sup_lists(Elements1, Elements2));
+ Tag2 =:= ?any -> t_tuple(t_sup_lists(Elements1, Elements2));
+ Tag1 < Tag2 -> ?tuple_set([{Arity, [T1, T2]}]);
+ Tag1 > Tag2 -> ?tuple_set([{Arity, [T2, T1]}])
+ end;
+t_sup(?tuple(_, Arity1, _) = T1, ?tuple(_, Arity2, _) = T2) ->
+ sup_tuple_sets([{Arity1, [T1]}], [{Arity2, [T2]}]);
+t_sup(?tuple_set(List1), ?tuple_set(List2)) ->
+ sup_tuple_sets(List1, List2);
+t_sup(?tuple_set(List1), T2 = ?tuple(_, Arity, _)) ->
+ sup_tuple_sets(List1, [{Arity, [T2]}]);
+t_sup(?tuple(_, Arity, _) = T1, ?tuple_set(List2)) ->
+ sup_tuple_sets([{Arity, [T1]}], List2);
+t_sup(?map(_, ADefK, ADefV) = A, ?map(_, BDefK, BDefV) = B) ->
+ Pairs =
+ map_pairwise_merge(
+ fun(K, MNess, V1, MNess, V2) -> {K, MNess, t_sup(V1, V2)};
+ (K, _, V1, _, V2) -> {K, ?opt, t_sup(V1, V2)}
+ end, A, B),
+ t_map(Pairs, t_sup(ADefK, BDefK), t_sup(ADefV, BDefV));
+t_sup(T1, T2) ->
+ ?union(U1) = force_union(T1),
+ ?union(U2) = force_union(T2),
+ sup_union(U1, U2).
+
+sup_opaque([]) -> ?none;
+sup_opaque(List) ->
+ L = sup_opaq(List),
+ ?opaque(ordsets:from_list(L)).
+
+sup_opaq(L0) ->
+ L1 = [{{Mod,Name,Args}, T} ||
+ #opaque{mod = Mod, name = Name, args = Args}=T <- L0],
+ F = family(L1),
+ [supl(Ts) || {_, Ts} <- F].
+
+supl([O]) -> O;
+supl(Ts) -> supl(Ts, t_none()).
+
+supl([#opaque{struct = S}=O|L], S0) ->
+ S1 = t_sup(S, S0),
+ case L =:= [] of
+ true -> O#opaque{struct = S1};
+ false -> supl(L, S1)
+ end.
+
+-spec t_sup_lists([erl_type()], [erl_type()]) -> [erl_type()].
+
+t_sup_lists([T1|Left1], [T2|Left2]) ->
+ [t_sup(T1, T2)|t_sup_lists(Left1, Left2)];
+t_sup_lists([], []) ->
+ [].
+
+sup_tuple_sets(L1, L2) ->
+ TotalArities = ordsets:union([Arity || {Arity, _} <- L1],
+ [Arity || {Arity, _} <- L2]),
+ if length(TotalArities) > ?TUPLE_ARITY_LIMIT -> t_tuple();
+ true ->
+ case sup_tuple_sets(L1, L2, []) of
+ [{_Arity, [OneTuple = ?tuple(_, _, _)]}] -> OneTuple;
+ List -> ?tuple_set(List)
+ end
+ end.
+
+sup_tuple_sets([{Arity, Tuples1}|Left1], [{Arity, Tuples2}|Left2], Acc) ->
+ NewAcc = [{Arity, sup_tuples_in_set(Tuples1, Tuples2)}|Acc],
+ sup_tuple_sets(Left1, Left2, NewAcc);
+sup_tuple_sets([{Arity1, _} = T1|Left1] = L1,
+ [{Arity2, _} = T2|Left2] = L2, Acc) ->
+ if Arity1 < Arity2 -> sup_tuple_sets(Left1, L2, [T1|Acc]);
+ Arity1 > Arity2 -> sup_tuple_sets(L1, Left2, [T2|Acc])
+ end;
+sup_tuple_sets([], L2, Acc) -> lists:reverse(Acc, L2);
+sup_tuple_sets(L1, [], Acc) -> lists:reverse(Acc, L1).
+
+sup_tuples_in_set([?tuple(_, _, ?any) = T], L) ->
+ [t_tuple(sup_tuple_elements([T|L]))];
+sup_tuples_in_set(L, [?tuple(_, _, ?any) = T]) ->
+ [t_tuple(sup_tuple_elements([T|L]))];
+sup_tuples_in_set(L1, L2) ->
+ FoldFun = fun(?tuple(_, _, Tag), AccTag) -> t_sup(Tag, AccTag) end,
+ TotalTag0 = lists:foldl(FoldFun, ?none, L1),
+ TotalTag = lists:foldl(FoldFun, TotalTag0, L2),
+ case TotalTag of
+ ?atom(?any) ->
+ %% We will reach the set limit. Widen now.
+ [t_tuple(sup_tuple_elements(L1 ++ L2))];
+ ?atom(Set) ->
+ case set_size(Set) > ?TUPLE_TAG_LIMIT of
+ true ->
+ %% We will reach the set limit. Widen now.
+ [t_tuple(sup_tuple_elements(L1 ++ L2))];
+ false ->
+ %% We can go on and build the tuple set.
+ sup_tuples_in_set(L1, L2, [])
+ end
+ end.
+
+sup_tuple_elements([?tuple(Elements, _, _)|L]) ->
+ lists:foldl(fun (?tuple(Es, _, _), Acc) -> t_sup_lists(Es, Acc) end,
+ Elements, L).
+
+sup_tuples_in_set([?tuple(Elements1, Arity, Tag1) = T1|Left1] = L1,
+ [?tuple(Elements2, Arity, Tag2) = T2|Left2] = L2, Acc) ->
+ if
+ Tag1 < Tag2 -> sup_tuples_in_set(Left1, L2, [T1|Acc]);
+ Tag1 > Tag2 -> sup_tuples_in_set(L1, Left2, [T2|Acc]);
+ Tag2 =:= Tag2 -> NewElements = t_sup_lists(Elements1, Elements2),
+ NewAcc = [?tuple(NewElements, Arity, Tag1)|Acc],
+ sup_tuples_in_set(Left1, Left2, NewAcc)
+ end;
+sup_tuples_in_set([], L2, Acc) -> lists:reverse(Acc, L2);
+sup_tuples_in_set(L1, [], Acc) -> lists:reverse(Acc, L1).
+
+sup_union(U1, U2) ->
+ sup_union(U1, U2, 0, []).
+
+sup_union([?none|Left1], [?none|Left2], N, Acc) ->
+ sup_union(Left1, Left2, N, [?none|Acc]);
+sup_union([T1|Left1], [T2|Left2], N, Acc) ->
+ sup_union(Left1, Left2, N+1, [t_sup(T1, T2)|Acc]);
+sup_union([], [], N, Acc) ->
+ if N =:= 0 -> ?none;
+ N =:= 1 ->
+ [Type] = [T || T <- Acc, T =/= ?none],
+ Type;
+ N =:= length(Acc) -> ?any;
+ true -> ?union(lists:reverse(Acc))
+ end.
+
+force_union(T = ?atom(_)) -> ?atom_union(T);
+force_union(T = ?bitstr(_, _)) -> ?bitstr_union(T);
+force_union(T = ?function(_, _)) -> ?function_union(T);
+force_union(T = ?identifier(_)) -> ?identifier_union(T);
+force_union(T = ?list(_, _, _)) -> ?list_union(T);
+force_union(T = ?nil) -> ?list_union(T);
+force_union(T = ?number(_, _)) -> ?number_union(T);
+force_union(T = ?opaque(_)) -> ?opaque_union(T);
+force_union(T = ?map(_,_,_)) -> ?map_union(T);
+force_union(T = ?tuple(_, _, _)) -> ?tuple_union(T);
+force_union(T = ?tuple_set(_)) -> ?tuple_union(T);
+force_union(T = ?matchstate(_, _)) -> ?matchstate_union(T);
+force_union(T = ?union(_)) -> T.
+
+%%-----------------------------------------------------------------------------
+%% An attempt to write the inverse operation of t_sup/1 -- XXX: INCOMPLETE !!
+%%
+
+-spec t_elements(erl_type()) -> [erl_type()].
+
+t_elements(?none) -> [];
+t_elements(?unit) -> [];
+t_elements(?any = T) -> [T];
+t_elements(?nil = T) -> [T];
+t_elements(?atom(?any) = T) -> [T];
+t_elements(?atom(Atoms)) ->
+ [t_atom(A) || A <- Atoms];
+t_elements(?bitstr(_, _) = T) -> [T];
+t_elements(?function(_, _) = T) -> [T];
+t_elements(?identifier(?any) = T) -> [T];
+t_elements(?identifier(IDs)) ->
+ [?identifier([T]) || T <- IDs];
+t_elements(?list(_, _, _) = T) -> [T];
+t_elements(?number(_, _) = T) ->
+ case T of
+ ?number(?any, ?unknown_qual) ->
+ [?float, ?integer(?any)];
+ ?float -> [T];
+ ?integer(?any) -> [T];
+ ?int_range(_, _) -> [T];
+ ?int_set(Set) ->
+ [t_integer(I) || I <- Set]
+ end;
+t_elements(?opaque(_) = T) ->
+ do_elements(T);
+t_elements(?map(_,_,_) = T) -> [T];
+t_elements(?tuple(_, _, _) = T) -> [T];
+t_elements(?tuple_set(_) = TS) ->
+ case t_tuple_subtypes(TS) of
+ unknown -> [];
+ Elems -> Elems
+ end;
+t_elements(?union(_) = T) ->
+ do_elements(T);
+t_elements(?var(_)) -> [?any]. %% yes, vars exist -- what else to do here?
+%% t_elements(T) ->
+%% io:format("T_ELEMENTS => ~p\n", [T]).
+
+do_elements(Type0) ->
+ case do_opaque(Type0, 'universe', fun(T) -> T end) of
+ ?union(List) -> lists:append([t_elements(T) || T <- List]);
+ Type -> t_elements(Type)
+ end.
+
+%%-----------------------------------------------------------------------------
+%% Infimum
+%%
+
+-spec t_inf([erl_type()]) -> erl_type().
+
+t_inf([H1, H2|T]) ->
+ case t_inf(H1, H2) of
+ ?none -> ?none;
+ NewH -> t_inf([NewH|T])
+ end;
+t_inf([H]) -> H;
+t_inf([]) -> ?none.
+
+-spec t_inf(erl_type(), erl_type()) -> erl_type().
+
+t_inf(T1, T2) ->
+ t_inf(T1, T2, 'universe').
+
+%% 'match' should be used from t_find_unknown_opaque() only
+-type t_inf_opaques() :: opaques() | {'match', [erl_type() | 'universe']}.
+
+-spec t_inf(erl_type(), erl_type(), t_inf_opaques()) -> erl_type().
+
+t_inf(?var(_), ?var(_), _Opaques) -> ?any;
+t_inf(?var(_), T, _Opaques) -> subst_all_vars_to_any(T);
+t_inf(T, ?var(_), _Opaques) -> subst_all_vars_to_any(T);
+t_inf(?any, T, _Opaques) -> subst_all_vars_to_any(T);
+t_inf(T, ?any, _Opaques) -> subst_all_vars_to_any(T);
+t_inf(?none, _, _Opaques) -> ?none;
+t_inf(_, ?none, _Opaques) -> ?none;
+t_inf(?unit, _, _Opaques) -> ?unit; % ?unit cases should appear below ?none
+t_inf(_, ?unit, _Opaques) -> ?unit;
+t_inf(T, T, _Opaques) -> subst_all_vars_to_any(T);
+t_inf(?atom(Set1), ?atom(Set2), _) ->
+ case set_intersection(Set1, Set2) of
+ ?none -> ?none;
+ NewSet -> ?atom(NewSet)
+ end;
+t_inf(?bitstr(U1, B1), ?bitstr(0, B2), _Opaques) ->
+ if B2 >= B1 andalso (B2-B1) rem U1 =:= 0 -> t_bitstr(0, B2);
+ true -> ?none
+ end;
+t_inf(?bitstr(0, B1), ?bitstr(U2, B2), _Opaques) ->
+ if B1 >= B2 andalso (B1-B2) rem U2 =:= 0 -> t_bitstr(0, B1);
+ true -> ?none
+ end;
+t_inf(?bitstr(U1, B1), ?bitstr(U1, B1), _Opaques) ->
+ t_bitstr(U1, B1);
+t_inf(?bitstr(U1, B1), ?bitstr(U2, B2), _Opaques) when U2 > U1 ->
+ inf_bitstr(U2, B2, U1, B1);
+t_inf(?bitstr(U1, B1), ?bitstr(U2, B2), _Opaques) ->
+ inf_bitstr(U1, B1, U2, B2);
+t_inf(?function(Domain1, Range1), ?function(Domain2, Range2), Opaques) ->
+ case t_inf(Domain1, Domain2, Opaques) of
+ ?none -> ?none;
+ Domain -> ?function(Domain, t_inf(Range1, Range2, Opaques))
+ end;
+t_inf(?identifier(Set1), ?identifier(Set2), _Opaques) ->
+ case set_intersection(Set1, Set2) of
+ ?none -> ?none;
+ Set -> ?identifier(Set)
+ end;
+t_inf(?map(_, ADefK, ADefV) = A, ?map(_, BDefK, BDefV) = B, _Opaques) ->
+ %% Because it simplifies the anonymous function, we allow Pairs to temporarily
+ %% contain mandatory pairs with none values, since all such cases should
+ %% result in a none result.
+ Pairs =
+ map_pairwise_merge(
+ %% For optional keys in both maps, when the infinimum is none, we have
+ %% essentially concluded that K must not be a key in the map.
+ fun(K, ?opt, V1, ?opt, V2) -> {K, ?opt, t_inf(V1, V2)};
+ %% When a key is optional in one map, but mandatory in another, it
+ %% becomes mandatory in the infinumum
+ (K, _, V1, _, V2) -> {K, ?mand, t_inf(V1, V2)}
+ end, A, B),
+ %% If the infinimum of any mandatory values is ?none, the entire map infinimum
+ %% is ?none.
+ case lists:any(fun({_,?mand,?none})->true; ({_,_,_}) -> false end, Pairs) of
+ true -> t_none();
+ false -> t_map(Pairs, t_inf(ADefK, BDefK), t_inf(ADefV, BDefV))
+ end;
+t_inf(?matchstate(Pres1, Slots1), ?matchstate(Pres2, Slots2), _Opaques) ->
+ ?matchstate(t_inf(Pres1, Pres2), t_inf(Slots1, Slots2));
+t_inf(?nil, ?nil, _Opaques) -> ?nil;
+t_inf(?nil, ?nonempty_list(_, _), _Opaques) ->
+ ?none;
+t_inf(?nonempty_list(_, _), ?nil, _Opaques) ->
+ ?none;
+t_inf(?nil, ?list(_Contents, Termination, _), Opaques) ->
+ t_inf(?nil, t_unopaque(Termination), Opaques);
+t_inf(?list(_Contents, Termination, _), ?nil, Opaques) ->
+ t_inf(?nil, t_unopaque(Termination), Opaques);
+t_inf(?list(Contents1, Termination1, Size1),
+ ?list(Contents2, Termination2, Size2), Opaques) ->
+ case t_inf(Termination1, Termination2, Opaques) of
+ ?none -> ?none;
+ Termination ->
+ case t_inf(Contents1, Contents2, Opaques) of
+ ?none ->
+ %% If none of the lists are nonempty, then the infimum is nil.
+ case (Size1 =:= ?unknown_qual) andalso (Size2 =:= ?unknown_qual) of
+ true -> t_nil();
+ false -> ?none
+ end;
+ Contents ->
+ Size =
+ case {Size1, Size2} of
+ {?unknown_qual, ?unknown_qual} -> ?unknown_qual;
+ {?unknown_qual, ?nonempty_qual} -> ?nonempty_qual;
+ {?nonempty_qual, ?unknown_qual} -> ?nonempty_qual;
+ {?nonempty_qual, ?nonempty_qual} -> ?nonempty_qual
+ end,
+ ?list(Contents, Termination, Size)
+ end
+ end;
+t_inf(?number(_, _) = T1, ?number(_, _) = T2, _Opaques) ->
+ case {T1, T2} of
+ {T, T} -> T;
+ {_, ?number(?any, ?unknown_qual)} -> T1;
+ {?number(?any, ?unknown_qual), _} -> T2;
+ {?float, ?integer(_)} -> ?none;
+ {?integer(_), ?float} -> ?none;
+ {?integer(?any), ?integer(_)} -> T2;
+ {?integer(_), ?integer(?any)} -> T1;
+ {?int_set(Set1), ?int_set(Set2)} ->
+ case set_intersection(Set1, Set2) of
+ ?none -> ?none;
+ Set -> ?int_set(Set)
+ end;
+ {?int_range(From1, To1), ?int_range(From2, To2)} ->
+ t_from_range(max(From1, From2), min(To1, To2));
+ {Range = ?int_range(_, _), ?int_set(Set)} ->
+ %% io:format("t_inf range, set args ~p ~p ~n", [T1, T2]),
+ Ans2 =
+ case set_filter(fun(X) -> in_range(X, Range) end, Set) of
+ ?none -> ?none;
+ NewSet -> ?int_set(NewSet)
+ end,
+ %% io:format("Ans2 ~p ~n", [Ans2]),
+ Ans2;
+ {?int_set(Set), ?int_range(_, _) = Range} ->
+ case set_filter(fun(X) -> in_range(X, Range) end, Set) of
+ ?none -> ?none;
+ NewSet -> ?int_set(NewSet)
+ end
+ end;
+t_inf(?product(Types1), ?product(Types2), Opaques) ->
+ L1 = length(Types1),
+ L2 = length(Types2),
+ if L1 =:= L2 -> ?product(t_inf_lists(Types1, Types2, Opaques));
+ true -> ?none
+ end;
+t_inf(?product(_), _, _Opaques) ->
+ ?none;
+t_inf(_, ?product(_), _Opaques) ->
+ ?none;
+t_inf(?tuple(?any, ?any, ?any), ?tuple(_, _, _) = T, _Opaques) ->
+ subst_all_vars_to_any(T);
+t_inf(?tuple(_, _, _) = T, ?tuple(?any, ?any, ?any), _Opaques) ->
+ subst_all_vars_to_any(T);
+t_inf(?tuple(?any, ?any, ?any), ?tuple_set(_) = T, _Opaques) ->
+ subst_all_vars_to_any(T);
+t_inf(?tuple_set(_) = T, ?tuple(?any, ?any, ?any), _Opaques) ->
+ subst_all_vars_to_any(T);
+t_inf(?tuple(Elements1, Arity, _Tag1), ?tuple(Elements2, Arity, _Tag2), Opaques) ->
+ case t_inf_lists_strict(Elements1, Elements2, Opaques) of
+ bottom -> ?none;
+ NewElements -> t_tuple(NewElements)
+ end;
+t_inf(?tuple_set(List1), ?tuple_set(List2), Opaques) ->
+ inf_tuple_sets(List1, List2, Opaques);
+t_inf(?tuple_set(List), ?tuple(_, Arity, _) = T, Opaques) ->
+ inf_tuple_sets(List, [{Arity, [T]}], Opaques);
+t_inf(?tuple(_, Arity, _) = T, ?tuple_set(List), Opaques) ->
+ inf_tuple_sets(List, [{Arity, [T]}], Opaques);
+%% be careful: here and in the next clause T can be ?opaque
+t_inf(?union(U1), T, Opaques) ->
+ ?union(U2) = force_union(T),
+ inf_union(U1, U2, Opaques);
+t_inf(T, ?union(U2), Opaques) ->
+ ?union(U1) = force_union(T),
+ inf_union(U1, U2, Opaques);
+t_inf(?opaque(Set1), ?opaque(Set2), Opaques) ->
+ inf_opaque(Set1, Set2, Opaques);
+t_inf(?opaque(_) = T1, T2, Opaques) ->
+ inf_opaque1(T2, T1, 1, Opaques);
+t_inf(T1, ?opaque(_) = T2, Opaques) ->
+ inf_opaque1(T1, T2, 2, Opaques);
+%% and as a result, the cases for ?opaque should appear *after* ?union
+t_inf(#c{}, #c{}, _) ->
+ ?none.
+
+inf_opaque1(T1, ?opaque(Set2)=T2, Pos, Opaques) ->
+ case Opaques =:= 'universe' orelse inf_is_opaque_type(T2, Pos, Opaques) of
+ false -> ?none;
+ true ->
+ List2 = set_to_list(Set2),
+ case inf_collect(T1, List2, Opaques, []) of
+ [] -> ?none;
+ OpL -> ?opaque(ordsets:from_list(OpL))
+ end
+ end.
+
+inf_is_opaque_type(T, Pos, {match, Opaques}) ->
+ is_opaque_type(T, Opaques) orelse throw({pos, [Pos]});
+inf_is_opaque_type(T, _Pos, Opaques) ->
+ is_opaque_type(T, Opaques).
+
+inf_collect(T1, [T2|List2], Opaques, OpL) ->
+ #opaque{struct = S2} = T2,
+ case t_inf(T1, S2, Opaques) of
+ ?none -> inf_collect(T1, List2, Opaques, OpL);
+ Inf ->
+ Op = T2#opaque{struct = Inf},
+ inf_collect(T1, List2, Opaques, [Op|OpL])
+ end;
+inf_collect(_T1, [], _Opaques, OpL) ->
+ OpL.
+
+combine(S, T1, T2) ->
+ #opaque{mod = Mod1, name = Name1, args = Args1} = T1,
+ #opaque{mod = Mod2, name = Name2, args = Args2} = T2,
+ Comb1 = comb(Mod1, Name1, Args1, S, T1),
+ case is_compat_opaque_names({Mod1, Name1, Args1}, {Mod2, Name2, Args2}) of
+ true -> Comb1;
+ false -> Comb1 ++ comb(Mod2, Name2, Args2, S, T2)
+ end.
+
+comb(Mod, Name, Args, S, T) ->
+ case can_combine_opaque_names(Mod, Name, Args, S) of
+ true ->
+ ?opaque(Set) = S,
+ Set;
+ false ->
+ [T#opaque{struct = S}]
+ end.
+
+can_combine_opaque_names(Mod1, Name1, Args1,
+ ?opaque([#opaque{mod = Mod2, name = Name2, args = Args2}])) ->
+ is_compat_opaque_names({Mod1, Name1, Args1}, {Mod2, Name2, Args2});
+can_combine_opaque_names(_, _, _, _) -> false.
+
+%% Combining two lists this way can be very time consuming...
+%% Note: two parameterized opaque types are not the same if their
+%% actual parameters differ
+inf_opaque(Set1, Set2, Opaques) ->
+ List1 = inf_look_up(Set1, Opaques),
+ List2 = inf_look_up(Set2, Opaques),
+ List0 = [combine(Inf, T1, T2) ||
+ {Is1, ModNameArgs1, T1} <- List1,
+ {Is2, ModNameArgs2, T2} <- List2,
+ not t_is_none(Inf = inf_opaque_types(Is1, ModNameArgs1, T1,
+ Is2, ModNameArgs2, T2,
+ Opaques))],
+ List = lists:sort(lists:append(List0)),
+ sup_opaque(List).
+
+%% Optimization: do just one lookup.
+inf_look_up(Set, Opaques) ->
+ [{Opaques =:= 'universe' orelse inf_is_opaque_type2(T, Opaques),
+ {M, N, Args}, T} ||
+ #opaque{mod = M, name = N, args = Args} = T <- set_to_list(Set)].
+
+inf_is_opaque_type2(T, {match, Opaques}) ->
+ is_opaque_type2(T, Opaques);
+inf_is_opaque_type2(T, Opaques) ->
+ is_opaque_type2(T, Opaques).
+
+inf_opaque_types(IsOpaque1, ModNameArgs1, T1,
+ IsOpaque2, ModNameArgs2, T2, Opaques) ->
+ #opaque{struct = S1}=T1,
+ #opaque{struct = S2}=T2,
+ case
+ Opaques =:= 'universe' orelse
+ is_compat_opaque_names(ModNameArgs1, ModNameArgs2)
+ of
+ true -> t_inf(S1, S2, Opaques);
+ false ->
+ case {IsOpaque1, IsOpaque2} of
+ {true, true} -> t_inf(S1, S2, Opaques);
+ {true, false} -> t_inf(S1, ?opaque(set_singleton(T2)), Opaques);
+ {false, true} -> t_inf(?opaque(set_singleton(T1)), S2, Opaques);
+ {false, false} when element(1, Opaques) =:= match ->
+ throw({pos, [1, 2]});
+ {false, false} -> t_none()
+ end
+ end.
+
+is_compat_opaque_names(ModNameArgs, ModNameArgs) -> true;
+is_compat_opaque_names({Mod,Name,Args1}, {Mod,Name,Args2}) ->
+ is_compat_args(Args1, Args2);
+is_compat_opaque_names(_, _) -> false.
+
+is_compat_args([A1|Args1], [A2|Args2]) ->
+ is_compat_arg(A1, A2) andalso is_compat_args(Args1, Args2);
+is_compat_args([], []) -> true;
+is_compat_args(_, _) -> false.
+
+is_compat_arg(A1, A2) ->
+ is_specialization(A1, A2) orelse is_specialization(A2, A1).
+
+-spec is_specialization(erl_type(), erl_type()) -> boolean().
+
+%% Returns true if the first argument is a specialization of the
+%% second argument in the sense that every type is a specialization of
+%% any(). For example, {_,_} is a specialization of any(), but not of
+%% tuple(). Does not handle variables, but any() and unions (sort of).
+
+is_specialization(T, T) -> true;
+is_specialization(_, ?any) -> true;
+is_specialization(?any, _) -> false;
+is_specialization(?function(Domain1, Range1), ?function(Domain2, Range2)) ->
+ (is_specialization(Domain1, Domain2) andalso
+ is_specialization(Range1, Range2));
+is_specialization(?list(Contents1, Termination1, Size1),
+ ?list(Contents2, Termination2, Size2)) ->
+ (Size1 =:= Size2 andalso
+ is_specialization(Contents1, Contents2) andalso
+ is_specialization(Termination1, Termination2));
+is_specialization(?product(Types1), ?product(Types2)) ->
+ specialization_list(Types1, Types2);
+is_specialization(?tuple(?any, ?any, ?any), ?tuple(_, _, _)) -> false;
+is_specialization(?tuple(_, _, _), ?tuple(?any, ?any, ?any)) -> false;
+is_specialization(?tuple(Elements1, Arity, _),
+ ?tuple(Elements2, Arity, _)) when Arity =/= ?any ->
+ specialization_list(Elements1, Elements2);
+is_specialization(?tuple_set([{Arity, List}]),
+ ?tuple(Elements2, Arity, _)) when Arity =/= ?any ->
+ specialization_list(sup_tuple_elements(List), Elements2);
+is_specialization(?tuple(Elements1, Arity, _),
+ ?tuple_set([{Arity, List}])) when Arity =/= ?any ->
+ specialization_list(Elements1, sup_tuple_elements(List));
+is_specialization(?tuple_set(List1), ?tuple_set(List2)) ->
+ try
+ specialization_list_list([sup_tuple_elements(T) || {_Arity, T} <- List1],
+ [sup_tuple_elements(T) || {_Arity, T} <- List2])
+ catch _:_ -> false
+ end;
+is_specialization(?union(List1)=T1, ?union(List2)=T2) ->
+ case specialization_union2(T1, T2) of
+ {yes, Type1, Type2} -> is_specialization(Type1, Type2);
+ no -> specialization_list(List1, List2)
+ end;
+is_specialization(?union(List), T2) ->
+ case unify_union(List) of
+ {yes, Type} -> is_specialization(Type, T2);
+ no -> false
+ end;
+is_specialization(T1, ?union(List)) ->
+ case unify_union(List) of
+ {yes, Type} -> is_specialization(T1, Type);
+ no -> false
+ end;
+is_specialization(?opaque(_) = T1, T2) ->
+ is_specialization(t_opaque_structure(T1), T2);
+is_specialization(T1, ?opaque(_) = T2) ->
+ is_specialization(T1, t_opaque_structure(T2));
+is_specialization(?var(_), _) -> exit(error);
+is_specialization(_, ?var(_)) -> exit(error);
+is_specialization(?none, _) -> false;
+is_specialization(_, ?none) -> false;
+is_specialization(?unit, _) -> false;
+is_specialization(_, ?unit) -> false;
+is_specialization(#c{}, #c{}) -> false.
+
+specialization_list_list(LL1, LL2) ->
+ length(LL1) =:= length(LL2) andalso specialization_list_list1(LL1, LL2).
+
+specialization_list_list1([], []) -> true;
+specialization_list_list1([L1|LL1], [L2|LL2]) ->
+ specialization_list(L1, L2) andalso specialization_list_list1(LL1, LL2).
+
+specialization_list(L1, L2) ->
+ length(L1) =:= length(L2) andalso specialization_list1(L1, L2).
+
+specialization_list1([], []) -> true;
+specialization_list1([T1|L1], [T2|L2]) ->
+ is_specialization(T1, T2) andalso specialization_list1(L1, L2).
+
+specialization_union2(?union(List1)=T1, ?union(List2)=T2) ->
+ case {unify_union(List1), unify_union(List2)} of
+ {{yes, Type1}, {yes, Type2}} -> {yes, Type1, Type2};
+ {{yes, Type1}, no} -> {yes, Type1, T2};
+ {no, {yes, Type2}} -> {yes, T1, Type2};
+ {no, no} -> no
+ end.
+
+-spec t_inf_lists([erl_type()], [erl_type()]) -> [erl_type()].
+
+t_inf_lists(L1, L2) ->
+ t_inf_lists(L1, L2, 'universe').
+
+-spec t_inf_lists([erl_type()], [erl_type()], t_inf_opaques()) -> [erl_type()].
+
+t_inf_lists(L1, L2, Opaques) ->
+ t_inf_lists(L1, L2, [], Opaques).
+
+-spec t_inf_lists([erl_type()], [erl_type()], [erl_type()], [erl_type()]) -> [erl_type()].
+
+t_inf_lists([T1|Left1], [T2|Left2], Acc, Opaques) ->
+ t_inf_lists(Left1, Left2, [t_inf(T1, T2, Opaques)|Acc], Opaques);
+t_inf_lists([], [], Acc, _Opaques) ->
+ lists:reverse(Acc).
+
+%% Infimum of lists with strictness.
+%% If any element is the ?none type, the value 'bottom' is returned.
+
+-spec t_inf_lists_strict([erl_type()], [erl_type()], [erl_type()]) -> 'bottom' | [erl_type()].
+
+t_inf_lists_strict(L1, L2, Opaques) ->
+ t_inf_lists_strict(L1, L2, [], Opaques).
+
+-spec t_inf_lists_strict([erl_type()], [erl_type()], [erl_type()], [erl_type()]) -> 'bottom' | [erl_type()].
+
+t_inf_lists_strict([T1|Left1], [T2|Left2], Acc, Opaques) ->
+ case t_inf(T1, T2, Opaques) of
+ ?none -> bottom;
+ T -> t_inf_lists_strict(Left1, Left2, [T|Acc], Opaques)
+ end;
+t_inf_lists_strict([], [], Acc, _Opaques) ->
+ lists:reverse(Acc).
+
+inf_tuple_sets(L1, L2, Opaques) ->
+ case inf_tuple_sets(L1, L2, [], Opaques) of
+ [] -> ?none;
+ [{_Arity, [?tuple(_, _, _) = OneTuple]}] -> OneTuple;
+ List -> ?tuple_set(List)
+ end.
+
+inf_tuple_sets([{Arity, Tuples1}|Ts1], [{Arity, Tuples2}|Ts2], Acc, Opaques) ->
+ case inf_tuples_in_sets(Tuples1, Tuples2, Opaques) of
+ [] -> inf_tuple_sets(Ts1, Ts2, Acc, Opaques);
+ [?tuple_set([{Arity, NewTuples}])] ->
+ inf_tuple_sets(Ts1, Ts2, [{Arity, NewTuples}|Acc], Opaques);
+ NewTuples -> inf_tuple_sets(Ts1, Ts2, [{Arity, NewTuples}|Acc], Opaques)
+ end;
+inf_tuple_sets([{Arity1, _}|Ts1] = L1, [{Arity2, _}|Ts2] = L2, Acc, Opaques) ->
+ if Arity1 < Arity2 -> inf_tuple_sets(Ts1, L2, Acc, Opaques);
+ Arity1 > Arity2 -> inf_tuple_sets(L1, Ts2, Acc, Opaques)
+ end;
+inf_tuple_sets([], _, Acc, _Opaques) -> lists:reverse(Acc);
+inf_tuple_sets(_, [], Acc, _Opaques) -> lists:reverse(Acc).
+
+inf_tuples_in_sets([?tuple(Elements1, _, ?any)], L2, Opaques) ->
+ NewList = [t_inf_lists_strict(Elements1, Elements2, Opaques)
+ || ?tuple(Elements2, _, _) <- L2],
+ [t_tuple(Es) || Es <- NewList, Es =/= bottom];
+inf_tuples_in_sets(L1, [?tuple(Elements2, _, ?any)], Opaques) ->
+ NewList = [t_inf_lists_strict(Elements1, Elements2, Opaques)
+ || ?tuple(Elements1, _, _) <- L1],
+ [t_tuple(Es) || Es <- NewList, Es =/= bottom];
+inf_tuples_in_sets(L1, L2, Opaques) ->
+ inf_tuples_in_sets2(L1, L2, [], Opaques).
+
+inf_tuples_in_sets2([?tuple(Elements1, Arity, Tag)|Ts1],
+ [?tuple(Elements2, Arity, Tag)|Ts2], Acc, Opaques) ->
+ case t_inf_lists_strict(Elements1, Elements2, Opaques) of
+ bottom -> inf_tuples_in_sets2(Ts1, Ts2, Acc, Opaques);
+ NewElements ->
+ inf_tuples_in_sets2(Ts1, Ts2, [?tuple(NewElements, Arity, Tag)|Acc],
+ Opaques)
+ end;
+inf_tuples_in_sets2([?tuple(_, _, Tag1)|Ts1] = L1,
+ [?tuple(_, _, Tag2)|Ts2] = L2, Acc, Opaques) ->
+ if Tag1 < Tag2 -> inf_tuples_in_sets2(Ts1, L2, Acc, Opaques);
+ Tag1 > Tag2 -> inf_tuples_in_sets2(L1, Ts2, Acc, Opaques)
+ end;
+inf_tuples_in_sets2([], _, Acc, _Opaques) -> lists:reverse(Acc);
+inf_tuples_in_sets2(_, [], Acc, _Opaques) -> lists:reverse(Acc).
+
+inf_union(U1, U2, Opaques) ->
+ OpaqueFun =
+ fun(Union1, Union2, InfFun) ->
+ [_,_,_,_,_,_,_,_,Opaque,_] = Union1,
+ [A,B,F,I,L,N,T,M,_,Map] = Union2,
+ List = [A,B,F,I,L,N,T,M,Map],
+ inf_union_collect(List, Opaque, InfFun, [], [])
+ end,
+ {O1, ThrowList1} =
+ OpaqueFun(U1, U2, fun(E, Opaque) -> t_inf(Opaque, E, Opaques) end),
+ {O2, ThrowList2}
+ = OpaqueFun(U2, U1, fun(E, Opaque) -> t_inf(E, Opaque, Opaques) end),
+ {Union, ThrowList3} = inf_union(U1, U2, 0, [], [], Opaques),
+ ThrowList = lists:merge3(ThrowList1, ThrowList2, ThrowList3),
+ case t_sup([O1, O2, Union]) of
+ ?none when ThrowList =/= [] -> throw({pos, lists:usort(ThrowList)});
+ Sup -> Sup
+ end.
+
+inf_union_collect([], _Opaque, _InfFun, InfList, ThrowList) ->
+ {t_sup(InfList), lists:usort(ThrowList)};
+inf_union_collect([?none|L], Opaque, InfFun, InfList, ThrowList) ->
+ inf_union_collect(L, Opaque, InfFun, [?none|InfList], ThrowList);
+inf_union_collect([E|L], Opaque, InfFun, InfList, ThrowList) ->
+ try InfFun(E, Opaque)of
+ Inf ->
+ inf_union_collect(L, Opaque, InfFun, [Inf|InfList], ThrowList)
+ catch throw:{pos, Ns} ->
+ inf_union_collect(L, Opaque, InfFun, InfList, Ns ++ ThrowList)
+ end.
+
+inf_union([?none|Left1], [?none|Left2], N, Acc, ThrowList, Opaques) ->
+ inf_union(Left1, Left2, N, [?none|Acc], ThrowList, Opaques);
+inf_union([T1|Left1], [T2|Left2], N, Acc, ThrowList, Opaques) ->
+ try t_inf(T1, T2, Opaques) of
+ ?none -> inf_union(Left1, Left2, N, [?none|Acc], ThrowList, Opaques);
+ T -> inf_union(Left1, Left2, N+1, [T|Acc], ThrowList, Opaques)
+ catch throw:{pos, Ns} ->
+ inf_union(Left1, Left2, N, [?none|Acc], Ns ++ ThrowList, Opaques)
+ end;
+inf_union([], [], N, Acc, ThrowList, _Opaques) ->
+ if N =:= 0 -> {?none, ThrowList};
+ N =:= 1 ->
+ [Type] = [T || T <- Acc, T =/= ?none],
+ {Type, ThrowList};
+ N >= 2 -> {?union(lists:reverse(Acc)), ThrowList}
+ end.
+
+inf_bitstr(U1, B1, U2, B2) ->
+ GCD = gcd(U1, U2),
+ case (B2-B1) rem GCD of
+ 0 ->
+ U = (U1*U2) div GCD,
+ B = findfirst(0, 0, U1, B1, U2, B2),
+ t_bitstr(U, B);
+ _ ->
+ ?none
+ end.
+
+findfirst(N1, N2, U1, B1, U2, B2) ->
+ Val1 = U1*N1+B1,
+ Val2 = U2*N2+B2,
+ if Val1 =:= Val2 ->
+ Val1;
+ Val1 > Val2 ->
+ findfirst(N1, N2+1, U1, B1, U2, B2);
+ Val1 < Val2 ->
+ findfirst(N1+1, N2, U1, B1, U2, B2)
+ end.
+
+%%-----------------------------------------------------------------------------
+%% Substitution of variables
+%%
+
+-type subst_table() :: #{any() => erl_type()}.
+
+-spec t_subst(erl_type(), subst_table()) -> erl_type().
+
+t_subst(T, Map) ->
+ case t_has_var(T) of
+ true -> t_subst_aux(T, Map);
+ false -> T
+ end.
+
+-spec subst_all_vars_to_any(erl_type()) -> erl_type().
+
+subst_all_vars_to_any(T) ->
+ t_subst(T, #{}).
+
+t_subst_aux(?var(Id), Map) ->
+ case maps:find(Id, Map) of
+ error -> ?any;
+ {ok, Type} -> Type
+ end;
+t_subst_aux(?list(Contents, Termination, Size), Map) ->
+ case t_subst_aux(Contents, Map) of
+ ?none -> ?none;
+ NewContents ->
+ %% Be careful here to make the termination collapse if necessary.
+ case t_subst_aux(Termination, Map) of
+ ?nil -> ?list(NewContents, ?nil, Size);
+ ?any -> ?list(NewContents, ?any, Size);
+ Other ->
+ ?list(NewContents2, NewTermination, _) = t_cons(NewContents, Other),
+ ?list(NewContents2, NewTermination, Size)
+ end
+ end;
+t_subst_aux(?function(Domain, Range), Map) ->
+ ?function(t_subst_aux(Domain, Map), t_subst_aux(Range, Map));
+t_subst_aux(?product(Types), Map) ->
+ ?product([t_subst_aux(T, Map) || T <- Types]);
+t_subst_aux(?tuple(?any, ?any, ?any) = T, _Map) ->
+ T;
+t_subst_aux(?tuple(Elements, _Arity, _Tag), Map) ->
+ t_tuple([t_subst_aux(E, Map) || E <- Elements]);
+t_subst_aux(?tuple_set(_) = TS, Map) ->
+ t_sup([t_subst_aux(T, Map) || T <- t_tuple_subtypes(TS)]);
+t_subst_aux(?map(Pairs, DefK, DefV), Map) ->
+ t_map([{K, MNess, t_subst_aux(V, Map)} || {K, MNess, V} <- Pairs],
+ t_subst_aux(DefK, Map), t_subst_aux(DefV, Map));
+t_subst_aux(?opaque(Es), Map) ->
+ List = [Opaque#opaque{args = [t_subst_aux(Arg, Map) || Arg <- Args],
+ struct = t_subst_aux(S, Map)} ||
+ Opaque = #opaque{args = Args, struct = S} <- set_to_list(Es)],
+ ?opaque(ordsets:from_list(List));
+t_subst_aux(?union(List), Map) ->
+ ?union([t_subst_aux(E, Map) || E <- List]);
+t_subst_aux(T, _Map) ->
+ T.
+
+%%-----------------------------------------------------------------------------
+%% Unification
+%%
+
+-type t_unify_ret() :: {erl_type(), [{_, erl_type()}]}.
+
+-spec t_unify(erl_type(), erl_type()) -> t_unify_ret().
+
+t_unify(T1, T2) ->
+ {T, VarMap} = t_unify(T1, T2, #{}),
+ {t_subst(T, VarMap), lists:keysort(1, maps:to_list(VarMap))}.
+
+t_unify(?var(Id) = T, ?var(Id), VarMap) ->
+ {T, VarMap};
+t_unify(?var(Id1) = T, ?var(Id2), VarMap) ->
+ case maps:find(Id1, VarMap) of
+ error ->
+ case maps:find(Id2, VarMap) of
+ error -> {T, VarMap#{Id2 => T}};
+ {ok, Type} -> t_unify(T, Type, VarMap)
+ end;
+ {ok, Type1} ->
+ case maps:find(Id2, VarMap) of
+ error -> {Type1, VarMap#{Id2 => T}};
+ {ok, Type2} -> t_unify(Type1, Type2, VarMap)
+ end
+ end;
+t_unify(?var(Id), Type, VarMap) ->
+ case maps:find(Id, VarMap) of
+ error -> {Type, VarMap#{Id => Type}};
+ {ok, VarType} -> t_unify(VarType, Type, VarMap)
+ end;
+t_unify(Type, ?var(Id), VarMap) ->
+ case maps:find(Id, VarMap) of
+ error -> {Type, VarMap#{Id => Type}};
+ {ok, VarType} -> t_unify(VarType, Type, VarMap)
+ end;
+t_unify(?function(Domain1, Range1), ?function(Domain2, Range2), VarMap) ->
+ {Domain, VarMap1} = t_unify(Domain1, Domain2, VarMap),
+ {Range, VarMap2} = t_unify(Range1, Range2, VarMap1),
+ {?function(Domain, Range), VarMap2};
+t_unify(?list(Contents1, Termination1, Size),
+ ?list(Contents2, Termination2, Size), VarMap) ->
+ {Contents, VarMap1} = t_unify(Contents1, Contents2, VarMap),
+ {Termination, VarMap2} = t_unify(Termination1, Termination2, VarMap1),
+ {?list(Contents, Termination, Size), VarMap2};
+t_unify(?product(Types1), ?product(Types2), VarMap) ->
+ {Types, VarMap1} = unify_lists(Types1, Types2, VarMap),
+ {?product(Types), VarMap1};
+t_unify(?tuple(?any, ?any, ?any) = T, ?tuple(?any, ?any, ?any), VarMap) ->
+ {T, VarMap};
+t_unify(?tuple(Elements1, Arity, _),
+ ?tuple(Elements2, Arity, _), VarMap) when Arity =/= ?any ->
+ {NewElements, VarMap1} = unify_lists(Elements1, Elements2, VarMap),
+ {t_tuple(NewElements), VarMap1};
+t_unify(?tuple_set([{Arity, _}]) = T1,
+ ?tuple(_, Arity, _) = T2, VarMap) when Arity =/= ?any ->
+ unify_tuple_set_and_tuple1(T1, T2, VarMap);
+t_unify(?tuple(_, Arity, _) = T1,
+ ?tuple_set([{Arity, _}]) = T2, VarMap) when Arity =/= ?any ->
+ unify_tuple_set_and_tuple2(T1, T2, VarMap);
+t_unify(?tuple_set(List1) = T1, ?tuple_set(List2) = T2, VarMap) ->
+ try
+ unify_lists(lists:append([T || {_Arity, T} <- List1]),
+ lists:append([T || {_Arity, T} <- List2]), VarMap)
+ of
+ {Tuples, NewVarMap} -> {t_sup(Tuples), NewVarMap}
+ catch _:_ -> throw({mismatch, T1, T2})
+ end;
+t_unify(?map(_, ADefK, ADefV) = A, ?map(_, BDefK, BDefV) = B, VarMap0) ->
+ {DefK, VarMap1} = t_unify(ADefK, BDefK, VarMap0),
+ {DefV, VarMap2} = t_unify(ADefV, BDefV, VarMap1),
+ {Pairs, VarMap} =
+ map_pairwise_merge_foldr(
+ fun(K, MNess, V1, MNess, V2, {Pairs0, VarMap3}) ->
+ %% We know that the keys unify and do not contain variables, or they
+ %% would not be singletons
+ %% TODO: Should V=?none (known missing keys) be handled special?
+ {V, VarMap4} = t_unify(V1, V2, VarMap3),
+ {[{K,MNess,V}|Pairs0], VarMap4};
+ (K, _, V1, _, V2, {Pairs0, VarMap3}) ->
+ %% One mandatory and one optional; what should be done in this case?
+ {V, VarMap4} = t_unify(V1, V2, VarMap3),
+ {[{K,?mand,V}|Pairs0], VarMap4}
+ end, {[], VarMap2}, A, B),
+ {t_map(Pairs, DefK, DefV), VarMap};
+t_unify(?opaque(_) = T1, ?opaque(_) = T2, VarMap) ->
+ t_unify(t_opaque_structure(T1), t_opaque_structure(T2), VarMap);
+t_unify(T1, ?opaque(_) = T2, VarMap) ->
+ t_unify(T1, t_opaque_structure(T2), VarMap);
+t_unify(?opaque(_) = T1, T2, VarMap) ->
+ t_unify(t_opaque_structure(T1), T2, VarMap);
+t_unify(T, T, VarMap) ->
+ {T, VarMap};
+t_unify(?union(_)=T1, ?union(_)=T2, VarMap) ->
+ {Type1, Type2} = unify_union2(T1, T2),
+ t_unify(Type1, Type2, VarMap);
+t_unify(?union(_)=T1, T2, VarMap) ->
+ t_unify(unify_union1(T1, T1, T2), T2, VarMap);
+t_unify(T1, ?union(_)=T2, VarMap) ->
+ t_unify(T1, unify_union1(T2, T1, T2), VarMap);
+t_unify(T1, T2, _) ->
+ throw({mismatch, T1, T2}).
+
+unify_union2(?union(List1)=T1, ?union(List2)=T2) ->
+ case {unify_union(List1), unify_union(List2)} of
+ {{yes, Type1}, {yes, Type2}} -> {Type1, Type2};
+ {{yes, Type1}, no} -> {Type1, T2};
+ {no, {yes, Type2}} -> {T1, Type2};
+ {no, no} -> throw({mismatch, T1, T2})
+ end.
+
+unify_union1(?union(List), T1, T2) ->
+ case unify_union(List) of
+ {yes, Type} -> Type;
+ no -> throw({mismatch, T1, T2})
+ end.
+
+unify_union(List) ->
+ [A,B,F,I,L,N,T,M,O,Map] = List,
+ if O =:= ?none -> no;
+ true ->
+ S = t_opaque_structure(O),
+ {yes, t_sup([A,B,F,I,L,N,T,M,S,Map])}
+ end.
+
+-spec is_opaque_type(erl_type(), [erl_type()]) -> boolean().
+
+%% An opaque type is a union of types. Returns true iff any of the type
+%% names (Module and Name) of the first argument (the opaque type to
+%% check) occurs in any of the opaque types of the second argument.
+is_opaque_type(?opaque(Elements), Opaques) ->
+ lists:any(fun(Opaque) -> is_opaque_type2(Opaque, Opaques) end, Elements).
+
+is_opaque_type2(#opaque{mod = Mod1, name = Name1, args = Args1}, Opaques) ->
+ F1 = fun(?opaque(Es)) ->
+ F2 = fun(#opaque{mod = Mod, name = Name, args = Args}) ->
+ is_type_name(Mod1, Name1, Args1, Mod, Name, Args)
+ end,
+ lists:any(F2, Es)
+ end,
+ lists:any(F1, Opaques).
+
+is_type_name(Mod, Name, Args1, Mod, Name, Args2) ->
+ length(Args1) =:= length(Args2);
+is_type_name(_Mod1, _Name1, _Args1, _Mod2, _Name2, _Args2) ->
+ false.
+
+%% Two functions since t_unify is not symmetric.
+unify_tuple_set_and_tuple1(?tuple_set([{Arity, List}]),
+ ?tuple(Elements2, Arity, _), VarMap) ->
+ %% Can only work if the single tuple has variables at correct places.
+ %% Collapse the tuple set.
+ {NewElements, VarMap1} =
+ unify_lists(sup_tuple_elements(List), Elements2, VarMap),
+ {t_tuple(NewElements), VarMap1}.
+
+unify_tuple_set_and_tuple2(?tuple(Elements2, Arity, _),
+ ?tuple_set([{Arity, List}]), VarMap) ->
+ %% Can only work if the single tuple has variables at correct places.
+ %% Collapse the tuple set.
+ {NewElements, VarMap1} =
+ unify_lists(Elements2, sup_tuple_elements(List), VarMap),
+ {t_tuple(NewElements), VarMap1}.
+
+unify_lists(L1, L2, VarMap) ->
+ unify_lists(L1, L2, VarMap, []).
+
+unify_lists([T1|Left1], [T2|Left2], VarMap, Acc) ->
+ {NewT, NewVarMap} = t_unify(T1, T2, VarMap),
+ unify_lists(Left1, Left2, NewVarMap, [NewT|Acc]);
+unify_lists([], [], VarMap, Acc) ->
+ {lists:reverse(Acc), VarMap}.
+
+%%t_assign_variables_to_subtype(T1, T2) ->
+%% try
+%% Dict = assign_vars(T1, T2, dict:new()),
+%% {ok, dict:map(fun(_Param, List) -> t_sup(List) end, Dict)}
+%% catch
+%% throw:error -> error
+%% end.
+
+%%assign_vars(_, ?var(_), _Dict) ->
+%% erlang:error("Variable in right hand side of assignment");
+%%assign_vars(?any, _, Dict) ->
+%% Dict;
+%%assign_vars(?var(_) = Var, Type, Dict) ->
+%% store_var(Var, Type, Dict);
+%%assign_vars(?function(Domain1, Range1), ?function(Domain2, Range2), Dict) ->
+%% DomainList =
+%% case Domain2 of
+%% ?any -> [];
+%% ?product(List) -> List
+%% end,
+%% case any_none([Range2|DomainList]) of
+%% true -> throw(error);
+%% false ->
+%% Dict1 = assign_vars(Domain1, Domain2, Dict),
+%% assign_vars(Range1, Range2, Dict1)
+%% end;
+%%assign_vars(?list(_Contents, _Termination, ?any), ?nil, Dict) ->
+%% Dict;
+%%assign_vars(?list(Contents1, Termination1, Size1),
+%% ?list(Contents2, Termination2, Size2), Dict) ->
+%% Dict1 = assign_vars(Contents1, Contents2, Dict),
+%% Dict2 = assign_vars(Termination1, Termination2, Dict1),
+%% case {Size1, Size2} of
+%% {S, S} -> Dict2;
+%% {?any, ?nonempty_qual} -> Dict2;
+%% {_, _} -> throw(error)
+%% end;
+%%assign_vars(?product(Types1), ?product(Types2), Dict) ->
+%% case length(Types1) =:= length(Types2) of
+%% true -> assign_vars_lists(Types1, Types2, Dict);
+%% false -> throw(error)
+%% end;
+%%assign_vars(?tuple(?any, ?any, ?any), ?tuple(?any, ?any, ?any), Dict) ->
+%% Dict;
+%%assign_vars(?tuple(?any, ?any, ?any), ?tuple(_, _, _), Dict) ->
+%% Dict;
+%%assign_vars(?tuple(Elements1, Arity, _),
+%% ?tuple(Elements2, Arity, _), Dict) when Arity =/= ?any ->
+%% assign_vars_lists(Elements1, Elements2, Dict);
+%%assign_vars(?tuple_set(_) = T, ?tuple_set(List2), Dict) ->
+%% %% All Rhs tuples must already be subtypes of Lhs, so we can take
+%% %% each one separatly.
+%% assign_vars_lists([T || _ <- List2], List2, Dict);
+%%assign_vars(?tuple(?any, ?any, ?any), ?tuple_set(_), Dict) ->
+%% Dict;
+%%assign_vars(?tuple(_, Arity, _) = T1, ?tuple_set(List), Dict) ->
+%% case reduce_tuple_tags(List) of
+%% [Tuple = ?tuple(_, Arity, _)] -> assign_vars(T1, Tuple, Dict);
+%% _ -> throw(error)
+%% end;
+%%assign_vars(?tuple_set(List), ?tuple(_, Arity, Tag) = T2, Dict) ->
+%% case [T || ?tuple(_, Arity1, Tag1) = T <- List,
+%% Arity1 =:= Arity, Tag1 =:= Tag] of
+%% [] -> throw(error);
+%% [T1] -> assign_vars(T1, T2, Dict)
+%% end;
+%%assign_vars(?union(U1), T2, Dict) ->
+%% ?union(U2) = force_union(T2),
+%% assign_vars_lists(U1, U2, Dict);
+%%assign_vars(T, T, Dict) ->
+%% Dict;
+%%assign_vars(T1, T2, Dict) ->
+%% case t_is_subtype(T2, T1) of
+%% false -> throw(error);
+%% true -> Dict
+%% end.
+
+%%assign_vars_lists([T1|Left1], [T2|Left2], Dict) ->
+%% assign_vars_lists(Left1, Left2, assign_vars(T1, T2, Dict));
+%%assign_vars_lists([], [], Dict) ->
+%% Dict.
+
+%%store_var(?var(Id), Type, Dict) ->
+%% case dict:find(Id, Dict) of
+%% error -> dict:store(Id, [Type], Dict);
+%% {ok, _VarType0} -> dict:update(Id, fun(X) -> [Type|X] end, Dict)
+%% end.
+
+%%-----------------------------------------------------------------------------
+%% Subtraction.
+%%
+%% Note that the subtraction is an approximation since we do not have
+%% negative types. Also, tuples and products should be handled using
+%% the cartesian product of the elements, but this is not feasible to
+%% do.
+%%
+%% Example: {a|b,c|d}\{a,d} = {a,c}|{a,d}|{b,c}|{b,d} \ {a,d} =
+%% = {a,c}|{b,c}|{b,d} = {a|b,c|d}
+%%
+%% Instead, we can subtract if all elements but one becomes none after
+%% subtracting element-wise.
+%%
+%% Example: {a|b,c|d}\{a|b,d} = {a,c}|{a,d}|{b,c}|{b,d} \ {a,d}|{b,d} =
+%% = {a,c}|{b,c} = {a|b,c}
+
+-spec t_subtract_list(erl_type(), [erl_type()]) -> erl_type().
+
+t_subtract_list(T1, [T2|Left]) ->
+ t_subtract_list(t_subtract(T1, T2), Left);
+t_subtract_list(T, []) ->
+ T.
+
+-spec t_subtract(erl_type(), erl_type()) -> erl_type().
+
+t_subtract(_, ?any) -> ?none;
+t_subtract(T, ?var(_)) -> T;
+t_subtract(?any, _) -> ?any;
+t_subtract(?var(_) = T, _) -> T;
+t_subtract(T, ?unit) -> T;
+t_subtract(?unit, _) -> ?unit;
+t_subtract(?none, _) -> ?none;
+t_subtract(T, ?none) -> T;
+t_subtract(?atom(Set1), ?atom(Set2)) ->
+ case set_subtract(Set1, Set2) of
+ ?none -> ?none;
+ Set -> ?atom(Set)
+ end;
+t_subtract(?bitstr(U1, B1), ?bitstr(U2, B2)) ->
+ subtract_bin(t_bitstr(U1, B1), t_inf(t_bitstr(U1, B1), t_bitstr(U2, B2)));
+t_subtract(?function(_, _) = T1, ?function(_, _) = T2) ->
+ case t_is_subtype(T1, T2) of
+ true -> ?none;
+ false -> T1
+ end;
+t_subtract(?identifier(Set1), ?identifier(Set2)) ->
+ case set_subtract(Set1, Set2) of
+ ?none -> ?none;
+ Set -> ?identifier(Set)
+ end;
+t_subtract(?opaque(_)=T1, ?opaque(_)=T2) ->
+ opaque_subtract(T1, t_opaque_structure(T2));
+t_subtract(?opaque(_)=T1, T2) ->
+ opaque_subtract(T1, T2);
+t_subtract(T1, ?opaque(_)=T2) ->
+ t_subtract(T1, t_opaque_structure(T2));
+t_subtract(?matchstate(Pres1, Slots1), ?matchstate(Pres2, _Slots2)) ->
+ Pres = t_subtract(Pres1, Pres2),
+ case t_is_none(Pres) of
+ true -> ?none;
+ false -> ?matchstate(Pres, Slots1)
+ end;
+t_subtract(?matchstate(Present, Slots), _) ->
+ ?matchstate(Present, Slots);
+t_subtract(?nil, ?nil) ->
+ ?none;
+t_subtract(?nil, ?nonempty_list(_, _)) ->
+ ?nil;
+t_subtract(?nil, ?list(_, _, _)) ->
+ ?none;
+t_subtract(?list(Contents, Termination, _Size) = T, ?nil) ->
+ case Termination =:= ?nil of
+ true -> ?nonempty_list(Contents, Termination);
+ false -> T
+ end;
+t_subtract(?list(Contents1, Termination1, Size1) = T,
+ ?list(Contents2, Termination2, Size2)) ->
+ case t_is_subtype(Contents1, Contents2) of
+ true ->
+ case t_is_subtype(Termination1, Termination2) of
+ true ->
+ case {Size1, Size2} of
+ {?nonempty_qual, ?unknown_qual} -> ?none;
+ {?unknown_qual, ?nonempty_qual} -> ?nil;
+ {S, S} -> ?none
+ end;
+ false ->
+ %% If the termination is not covered by the subtracted type
+ %% we cannot really say anything about the result.
+ T
+ end;
+ false ->
+ %% All contents must be covered if there is going to be any
+ %% change to the list.
+ T
+ end;
+t_subtract(?float, ?float) -> ?none;
+t_subtract(?number(_, _) = T1, ?float) -> t_inf(T1, t_integer());
+t_subtract(?float, ?number(_Set, Tag)) ->
+ case Tag of
+ ?unknown_qual -> ?none;
+ _ -> ?float
+ end;
+t_subtract(?number(_, _), ?number(?any, ?unknown_qual)) -> ?none;
+t_subtract(?number(_, _) = T1, ?integer(?any)) -> t_inf(?float, T1);
+t_subtract(?int_set(Set1), ?int_set(Set2)) ->
+ case set_subtract(Set1, Set2) of
+ ?none -> ?none;
+ Set -> ?int_set(Set)
+ end;
+t_subtract(?int_range(From1, To1) = T1, ?int_range(_, _) = T2) ->
+ case t_inf(T1, T2) of
+ ?none -> T1;
+ ?int_range(From1, To1) -> ?none;
+ ?int_range(neg_inf, To) -> t_from_range(To + 1, To1);
+ ?int_range(From, pos_inf) -> t_from_range(From1, From - 1);
+ ?int_range(From, To) -> t_sup(t_from_range(From1, From - 1),
+ t_from_range(To + 1, To))
+ end;
+t_subtract(?int_range(From, To) = T1, ?int_set(Set)) ->
+ NewFrom = case set_is_element(From, Set) of
+ true -> From + 1;
+ false -> From
+ end,
+ NewTo = case set_is_element(To, Set) of
+ true -> To - 1;
+ false -> To
+ end,
+ if (NewFrom =:= From) and (NewTo =:= To) -> T1;
+ true -> t_from_range(NewFrom, NewTo)
+ end;
+t_subtract(?int_set(Set), ?int_range(From, To)) ->
+ case set_filter(fun(X) -> not ((X =< From) orelse (X >= To)) end, Set) of
+ ?none -> ?none;
+ NewSet -> ?int_set(NewSet)
+ end;
+t_subtract(?integer(?any) = T1, ?integer(_)) -> T1;
+t_subtract(?number(_, _) = T1, ?number(_, _)) -> T1;
+t_subtract(?tuple(_, _, _), ?tuple(?any, ?any, ?any)) -> ?none;
+t_subtract(?tuple_set(_), ?tuple(?any, ?any, ?any)) -> ?none;
+t_subtract(?tuple(?any, ?any, ?any) = T1, ?tuple_set(_)) -> T1;
+t_subtract(?tuple(Elements1, Arity1, _Tag1) = T1,
+ ?tuple(Elements2, Arity2, _Tag2)) ->
+ if Arity1 =/= Arity2 -> T1;
+ Arity1 =:= Arity2 ->
+ NewElements = t_subtract_lists(Elements1, Elements2),
+ case [E || E <- NewElements, E =/= ?none] of
+ [] -> ?none;
+ [_] -> t_tuple(replace_nontrivial_element(Elements1, NewElements));
+ _ -> T1
+ end
+ end;
+t_subtract(?tuple_set(List1) = T1, ?tuple(_, Arity, _) = T2) ->
+ case orddict:find(Arity, List1) of
+ error -> T1;
+ {ok, List2} ->
+ TuplesLeft0 = [Tuple || {_Arity, Tuple} <- orddict:erase(Arity, List1)],
+ TuplesLeft1 = lists:append(TuplesLeft0),
+ t_sup([t_subtract(L, T2) || L <- List2] ++ TuplesLeft1)
+ end;
+t_subtract(?tuple(_, Arity, _) = T1, ?tuple_set(List1)) ->
+ case orddict:find(Arity, List1) of
+ error -> T1;
+ {ok, List2} -> t_inf([t_subtract(T1, L) || L <- List2])
+ end;
+t_subtract(?tuple_set(_) = T1, ?tuple_set(_) = T2) ->
+ t_sup([t_subtract(T, T2) || T <- t_tuple_subtypes(T1)]);
+t_subtract(?product(Elements1) = T1, ?product(Elements2)) ->
+ Arity1 = length(Elements1),
+ Arity2 = length(Elements2),
+ if Arity1 =/= Arity2 -> T1;
+ Arity1 =:= Arity2 ->
+ NewElements = t_subtract_lists(Elements1, Elements2),
+ case [E || E <- NewElements, E =/= ?none] of
+ [] -> ?none;
+ [_] -> t_product(replace_nontrivial_element(Elements1, NewElements));
+ _ -> T1
+ end
+ end;
+t_subtract(?map(APairs, ADefK, ADefV) = A, ?map(_, BDefK, BDefV) = B) ->
+ case t_is_subtype(ADefK, BDefK) andalso t_is_subtype(ADefV, BDefV) of
+ false -> A;
+ true ->
+ %% We fold over the maps to produce a list of constraints, where
+ %% constraints are additional key-value pairs to put in Pairs. Only one
+ %% constraint need to be applied to produce a type that excludes the
+ %% right-hand-side type, so if more than one constraint is produced, we
+ %% just return the left-hand-side argument.
+ %%
+ %% Each case of the fold may either conclude that
+ %% * The arguments constrain A at least as much as B, i.e. that A so far
+ %% is a subtype of B. In that case they return false
+ %% * That for the particular arguments, A being a subtype of B does not
+ %% hold, but the infinimum of A and B is nonempty, and by narrowing a
+ %% pair in A, we can create a type that excludes some elements in the
+ %% infinumum. In that case, they will return that pair.
+ %% * That for the particular arguments, A being a subtype of B does not
+ %% hold, and either the infinumum of A and B is empty, or it is not
+ %% possible with the current representation to create a type that
+ %% excludes elements from B without also excluding elements that are
+ %% only in A. In that case, it will return the pair from A unchanged.
+ case
+ map_pairwise_merge(
+ %% If V1 is a subtype of V2, the case that K does not exist in A
+ %% remain.
+ fun(K, ?opt, V1, ?mand, V2) -> {K, ?opt, t_subtract(V1, V2)};
+ (K, _, V1, _, V2) ->
+ %% If we subtract an optional key, that leaves a mandatory key
+ case t_subtract(V1, V2) of
+ ?none -> false;
+ Partial -> {K, ?mand, Partial}
+ end
+ end, A, B)
+ of
+ %% We produce a list of keys that are constrained. As only one of
+ %% these should apply at a time, we can't represent the difference if
+ %% more than one constraint is produced. If we applied all of them,
+ %% that would make an underapproximation, which we must not do.
+ [] -> ?none; %% A is a subtype of B
+ [E] -> t_map(mapdict_store(E, APairs), ADefK, ADefV);
+ _ -> A
+ end
+ end;
+t_subtract(?product(P1), _) ->
+ ?product(P1);
+t_subtract(T, ?product(_)) ->
+ T;
+t_subtract(?union(U1), ?union(U2)) ->
+ subtract_union(U1, U2);
+t_subtract(T1, T2) ->
+ ?union(U1) = force_union(T1),
+ ?union(U2) = force_union(T2),
+ subtract_union(U1, U2).
+
+-spec opaque_subtract(erl_type(), erl_type()) -> erl_type().
+
+opaque_subtract(?opaque(Set1), T2) ->
+ List = [T1#opaque{struct = Sub} ||
+ #opaque{struct = S1}=T1 <- set_to_list(Set1),
+ not t_is_none(Sub = t_subtract(S1, T2))],
+ case List of
+ [] -> ?none;
+ _ -> ?opaque(ordsets:from_list(List))
+ end.
+
+-spec t_subtract_lists([erl_type()], [erl_type()]) -> [erl_type()].
+
+t_subtract_lists(L1, L2) ->
+ t_subtract_lists(L1, L2, []).
+
+-spec t_subtract_lists([erl_type()], [erl_type()], [erl_type()]) -> [erl_type()].
+
+t_subtract_lists([T1|Left1], [T2|Left2], Acc) ->
+ t_subtract_lists(Left1, Left2, [t_subtract(T1, T2)|Acc]);
+t_subtract_lists([], [], Acc) ->
+ lists:reverse(Acc).
+
+-spec subtract_union([erl_type(),...], [erl_type(),...]) -> erl_type().
+
+subtract_union(U1, U2) ->
+ [A1,B1,F1,I1,L1,N1,T1,M1,O1,Map1] = U1,
+ [A2,B2,F2,I2,L2,N2,T2,M2,O2,Map2] = U2,
+ List1 = [A1,B1,F1,I1,L1,N1,T1,M1,?none,Map1],
+ List2 = [A2,B2,F2,I2,L2,N2,T2,M2,?none,Map2],
+ Sub1 = subtract_union(List1, List2, 0, []),
+ O = if O1 =:= ?none -> O1;
+ true -> t_subtract(O1, ?union(U2))
+ end,
+ Sub2 = if O2 =:= ?none -> Sub1;
+ true -> t_subtract(Sub1, t_opaque_structure(O2))
+ end,
+ t_sup(O, Sub2).
+
+-spec subtract_union([erl_type()], [erl_type()], non_neg_integer(), [erl_type()]) -> erl_type().
+
+subtract_union([T1|Left1], [T2|Left2], N, Acc) ->
+ case t_subtract(T1, T2) of
+ ?none -> subtract_union(Left1, Left2, N, [?none|Acc]);
+ T -> subtract_union(Left1, Left2, N+1, [T|Acc])
+ end;
+subtract_union([], [], 0, _Acc) ->
+ ?none;
+subtract_union([], [], 1, Acc) ->
+ [T] = [X || X <- Acc, X =/= ?none],
+ T;
+subtract_union([], [], N, Acc) when is_integer(N), N > 1 ->
+ ?union(lists:reverse(Acc)).
+
+replace_nontrivial_element(El1, El2) ->
+ replace_nontrivial_element(El1, El2, []).
+
+replace_nontrivial_element([T1|Left1], [?none|Left2], Acc) ->
+ replace_nontrivial_element(Left1, Left2, [T1|Acc]);
+replace_nontrivial_element([_|Left1], [T2|_], Acc) ->
+ lists:reverse(Acc) ++ [T2|Left1].
+
+subtract_bin(?bitstr(U1, B1), ?bitstr(U1, B1)) ->
+ ?none;
+subtract_bin(?bitstr(U1, B1), ?none) ->
+ t_bitstr(U1, B1);
+subtract_bin(?bitstr(U1, B1), ?bitstr(0, B1)) ->
+ t_bitstr(U1, B1+U1);
+subtract_bin(?bitstr(U1, B1), ?bitstr(U1, B2)) ->
+ if (B1+U1) =/= B2 -> t_bitstr(0, B1);
+ true -> t_bitstr(U1, B1)
+ end;
+subtract_bin(?bitstr(U1, B1), ?bitstr(U2, B2)) ->
+ if (2 * U1) =:= U2 ->
+ if B1 =:= B2 ->
+ t_bitstr(U2, B1+U1);
+ (B1 + U1) =:= B2 ->
+ t_bitstr(U2, B1);
+ true ->
+ t_bitstr(U1, B1)
+ end;
+ true ->
+ t_bitstr(U1, B1)
+ end.
+
+%%-----------------------------------------------------------------------------
+%% Relations
+%%
+
+-spec t_is_equal(erl_type(), erl_type()) -> boolean().
+
+t_is_equal(T, T) -> true;
+t_is_equal(_, _) -> false.
+
+-spec t_is_subtype(erl_type(), erl_type()) -> boolean().
+
+t_is_subtype(T1, T2) ->
+ Inf = t_inf(T1, T2),
+ subtype_is_equal(T1, Inf).
+
+%% The subtype relation has to behave correctly irrespective of opaque
+%% types.
+subtype_is_equal(T, T) -> true;
+subtype_is_equal(T1, T2) ->
+ t_is_equal(case t_contains_opaque(T1) of
+ true -> t_unopaque(T1);
+ false -> T1
+ end,
+ case t_contains_opaque(T2) of
+ true -> t_unopaque(T2);
+ false -> T2
+ end).
+
+-spec t_is_instance(erl_type(), erl_type()) -> boolean().
+
+%% XXX. To be removed.
+t_is_instance(ConcreteType, Type) ->
+ t_is_subtype(ConcreteType, t_unopaque(Type)).
+
+-spec t_do_overlap(erl_type(), erl_type()) -> boolean().
+
+t_do_overlap(TypeA, TypeB) ->
+ not (t_is_none_or_unit(t_inf(TypeA, TypeB))).
+
+-spec t_unopaque(erl_type()) -> erl_type().
+
+t_unopaque(T) ->
+ t_unopaque(T, 'universe').
+
+-spec t_unopaque(erl_type(), opaques()) -> erl_type().
+
+t_unopaque(?opaque(_) = T, Opaques) ->
+ case Opaques =:= 'universe' orelse is_opaque_type(T, Opaques) of
+ true -> t_unopaque(t_opaque_structure(T), Opaques);
+ false -> T
+ end;
+t_unopaque(?list(ElemT, Termination, Sz), Opaques) ->
+ ?list(t_unopaque(ElemT, Opaques), t_unopaque(Termination, Opaques), Sz);
+t_unopaque(?tuple(?any, _, _) = T, _) -> T;
+t_unopaque(?tuple(ArgTs, Sz, Tag), Opaques) when is_list(ArgTs) ->
+ NewArgTs = [t_unopaque(A, Opaques) || A <- ArgTs],
+ ?tuple(NewArgTs, Sz, Tag);
+t_unopaque(?tuple_set(Set), Opaques) ->
+ NewSet = [{Sz, [t_unopaque(T, Opaques) || T <- Tuples]}
+ || {Sz, Tuples} <- Set],
+ ?tuple_set(NewSet);
+t_unopaque(?product(Types), Opaques) ->
+ ?product([t_unopaque(T, Opaques) || T <- Types]);
+t_unopaque(?function(Domain, Range), Opaques) ->
+ ?function(t_unopaque(Domain, Opaques), t_unopaque(Range, Opaques));
+t_unopaque(?union([A,B,F,I,L,N,T,M,O,Map]), Opaques) ->
+ UL = t_unopaque(L, Opaques),
+ UT = t_unopaque(T, Opaques),
+ UF = t_unopaque(F, Opaques),
+ UM = t_unopaque(M, Opaques),
+ UMap = t_unopaque(Map, Opaques),
+ {OF,UO} = case t_unopaque(O, Opaques) of
+ ?opaque(_) = O1 -> {O1, []};
+ Type -> {?none, [Type]}
+ end,
+ t_sup([?union([A,B,UF,I,UL,N,UT,UM,OF,UMap])|UO]);
+t_unopaque(?map(Pairs,DefK,DefV), Opaques) ->
+ t_map([{K, MNess, t_unopaque(V, Opaques)} || {K, MNess, V} <- Pairs],
+ t_unopaque(DefK, Opaques),
+ t_unopaque(DefV, Opaques));
+t_unopaque(T, _) ->
+ T.
+
+%%-----------------------------------------------------------------------------
+%% K-depth abstraction.
+%%
+%% t_limit/2 is the exported function, which checks the type of the
+%% second argument and calls the module local t_limit_k/2 function.
+%%
+
+-spec t_limit(erl_type(), integer()) -> erl_type().
+
+t_limit(Term, K) when is_integer(K) ->
+ t_limit_k(Term, K).
+
+t_limit_k(_, K) when K =< 0 -> ?any;
+t_limit_k(?tuple(?any, ?any, ?any) = T, _K) -> T;
+t_limit_k(?tuple(Elements, Arity, _), K) ->
+ if K =:= 1 -> t_tuple(Arity);
+ true -> t_tuple([t_limit_k(E, K-1) || E <- Elements])
+ end;
+t_limit_k(?tuple_set(_) = T, K) ->
+ t_sup([t_limit_k(Tuple, K) || Tuple <- t_tuple_subtypes(T)]);
+t_limit_k(?list(Elements, Termination, Size), K) ->
+ NewTermination =
+ if K =:= 1 ->
+ %% We do not want to lose the termination information.
+ t_limit_k(Termination, K);
+ true -> t_limit_k(Termination, K - 1)
+ end,
+ NewElements = t_limit_k(Elements, K - 1),
+ TmpList = t_cons(NewElements, NewTermination),
+ case Size of
+ ?nonempty_qual -> TmpList;
+ ?unknown_qual ->
+ ?list(NewElements1, NewTermination1, _) = TmpList,
+ ?list(NewElements1, NewTermination1, ?unknown_qual)
+ end;
+t_limit_k(?function(Domain, Range), K) ->
+ %% The domain is either a product or any() so we do not decrease the K.
+ ?function(t_limit_k(Domain, K), t_limit_k(Range, K-1));
+t_limit_k(?product(Elements), K) ->
+ ?product([t_limit_k(X, K - 1) || X <- Elements]);
+t_limit_k(?union(Elements), K) ->
+ ?union([t_limit_k(X, K) || X <- Elements]);
+t_limit_k(?opaque(Es), K) ->
+ List = [begin
+ NewS = t_limit_k(S, K),
+ Opaque#opaque{struct = NewS}
+ end || #opaque{struct = S} = Opaque <- set_to_list(Es)],
+ ?opaque(ordsets:from_list(List));
+t_limit_k(?map(Pairs0, DefK0, DefV0), K) ->
+ Fun = fun({EK, MNess, EV}, {Exact, DefK1, DefV1}) ->
+ LV = t_limit_k(EV, K - 1),
+ case t_limit_k(EK, K - 1) of
+ EK -> {[{EK,MNess,LV}|Exact], DefK1, DefV1};
+ LK -> {Exact, t_sup(LK, DefK1), t_sup(LV, DefV1)}
+ end
+ end,
+ {Pairs, DefK2, DefV2} = lists:foldr(Fun, {[], DefK0, DefV0}, Pairs0),
+ t_map(Pairs, t_limit_k(DefK2, K - 1), t_limit_k(DefV2, K - 1));
+t_limit_k(T, _K) -> T.
+
+%%============================================================================
+%%
+%% Abstract records. Used for comparing contracts.
+%%
+%%============================================================================
+
+-spec t_abstract_records(erl_type(), type_table()) -> erl_type().
+
+t_abstract_records(?list(Contents, Termination, Size), RecDict) ->
+ case t_abstract_records(Contents, RecDict) of
+ ?none -> ?none;
+ NewContents ->
+ %% Be careful here to make the termination collapse if necessary.
+ case t_abstract_records(Termination, RecDict) of
+ ?nil -> ?list(NewContents, ?nil, Size);
+ ?any -> ?list(NewContents, ?any, Size);
+ Other ->
+ ?list(NewContents2, NewTermination, _) = t_cons(NewContents, Other),
+ ?list(NewContents2, NewTermination, Size)
+ end
+ end;
+t_abstract_records(?function(Domain, Range), RecDict) ->
+ ?function(t_abstract_records(Domain, RecDict),
+ t_abstract_records(Range, RecDict));
+t_abstract_records(?product(Types), RecDict) ->
+ ?product([t_abstract_records(T, RecDict) || T <- Types]);
+t_abstract_records(?union(Types), RecDict) ->
+ t_sup([t_abstract_records(T, RecDict) || T <- Types]);
+t_abstract_records(?tuple(?any, ?any, ?any) = T, _RecDict) ->
+ T;
+t_abstract_records(?tuple(Elements, Arity, ?atom(_) = Tag), RecDict) ->
+ [TagAtom] = atom_vals(Tag),
+ case lookup_record(TagAtom, Arity - 1, RecDict) of
+ error -> t_tuple([t_abstract_records(E, RecDict) || E <- Elements]);
+ {ok, Fields} -> t_tuple([Tag|[T || {_Name, _Abstr, T} <- Fields]])
+ end;
+t_abstract_records(?tuple(Elements, _Arity, _Tag), RecDict) ->
+ t_tuple([t_abstract_records(E, RecDict) || E <- Elements]);
+t_abstract_records(?tuple_set(_) = Tuples, RecDict) ->
+ t_sup([t_abstract_records(T, RecDict) || T <- t_tuple_subtypes(Tuples)]);
+t_abstract_records(?opaque(_)=Type, RecDict) ->
+ t_abstract_records(t_opaque_structure(Type), RecDict);
+t_abstract_records(T, _RecDict) ->
+ T.
+
+%% Map over types. Depth first. Used by the contract checker. ?list is
+%% not fully implemented so take care when changing the type in Termination.
+
+-spec t_map(fun((erl_type()) -> erl_type()), erl_type()) -> erl_type().
+
+t_map(Fun, ?list(Contents, Termination, Size)) ->
+ Fun(?list(t_map(Fun, Contents), t_map(Fun, Termination), Size));
+t_map(Fun, ?function(Domain, Range)) ->
+ Fun(?function(t_map(Fun, Domain), t_map(Fun, Range)));
+t_map(Fun, ?product(Types)) ->
+ Fun(?product([t_map(Fun, T) || T <- Types]));
+t_map(Fun, ?union(Types)) ->
+ Fun(t_sup([t_map(Fun, T) || T <- Types]));
+t_map(Fun, ?tuple(?any, ?any, ?any) = T) ->
+ Fun(T);
+t_map(Fun, ?tuple(Elements, _Arity, _Tag)) ->
+ Fun(t_tuple([t_map(Fun, E) || E <- Elements]));
+t_map(Fun, ?tuple_set(_) = Tuples) ->
+ Fun(t_sup([t_map(Fun, T) || T <- t_tuple_subtypes(Tuples)]));
+t_map(Fun, ?opaque(Set)) ->
+ L = [Opaque#opaque{struct = NewS} ||
+ #opaque{struct = S} = Opaque <- set_to_list(Set),
+ not t_is_none(NewS = t_map(Fun, S))],
+ Fun(case L of
+ [] -> ?none;
+ _ -> ?opaque(ordsets:from_list(L))
+ end);
+t_map(Fun, ?map(Pairs,DefK,DefV)) ->
+ %% TODO:
+ Fun(t_map(Pairs, Fun(DefK), Fun(DefV)));
+t_map(Fun, T) ->
+ Fun(T).
+
+%%=============================================================================
+%%
+%% Prettyprinter
+%%
+%%=============================================================================
+
+-spec t_to_string(erl_type()) -> string().
+
+t_to_string(T) ->
+ t_to_string(T, dict:new()).
+
+-spec t_to_string(erl_type(), type_table()) -> string().
+
+t_to_string(?any, _RecDict) ->
+ "any()";
+t_to_string(?none, _RecDict) ->
+ "none()";
+t_to_string(?unit, _RecDict) ->
+ "no_return()";
+t_to_string(?atom(?any), _RecDict) ->
+ "atom()";
+t_to_string(?atom(Set), _RecDict) ->
+ case set_size(Set) of
+ 2 ->
+ case set_is_element(true, Set) andalso set_is_element(false, Set) of
+ true -> "boolean()";
+ false -> set_to_string(Set)
+ end;
+ _ ->
+ set_to_string(Set)
+ end;
+t_to_string(?bitstr(0, 0), _RecDict) ->
+ "<<>>";
+t_to_string(?bitstr(8, 0), _RecDict) ->
+ "binary()";
+t_to_string(?bitstr(1, 0), _RecDict) ->
+ "bitstring()";
+t_to_string(?bitstr(0, B), _RecDict) ->
+ flat_format("<<_:~w>>", [B]);
+t_to_string(?bitstr(U, 0), _RecDict) ->
+ flat_format("<<_:_*~w>>", [U]);
+t_to_string(?bitstr(U, B), _RecDict) ->
+ flat_format("<<_:~w,_:_*~w>>", [B, U]);
+t_to_string(?function(?any, ?any), _RecDict) ->
+ "fun()";
+t_to_string(?function(?any, Range), RecDict) ->
+ "fun((...) -> " ++ t_to_string(Range, RecDict) ++ ")";
+t_to_string(?function(?product(ArgList), Range), RecDict) ->
+ "fun((" ++ comma_sequence(ArgList, RecDict) ++ ") -> "
+ ++ t_to_string(Range, RecDict) ++ ")";
+t_to_string(?identifier(Set), _RecDict) ->
+ case Set of
+ ?any -> "identifier()";
+ _ ->
+ string:join([flat_format("~w()", [T]) || T <- set_to_list(Set)], " | ")
+ end;
+t_to_string(?opaque(Set), RecDict) ->
+ string:join([opaque_type(Mod, Name, Args, S, RecDict) ||
+ #opaque{mod = Mod, name = Name, struct = S, args = Args}
+ <- set_to_list(Set)],
+ " | ");
+t_to_string(?matchstate(Pres, Slots), RecDict) ->
+ flat_format("ms(~s,~s)", [t_to_string(Pres, RecDict),
+ t_to_string(Slots,RecDict)]);
+t_to_string(?nil, _RecDict) ->
+ "[]";
+t_to_string(?nonempty_list(Contents, Termination), RecDict) ->
+ ContentString = t_to_string(Contents, RecDict),
+ case Termination of
+ ?nil ->
+ case Contents of
+ ?char -> "nonempty_string()";
+ _ -> "["++ContentString++",...]"
+ end;
+ ?any ->
+ %% Just a safety check.
+ case Contents =:= ?any of
+ true -> ok;
+ false ->
+ %% XXX. See comment below.
+ %% erlang:error({illegal_list, ?nonempty_list(Contents, Termination)})
+ ok
+ end,
+ "nonempty_maybe_improper_list()";
+ _ ->
+ case t_is_subtype(t_nil(), Termination) of
+ true ->
+ "nonempty_maybe_improper_list("++ContentString++","
+ ++t_to_string(Termination, RecDict)++")";
+ false ->
+ "nonempty_improper_list("++ContentString++","
+ ++t_to_string(Termination, RecDict)++")"
+ end
+ end;
+t_to_string(?list(Contents, Termination, ?unknown_qual), RecDict) ->
+ ContentString = t_to_string(Contents, RecDict),
+ case Termination of
+ ?nil ->
+ case Contents of
+ ?char -> "string()";
+ _ -> "["++ContentString++"]"
+ end;
+ ?any ->
+ %% Just a safety check.
+ %% XXX. Types such as "maybe_improper_list(integer(), any())"
+ %% are OK, but cannot be printed!?
+ case Contents =:= ?any of
+ true -> ok;
+ false ->
+ ok
+ %% L = ?list(Contents, Termination, ?unknown_qual),
+ %% erlang:error({illegal_list, L})
+ end,
+ "maybe_improper_list()";
+ _ ->
+ case t_is_subtype(t_nil(), Termination) of
+ true ->
+ "maybe_improper_list("++ContentString++","
+ ++t_to_string(Termination, RecDict)++")";
+ false ->
+ "improper_list("++ContentString++","
+ ++t_to_string(Termination, RecDict)++")"
+ end
+ end;
+t_to_string(?int_set(Set), _RecDict) ->
+ set_to_string(Set);
+t_to_string(?byte, _RecDict) -> "byte()";
+t_to_string(?char, _RecDict) -> "char()";
+t_to_string(?integer_pos, _RecDict) -> "pos_integer()";
+t_to_string(?integer_non_neg, _RecDict) -> "non_neg_integer()";
+t_to_string(?integer_neg, _RecDict) -> "neg_integer()";
+t_to_string(?int_range(From, To), _RecDict) ->
+ flat_format("~w..~w", [From, To]);
+t_to_string(?integer(?any), _RecDict) -> "integer()";
+t_to_string(?float, _RecDict) -> "float()";
+t_to_string(?number(?any, ?unknown_qual), _RecDict) -> "number()";
+t_to_string(?product(List), RecDict) ->
+ "<" ++ comma_sequence(List, RecDict) ++ ">";
+t_to_string(?map([],?any,?any), _RecDict) -> "map()";
+t_to_string(?map(Pairs0,DefK,DefV), RecDict) ->
+ {Pairs, ExtraEl} =
+ case {DefK, DefV} of
+ {?none, ?none} -> {Pairs0, []};
+ _ -> {Pairs0 ++ [{DefK,?opt,DefV}], []}
+ end,
+ Tos = fun(T) -> case T of
+ ?any -> "_";
+ _ -> t_to_string(T, RecDict)
+ end end,
+ StrMand = [{Tos(K),Tos(V)}||{K,?mand,V}<-Pairs],
+ StrOpt = [{Tos(K),Tos(V)}||{K,?opt,V}<-Pairs],
+ "#{" ++ string:join([K ++ ":=" ++ V||{K,V}<-StrMand]
+ ++ [K ++ "=>" ++ V||{K,V}<-StrOpt]
+ ++ ExtraEl, ", ") ++ "}";
+t_to_string(?tuple(?any, ?any, ?any), _RecDict) -> "tuple()";
+t_to_string(?tuple(Elements, _Arity, ?any), RecDict) ->
+ "{" ++ comma_sequence(Elements, RecDict) ++ "}";
+t_to_string(?tuple(Elements, Arity, Tag), RecDict) ->
+ [TagAtom] = atom_vals(Tag),
+ case lookup_record(TagAtom, Arity-1, RecDict) of
+ error -> "{" ++ comma_sequence(Elements, RecDict) ++ "}";
+ {ok, FieldNames} ->
+ record_to_string(TagAtom, Elements, FieldNames, RecDict)
+ end;
+t_to_string(?tuple_set(_) = T, RecDict) ->
+ union_sequence(t_tuple_subtypes(T), RecDict);
+t_to_string(?union(Types), RecDict) ->
+ union_sequence([T || T <- Types, T =/= ?none], RecDict);
+t_to_string(?var(Id), _RecDict) when is_atom(Id) ->
+ flat_format("~s", [atom_to_list(Id)]);
+t_to_string(?var(Id), _RecDict) when is_integer(Id) ->
+ flat_format("var(~w)", [Id]).
+
+
+record_to_string(Tag, [_|Fields], FieldNames, RecDict) ->
+ FieldStrings = record_fields_to_string(Fields, FieldNames, RecDict, []),
+ "#" ++ atom_to_string(Tag) ++ "{" ++ string:join(FieldStrings, ",") ++ "}".
+
+record_fields_to_string([F|Fs], [{FName, _Abstr, DefType}|FDefs],
+ RecDict, Acc) ->
+ NewAcc =
+ case
+ t_is_equal(F, t_any()) orelse
+ (t_is_any_atom('undefined', F) andalso
+ not t_is_none(t_inf(F, DefType)))
+ of
+ true -> Acc;
+ false ->
+ StrFV = atom_to_string(FName) ++ "::" ++ t_to_string(F, RecDict),
+ [StrFV|Acc]
+ end,
+ record_fields_to_string(Fs, FDefs, RecDict, NewAcc);
+record_fields_to_string([], [], _RecDict, Acc) ->
+ lists:reverse(Acc).
+
+-spec record_field_diffs_to_string(erl_type(), type_table()) -> string().
+
+record_field_diffs_to_string(?tuple([_|Fs], Arity, Tag), RecDict) ->
+ [TagAtom] = atom_vals(Tag),
+ {ok, FieldNames} = lookup_record(TagAtom, Arity-1, RecDict),
+ %% io:format("RecCElems = ~p\nRecTypes = ~p\n", [Fs, FieldNames]),
+ FieldDiffs = field_diffs(Fs, FieldNames, RecDict, []),
+ string:join(FieldDiffs, " and ").
+
+field_diffs([F|Fs], [{FName, _Abstr, DefType}|FDefs], RecDict, Acc) ->
+ %% Don't care about opaqueness for now.
+ NewAcc =
+ case not t_is_none(t_inf(F, DefType)) of
+ true -> Acc;
+ false ->
+ Str = atom_to_string(FName) ++ "::" ++ t_to_string(DefType, RecDict),
+ [Str|Acc]
+ end,
+ field_diffs(Fs, FDefs, RecDict, NewAcc);
+field_diffs([], [], _, Acc) ->
+ lists:reverse(Acc).
+
+comma_sequence(Types, RecDict) ->
+ List = [case T =:= ?any of
+ true -> "_";
+ false -> t_to_string(T, RecDict)
+ end || T <- Types],
+ string:join(List, ",").
+
+union_sequence(Types, RecDict) ->
+ List = [t_to_string(T, RecDict) || T <- Types],
+ string:join(List, " | ").
+
+-ifdef(DEBUG).
+opaque_type(Mod, Name, _Args, S, RecDict) ->
+ ArgsString = comma_sequence(_Args, RecDict),
+ String = t_to_string(S, RecDict),
+ opaque_name(Mod, Name, ArgsString) ++ "[" ++ String ++ "]".
+-else.
+opaque_type(Mod, Name, Args, _S, RecDict) ->
+ ArgsString = comma_sequence(Args, RecDict),
+ opaque_name(Mod, Name, ArgsString).
+-endif.
+
+opaque_name(Mod, Name, Extra) ->
+ S = mod_name(Mod, Name),
+ flat_format("~s(~s)", [S, Extra]).
+
+mod_name(Mod, Name) ->
+ flat_format("~w:~w", [Mod, Name]).
+
+%%=============================================================================
+%%
+%% Build a type from parse forms.
+%%
+%%=============================================================================
+
+-type type_names() :: [type_key() | record_key()].
+
+-type mta() :: {module(), atom(), arity()}.
+-type mra() :: {module(), atom(), arity()}.
+-type site() :: {'type', mta()} | {'spec', mfa()} | {'record', mra()}.
+-type cache_key() :: {module(), atom(), expand_depth(),
+ [erl_type()], type_names()}.
+-opaque cache() :: #{cache_key() => {erl_type(), expand_limit()}}.
+
+-spec t_from_form(parse_form(), sets:set(mfa()), site(), mod_records(),
+ var_table(), cache()) -> {erl_type(), cache()}.
+
+t_from_form(Form, ExpTypes, Site, RecDict, VarTab, Cache) ->
+ t_from_form1(Form, ExpTypes, Site, RecDict, VarTab, Cache).
+
+%% Replace external types with with none().
+-spec t_from_form_without_remote(parse_form(), site(), type_table()) ->
+ {erl_type(), cache()}.
+
+t_from_form_without_remote(Form, Site, TypeTable) ->
+ Module = site_module(Site),
+ RecDict = dict:from_list([{Module, TypeTable}]),
+ ExpTypes = replace_by_none,
+ VarTab = var_table__new(),
+ Cache = cache__new(),
+ t_from_form1(Form, ExpTypes, Site, RecDict, VarTab, Cache).
+
+%% REC_TYPE_LIMIT is used for limiting the depth of recursive types.
+%% EXPAND_LIMIT is used for limiting the size of types by
+%% limiting the number of elements of lists within one type form.
+%% EXPAND_DEPTH is used in conjunction with EXPAND_LIMIT to make the
+%% types balanced (unions will otherwise collapse to any()) by limiting
+%% the depth the same way as t_limit/2 does.
+
+-type expand_limit() :: integer().
+
+-type expand_depth() :: integer().
+
+-record(from_form, {site :: site(),
+ xtypes :: sets:set(mfa()) | 'replace_by_none',
+ mrecs :: mod_records(),
+ vtab :: var_table(),
+ tnames :: type_names()}).
+
+-spec t_from_form1(parse_form(), sets:set(mfa()) | 'replace_by_none',
+ site(), mod_records(), var_table(), cache()) ->
+ {erl_type(), cache()}.
+
+t_from_form1(Form, ET, Site, MR, V, C) ->
+ TypeNames = initial_typenames(Site),
+ State = #from_form{site = Site,
+ xtypes = ET,
+ mrecs = MR,
+ vtab = V,
+ tnames = TypeNames},
+ L = ?EXPAND_LIMIT,
+ {T1, L1, C1} = from_form(Form, State, ?EXPAND_DEPTH, L, C),
+ if
+ L1 =< 0 ->
+ from_form_loop(Form, State, 1, L, C1);
+ true ->
+ {T1, C1}
+ end.
+
+initial_typenames({type, _MTA}=Site) -> [Site];
+initial_typenames({spec, _MFA}) -> [];
+initial_typenames({record, _MRA}) -> [].
+
+from_form_loop(Form, State, D, Limit, C) ->
+ {T1, L1, C1} = from_form(Form, State, D, Limit, C),
+ Delta = Limit - L1,
+ if
+ %% Save some time by assuming next depth will exceed the limit.
+ Delta * 8 > Limit ->
+ {T1, C1};
+ true ->
+ D1 = D + 1,
+ from_form_loop(Form, State, D1, Limit, C1)
+ end.
+
+-spec from_form(parse_form(),
+ #from_form{},
+ expand_depth(),
+ expand_limit(),
+ cache()) -> {erl_type(), expand_limit(), cache()}.
+
+%% If there is something wrong with parse_form()
+%% throw({error, io_lib:chars()} is called;
+%% for unknown remote types
+%% self() ! {self(), ext_types, {RemMod, Name, ArgsLen}}
+%% is called, unless 'replace_by_none' is given.
+%%
+%% It is assumed that site_module(S) can be found in MR.
+
+from_form(_, _S, D, L, C) when D =< 0 ; L =< 0 ->
+ {t_any(), L, C};
+from_form({var, _L, '_'}, _S, _D, L, C) ->
+ {t_any(), L, C};
+from_form({var, _L, Name}, S, _D, L, C) ->
+ V = S#from_form.vtab,
+ case maps:find(Name, V) of
+ error -> {t_var(Name), L, C};
+ {ok, Val} -> {Val, L, C}
+ end;
+from_form({ann_type, _L, [_Var, Type]}, S, D, L, C) ->
+ from_form(Type, S, D, L, C);
+from_form({paren_type, _L, [Type]}, S, D, L, C) ->
+ from_form(Type, S, D, L, C);
+from_form({remote_type, _L, [{atom, _, Module}, {atom, _, Type}, Args]},
+ S, D, L, C) ->
+ remote_from_form(Module, Type, Args, S, D, L, C);
+from_form({atom, _L, Atom}, _S, _D, L, C) ->
+ {t_atom(Atom), L, C};
+from_form({integer, _L, Int}, _S, _D, L, C) ->
+ {t_integer(Int), L, C};
+from_form({op, _L, _Op, _Arg} = Op, _S, _D, L, C) ->
+ case erl_eval:partial_eval(Op) of
+ {integer, _, Val} ->
+ {t_integer(Val), L, C};
+ _ -> throw({error, io_lib:format("Unable to evaluate type ~w\n", [Op])})
+ end;
+from_form({op, _L, _Op, _Arg1, _Arg2} = Op, _S, _D, L, C) ->
+ case erl_eval:partial_eval(Op) of
+ {integer, _, Val} ->
+ {t_integer(Val), L, C};
+ _ -> throw({error, io_lib:format("Unable to evaluate type ~w\n", [Op])})
+ end;
+from_form({type, _L, any, []}, _S, _D, L, C) ->
+ {t_any(), L, C};
+from_form({type, _L, arity, []}, _S, _D, L, C) ->
+ {t_arity(), L, C};
+from_form({type, _L, atom, []}, _S, _D, L, C) ->
+ {t_atom(), L, C};
+from_form({type, _L, binary, []}, _S, _D, L, C) ->
+ {t_binary(), L, C};
+from_form({type, _L, binary, [Base, Unit]} = Type, _S, _D, L, C) ->
+ case {erl_eval:partial_eval(Base), erl_eval:partial_eval(Unit)} of
+ {{integer, _, B}, {integer, _, U}} when B >= 0, U >= 0 ->
+ {t_bitstr(U, B), L, C};
+ _ -> throw({error, io_lib:format("Unable to evaluate type ~w\n", [Type])})
+ end;
+from_form({type, _L, bitstring, []}, _S, _D, L, C) ->
+ {t_bitstr(), L, C};
+from_form({type, _L, bool, []}, _S, _D, L, C) ->
+ {t_boolean(), L, C}; % XXX: Temporarily
+from_form({type, _L, boolean, []}, _S, _D, L, C) ->
+ {t_boolean(), L, C};
+from_form({type, _L, byte, []}, _S, _D, L, C) ->
+ {t_byte(), L, C};
+from_form({type, _L, char, []}, _S, _D, L, C) ->
+ {t_char(), L, C};
+from_form({type, _L, float, []}, _S, _D, L, C) ->
+ {t_float(), L, C};
+from_form({type, _L, function, []}, _S, _D, L, C) ->
+ {t_fun(), L, C};
+from_form({type, _L, 'fun', []}, _S, _D, L, C) ->
+ {t_fun(), L, C};
+from_form({type, _L, 'fun', [{type, _, any}, Range]}, S, D, L, C) ->
+ {T, L1, C1} = from_form(Range, S, D - 1, L - 1, C),
+ {t_fun(T), L1, C1};
+from_form({type, _L, 'fun', [{type, _, product, Domain}, Range]},
+ S, D, L, C) ->
+ {Dom1, L1, C1} = list_from_form(Domain, S, D, L, C),
+ {Ran1, L2, C2} = from_form(Range, S, D, L1, C1),
+ {t_fun(Dom1, Ran1), L2, C2};
+from_form({type, _L, identifier, []}, _S, _D, L, C) ->
+ {t_identifier(), L, C};
+from_form({type, _L, integer, []}, _S, _D, L, C) ->
+ {t_integer(), L, C};
+from_form({type, _L, iodata, []}, _S, _D, L, C) ->
+ {t_iodata(), L, C};
+from_form({type, _L, iolist, []}, _S, _D, L, C) ->
+ {t_iolist(), L, C};
+from_form({type, _L, list, []}, _S, _D, L, C) ->
+ {t_list(), L, C};
+from_form({type, _L, list, [Type]}, S, D, L, C) ->
+ {T, L1, C1} = from_form(Type, S, D - 1, L - 1, C),
+ {t_list(T), L1, C1};
+from_form({type, _L, map, any}, S, D, L, C) ->
+ builtin_type(map, t_map(), S, D, L, C);
+from_form({type, _L, map, List}, S, D0, L, C) ->
+ {Pairs1, L5, C5} =
+ fun PairsFromForm(_, L1, C1) when L1 =< 0 -> {[{?any,?opt,?any}], L1, C1};
+ PairsFromForm([], L1, C1) -> {[], L1, C1};
+ PairsFromForm([{type, _, Oper, [KF, VF]}|T], L1, C1) ->
+ D = D0 - 1,
+ {Key, L2, C2} = from_form(KF, S, D, L1, C1),
+ {Val, L3, C3} = from_form(VF, S, D, L2, C2),
+ {Pairs0, L4, C4} = PairsFromForm(T, L3 - 1, C3),
+ case Oper of
+ map_field_assoc -> {[{Key,?opt, Val}|Pairs0], L4, C4};
+ map_field_exact -> {[{Key,?mand,Val}|Pairs0], L4, C4}
+ end
+ end(List, L, C),
+ try
+ {Pairs, DefK, DefV} = map_from_form(Pairs1, [], [], [], ?none, ?none),
+ {t_map(Pairs, DefK, DefV), L5, C5}
+ catch none -> {t_none(), L5, C5}
+ end;
+from_form({type, _L, mfa, []}, _S, _D, L, C) ->
+ {t_mfa(), L, C};
+from_form({type, _L, module, []}, _S, _D, L, C) ->
+ {t_module(), L, C};
+from_form({type, _L, nil, []}, _S, _D, L, C) ->
+ {t_nil(), L, C};
+from_form({type, _L, neg_integer, []}, _S, _D, L, C) ->
+ {t_neg_integer(), L, C};
+from_form({type, _L, non_neg_integer, []}, _S, _D, L, C) ->
+ {t_non_neg_integer(), L, C};
+from_form({type, _L, no_return, []}, _S, _D, L, C) ->
+ {t_unit(), L, C};
+from_form({type, _L, node, []}, _S, _D, L, C) ->
+ {t_node(), L, C};
+from_form({type, _L, none, []}, _S, _D, L, C) ->
+ {t_none(), L, C};
+from_form({type, _L, nonempty_list, []}, _S, _D, L, C) ->
+ {t_nonempty_list(), L, C};
+from_form({type, _L, nonempty_list, [Type]}, S, D, L, C) ->
+ {T, L1, C1} = from_form(Type, S, D, L - 1, C),
+ {t_nonempty_list(T), L1, C1};
+from_form({type, _L, nonempty_improper_list, [Cont, Term]}, S, D, L, C) ->
+ {T1, L1, C1} = from_form(Cont, S, D, L - 1, C),
+ {T2, L2, C2} = from_form(Term, S, D, L1, C1),
+ {t_cons(T1, T2), L2, C2};
+from_form({type, _L, nonempty_maybe_improper_list, []}, _S, _D, L, C) ->
+ {t_cons(?any, ?any), L, C};
+from_form({type, _L, nonempty_maybe_improper_list, [Cont, Term]},
+ S, D, L, C) ->
+ {T1, L1, C1} = from_form(Cont, S, D, L - 1, C),
+ {T2, L2, C2} = from_form(Term, S, D, L1, C1),
+ {t_cons(T1, T2), L2, C2};
+from_form({type, _L, nonempty_string, []}, _S, _D, L, C) ->
+ {t_nonempty_string(), L, C};
+from_form({type, _L, number, []}, _S, _D, L, C) ->
+ {t_number(), L, C};
+from_form({type, _L, pid, []}, _S, _D, L, C) ->
+ {t_pid(), L, C};
+from_form({type, _L, port, []}, _S, _D, L, C) ->
+ {t_port(), L, C};
+from_form({type, _L, pos_integer, []}, _S, _D, L, C) ->
+ {t_pos_integer(), L, C};
+from_form({type, _L, maybe_improper_list, []}, _S, _D, L, C) ->
+ {t_maybe_improper_list(), L, C};
+from_form({type, _L, maybe_improper_list, [Content, Termination]},
+ S, D, L, C) ->
+ {T1, L1, C1} = from_form(Content, S, D, L - 1, C),
+ {T2, L2, C2} = from_form(Termination, S, D, L1, C1),
+ {t_maybe_improper_list(T1, T2), L2, C2};
+from_form({type, _L, product, Elements}, S, D, L, C) ->
+ {Lst, L1, C1} = list_from_form(Elements, S, D - 1, L, C),
+ {t_product(Lst), L1, C1};
+from_form({type, _L, range, [From, To]} = Type, _S, _D, L, C) ->
+ case {erl_eval:partial_eval(From), erl_eval:partial_eval(To)} of
+ {{integer, _, FromVal}, {integer, _, ToVal}} ->
+ {t_from_range(FromVal, ToVal), L, C};
+ _ -> throw({error, io_lib:format("Unable to evaluate type ~w\n", [Type])})
+ end;
+from_form({type, _L, record, [Name|Fields]}, S, D, L, C) ->
+ record_from_form(Name, Fields, S, D, L, C);
+from_form({type, _L, reference, []}, _S, _D, L, C) ->
+ {t_reference(), L, C};
+from_form({type, _L, string, []}, _S, _D, L, C) ->
+ {t_string(), L, C};
+from_form({type, _L, term, []}, _S, _D, L, C) ->
+ {t_any(), L, C};
+from_form({type, _L, timeout, []}, _S, _D, L, C) ->
+ {t_timeout(), L, C};
+from_form({type, _L, tuple, any}, _S, _D, L, C) ->
+ {t_tuple(), L, C};
+from_form({type, _L, tuple, Args}, S, D, L, C) ->
+ {Lst, L1, C1} = list_from_form(Args, S, D - 1, L, C),
+ {t_tuple(Lst), L1, C1};
+from_form({type, _L, union, Args}, S, D, L, C) ->
+ {Lst, L1, C1} = list_from_form(Args, S, D, L, C),
+ {t_sup(Lst), L1, C1};
+from_form({user_type, _L, Name, Args}, S, D, L, C) ->
+ type_from_form(Name, Args, S, D, L, C);
+from_form({type, _L, Name, Args}, S, D, L, C) ->
+ %% Compatibility: modules compiled before Erlang/OTP 18.0.
+ type_from_form(Name, Args, S, D, L, C);
+from_form({opaque, _L, Name, {Mod, Args, Rep}}, _S, _D, L, C) ->
+ %% XXX. To be removed.
+ {t_opaque(Mod, Name, Args, Rep), L, C}.
+
+builtin_type(Name, Type, S, D, L, C) ->
+ #from_form{site = Site, mrecs = MR} = S,
+ M = site_module(Site),
+ case dict:find(M, MR) of
+ {ok, R} ->
+ case lookup_type(Name, 0, R) of
+ {_, {{_M, _FL, _F, _A}, _T}} ->
+ type_from_form(Name, [], S, D, L, C);
+ error ->
+ {Type, L, C}
+ end;
+ error ->
+ {Type, L, C}
+ end.
+
+type_from_form(Name, Args, S, D, L, C) ->
+ #from_form{site = Site, mrecs = MR, tnames = TypeNames} = S,
+ ArgsLen = length(Args),
+ Module = site_module(Site),
+ TypeName = {type, {Module, Name, ArgsLen}},
+ case can_unfold_more(TypeName, TypeNames) of
+ true ->
+ {ok, R} = dict:find(Module, MR),
+ type_from_form1(Name, Args, ArgsLen, R, TypeName, TypeNames,
+ S, D, L, C);
+ false ->
+ {t_any(), L, C}
+ end.
+
+type_from_form1(Name, Args, ArgsLen, R, TypeName, TypeNames, S, D, L, C) ->
+ case lookup_type(Name, ArgsLen, R) of
+ {Tag, {{Module, _FileName, Form, ArgNames}, Type}} ->
+ NewTypeNames = [TypeName|TypeNames],
+ S1 = S#from_form{tnames = NewTypeNames},
+ {ArgTypes, L1, C1} = list_from_form(Args, S1, D, L, C),
+ CKey = cache_key(Module, Name, ArgTypes, TypeNames, D),
+ case cache_find(CKey, C) of
+ {CachedType, DeltaL} ->
+ {CachedType, L1 - DeltaL, C};
+ error ->
+ List = lists:zip(ArgNames, ArgTypes),
+ TmpV = maps:from_list(List),
+ S2 = S1#from_form{site = TypeName, vtab = TmpV},
+ Fun = fun(DD, LL) -> from_form(Form, S2, DD, LL, C1) end,
+ {NewType, L3, C3} =
+ case Tag of
+ type ->
+ recur_limit(Fun, D, L1, TypeName, TypeNames);
+ opaque ->
+ {Rep, L2, C2} = recur_limit(Fun, D, L1, TypeName, TypeNames),
+ Rep1 = choose_opaque_type(Rep, Type),
+ Rep2 = case cannot_have_opaque(Rep1, TypeName, TypeNames) of
+ true -> Rep1;
+ false ->
+ ArgTypes2 = subst_all_vars_to_any_list(ArgTypes),
+ t_opaque(Module, Name, ArgTypes2, Rep1)
+ end,
+ {Rep2, L2, C2}
+ end,
+ C4 = cache_put(CKey, NewType, L1 - L3, C3),
+ {NewType, L3, C4}
+ end;
+ error ->
+ Msg = io_lib:format("Unable to find type ~w/~w\n",
+ [Name, ArgsLen]),
+ throw({error, Msg})
+ end.
+
+remote_from_form(RemMod, Name, Args, S, D, L, C) ->
+ #from_form{xtypes = ET, mrecs = MR, tnames = TypeNames} = S,
+ if
+ ET =:= replace_by_none ->
+ {t_none(), L, C};
+ true ->
+ ArgsLen = length(Args),
+ MFA = {RemMod, Name, ArgsLen},
+ case dict:find(RemMod, MR) of
+ error ->
+ self() ! {self(), ext_types, MFA},
+ {t_any(), L, C};
+ {ok, RemDict} ->
+ case sets:is_element(MFA, ET) of
+ true ->
+ RemType = {type, MFA},
+ case can_unfold_more(RemType, TypeNames) of
+ true ->
+ remote_from_form1(RemMod, Name, Args, ArgsLen, RemDict,
+ RemType, TypeNames, S, D, L, C);
+ false ->
+ {t_any(), L, C}
+ end;
+ false ->
+ self() ! {self(), ext_types, {RemMod, Name, ArgsLen}},
+ {t_any(), L, C}
+ end
+ end
+ end.
+
+remote_from_form1(RemMod, Name, Args, ArgsLen, RemDict, RemType, TypeNames,
+ S, D, L, C) ->
+ case lookup_type(Name, ArgsLen, RemDict) of
+ {Tag, {{Mod, _FileLine, Form, ArgNames}, Type}} ->
+ NewTypeNames = [RemType|TypeNames],
+ S1 = S#from_form{tnames = NewTypeNames},
+ {ArgTypes, L1, C1} = list_from_form(Args, S1, D, L, C),
+ CKey = cache_key(RemMod, Name, ArgTypes, TypeNames, D),
+ %% case error of
+ case cache_find(CKey, C) of
+ {CachedType, DeltaL} ->
+ {CachedType, L - DeltaL, C};
+ error ->
+ List = lists:zip(ArgNames, ArgTypes),
+ TmpVarTab = maps:from_list(List),
+ S2 = S1#from_form{site = RemType, vtab = TmpVarTab},
+ Fun = fun(DD, LL) -> from_form(Form, S2, DD, LL, C1) end,
+ {NewType, L3, C3} =
+ case Tag of
+ type ->
+ recur_limit(Fun, D, L1, RemType, TypeNames);
+ opaque ->
+ {NewRep, L2, C2} = recur_limit(Fun, D, L1, RemType, TypeNames),
+ NewRep1 = choose_opaque_type(NewRep, Type),
+ NewRep2 =
+ case cannot_have_opaque(NewRep1, RemType, TypeNames) of
+ true -> NewRep1;
+ false ->
+ ArgTypes2 = subst_all_vars_to_any_list(ArgTypes),
+ t_opaque(Mod, Name, ArgTypes2, NewRep1)
+ end,
+ {NewRep2, L2, C2}
+ end,
+ C4 = cache_put(CKey, NewType, L1 - L3, C3),
+ {NewType, L3, C4}
+ end;
+ error ->
+ Msg = io_lib:format("Unable to find remote type ~w:~w()\n",
+ [RemMod, Name]),
+ throw({error, Msg})
+ end.
+
+subst_all_vars_to_any_list(Types) ->
+ [subst_all_vars_to_any(Type) || Type <- Types].
+
+%% Opaque types (both local and remote) are problematic when it comes
+%% to the limits (TypeNames, D, and L). The reason is that if any() is
+%% substituted for a more specialized subtype of an opaque type, the
+%% property stated along with decorate_with_opaque() (the type has to
+%% be a subtype of the declared type) no longer holds.
+%%
+%% The less than perfect remedy: if the opaque type created from a
+%% form is not a subset of the declared type, the declared type is
+%% used instead, effectively bypassing the limits, and potentially
+%% resulting in huge types.
+choose_opaque_type(Type, DeclType) ->
+ case
+ t_is_subtype(subst_all_vars_to_any(Type),
+ subst_all_vars_to_any(DeclType))
+ of
+ true -> Type;
+ false -> DeclType
+ end.
+
+record_from_form({atom, _, Name}, ModFields, S, D0, L0, C) ->
+ #from_form{site = Site, mrecs = MR, tnames = TypeNames} = S,
+ RecordType = {record, Name},
+ case can_unfold_more(RecordType, TypeNames) of
+ true ->
+ M = site_module(Site),
+ {ok, R} = dict:find(M, MR),
+ case lookup_record(Name, R) of
+ {ok, DeclFields} ->
+ NewTypeNames = [RecordType|TypeNames],
+ Site1 = {record, {M, Name, length(DeclFields)}},
+ S1 = S#from_form{site = Site1, tnames = NewTypeNames},
+ Fun = fun(D, L) ->
+ {GetModRec, L1, C1} =
+ get_mod_record(ModFields, DeclFields, S1, D, L, C),
+ case GetModRec of
+ {error, FieldName} ->
+ throw({error,
+ io_lib:format("Illegal declaration of #~w{~w}\n",
+ [Name, FieldName])});
+ {ok, NewFields} ->
+ S2 = S1#from_form{vtab = var_table__new()},
+ {NewFields1, L2, C2} =
+ fields_from_form(NewFields, S2, D, L1, C1),
+ Rec = t_tuple(
+ [t_atom(Name)|[Type
+ || {_FieldName, Type} <- NewFields1]]),
+ {Rec, L2, C2}
+ end
+ end,
+ recur_limit(Fun, D0, L0, RecordType, TypeNames);
+ error ->
+ throw({error, io_lib:format("Unknown record #~w{}\n", [Name])})
+ end;
+ false ->
+ {t_any(), L0, C}
+ end.
+
+get_mod_record([], DeclFields, _S, _D, L, C) ->
+ {{ok, DeclFields}, L, C};
+get_mod_record(ModFields, DeclFields, S, D, L, C) ->
+ DeclFieldsDict = lists:keysort(1, DeclFields),
+ {ModFieldsDict, L1, C1} = build_field_dict(ModFields, S, D, L, C),
+ case get_mod_record_types(DeclFieldsDict, ModFieldsDict, []) of
+ {error, _FieldName} = Error -> {Error, L1, C1};
+ {ok, FinalKeyDict} ->
+ Fields = [lists:keyfind(FieldName, 1, FinalKeyDict)
+ || {FieldName, _, _} <- DeclFields],
+ {{ok, Fields}, L1, C1}
+ end.
+
+build_field_dict(FieldTypes, S, D, L, C) ->
+ build_field_dict(FieldTypes, S, D, L, C, []).
+
+build_field_dict([{type, _, field_type, [{atom, _, Name}, Type]}|Left],
+ S, D, L, C, Acc) ->
+ {T, L1, C1} = from_form(Type, S, D, L - 1, C),
+ NewAcc = [{Name, Type, T}|Acc],
+ build_field_dict(Left, S, D, L1, C1, NewAcc);
+build_field_dict([], _S, _D, L, C, Acc) ->
+ {lists:keysort(1, Acc), L, C}.
+
+get_mod_record_types([{FieldName, _Abstr, _DeclType}|Left1],
+ [{FieldName, TypeForm, ModType}|Left2],
+ Acc) ->
+ get_mod_record_types(Left1, Left2, [{FieldName, TypeForm, ModType}|Acc]);
+get_mod_record_types([{FieldName1, _Abstr, _DeclType} = DT|Left1],
+ [{FieldName2, _FormType, _ModType}|_] = List2,
+ Acc) when FieldName1 < FieldName2 ->
+ get_mod_record_types(Left1, List2, [DT|Acc]);
+get_mod_record_types(Left1, [], Acc) ->
+ {ok, lists:keysort(1, Left1++Acc)};
+get_mod_record_types(_, [{FieldName2, _FormType, _ModType}|_], _Acc) ->
+ {error, FieldName2}.
+
+%% It is important to create a limited version of the record type
+%% since nested record types can otherwise easily result in huge
+%% terms.
+fields_from_form([], _S, _D, L, C) ->
+ {[], L, C};
+fields_from_form([{Name, Abstr, _Type}|Tail], S, D, L, C) ->
+ {T, L1, C1} = from_form(Abstr, S, D, L, C),
+ {F, L2, C2} = fields_from_form(Tail, S, D, L1, C1),
+ {[{Name, T}|F], L2, C2}.
+
+list_from_form([], _S, _D, L, C) ->
+ {[], L, C};
+list_from_form([H|Tail], S, D, L, C) ->
+ {H1, L1, C1} = from_form(H, S, D, L - 1, C),
+ {T1, L2, C2} = list_from_form(Tail, S, D, L1, C1),
+ {[H1|T1], L2, C2}.
+
+%% Sorts, combines non-singleton pairs, and applies precendence and
+%% mandatoriness rules.
+map_from_form([], ShdwPs, MKs, Pairs, DefK, DefV) ->
+ verify_possible(MKs, ShdwPs),
+ {promote_to_mand(MKs, Pairs), DefK, DefV};
+map_from_form([{SKey,MNess,Val}|SPairs], ShdwPs0, MKs0, Pairs0, DefK0, DefV0) ->
+ Key = lists:foldl(fun({K,_},S)->t_subtract(S,K)end, SKey, ShdwPs0),
+ ShdwPs = case Key of ?none -> ShdwPs0; _ -> [{Key,Val}|ShdwPs0] end,
+ MKs = case MNess of ?mand -> [SKey|MKs0]; ?opt -> MKs0 end,
+ if MNess =:= ?mand, SKey =:= ?none -> throw(none);
+ true -> ok
+ end,
+ {Pairs, DefK, DefV} =
+ case is_singleton_type(Key) of
+ true ->
+ MNess1 = case Val =:= ?none of true -> ?opt; false -> MNess end,
+ {mapdict_insert({Key,MNess1,Val}, Pairs0), DefK0, DefV0};
+ false ->
+ case Key =:= ?none orelse Val =:= ?none of
+ true -> {Pairs0, DefK0, DefV0};
+ false -> {Pairs0, t_sup(DefK0, Key), t_sup(DefV0, Val)}
+ end
+ end,
+ map_from_form(SPairs, ShdwPs, MKs, Pairs, DefK, DefV).
+
+%% Verifies that all mandatory keys are possible, throws 'none' otherwise
+verify_possible(MKs, ShdwPs) ->
+ lists:foreach(fun(M) -> verify_possible_1(M, ShdwPs) end, MKs).
+
+verify_possible_1(M, ShdwPs) ->
+ case lists:any(fun({K,_}) -> t_inf(M, K) =/= ?none end, ShdwPs) of
+ true -> ok;
+ false -> throw(none)
+ end.
+
+-spec promote_to_mand([erl_type()], t_map_dict()) -> t_map_dict().
+
+promote_to_mand(_, []) -> [];
+promote_to_mand(MKs, [E={K,_,V}|T]) ->
+ [case lists:any(fun(M) -> t_is_equal(K,M) end, MKs) of
+ true -> {K, ?mand, V};
+ false -> E
+ end|promote_to_mand(MKs, T)].
+
+-define(RECUR_EXPAND_LIMIT, 10).
+-define(RECUR_EXPAND_DEPTH, 2).
+
+%% If more of the limited resources is spent on the non-recursive
+%% forms, more warnings are found. And the analysis is also a bit
+%% faster.
+%%
+%% Setting REC_TYPE_LIMIT to 1 would work also work well.
+
+recur_limit(Fun, D, L, _, _) when L =< ?RECUR_EXPAND_DEPTH,
+ D =< ?RECUR_EXPAND_LIMIT ->
+ Fun(D, L);
+recur_limit(Fun, D, L, TypeName, TypeNames) ->
+ case is_recursive(TypeName, TypeNames) of
+ true ->
+ {T, L1, C1} = Fun(?RECUR_EXPAND_DEPTH, ?RECUR_EXPAND_LIMIT),
+ {T, L - L1, C1};
+ false ->
+ Fun(D, L)
+ end.
+
+-spec t_check_record_fields(parse_form(), sets:set(mfa()), site(),
+ mod_records(), var_table(), cache()) -> cache().
+
+t_check_record_fields(Form, ExpTypes, Site, RecDict, VarTable, Cache) ->
+ State = #from_form{site = Site,
+ xtypes = ExpTypes,
+ mrecs = RecDict,
+ vtab = VarTable,
+ tnames = []},
+ check_record_fields(Form, State, Cache).
+
+-spec check_record_fields(parse_form(), #from_form{}, cache()) -> cache().
+
+%% If there is something wrong with parse_form()
+%% throw({error, io_lib:chars()} is called.
+
+check_record_fields({var, _L, _}, _S, C) -> C;
+check_record_fields({ann_type, _L, [_Var, Type]}, S, C) ->
+ check_record_fields(Type, S, C);
+check_record_fields({paren_type, _L, [Type]}, S, C) ->
+ check_record_fields(Type, S, C);
+check_record_fields({remote_type, _L, [{atom, _, _}, {atom, _, _}, Args]},
+ S, C) ->
+ list_check_record_fields(Args, S, C);
+check_record_fields({atom, _L, _}, _S, C) -> C;
+check_record_fields({integer, _L, _}, _S, C) -> C;
+check_record_fields({op, _L, _Op, _Arg}, _S, C) -> C;
+check_record_fields({op, _L, _Op, _Arg1, _Arg2}, _S, C) -> C;
+check_record_fields({type, _L, tuple, any}, _S, C) -> C;
+check_record_fields({type, _L, map, any}, _S, C) -> C;
+check_record_fields({type, _L, binary, [_Base, _Unit]}, _S, C) -> C;
+check_record_fields({type, _L, 'fun', [{type, _, any}, Range]}, S, C) ->
+ check_record_fields(Range, S, C);
+check_record_fields({type, _L, range, [_From, _To]}, _S, C) -> C;
+check_record_fields({type, _L, record, [Name|Fields]}, S, C) ->
+ check_record(Name, Fields, S, C);
+check_record_fields({type, _L, _, Args}, S, C) ->
+ list_check_record_fields(Args, S, C);
+check_record_fields({user_type, _L, _Name, Args}, S, C) ->
+ list_check_record_fields(Args, S, C).
+
+check_record({atom, _, Name}, ModFields, S, C) ->
+ #from_form{site = Site, mrecs = MR} = S,
+ M = site_module(Site),
+ {ok, R} = dict:find(M, MR),
+ {ok, DeclFields} = lookup_record(Name, R),
+ case check_fields(Name, ModFields, DeclFields, S, C) of
+ {error, FieldName} ->
+ throw({error, io_lib:format("Illegal declaration of #~w{~w}\n",
+ [Name, FieldName])});
+ C1 -> C1
+ end.
+
+check_fields(RecName, [{type, _, field_type, [{atom, _, Name}, Abstr]}|Left],
+ DeclFields, S, C) ->
+ #from_form{site = Site0, xtypes = ET, mrecs = MR, vtab = V} = S,
+ M = site_module(Site0),
+ Site = {record, {M, RecName, length(DeclFields)}},
+ {Type, C1} = t_from_form(Abstr, ET, Site, MR, V, C),
+ {Name, _, DeclType} = lists:keyfind(Name, 1, DeclFields),
+ TypeNoVars = subst_all_vars_to_any(Type),
+ case t_is_subtype(TypeNoVars, DeclType) of
+ false -> {error, Name};
+ true -> check_fields(RecName, Left, DeclFields, S, C1)
+ end;
+check_fields(_RecName, [], _Decl, _S, C) ->
+ C.
+
+list_check_record_fields([], _S, C) ->
+ C;
+list_check_record_fields([H|Tail], S, C) ->
+ C1 = check_record_fields(H, S, C),
+ list_check_record_fields(Tail, S, C1).
+
+site_module({_, {Module, _, _}}) ->
+ Module.
+
+-spec cache__new() -> cache().
+
+cache__new() ->
+ maps:new().
+
+-spec cache_key(module(), atom(), [erl_type()],
+ type_names(), expand_depth()) -> cache_key().
+
+%% If TypeNames is left out from the key, the cache is smaller, and
+%% the form-to-type translation is faster. But it would be a shame if,
+%% for example, any() is used, where a more complex type should be
+%% used. There is also a slight risk of creating unnecessarily big
+%% types.
+
+cache_key(Module, Name, ArgTypes, TypeNames, D) ->
+ {Module, Name, D, ArgTypes, TypeNames}.
+
+-spec cache_find(cache_key(), cache()) ->
+ {erl_type(), expand_limit()} | 'error'.
+
+cache_find(Key, Cache) ->
+ case maps:find(Key, Cache) of
+ {ok, Value} ->
+ Value;
+ error ->
+ error
+ end.
+
+-spec cache_put(cache_key(), erl_type(), expand_limit(), cache()) -> cache().
+
+cache_put(_Key, _Type, DeltaL, Cache) when DeltaL < 0 ->
+ %% The type is truncated; do not reuse it.
+ Cache;
+cache_put(Key, Type, DeltaL, Cache) ->
+ maps:put(Key, {Type, DeltaL}, Cache).
+
+-spec t_var_names([erl_type()]) -> [atom()].
+
+t_var_names([{var, _, Name}|L]) when L =/= '_' ->
+ [Name|t_var_names(L)];
+t_var_names([]) ->
+ [].
+
+-spec t_form_to_string(parse_form()) -> string().
+
+t_form_to_string({var, _L, '_'}) -> "_";
+t_form_to_string({var, _L, Name}) -> atom_to_list(Name);
+t_form_to_string({atom, _L, Atom}) ->
+ io_lib:write_string(atom_to_list(Atom), $'); % To quote or not to quote... '
+t_form_to_string({integer, _L, Int}) -> integer_to_list(Int);
+t_form_to_string({op, _L, _Op, _Arg} = Op) ->
+ case erl_eval:partial_eval(Op) of
+ {integer, _, _} = Int -> t_form_to_string(Int);
+ _ -> io_lib:format("Badly formed type ~w", [Op])
+ end;
+t_form_to_string({op, _L, _Op, _Arg1, _Arg2} = Op) ->
+ case erl_eval:partial_eval(Op) of
+ {integer, _, _} = Int -> t_form_to_string(Int);
+ _ -> io_lib:format("Badly formed type ~w", [Op])
+ end;
+t_form_to_string({ann_type, _L, [Var, Type]}) ->
+ t_form_to_string(Var) ++ "::" ++ t_form_to_string(Type);
+t_form_to_string({paren_type, _L, [Type]}) ->
+ flat_format("(~s)", [t_form_to_string(Type)]);
+t_form_to_string({remote_type, _L, [{atom, _, Mod}, {atom, _, Name}, Args]}) ->
+ ArgString = "(" ++ string:join(t_form_to_string_list(Args), ",") ++ ")",
+ flat_format("~w:~w", [Mod, Name]) ++ ArgString;
+t_form_to_string({type, _L, arity, []}) -> "arity()";
+t_form_to_string({type, _L, binary, []}) -> "binary()";
+t_form_to_string({type, _L, binary, [Base, Unit]} = Type) ->
+ case {erl_eval:partial_eval(Base), erl_eval:partial_eval(Unit)} of
+ {{integer, _, B}, {integer, _, U}} ->
+ %% the following mirrors the clauses of t_to_string/2
+ case {U, B} of
+ {0, 0} -> "<<>>";
+ {8, 0} -> "binary()";
+ {1, 0} -> "bitstring()";
+ {0, B} -> flat_format("<<_:~w>>", [B]);
+ {U, 0} -> flat_format("<<_:_*~w>>", [U]);
+ {U, B} -> flat_format("<<_:~w,_:_*~w>>", [B, U])
+ end;
+ _ -> io_lib:format("Badly formed bitstr type ~w", [Type])
+ end;
+t_form_to_string({type, _L, bitstring, []}) -> "bitstring()";
+t_form_to_string({type, _L, 'fun', []}) -> "fun()";
+t_form_to_string({type, _L, 'fun', [{type, _, any}, Range]}) ->
+ "fun(...) -> " ++ t_form_to_string(Range);
+t_form_to_string({type, _L, 'fun', [{type, _, product, Domain}, Range]}) ->
+ "fun((" ++ string:join(t_form_to_string_list(Domain), ",") ++ ") -> "
+ ++ t_form_to_string(Range) ++ ")";
+t_form_to_string({type, _L, iodata, []}) -> "iodata()";
+t_form_to_string({type, _L, iolist, []}) -> "iolist()";
+t_form_to_string({type, _L, list, [Type]}) ->
+ "[" ++ t_form_to_string(Type) ++ "]";
+t_form_to_string({type, _L, map, any}) -> "map()";
+t_form_to_string({type, _L, map, Args}) ->
+ "#{" ++ string:join(t_form_to_string_list(Args), ",") ++ "}";
+t_form_to_string({type, _L, map_field_assoc, [Key, Val]}) ->
+ t_form_to_string(Key) ++ "=>" ++ t_form_to_string(Val);
+t_form_to_string({type, _L, map_field_exact, [Key, Val]}) ->
+ t_form_to_string(Key) ++ ":=" ++ t_form_to_string(Val);
+t_form_to_string({type, _L, mfa, []}) -> "mfa()";
+t_form_to_string({type, _L, module, []}) -> "module()";
+t_form_to_string({type, _L, node, []}) -> "node()";
+t_form_to_string({type, _L, nonempty_list, [Type]}) ->
+ "[" ++ t_form_to_string(Type) ++ ",...]";
+t_form_to_string({type, _L, nonempty_string, []}) -> "nonempty_string()";
+t_form_to_string({type, _L, product, Elements}) ->
+ "<" ++ string:join(t_form_to_string_list(Elements), ",") ++ ">";
+t_form_to_string({type, _L, range, [From, To]} = Type) ->
+ case {erl_eval:partial_eval(From), erl_eval:partial_eval(To)} of
+ {{integer, _, FromVal}, {integer, _, ToVal}} ->
+ flat_format("~w..~w", [FromVal, ToVal]);
+ _ -> flat_format("Badly formed type ~w",[Type])
+ end;
+t_form_to_string({type, _L, record, [{atom, _, Name}]}) ->
+ flat_format("#~w{}", [Name]);
+t_form_to_string({type, _L, record, [{atom, _, Name}|Fields]}) ->
+ FieldString = string:join(t_form_to_string_list(Fields), ","),
+ flat_format("#~w{~s}", [Name, FieldString]);
+t_form_to_string({type, _L, field_type, [{atom, _, Name}, Type]}) ->
+ flat_format("~w::~s", [Name, t_form_to_string(Type)]);
+t_form_to_string({type, _L, term, []}) -> "term()";
+t_form_to_string({type, _L, timeout, []}) -> "timeout()";
+t_form_to_string({type, _L, tuple, any}) -> "tuple()";
+t_form_to_string({type, _L, tuple, Args}) ->
+ "{" ++ string:join(t_form_to_string_list(Args), ",") ++ "}";
+t_form_to_string({type, _L, union, Args}) ->
+ string:join(t_form_to_string_list(Args), " | ");
+t_form_to_string({type, _L, Name, []} = T) ->
+ try
+ M = mod,
+ D0 = dict:new(),
+ MR = dict:from_list([{M, D0}]),
+ Site = {type, {M,Name,0}},
+ V = var_table__new(),
+ C = cache__new(),
+ State = #from_form{site = Site,
+ xtypes = sets:new(),
+ mrecs = MR,
+ vtab = V,
+ tnames = []},
+ {T1, _, _} = from_form(T, State, _Deep=1000, _ALot=1000000, C),
+ t_to_string(T1)
+ catch throw:{error, _} -> atom_to_string(Name) ++ "()"
+ end;
+t_form_to_string({user_type, _L, Name, List}) ->
+ flat_format("~w(~s)",
+ [Name, string:join(t_form_to_string_list(List), ",")]);
+t_form_to_string({type, L, Name, List}) ->
+ %% Compatibility: modules compiled before Erlang/OTP 18.0.
+ t_form_to_string({user_type, L, Name, List}).
+
+t_form_to_string_list(List) ->
+ t_form_to_string_list(List, []).
+
+t_form_to_string_list([H|T], Acc) ->
+ t_form_to_string_list(T, [t_form_to_string(H)|Acc]);
+t_form_to_string_list([], Acc) ->
+ lists:reverse(Acc).
+
+-spec atom_to_string(atom()) -> string().
+
+atom_to_string(Atom) ->
+ flat_format("~w", [Atom]).
+
+%%=============================================================================
+%%
+%% Utilities
+%%
+%%=============================================================================
+
+-spec any_none([erl_type()]) -> boolean().
+
+any_none([?none|_Left]) -> true;
+any_none([_|Left]) -> any_none(Left);
+any_none([]) -> false.
+
+-spec any_none_or_unit([erl_type()]) -> boolean().
+
+any_none_or_unit([?none|_]) -> true;
+any_none_or_unit([?unit|_]) -> true;
+any_none_or_unit([_|Left]) -> any_none_or_unit(Left);
+any_none_or_unit([]) -> false.
+
+-spec is_erl_type(any()) -> boolean().
+
+is_erl_type(?any) -> true;
+is_erl_type(?none) -> true;
+is_erl_type(?unit) -> true;
+is_erl_type(#c{}) -> true;
+is_erl_type(_) -> false.
+
+-spec lookup_record(atom(), type_table()) ->
+ 'error' | {'ok', [{atom(), parse_form(), erl_type()}]}.
+
+lookup_record(Tag, RecDict) when is_atom(Tag) ->
+ case dict:find({record, Tag}, RecDict) of
+ {ok, {_FileLine, [{_Arity, Fields}]}} ->
+ {ok, Fields};
+ {ok, {_FileLine, List}} when is_list(List) ->
+ %% This will have to do, since we do not know which record we
+ %% are looking for.
+ error;
+ error ->
+ error
+ end.
+
+-spec lookup_record(atom(), arity(), type_table()) ->
+ 'error' | {'ok', [{atom(), parse_form(), erl_type()}]}.
+
+lookup_record(Tag, Arity, RecDict) when is_atom(Tag) ->
+ case dict:find({record, Tag}, RecDict) of
+ {ok, {_FileLine, [{Arity, Fields}]}} -> {ok, Fields};
+ {ok, {_FileLine, OrdDict}} -> orddict:find(Arity, OrdDict);
+ error -> error
+ end.
+
+-spec lookup_type(_, _, _) -> {'type' | 'opaque', type_value()} | 'error'.
+lookup_type(Name, Arity, RecDict) ->
+ case dict:find({type, Name, Arity}, RecDict) of
+ error ->
+ case dict:find({opaque, Name, Arity}, RecDict) of
+ error -> error;
+ {ok, Found} -> {opaque, Found}
+ end;
+ {ok, Found} -> {type, Found}
+ end.
+
+-spec type_is_defined('type' | 'opaque', atom(), arity(), type_table()) ->
+ boolean().
+
+type_is_defined(TypeOrOpaque, Name, Arity, RecDict) ->
+ dict:is_key({TypeOrOpaque, Name, Arity}, RecDict).
+
+cannot_have_opaque(Type, TypeName, TypeNames) ->
+ t_is_none(Type) orelse is_recursive(TypeName, TypeNames).
+
+is_recursive(TypeName, TypeNames) ->
+ lists:member(TypeName, TypeNames).
+
+can_unfold_more(TypeName, TypeNames) ->
+ Fun = fun(E, Acc) -> case E of TypeName -> Acc + 1; _ -> Acc end end,
+ lists:foldl(Fun, 0, TypeNames) < ?REC_TYPE_LIMIT.
+
+-spec do_opaque(erl_type(), opaques(), fun((_) -> T)) -> T.
+
+%% Probably a little faster than calling t_unopaque/2.
+%% Unions that are due to opaque types are unopaqued.
+do_opaque(?opaque(_) = Type, Opaques, Pred) ->
+ case Opaques =:= 'universe' orelse is_opaque_type(Type, Opaques) of
+ true -> do_opaque(t_opaque_structure(Type), Opaques, Pred);
+ false -> Pred(Type)
+ end;
+do_opaque(?union(List) = Type, Opaques, Pred) ->
+ [A,B,F,I,L,N,T,M,O,Map] = List,
+ if O =:= ?none -> Pred(Type);
+ true ->
+ case Opaques =:= 'universe' orelse is_opaque_type(O, Opaques) of
+ true ->
+ S = t_opaque_structure(O),
+ do_opaque(t_sup([A,B,F,I,L,N,T,M,S,Map]), Opaques, Pred);
+ false -> Pred(Type)
+ end
+ end;
+do_opaque(Type, _Opaques, Pred) ->
+ Pred(Type).
+
+map_all_values(?map(Pairs,_,DefV)) ->
+ [DefV|[V || {V, _, _} <- Pairs]].
+
+map_all_keys(?map(Pairs,DefK,_)) ->
+ [DefK|[K || {_, _, K} <- Pairs]].
+
+map_all_types(M) ->
+ map_all_keys(M) ++ map_all_values(M).
+
+%% Tests if a type has exactly one possible value.
+-spec t_is_singleton(erl_type()) -> boolean().
+
+t_is_singleton(Type) ->
+ t_is_singleton(Type, 'universe').
+
+-spec t_is_singleton(erl_type(), opaques()) -> boolean().
+
+t_is_singleton(Type, Opaques) ->
+ do_opaque(Type, Opaques, fun is_singleton_type/1).
+
+%% Incomplete; not all representable singleton types are included.
+is_singleton_type(?nil) -> true;
+is_singleton_type(?atom(?any)) -> false;
+is_singleton_type(?atom(Set)) ->
+ ordsets:size(Set) =:= 1;
+is_singleton_type(?int_range(V, V)) -> true;
+is_singleton_type(?int_set(Set)) ->
+ ordsets:size(Set) =:= 1;
+is_singleton_type(?tuple(Types, Arity, _)) when is_integer(Arity) ->
+ lists:all(fun is_singleton_type/1, Types);
+is_singleton_type(?tuple_set([{Arity, [OnlyTuple]}])) when is_integer(Arity) ->
+ is_singleton_type(OnlyTuple);
+is_singleton_type(?map(Pairs, ?none, ?none)) ->
+ lists:all(fun({_,MNess,V}) -> MNess =:= ?mand andalso is_singleton_type(V)
+ end, Pairs);
+is_singleton_type(_) ->
+ false.
+
+%% Returns the only possible value of a singleton type.
+-spec t_singleton_to_term(erl_type(), opaques()) -> term().
+
+t_singleton_to_term(Type, Opaques) ->
+ do_opaque(Type, Opaques, fun singleton_type_to_term/1).
+
+singleton_type_to_term(?nil) -> [];
+singleton_type_to_term(?atom(Set)) when Set =/= ?any ->
+ case ordsets:size(Set) of
+ 1 -> hd(ordsets:to_list(Set));
+ _ -> error(badarg)
+ end;
+singleton_type_to_term(?int_range(V, V)) -> V;
+singleton_type_to_term(?int_set(Set)) ->
+ case ordsets:size(Set) of
+ 1 -> hd(ordsets:to_list(Set));
+ _ -> error(badarg)
+ end;
+singleton_type_to_term(?tuple(Types, Arity, _)) when is_integer(Arity) ->
+ lists:map(fun singleton_type_to_term/1, Types);
+singleton_type_to_term(?tuple_set([{Arity, [OnlyTuple]}]))
+ when is_integer(Arity) ->
+ singleton_type_to_term(OnlyTuple);
+singleton_type_to_term(?map(Pairs, ?none, ?none)) ->
+ maps:from_list([{singleton_type_to_term(K), singleton_type_to_term(V)}
+ || {K,?mand,V} <- Pairs]).
+
+%% -----------------------------------
+%% Set
+%%
+
+set_singleton(Element) ->
+ ordsets:from_list([Element]).
+
+set_is_singleton(Element, Set) ->
+ set_singleton(Element) =:= Set.
+
+set_is_element(Element, Set) ->
+ ordsets:is_element(Element, Set).
+
+set_union(?any, _) -> ?any;
+set_union(_, ?any) -> ?any;
+set_union(S1, S2) ->
+ case ordsets:union(S1, S2) of
+ S when length(S) =< ?SET_LIMIT -> S;
+ _ -> ?any
+ end.
+
+%% The intersection and subtraction can return ?none.
+%% This should always be handled right away since ?none is not a valid set.
+%% However, ?any is considered a valid set.
+
+set_intersection(?any, S) -> S;
+set_intersection(S, ?any) -> S;
+set_intersection(S1, S2) ->
+ case ordsets:intersection(S1, S2) of
+ [] -> ?none;
+ S -> S
+ end.
+
+set_subtract(_, ?any) -> ?none;
+set_subtract(?any, _) -> ?any;
+set_subtract(S1, S2) ->
+ case ordsets:subtract(S1, S2) of
+ [] -> ?none;
+ S -> S
+ end.
+
+set_from_list(List) ->
+ case length(List) of
+ L when L =< ?SET_LIMIT -> ordsets:from_list(List);
+ L when L > ?SET_LIMIT -> ?any
+ end.
+
+set_to_list(Set) ->
+ ordsets:to_list(Set).
+
+set_filter(Fun, Set) ->
+ case ordsets:filter(Fun, Set) of
+ [] -> ?none;
+ NewSet -> NewSet
+ end.
+
+set_size(Set) ->
+ ordsets:size(Set).
+
+set_to_string(Set) ->
+ L = [case is_atom(X) of
+ true -> io_lib:write_string(atom_to_list(X), $'); % stupid emacs '
+ false -> flat_format("~w", [X])
+ end || X <- set_to_list(Set)],
+ string:join(L, " | ").
+
+set_min([H|_]) -> H.
+
+set_max(Set) ->
+ hd(lists:reverse(Set)).
+
+flat_format(F, S) ->
+ lists:flatten(io_lib:format(F, S)).
+
+%%=============================================================================
+%%
+%% Utilities for the binary type
+%%
+%%=============================================================================
+
+-spec gcd(integer(), integer()) -> integer().
+
+gcd(A, B) when B > A ->
+ gcd1(B, A);
+gcd(A, B) ->
+ gcd1(A, B).
+
+-spec gcd1(integer(), integer()) -> integer().
+
+gcd1(A, 0) -> A;
+gcd1(A, B) ->
+ case A rem B of
+ 0 -> B;
+ X -> gcd1(B, X)
+ end.
+
+-spec bitstr_concat(erl_type(), erl_type()) -> erl_type().
+
+bitstr_concat(?none, _) -> ?none;
+bitstr_concat(_, ?none) -> ?none;
+bitstr_concat(?bitstr(U1, B1), ?bitstr(U2, B2)) ->
+ t_bitstr(gcd(U1, U2), B1+B2).
+
+-spec bitstr_match(erl_type(), erl_type()) -> erl_type().
+
+bitstr_match(?none, _) -> ?none;
+bitstr_match(_, ?none) -> ?none;
+bitstr_match(?bitstr(0, B1), ?bitstr(0, B2)) when B1 =< B2 ->
+ t_bitstr(0, B2-B1);
+bitstr_match(?bitstr(0, _B1), ?bitstr(0, _B2)) ->
+ ?none;
+bitstr_match(?bitstr(0, B1), ?bitstr(U2, B2)) when B1 =< B2 ->
+ t_bitstr(U2, B2-B1);
+bitstr_match(?bitstr(0, B1), ?bitstr(U2, B2)) ->
+ t_bitstr(U2, handle_base(U2, B2-B1));
+bitstr_match(?bitstr(_, B1), ?bitstr(0, B2)) when B1 > B2 ->
+ ?none;
+bitstr_match(?bitstr(U1, B1), ?bitstr(U2, B2)) ->
+ GCD = gcd(U1, U2),
+ t_bitstr(GCD, handle_base(GCD, B2-B1)).
+
+-spec handle_base(integer(), integer()) -> integer().
+
+handle_base(Unit, Pos) when Pos >= 0 ->
+ Pos rem Unit;
+handle_base(Unit, Neg) ->
+ (Unit+(Neg rem Unit)) rem Unit.
+
+family(L) ->
+ R = sofs:relation(L),
+ F = sofs:relation_to_family(R),
+ sofs:to_external(F).
+
+%%=============================================================================
+%%
+%% Interface functions for abstract data types defined in this module
+%%
+%%=============================================================================
+
+-spec var_table__new() -> var_table().
+
+var_table__new() ->
+ maps:new().
+
+%%=============================================================================
+%% Consistency-testing function(s) below
+%%=============================================================================
+
+-ifdef(DO_ERL_TYPES_TEST).
+
+test() ->
+ Atom1 = t_atom(),
+ Atom2 = t_atom(foo),
+ Atom3 = t_atom(bar),
+ true = t_is_atom(Atom2),
+
+ True = t_atom(true),
+ False = t_atom(false),
+ Bool = t_boolean(),
+ true = t_is_boolean(True),
+ true = t_is_boolean(Bool),
+ false = t_is_boolean(Atom1),
+
+ Binary = t_binary(),
+ true = t_is_binary(Binary),
+
+ Bitstr = t_bitstr(),
+ true = t_is_bitstr(Bitstr),
+
+ Bitstr1 = t_bitstr(7, 3),
+ true = t_is_bitstr(Bitstr1),
+ false = t_is_binary(Bitstr1),
+
+ Bitstr2 = t_bitstr(16, 8),
+ true = t_is_bitstr(Bitstr2),
+ true = t_is_binary(Bitstr2),
+
+ ?bitstr(8, 16) = t_subtract(t_bitstr(4, 12), t_bitstr(8, 12)),
+ ?bitstr(8, 16) = t_subtract(t_bitstr(4, 12), t_bitstr(8, 12)),
+
+ Int1 = t_integer(),
+ Int2 = t_integer(1),
+ Int3 = t_integer(16#ffffffff),
+ true = t_is_integer(Int2),
+ true = t_is_byte(Int2),
+ false = t_is_byte(Int3),
+ false = t_is_byte(t_from_range(-1, 1)),
+ true = t_is_byte(t_from_range(1, ?MAX_BYTE)),
+
+ Tuple1 = t_tuple(),
+ Tuple2 = t_tuple(3),
+ Tuple3 = t_tuple([Atom1, Int1]),
+ Tuple4 = t_tuple([Tuple1, Tuple2]),
+ Tuple5 = t_tuple([Tuple3, Tuple4]),
+ Tuple6 = t_limit(Tuple5, 2),
+ Tuple7 = t_limit(Tuple5, 3),
+ true = t_is_tuple(Tuple1),
+
+ Port = t_port(),
+ Pid = t_pid(),
+ Ref = t_reference(),
+ Identifier = t_identifier(),
+ false = t_is_reference(Port),
+ true = t_is_identifier(Port),
+
+ Function1 = t_fun(),
+ Function2 = t_fun(Pid),
+ Function3 = t_fun([], Pid),
+ Function4 = t_fun([Port, Pid], Pid),
+ Function5 = t_fun([Pid, Atom1], Int2),
+ true = t_is_fun(Function3),
+
+ List1 = t_list(),
+ List2 = t_list(t_boolean()),
+ List3 = t_cons(t_boolean(), List2),
+ List4 = t_cons(t_boolean(), t_atom()),
+ List5 = t_cons(t_boolean(), t_nil()),
+ List6 = t_cons_tl(List5),
+ List7 = t_sup(List4, List5),
+ List8 = t_inf(List7, t_list()),
+ List9 = t_cons(),
+ List10 = t_cons_tl(List9),
+ true = t_is_boolean(t_cons_hd(List5)),
+ true = t_is_list(List5),
+ false = t_is_list(List4),
+
+ Product1 = t_product([Atom1, Atom2]),
+ Product2 = t_product([Atom3, Atom1]),
+ Product3 = t_product([Atom3, Atom2]),
+
+ Union1 = t_sup(Atom2, Atom3),
+ Union2 = t_sup(Tuple2, Tuple3),
+ Union3 = t_sup(Int2, Atom3),
+ Union4 = t_sup(Port, Pid),
+ Union5 = t_sup(Union4, Int1),
+ Union6 = t_sup(Function1, Function2),
+ Union7 = t_sup(Function4, Function5),
+ Union8 = t_sup(True, False),
+ true = t_is_boolean(Union8),
+ Union9 = t_sup(Int2, t_integer(2)),
+ true = t_is_byte(Union9),
+ Union10 = t_sup(t_tuple([t_atom(true), ?any]),
+ t_tuple([t_atom(false), ?any])),
+
+ ?any = t_sup(Product3, Function5),
+
+ Atom3 = t_inf(Union3, Atom1),
+ Union2 = t_inf(Union2, Tuple1),
+ Int2 = t_inf(Int1, Union3),
+ Union4 = t_inf(Union4, Identifier),
+ Port = t_inf(Union5, Port),
+ Function4 = t_inf(Union7, Function4),
+ ?none = t_inf(Product2, Atom1),
+ Product3 = t_inf(Product1, Product2),
+ Function5 = t_inf(Union7, Function5),
+ true = t_is_byte(t_inf(Union9, t_number())),
+ true = t_is_char(t_inf(Union9, t_number())),
+
+ io:format("3? ~p ~n", [?int_set([3])]),
+
+ RecDict = dict:store({foo, 2}, [bar, baz], dict:new()),
+ Record1 = t_from_term({foo, [1,2], {1,2,3}}),
+
+ Types = [
+ Atom1,
+ Atom2,
+ Atom3,
+ Binary,
+ Int1,
+ Int2,
+ Tuple1,
+ Tuple2,
+ Tuple3,
+ Tuple4,
+ Tuple5,
+ Tuple6,
+ Tuple7,
+ Ref,
+ Port,
+ Pid,
+ Identifier,
+ List1,
+ List2,
+ List3,
+ List4,
+ List5,
+ List6,
+ List7,
+ List8,
+ List9,
+ List10,
+ Function1,
+ Function2,
+ Function3,
+ Function4,
+ Function5,
+ Product1,
+ Product2,
+ Record1,
+ Union1,
+ Union2,
+ Union3,
+ Union4,
+ Union5,
+ Union6,
+ Union7,
+ Union8,
+ Union10,
+ t_inf(Union10, t_tuple([t_atom(true), t_integer()]))
+ ],
+ io:format("~p\n", [[t_to_string(X, RecDict) || X <- Types]]).
+
+-endif.