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+%% =====================================================================
+%% %CopyrightBegin%
+%%
+%% Copyright Ericsson AB 2004-2009. All Rights Reserved.
+%%
+%% The contents of this file are subject to the Erlang Public License,
+%% Version 1.1, (the "License"); you may not use this file except in
+%% compliance with the License. You should have received a copy of the
+%% Erlang Public License along with this software. If not, it can be
+%% retrieved online at http://www.erlang.org/.
+%%
+%% Software distributed under the License is distributed on an "AS IS"
+%% basis, WITHOUT WARRANTY OF ANY KIND, either express or implied. See
+%% the License for the specific language governing rights and limitations
+%% under the License.
+%%
+%% %CopyrightEnd%
+%%
+%% Message analysis of Core Erlang programs.
+%%
+%% Copyright (C) 2002 Richard Carlsson
+%%
+%% Author contact: [email protected]
+%% =====================================================================
+
+%% TODO: might need a "top" (`any') element for any-length value lists.
+
+-module(cerl_messagean).
+
+-export([annotate/1]).
+
+-import(cerl, [alias_pat/1, alias_var/1, ann_c_var/2, ann_c_fun/3,
+ apply_args/1, apply_op/1, atom_val/1, bitstr_size/1,
+ bitstr_val/1, binary_segments/1, c_letrec/2,
+ ann_c_tuple/2, c_nil/0, call_args/1, call_module/1,
+ call_name/1, case_arg/1, case_clauses/1, catch_body/1,
+ clause_body/1, clause_guard/1, clause_pats/1, cons_hd/1,
+ cons_tl/1, fun_body/1, fun_vars/1, get_ann/1, int_val/1,
+ is_c_atom/1, is_c_int/1, let_arg/1, let_body/1,
+ let_vars/1, letrec_body/1, letrec_defs/1, module_defs/1,
+ module_defs/1, module_exports/1, pat_vars/1,
+ primop_args/1, primop_name/1, receive_action/1,
+ receive_clauses/1, receive_timeout/1, seq_arg/1,
+ seq_body/1, set_ann/2, try_arg/1, try_body/1, try_vars/1,
+ try_evars/1, try_handler/1, tuple_es/1, type/1,
+ values_es/1]).
+
+-import(cerl_trees, [get_label/1]).
+
+-define(DEF_LIMIT, 4).
+
+%% -export([test/1, test1/1, ttest/1]).
+
+%% ttest(F) ->
+%% {T, _} = cerl_trees:label(user_default:read(F)),
+%% {Time0, _} = erlang:statistics(runtime),
+%% analyze(T),
+%% {Time1, _} = erlang:statistics(runtime),
+%% Time1 - Time0.
+
+%% test(F) ->
+%% {T, _} = cerl_trees:label(user_default:read(F)),
+%% {Time0, _} = erlang:statistics(runtime),
+%% {Esc, _Vars} = analyze(T),
+%% {Time1, _} = erlang:statistics(runtime),
+%% io:fwrite("messages: ~p.\n", [Esc]),
+%% Set = sets:from_list(Esc),
+%% H = fun (Node, Ctxt, Cont) ->
+%% Doc = case get_ann(Node) of
+%% [{label, L} | _] ->
+%% B = sets:is_element(L, Set),
+%% bf(Node, Ctxt, Cont, B);
+%% _ ->
+%% bf(Node, Ctxt, Cont, false)
+%% end,
+%% case type(Node) of
+%% cons -> color(Doc);
+%% tuple -> color(Doc);
+%% _ -> Doc
+%% end
+%% end,
+%% {ok, FD} = file:open("out.html",[write]),
+%% Txt = cerl_prettypr:format(T, [{hook, H},{user,false}]),
+%% io:put_chars(FD, "<pre>\n"),
+%% io:put_chars(FD, html(Txt)),
+%% io:put_chars(FD, "</pre>\n"),
+%% file:close(FD),
+%% {ok, Time1 - Time0}.
+
+%% test1(F) ->
+%% {T, _} = cerl_trees:label(user_default:read(F)),
+%% {Time0, _} = erlang:statistics(runtime),
+%% {T1, Esc, Vars} = annotate(T),
+%% {Time1, _} = erlang:statistics(runtime),
+%% io:fwrite("messages: ~p.\n", [Esc]),
+%% %%% io:fwrite("vars: ~p.\n", [[X || X <- dict:to_list(Vars)]]),
+%% T2 = hhl_transform:transform(T1, Vars),
+%% Set = sets:from_list(Esc),
+%% H = fun (Node, Ctxt, Cont) ->
+%% case get_ann(Node) of
+%% [{label, L} | _] ->
+%% B = sets:is_element(L, Set),
+%% bf(Node, Ctxt, Cont, B);
+%% _ ->
+%% bf(Node, Ctxt, Cont, false)
+%% end
+%% end,
+%% {ok, FD} = file:open("out.html",[write]),
+%% Txt = cerl_prettypr:format(T2, [{hook, H},{user,false}]),
+%% io:put_chars(FD, "<pre>\n"),
+%% io:put_chars(FD, html(Txt)),
+%% io:put_chars(FD, "</pre>\n"),
+%% file:close(FD),
+%% {ok, Time1 - Time0}.
+
+%% html(Cs) ->
+%% html(Cs, []).
+
+%% html([$#, $< | Cs], As) ->
+%% html_1(Cs, [$< | As]);
+%% html([$< | Cs], As) ->
+%% html(Cs, ";tl&" ++ As);
+%% html([$> | Cs], As) ->
+%% html(Cs, ";tg&" ++ As);
+%% html([$& | Cs], As) ->
+%% html(Cs, ";pma&" ++ As);
+%% html([C | Cs], As) ->
+%% html(Cs, [C | As]);
+%% html([], As) ->
+%% lists:reverse(As).
+
+%% html_1([$> | Cs], As) ->
+%% html(Cs, [$> | As]);
+%% html_1([C | Cs], As) ->
+%% html_1(Cs, [C | As]).
+
+%% bf(Node, Ctxt, Cont, B) ->
+%% B0 = cerl_prettypr:get_ctxt_user(Ctxt),
+%% if B /= B0 ->
+%% Ctxt1 = cerl_prettypr:set_ctxt_user(Ctxt, B),
+%% Doc = Cont(Node, Ctxt1),
+%% case B of
+%% true ->
+%% Start = "<b>",
+%% End = "</b>";
+%% false ->
+%% Start = "</b>",
+%% End = "<b>"
+%% end,
+%% markup(Doc, Start, End);
+%% true ->
+%% Cont(Node, Ctxt)
+%% end.
+
+%% color(Doc) ->
+%% % Doc.
+%% markup(Doc, "<font color=blue>", "</font>").
+
+%% markup(Doc, Start, End) ->
+%% prettypr:beside(
+%% prettypr:null_text([$# | Start]),
+%% prettypr:beside(Doc,
+%% prettypr:null_text([$# | End]))).
+
+
+%% =====================================================================
+%% annotate(Tree) -> {Tree1, Escapes, Vars}
+%%
+%% Tree = cerl:cerl()
+%%
+%% Analyzes `Tree' (see `analyze') and appends a term 'escapes', to
+%% the annotation list of each constructor expression node and of
+%% `Tree', corresponding to the escape information derived by the
+%% analysis. Any previous such annotations are removed from `Tree'.
+%% `Tree1' is the modified tree; for details on `OutList',
+%% `Outputs' , `Dependencies', `Escapes' and `Parents', see
+%% `analyze'.
+%%
+%% Note: `Tree' must be annotated with labels in order to use this
+%% function; see `analyze' for details.
+
+-type label() :: integer() | 'external' | 'top'.
+-type ordset(X) :: [X]. % XXX: TAKE ME OUT
+
+-spec annotate(cerl:cerl()) -> {cerl:cerl(), ordset(label()), dict()}.
+
+annotate(Tree) ->
+ {Esc0, Vars} = analyze(Tree),
+ Esc = sets:from_list(Esc0),
+ F = fun (T) ->
+ case type(T) of
+ literal -> T;
+%%% var ->
+%%% L = get_label(T),
+%%% T1 = ann_escape(T, L, Esc),
+%%% X = dict:fetch(L, Vars),
+%%% set_ann(T1, append_ann({s,X}, get_ann(T1)));
+ _ ->
+ L = get_label(T),
+ ann_escape(T, L, Esc)
+ end
+ end,
+ {cerl_trees:map(F, Tree), Esc0, Vars}.
+
+ann_escape(T, L, Esc) ->
+ case sets:is_element(L, Esc) of
+ true ->
+ set_ann(T, append_ann(escapes, get_ann(T)));
+ false ->
+ T
+ end.
+
+append_ann(Tag, [X | Xs]) ->
+ if tuple_size(X) >= 1, element(1, X) =:= Tag ->
+ append_ann(Tag, Xs);
+ true ->
+ [X | append_ann(Tag, Xs)]
+ end;
+append_ann(Tag, []) ->
+ [Tag].
+
+
+%% =====================================================================
+%% analyze(Tree) -> Escapes
+%%
+%% Tree = cerl:cerl()
+%% Escapes = ordset(Label)
+%% Label = integer() | external | top
+%%
+%% Analyzes a module or an expression represented by `Tree'.
+%%
+%% `Escapes' is the set of labels of constructor expressions in
+%% `Tree' such that the created values may be accessed from outside
+%% `Tree'.
+%%
+%% Note: `Tree' must be annotated with labels (as done by the
+%% function `cerl_trees:label/1') in order to use this function.
+%% The label annotation `{label, L}' (where L should be an integer)
+%% must be the first element of the annotation list of each node in
+%% the tree. Instances of variables bound in `Tree' which denote
+%% the same variable must have the same label; apart from this,
+%% labels should be unique. Constant literals do not need to be
+%% labeled.
+
+-record(state, {vars, out, dep, work, funs, k}).
+
+%% Note: We assume that all remote calls and primops return a single
+%% value.
+
+%% The analysis determines which objects (identified by the
+%% corresponding "cons-point" labels in the code) are likely to be
+%% passed in a message. (If so, we say that they "escape".) It is always
+%% safe to assume either case, because the send operation will assure
+%% that things are copied if necessary. This analysis tries to
+%% anticipate that copying will be done.
+%%
+%% Rules:
+%% 1) An object passed as message argument (or part of such an
+%% argument) to a known send-operation, will probably be a message.
+%% 2) A received value is always a message (safe).
+%% 3) The external function can return any object (unsafe).
+%% 4) A function called from the external function can receive any
+%% object (unsafe) as argument.
+%% 5) Unknown functions/operations can return any object (unsafe).
+
+%% We wrap the given syntax tree T in a fun-expression labeled `top',
+%% which is initially in the set of escaped labels. `top' will be
+%% visited at least once.
+%%
+%% We create a separate function labeled `external', defined as:
+%% "'external'/1 = fun () -> Any", which will represent any and all
+%% functions outside T, and which returns the 'unsafe' value.
+
+analyze(Tree) ->
+ analyze(Tree, ?DEF_LIMIT).
+
+analyze(Tree, Limit) ->
+ {_, _, Esc, Dep, _Par} = cerl_closurean:analyze(Tree),
+%%% io:fwrite("dependencies: ~w.\n", [dict:to_list(Dep)]),
+ analyze(Tree, Limit, Dep, Esc).
+
+analyze(Tree, Limit, Dep0, Esc0) ->
+ %% Note that we use different name spaces for variable labels and
+ %% function/call site labels, so we can reuse some names here. We
+ %% assume that the labeling of Tree only uses integers, not atoms.
+ Any = ann_c_var([{label, any}], 'Any'),
+ External = ann_c_var([{label, external}], {external, 1}),
+ ExtFun = ann_c_fun([{label, external}], [], Any),
+%%% io:fwrite("external fun:\n~s.\n",
+%%% [cerl_prettypr:format(ExtFun, [noann, {paper, 80}])]),
+ Top = ann_c_var([{label, top}], {top, 0}),
+ TopFun = ann_c_fun([{label, top}], [], Tree),
+
+ %% The "start fun" just makes the initialisation easier. It is not
+ %% itself in the call graph.
+ StartFun = ann_c_fun([{label, start}], [],
+ c_letrec([{External, ExtFun}, {Top, TopFun}],
+ c_nil())),
+%%% io:fwrite("start fun:\n~s.\n",
+%%% [cerl_prettypr:format(StartFun, [{paper, 80}])]),
+
+ %% Initialise the Any and Escape variables. Gather a database of all
+ %% fun-expressions in Tree and initialise their outputs and parameter
+ %% variables. All escaping functions can receive any values as
+ %% inputs. Bind all module- and letrec-defined variables to their
+ %% corresponding labels.
+ Esc = sets:from_list(Esc0),
+ Unsafe = unsafe(),
+ Empty = empty(),
+ Funs0 = dict:new(),
+ Vars0 = dict:store(escape, empty(),
+ dict:store(any, Unsafe, dict:new())),
+ Out0 = dict:new(),
+ F = fun (T, S = {Fs, Vs, Os}) ->
+ case type(T) of
+ 'fun' ->
+ L = get_label(T),
+ As = fun_vars(T),
+ X = case sets:is_element(L, Esc) of
+ true -> Unsafe;
+ false -> Empty
+ end,
+ {dict:store(L, T, Fs),
+ bind_vars_single(As, X, Vs),
+ dict:store(L, none, Os)};
+ letrec ->
+ {Fs, bind_defs(letrec_defs(T), Vs), Os};
+ module ->
+ {Fs, bind_defs(module_defs(T), Vs), Os};
+ _ ->
+ S
+ end
+ end,
+ {Funs, Vars, Out} = cerl_trees:fold(F, {Funs0, Vars0, Out0}, StartFun),
+
+ %% Add the dependency for the loop in 'external':
+ Dep = add_dep(loop, external, Dep0),
+
+ %% Enter the fixpoint iteration at the StartFun.
+ St = loop(StartFun, start, #state{vars = Vars,
+ out = Out,
+ dep = Dep,
+ work = init_work(),
+ funs = Funs,
+ k = Limit}),
+ Ms = labels(dict:fetch(escape, St#state.vars)),
+ {Ms, St#state.vars}.
+
+loop(T, L, St0) ->
+%%% io:fwrite("analyzing: ~w.\n",[L]),
+%%% io:fwrite("work: ~w.\n", [St0#state.work]),
+ Xs0 = dict:fetch(L, St0#state.out),
+ {Xs1, St1} = visit(fun_body(T), L, St0),
+ Xs = limit(Xs1, St1#state.k),
+ {W, M} = case equal(Xs0, Xs) of
+ true ->
+ {St1#state.work, St1#state.out};
+ false ->
+%%% io:fwrite("out (~w) changed: ~w <- ~w.\n",
+%%% [L, Xs, Xs0]),
+ M1 = dict:store(L, Xs, St1#state.out),
+ case dict:find(L, St1#state.dep) of
+ {ok, S} ->
+ {add_work(set__to_list(S), St1#state.work),
+ M1};
+ error ->
+ {St1#state.work, M1}
+ end
+ end,
+ St2 = St1#state{out = M},
+ case take_work(W) of
+ {ok, L1, W1} ->
+ T1 = dict:fetch(L1, St2#state.funs),
+ loop(T1, L1, St2#state{work = W1});
+ none ->
+ St2
+ end.
+
+visit(T, L, St) ->
+%%% io:fwrite("visiting: ~w.\n",[type(T)]),
+ case type(T) of
+ literal ->
+ %% This is (or should be) a constant, even if it's compound,
+ %% so it's bugger all whether it is sent or not.
+ case cerl:concrete(T) of
+ [] -> {[empty()], St};
+ X when is_atom(X) -> {[empty()], St};
+ X when is_integer(X) -> {[empty()], St};
+ X when is_float(X) -> {[empty()], St};
+ _ ->
+ exit({not_literal, T})
+ end;
+ var ->
+ %% If a variable is not already in the store here, it must
+ %% be free in the program.
+ L1 = get_label(T),
+ Vars = St#state.vars,
+ case dict:find(L1, Vars) of
+ {ok, X} ->
+ {[X], St};
+ error ->
+%%% io:fwrite("free var: ~w.\n",[L1]),
+ X = unsafe(),
+ St1 = St#state{vars = dict:store(L1, X, Vars)},
+ {[X], St1}
+ end;
+ 'fun' ->
+ %% Must revisit the fun also, because its environment might
+ %% have changed. (We don't keep track of such dependencies.)
+ L1 = get_label(T),
+ St1 = St#state{work = add_work([L1], St#state.work)},
+ %% Currently, lambda expressions can only be locally
+ %% allocated, and therefore we have to force copying by
+ %% treating them as "unsafe" for now.
+ {[unsafe()], St1};
+ %% {[singleton(L1)], St1};
+ values ->
+ visit_list(values_es(T), L, St);
+ cons ->
+ {[X1, X2], St1} = visit_list([cons_hd(T), cons_tl(T)], L, St),
+ L1 = get_label(T),
+ X = make_cons(L1, X1, X2),
+ %% Also store the values of the elements.
+ Hd = get_hd(X),
+ Tl = get_tl(X),
+ St2 = St1#state{vars = dict:store(L1, [Hd, Tl], St1#state.vars)},
+ {[X], St2};
+ tuple ->
+ {Xs, St1} = visit_list(tuple_es(T), L, St),
+ L1 = get_label(T),
+ %% Also store the values of the elements.
+ St2 = St1#state{vars = dict:store(L1, Xs, St1#state.vars)},
+ {[struct(L1, Xs)], St2};
+ 'let' ->
+ {Xs, St1} = visit(let_arg(T), L, St),
+ Vars = bind_vars(let_vars(T), Xs, St1#state.vars),
+ visit(let_body(T), L, St1#state{vars = Vars});
+ seq ->
+ {_, St1} = visit(seq_arg(T), L, St),
+ visit(seq_body(T), L, St1);
+ apply ->
+ {_F, St1} = visit(apply_op(T), L, St),
+ {As, St2} = visit_list(apply_args(T), L, St1),
+ L1 = get_label(T),
+ Ls = get_deps(L1, St#state.dep),
+ Out = St2#state.out,
+ Xs1 = join_list([dict:fetch(X, Out) || X <- Ls]),
+ {Xs1, call_site(Ls, As, St2)};
+ call ->
+ M = call_module(T),
+ F = call_name(T),
+ As = call_args(T),
+ {_, St1} = visit(M, L, St),
+ {_, St2} = visit(F, L, St1),
+ {Xs, St3} = visit_list(As, L, St2),
+ L1 = get_label(T),
+ remote_call(M, F, Xs, As, L1, St3);
+ primop ->
+ As = primop_args(T),
+ {Xs, St1} = visit_list(As, L, St),
+ F = atom_val(primop_name(T)),
+ primop_call(F, length(Xs), Xs, As, St1);
+ 'case' ->
+ {Xs, St1} = visit(case_arg(T), L, St),
+ visit_clauses(Xs, case_clauses(T), L, St1);
+ 'receive' ->
+ %% The received value is of course a message, so it
+ %% is 'empty()', not 'unsafe()'.
+ X = empty(),
+ {Xs1, St1} = visit_clauses([X], receive_clauses(T), L, St),
+ {_, St2} = visit(receive_timeout(T), L, St1),
+ {Xs2, St3} = visit(receive_action(T), L, St2),
+ {join(Xs1, Xs2), St3};
+ 'try' ->
+ {Xs1, St1} = visit(try_arg(T), L, St),
+ X = unsafe(),
+ Vars = bind_vars(try_vars(T), Xs1, St1#state.vars),
+ {Xs2, St2} = visit(try_body(T), L, St1#state{vars = Vars}),
+ EVars = bind_vars(try_evars(T), [X, X, X], St2#state.vars),
+ {Xs3, St3} = visit(try_handler(T), L, St2#state{vars = EVars}),
+ {join(Xs2, Xs3), St3};
+ 'catch' ->
+ %% If we catch an exception, we can get unsafe data.
+ {Xs, St1} = visit(catch_body(T), L, St),
+ {join([unsafe()], Xs), St1};
+ binary ->
+ %% Binaries are heap objects, but we don't have special
+ %% shared-heap allocation operators for them at the moment.
+ %% They must therefore be treated as unsafe.
+ {_, St1} = visit_list(binary_segments(T), L, St),
+ {[unsafe()], St1};
+ bitstr ->
+ %% The other fields are constant literals.
+ {_, St1} = visit(bitstr_val(T), L, St),
+ {_, St2} = visit(bitstr_size(T), L, St1),
+ {none, St2};
+ letrec ->
+ %% All the bound funs should be revisited, because the
+ %% environment might have changed.
+ Ls = [get_label(F) || {_, F} <- letrec_defs(T)],
+ St1 = St#state{work = add_work(Ls, St#state.work)},
+ visit(letrec_body(T), L, St1);
+ module ->
+ %% We regard a module as a tuple of function variables in
+ %% the body of a `letrec'.
+ visit(c_letrec(module_defs(T),
+ ann_c_tuple([{label, get_label(T)}],
+ module_exports(T))),
+ L, St)
+ end.
+
+visit_clause(T, Xs, L, St) ->
+ Vars = bind_pats(clause_pats(T), Xs, St#state.vars),
+ {_, St1} = visit(clause_guard(T), L, St#state{vars = Vars}),
+ visit(clause_body(T), L, St1).
+
+%% We assume correct value-list typing.
+
+visit_list([T | Ts], L, St) ->
+ {Xs, St1} = visit(T, L, St),
+ {Xs1, St2} = visit_list(Ts, L, St1),
+ X = case Xs of
+ [X1] -> X1;
+ _ -> empty()
+ end,
+ {[X | Xs1], St2};
+visit_list([], _L, St) ->
+ {[], St}.
+
+visit_clauses(Xs, [T | Ts], L, St) ->
+ {Xs1, St1} = visit_clause(T, Xs, L, St),
+ {Xs2, St2} = visit_clauses(Xs, Ts, L, St1),
+ {join(Xs1, Xs2), St2};
+visit_clauses(_, [], _L, St) ->
+ {none, St}.
+
+bind_defs([{V, F} | Ds], Vars) ->
+ bind_defs(Ds, dict:store(get_label(V), singleton(get_label(F)), Vars));
+bind_defs([], Vars) ->
+ Vars.
+
+bind_pats(Ps, none, Vars) ->
+ bind_pats_single(Ps, empty(), Vars);
+bind_pats(Ps, Xs, Vars) ->
+ if length(Xs) =:= length(Ps) ->
+ bind_pats_list(Ps, Xs, Vars);
+ true ->
+ bind_pats_single(Ps, empty(), Vars)
+ end.
+
+%% The lists might not be of the same length.
+
+bind_pats_list([P | Ps], [X | Xs], Vars) ->
+ bind_pats_list(Ps, Xs, bind_pat_vars(P, X, Vars));
+bind_pats_list(Ps, [], Vars) ->
+ bind_pats_single(Ps, empty(), Vars);
+bind_pats_list([], _, Vars) ->
+ Vars.
+
+bind_pats_single([P | Ps], X, Vars) ->
+ bind_pats_single(Ps, X, bind_pat_vars(P, X, Vars));
+bind_pats_single([], _X, Vars) ->
+ Vars.
+
+bind_pat_vars(P, X, Vars) ->
+ case type(P) of
+ var ->
+ dict:store(get_label(P), X, Vars);
+ literal ->
+ Vars;
+ cons ->
+ bind_pats_list([cons_hd(P), cons_tl(P)],
+ [get_hd(X), get_tl(X)], Vars);
+ tuple ->
+ case elements(X) of
+ none ->
+ bind_vars_single(pat_vars(P), X, Vars);
+ Xs ->
+ bind_pats_list(tuple_es(P), Xs, Vars)
+ end;
+ binary ->
+ %% See the handling of binary-expressions.
+ bind_pats_single(binary_segments(P), unsafe(), Vars);
+ bitstr ->
+ %% See the handling of binary-expressions.
+ bind_pats_single([bitstr_val(P), bitstr_size(P)],
+ unsafe(), Vars);
+ alias ->
+ P1 = alias_pat(P),
+ Vars1 = bind_pat_vars(P1, X, Vars),
+ dict:store(get_label(alias_var(P)), X, Vars1)
+ end.
+
+%%% %% This is the "exact" version of list representation, which simply
+%%% %% mimics the actual cons, head and tail operations.
+%%% make_cons(L, X1, X2) ->
+%%% struct(L1, [X1, X2]).
+%%% get_hd(X) ->
+%%% case elements(X) of
+%%% none -> X;
+%%% [X1 | _] -> X1;
+%%% _ -> empty()
+%%% end.
+%%% get_tl(X) ->
+%%% case elements(X) of
+%%% none -> X;
+%%% [_, X2 | _] -> X2;
+%%% _ -> empty()
+%%% end.
+
+%% This version does not unnecessarily confuse spine labels with element
+%% labels, and is safe. However, it loses precision if cons cells are
+%% used for other things than proper lists.
+
+make_cons(L, X1, X2) ->
+ %% join subtypes and cons locations
+ join_single(struct(L, [X1]), X2).
+
+get_hd(X) ->
+ case elements(X) of
+ none -> X;
+ [X1 | _] -> X1; % First element represents list subtype.
+ _ -> empty()
+ end.
+
+get_tl(X) -> X. % Tail of X has same type as X.
+
+bind_vars(Vs, none, Vars) ->
+ bind_vars_single(Vs, empty(), Vars);
+bind_vars(Vs, Xs, Vars) ->
+ if length(Vs) =:= length(Xs) ->
+ bind_vars_list(Vs, Xs, Vars);
+ true ->
+ bind_vars_single(Vs, empty(), Vars)
+ end.
+
+bind_vars_list([V | Vs], [X | Xs], Vars) ->
+ bind_vars_list(Vs, Xs, dict:store(get_label(V), X, Vars));
+bind_vars_list([], [], Vars) ->
+ Vars.
+
+bind_vars_single([V | Vs], X, Vars) ->
+ bind_vars_single(Vs, X, dict:store(get_label(V), X, Vars));
+bind_vars_single([], _X, Vars) ->
+ Vars.
+
+%% This handles a call site, updating parameter variables with respect
+%% to the actual parameters. The 'external' function is handled
+%% specially, since it can get an arbitrary number of arguments. For our
+%% purposes here, calls to the external function can be ignored.
+
+call_site(Ls, Xs, St) ->
+%%% io:fwrite("call site: ~w -> ~w (~w).\n", [L, Ls, Xs]),
+ {W, V} = call_site(Ls, Xs, St#state.work, St#state.vars,
+ St#state.funs, St#state.k),
+ St#state{work = W, vars = V}.
+
+call_site([external | Ls], Xs, W, V, Fs, Limit) ->
+ call_site(Ls, Xs, W, V, Fs, Limit);
+call_site([L | Ls], Xs, W, V, Fs, Limit) ->
+ Vs = fun_vars(dict:fetch(L, Fs)),
+ case bind_args(Vs, Xs, V, Limit) of
+ {V1, true} ->
+ call_site(Ls, Xs, add_work([L], W), V1, Fs, Limit);
+ {V1, false} ->
+ call_site(Ls, Xs, W, V1, Fs, Limit)
+ end;
+call_site([], _, W, V, _, _) ->
+ {W, V}.
+
+add_dep(Source, Target, Deps) ->
+ case dict:find(Source, Deps) of
+ {ok, X} ->
+ case set__is_member(Target, X) of
+ true ->
+ Deps;
+ false ->
+%%% io:fwrite("new dep: ~w <- ~w.\n", [Target, Source]),
+ dict:store(Source, set__add(Target, X), Deps)
+ end;
+ error ->
+%%% io:fwrite("new dep: ~w <- ~w.\n", [Target, Source]),
+ dict:store(Source, set__singleton(Target), Deps)
+ end.
+
+%% If the arity does not match the call, nothing is done here.
+
+bind_args(Vs, Xs, Vars, Limit) ->
+ if length(Vs) =:= length(Xs) ->
+ bind_args(Vs, Xs, Vars, Limit, false);
+ true ->
+ {Vars, false}
+ end.
+
+bind_args([V | Vs], [X | Xs], Vars, Limit, Ch) ->
+ L = get_label(V),
+ {Vars1, Ch1} = bind_arg(L, X, Vars, Limit, Ch),
+ bind_args(Vs, Xs, Vars1, Limit, Ch1);
+bind_args([], [], Vars, _Limit, Ch) ->
+ {Vars, Ch}.
+
+%% bind_arg(L, X, Vars, Limit) ->
+%% bind_arg(L, X, Vars, Limit, false).
+
+bind_arg(L, X, Vars, Limit, Ch) ->
+ X0 = dict:fetch(L, Vars),
+ X1 = limit_single(join_single(X, X0), Limit),
+ case equal_single(X0, X1) of
+ true ->
+ {Vars, Ch};
+ false ->
+%%% io:fwrite("arg (~w) changed: ~w <- ~w + ~w.\n",
+%%% [L, X1, X0, X]),
+ {dict:store(L, X1, Vars), true}
+ end.
+
+%% This handles escapes from things like primops and remote calls.
+
+escape(Xs, Ns, St) ->
+ escape(Xs, Ns, 1, St).
+
+escape([_ | Xs], Ns=[N1 | _], N, St) when is_integer(N1), N1 > N ->
+ escape(Xs, Ns, N + 1, St);
+escape([X | Xs], [N | Ns], N, St) ->
+ Vars = St#state.vars,
+ X0 = dict:fetch(escape, Vars),
+ X1 = join_single(X, X0),
+ case equal_single(X0, X1) of
+ true ->
+ escape(Xs, Ns, N + 1, St);
+ false ->
+%%% io:fwrite("escape changed: ~w <- ~w + ~w.\n", [X1, X0, X]),
+ Vars1 = dict:store(escape, X1, Vars),
+ escape(Xs, Ns, N + 1, St#state{vars = Vars1})
+ end;
+escape(Xs, [_ | Ns], N, St) ->
+ escape(Xs, Ns, N + 1, St);
+escape(_, _, _, St) ->
+ St.
+
+%% Handle primop calls: (At present, we assume that all unknown calls
+%% yield exactly one value. This might have to be changed.)
+
+primop_call(F, A, Xs, _As, St0) ->
+ %% St1 = case is_escape_op(F, A) of
+ %% [] -> St0;
+ %% Ns -> escape(Xs, Ns, St0)
+ %% end,
+ St1 = St0,
+ case is_imm_op(F, A) of
+ true ->
+ {[empty()], St1};
+ false ->
+ call_unknown(Xs, St1)
+ end.
+
+%% Handle remote-calls: (At present, we assume that all unknown calls
+%% yield exactly one value. This might have to be changed.)
+
+remote_call(M, F, Xs, As, L, St) ->
+ case is_c_atom(M) andalso is_c_atom(F) of
+ true ->
+ remote_call_1(atom_val(M), atom_val(F), length(Xs),
+ Xs, As, L, St);
+ false ->
+ %% Unknown function
+ call_unknown(Xs, St)
+ end.
+
+%% When calling an unknown function, we assume that the result does
+%% *not* contain any of the constructors in its arguments (but it could
+%% return locally allocated data that we don't know about). Note that
+%% even a "pure" function can still cons up new data.
+
+call_unknown(_Xs, St) ->
+ {[unsafe()], St}.
+
+%% We need to handle some important standard functions in order to get
+%% decent precision.
+%% TODO: foldl, map, mapfoldl
+
+remote_call_1(erlang, hd, 1, [X], _As, _L, St) ->
+ {[get_hd(X)], St};
+remote_call_1(erlang, tl, 1, [X], _As, _L, St) ->
+ {[get_tl(X)], St};
+remote_call_1(erlang, element, 2, [_,X], [N|_], _L, St) ->
+ case elements(X) of
+ none -> {[X], St};
+ Xs ->
+ case is_c_int(N) of
+ true ->
+ N1 = int_val(N),
+ if is_integer(N1), 1 =< N1, N1 =< length(Xs) ->
+ {[nth(N1, Xs)], St};
+ true ->
+ {none, St}
+ end;
+ false ->
+ %% Even if we don't know which element is selected,
+ %% we know that the top level is never part of the
+ %% returned value.
+ {[join_single_list(Xs)], St}
+ end
+ end;
+remote_call_1(erlang, setelement, 3, [_,X, Y], [N|_], L, St) ->
+ %% The constructor gets the label of the call operation.
+ case elements(X) of
+ none -> {[join_single(singleton(L), join_single(X, Y))], St};
+ Xs ->
+ case is_c_int(N) of
+ true ->
+ N1 = int_val(N),
+ if is_integer(N1), 1 =< N1, N1 =< length(Xs) ->
+ Xs1 = set_nth(N1, Y, Xs),
+ {[struct(L, Xs1)], St};
+ true ->
+ {none, St}
+ end;
+ false ->
+ %% Even if we don't know which element is selected,
+ %% we know that the top level is never part of the
+ %% returned value (a new tuple is always created).
+ Xs1 = [join_single(Y, X1) || X1 <- Xs],
+ {[struct(L, Xs1)], St}
+ end
+ end;
+remote_call_1(erlang, '++', 2, [X1,X2], _As, _L, St) ->
+ %% Note: this is unsafe for non-proper lists! (See make_cons/3).
+ %% No safe version is implemented.
+ {[join_single(X1, X2)], St};
+remote_call_1(erlang, '--', 2, [X1,_X2], _As, _L, St) ->
+ {[X1], St};
+remote_call_1(lists, append, 2, Xs, As, L, St) ->
+ remote_call_1(erlang, '++', 2, Xs, As, L, St);
+remote_call_1(lists, subtract, 2, Xs, As, L, St) ->
+ remote_call_1(erlang, '--', 2, Xs, As, L, St);
+remote_call_1(M, F, A, Xs, _As, _L, St0) ->
+ St1 = case is_escape_op(M, F, A) of
+ [] -> St0;
+ Ns -> escape(Xs, Ns, St0)
+ end,
+ case is_imm_op(M, F, A) of
+ true ->
+ {[empty()], St1};
+ false ->
+ call_unknown(Xs, St1)
+ end.
+
+%% 1-based n:th-element list selector and update function.
+
+nth(1, [X | _Xs]) -> X;
+nth(N, [_X | Xs]) when N > 1 -> nth(N - 1, Xs).
+
+set_nth(1, Y, [_X | Xs]) -> [Y | Xs];
+set_nth(N, Y, [X | Xs]) when N > 1 -> [X | set_nth(N - 1, Y, Xs)].
+
+%% Domain: none | [V], where V = {S, none} | {S, [V]}, S = set(integer()).
+
+join(none, Xs2) -> Xs2;
+join(Xs1, none) -> Xs1;
+join(Xs1, Xs2) ->
+ if length(Xs1) =:= length(Xs2) ->
+ join_1(Xs1, Xs2);
+ true ->
+ none
+ end.
+
+join_1([X1 | Xs1], [X2 | Xs2]) ->
+ [join_single(X1, X2) | join_1(Xs1, Xs2)];
+join_1([], []) ->
+ [].
+
+join_list([Xs | Xss]) ->
+ join(Xs, join_list(Xss));
+join_list([]) ->
+ none.
+
+empty() -> {set__new(), []}.
+
+singleton(X) -> {set__singleton(X), []}.
+
+struct(X, Xs) -> {set__singleton(X), Xs}.
+
+elements({_, Xs}) -> Xs.
+
+unsafe() -> {set__singleton(unsafe), none}.
+
+equal(none, none) -> true;
+equal(none, _) -> false;
+equal(_, none) -> false;
+equal(X1, X2) -> equal_1(X1, X2).
+
+equal_1([X1 | Xs1], [X2 | Xs2]) ->
+ equal_single(X1, X2) andalso equal_1(Xs1, Xs2);
+equal_1([], []) -> true;
+equal_1(_, _) -> false.
+
+equal_single({S1, none}, {S2, none}) ->
+ set__equal(S1, S2);
+equal_single({_, none}, _) ->
+ false;
+equal_single(_, {_, none}) ->
+ false;
+equal_single({S1, Vs1}, {S2, Vs2}) ->
+ set__equal(S1, S2) andalso equal_single_lists(Vs1, Vs2).
+
+equal_single_lists([X1 | Xs1], [X2 | Xs2]) ->
+ equal_single(X1, X2) andalso equal_single_lists(Xs1, Xs2);
+equal_single_lists([], []) ->
+ true;
+equal_single_lists(_, _) ->
+ false.
+
+join_single({S, none}, V) ->
+ {set__union(S, labels(V)), none};
+join_single(V, {S, none}) ->
+ {set__union(S, labels(V)), none};
+join_single({S1, Vs1}, {S2, Vs2}) ->
+ {set__union(S1, S2), join_single_lists(Vs1, Vs2)}.
+
+join_single_list([V | Vs]) ->
+ join_single(V, join_single_list(Vs));
+join_single_list([]) ->
+ empty().
+
+%% If one list has more elements that the other, and N is the length of
+%% the longer list, then the result has N elements.
+
+join_single_lists([V1], [V2]) ->
+ [join_single(V1, V2)];
+join_single_lists([V1 | Vs1], [V2 | Vs2]) ->
+ [join_single(V1, V2) | join_single_lists(Vs1, Vs2)];
+join_single_lists([], Vs) -> Vs;
+join_single_lists(Vs, []) -> Vs.
+
+collapse(V) ->
+ {labels(V), none}.
+
+%% collapse_list([]) ->
+%% empty();
+%% collapse_list(Vs) ->
+%% {labels_list(Vs), none}.
+
+labels({S, none}) -> S;
+labels({S, []}) -> S;
+labels({S, Vs}) -> set__union(S, labels_list(Vs)).
+
+labels_list([V]) ->
+ labels(V);
+labels_list([V | Vs]) ->
+ set__union(labels(V), labels_list(Vs)).
+
+limit(none, _K) -> none;
+limit(X, K) -> limit_list(X, K).
+
+limit_list([X | Xs], K) ->
+ [limit_single(X, K) | limit_list(Xs, K)];
+limit_list([], _) ->
+ [].
+
+limit_single({_, none} = V, _K) ->
+ V;
+limit_single({_, []} = V, _K) ->
+ V;
+limit_single({S, Vs}, K) when K > 0 ->
+ {S, limit_list(Vs, K - 1)};
+limit_single(V, _K) ->
+ collapse(V).
+
+%% Set abstraction for label sets in the domain.
+
+%% set__is_empty([]) -> true;
+%% set__is_empty(_) -> false.
+
+set__new() -> [].
+
+set__singleton(X) -> [X].
+
+set__to_list(S) -> S.
+
+%% set__from_list(S) -> ordsets:from_list(S).
+
+set__union(X, Y) -> ordsets:union(X, Y).
+
+set__add(X, S) -> ordsets:add_element(X, S).
+
+set__is_member(X, S) -> ordsets:is_element(X, S).
+
+%% set__subtract(X, Y) -> ordsets:subtract(X, Y).
+
+set__equal(X, Y) -> X =:= Y.
+
+%% A simple but efficient functional queue.
+
+queue__new() -> {[], []}.
+
+queue__put(X, {In, Out}) -> {[X | In], Out}.
+
+queue__get({In, [X | Out]}) -> {ok, X, {In, Out}};
+queue__get({[], _}) -> empty;
+queue__get({In, _}) ->
+ [X | In1] = lists:reverse(In),
+ {ok, X, {[], In1}}.
+
+%% The work list - a queue without repeated elements.
+
+init_work() ->
+ {queue__new(), sets:new()}.
+
+add_work(Ls, {Q, Set}) ->
+ add_work(Ls, Q, Set).
+
+%% Note that the elements are enqueued in order.
+
+add_work([L | Ls], Q, Set) ->
+ case sets:is_element(L, Set) of
+ true ->
+ add_work(Ls, Q, Set);
+ false ->
+ add_work(Ls, queue__put(L, Q), sets:add_element(L, Set))
+ end;
+add_work([], Q, Set) ->
+ {Q, Set}.
+
+take_work({Queue0, Set0}) ->
+ case queue__get(Queue0) of
+ {ok, L, Queue1} ->
+ Set1 = sets:del_element(L, Set0),
+ {ok, L, {Queue1, Set1}};
+ empty ->
+ none
+ end.
+
+get_deps(L, Dep) ->
+ case dict:find(L, Dep) of
+ {ok, Ls} -> Ls;
+ error -> []
+ end.
+
+%% Escape operators may let their arguments escape. For this analysis,
+%% only send-operations are considered as causing escapement, and only
+%% in specific arguments.
+
+%% is_escape_op(_F, _A) -> [].
+
+-spec is_escape_op(module(), atom(), arity()) -> [arity()].
+
+is_escape_op(erlang, '!', 2) -> [2];
+is_escape_op(erlang, send, 2) -> [2];
+is_escape_op(erlang, spawn, 1) -> [1];
+is_escape_op(erlang, spawn, 3) -> [3];
+is_escape_op(erlang, spawn, 4) -> [4];
+is_escape_op(erlang, spawn_link, 3) -> [3];
+is_escape_op(erlang, spawn_link, 4) -> [4];
+is_escape_op(_M, _F, _A) -> [].
+
+%% "Immediate" operators will never return heap allocated data. This is
+%% of course true for operators that never return, like 'exit/1'. (Note
+%% that floats are always heap allocated objects, and that most integer
+%% arithmetic can return a bignum on the heap.)
+
+-spec is_imm_op(atom(), arity()) -> boolean().
+
+is_imm_op(match_fail, 1) -> true;
+is_imm_op(_, _) -> false.
+
+-spec is_imm_op(module(), atom(), arity()) -> boolean().
+
+is_imm_op(erlang, self, 0) -> true;
+is_imm_op(erlang, '=:=', 2) -> true;
+is_imm_op(erlang, '==', 2) -> true;
+is_imm_op(erlang, '=/=', 2) -> true;
+is_imm_op(erlang, '/=', 2) -> true;
+is_imm_op(erlang, '<', 2) -> true;
+is_imm_op(erlang, '=<', 2) -> true;
+is_imm_op(erlang, '>', 2) -> true;
+is_imm_op(erlang, '>=', 2) -> true;
+is_imm_op(erlang, 'and', 2) -> true;
+is_imm_op(erlang, 'or', 2) -> true;
+is_imm_op(erlang, 'xor', 2) -> true;
+is_imm_op(erlang, 'not', 1) -> true;
+is_imm_op(erlang, is_alive, 0) -> true;
+is_imm_op(erlang, is_atom, 1) -> true;
+is_imm_op(erlang, is_binary, 1) -> true;
+is_imm_op(erlang, is_builtin, 3) -> true;
+is_imm_op(erlang, is_constant, 1) -> true;
+is_imm_op(erlang, is_float, 1) -> true;
+is_imm_op(erlang, is_function, 1) -> true;
+is_imm_op(erlang, is_integer, 1) -> true;
+is_imm_op(erlang, is_list, 1) -> true;
+is_imm_op(erlang, is_number, 1) -> true;
+is_imm_op(erlang, is_pid, 1) -> true;
+is_imm_op(erlang, is_port, 1) -> true;
+is_imm_op(erlang, is_process_alive, 1) -> true;
+is_imm_op(erlang, is_reference, 1) -> true;
+is_imm_op(erlang, is_tuple, 1) -> true;
+is_imm_op(erlang, length, 1) -> true; % never a bignum
+is_imm_op(erlang, list_to_atom, 1) -> true;
+is_imm_op(erlang, node, 0) -> true;
+is_imm_op(erlang, node, 1) -> true;
+is_imm_op(erlang, throw, 1) -> true;
+is_imm_op(erlang, exit, 1) -> true;
+is_imm_op(erlang, error, 1) -> true;
+is_imm_op(erlang, error, 2) -> true;
+is_imm_op(_, _, _) -> false.