diff options
Diffstat (limited to 'lib/hipe/cerl/erl_types.erl')
| -rw-r--r-- | lib/hipe/cerl/erl_types.erl | 2025 |
1 files changed, 1305 insertions, 720 deletions
diff --git a/lib/hipe/cerl/erl_types.erl b/lib/hipe/cerl/erl_types.erl index d7d8a878c5..cfa72d85b7 100644 --- a/lib/hipe/cerl/erl_types.erl +++ b/lib/hipe/cerl/erl_types.erl @@ -2,7 +2,7 @@ %% %% %CopyrightBegin% %% -%% Copyright Ericsson AB 2003-2013. All Rights Reserved. +%% Copyright Ericsson AB 2003-2014. 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 @@ -42,15 +42,15 @@ max/2, module_builtin_opaques/1, min/2, - number_max/1, - number_min/1, + 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/1, t_atom_vals/2, t_binary/0, t_bitstr/0, t_bitstr/2, @@ -66,12 +66,14 @@ t_collect_vars/1, t_cons/0, t_cons/2, - t_cons_hd/1, - t_cons_tl/1, + t_cons_hd/1, t_cons_hd/2, + t_cons_tl/1, t_cons_tl/2, t_constant/0, - t_contains_opaque/1, + t_contains_opaque/1, t_contains_opaque/2, + t_decorate_with_opaque/3, t_elements/1, t_find_opaque_mismatch/2, + t_find_unknown_opaque/3, t_fixnum/0, t_map/2, t_non_neg_fixnum/0, @@ -87,18 +89,18 @@ t_fun/0, t_fun/1, t_fun/2, - t_fun_args/1, - t_fun_arity/1, - t_fun_range/1, - t_has_opaque_subtype/1, + 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/2, - t_inf/3, - t_inf_lists/2, - t_inf_lists/3, - t_inf_lists_masked/3, + 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, @@ -107,44 +109,44 @@ t_iodata/0, t_iolist/0, t_is_any/1, - t_is_atom/1, - t_is_atom/2, - t_is_binary/1, - t_is_bitstr/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/1, t_is_boolean/2, %% t_is_byte/1, %% t_is_char/1, - t_is_cons/1, + t_is_cons/1, t_is_cons/2, t_is_constant/1, t_is_equal/2, t_is_fixnum/1, - t_is_float/1, - t_is_fun/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/1, t_is_integer/2, t_is_list/1, t_is_matchstate/1, - t_is_nil/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_opaque/1, - t_is_pid/1, - t_is_port/1, - t_is_maybe_improper_list/1, - t_is_reference/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_remote/1, t_is_string/1, t_is_subtype/2, - t_is_tuple/1, + 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/1, t_list_elements/2, t_list_termination/1, t_matchstate/0, t_matchstate/2, @@ -163,11 +165,8 @@ t_nonempty_string/0, t_number/0, t_number/1, - t_number_vals/1, + t_number_vals/1, t_number_vals/2, t_opaque_from_records/1, - t_opaque_match_atom/2, - t_opaque_match_record/2, - t_opaque_matching_structure/2, t_opaque_structure/1, %% t_parameterized_module/0, t_pid/0, @@ -192,16 +191,14 @@ t_to_tlist/1, t_tuple/0, t_tuple/1, - t_tuple_args/1, - t_tuple_size/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_unify/3, t_unit/0, - t_unopaque/1, - t_unopaque/2, - t_unopaque_on_mismatch/3, + t_unopaque/1, t_unopaque/2, t_var/1, t_var_name/1, %% t_assign_variables_to_subtype/2, @@ -209,6 +206,7 @@ record_field_diffs_to_string/2, subst_all_vars_to_any/1, lift_list_to_pos_empty/1, + is_opaque_type/2, is_erl_type/1, atom_to_string/1 ]). @@ -228,6 +226,14 @@ -export_type([erl_type/0]). +%%-define(DEBUG, true). + +-ifdef(DEBUG). +-define(debug(__A), __A). +-else. +-define(debug(__A), ok). +-endif. + %%============================================================================= %% %% Definition of the type structure @@ -310,6 +316,9 @@ -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()}). -record(remote, {mod:: module(), name :: atom(), args = [] :: [erl_type()]}). @@ -346,6 +355,8 @@ -define(integer_non_neg, ?int_range(0, pos_inf)). -define(integer_neg, ?int_range(neg_inf, -1)). +-type opaques() :: [erl_type()] | 'universe'. + %%----------------------------------------------------------------------------- %% Unions %% @@ -384,8 +395,11 @@ t_any() -> -spec t_is_any(erl_type()) -> boolean(). -t_is_any(?any) -> true; -t_is_any(_) -> false. +t_is_any(Type) -> + do_opaque(Type, 'universe', fun is_any/1). + +is_any(?any) -> true; +is_any(_) -> false. -spec t_none() -> erl_type(). @@ -407,16 +421,25 @@ 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()) -> boolean(). +-spec t_has_opaque_subtype(erl_type(), opaques()) -> boolean(). + +t_has_opaque_subtype(Type, Opaques) -> + do_opaque(Type, Opaques, fun has_opaque_subtype/1). -t_has_opaque_subtype(?union(Ts)) -> +has_opaque_subtype(?union(Ts)) -> lists:any(fun t_is_opaque/1, Ts); -t_has_opaque_subtype(T) -> +has_opaque_subtype(T) -> t_is_opaque(T). -spec t_opaque_structure(erl_type()) -> erl_type(). @@ -424,74 +447,62 @@ t_has_opaque_subtype(T) -> t_opaque_structure(?opaque(Elements)) -> t_sup([Struct || #opaque{struct = Struct} <- ordsets:to_list(Elements)]). --spec t_opaque_module(erl_type()) -> module(). +-spec t_opaque_modules(erl_type()) -> [module()]. -t_opaque_module(?opaque(Elements)) -> +t_opaque_modules(?opaque(Elements)) -> case ordsets:size(Elements) of 1 -> - [#opaque{mod = Module}] = ordsets:to_list(Elements), - Module; + [#opaque{mod = Mod}] = set_to_list(Elements), + [Mod]; _ -> throw({error, "Unexpected multiple opaque types"}) end. -%% This only makes sense if we know that Type matches Opaque --spec t_opaque_matching_structure(erl_type(), erl_type()) -> erl_type(). - -t_opaque_matching_structure(Type, Opaque) -> - OpaqueStruct = t_opaque_structure(Opaque), - case OpaqueStruct of - ?union(L1) -> - case Type of - ?union(_L2) -> OpaqueStruct; - _OtherType -> t_opaque_matching_structure_list(Type, L1) - end; - ?tuple_set(_Set1) = TupleSet -> - case Type of - ?tuple_set(_Set2) -> OpaqueStruct; - _ -> t_opaque_matching_structure_list(Type, t_tuple_subtypes(TupleSet)) - end; - _Other -> OpaqueStruct - end. - -t_opaque_matching_structure_list(Type, List) -> - NewList = [t_inf(Element, Type) || Element <- List], - Results = [NotNone || NotNone <- NewList, NotNone =/= ?none], - case Results of - [] -> ?none; - [First|_] -> First - end. - -spec t_contains_opaque(erl_type()) -> boolean(). -t_contains_opaque(?any) -> false; -t_contains_opaque(?none) -> false; -t_contains_opaque(?unit) -> false; -t_contains_opaque(?atom(_Set)) -> false; -t_contains_opaque(?bitstr(_Unit, _Base)) -> false; -t_contains_opaque(?float) -> false; -t_contains_opaque(?function(Domain, Range)) -> - t_contains_opaque(Domain) orelse t_contains_opaque(Range); -t_contains_opaque(?identifier(_Types)) -> false; -t_contains_opaque(?integer(_Types)) -> false; -t_contains_opaque(?int_range(_From, _To)) -> false; -t_contains_opaque(?int_set(_Set)) -> false; -t_contains_opaque(?list(Type, _, _)) -> t_contains_opaque(Type); -t_contains_opaque(?matchstate(_P, _Slots)) -> false; -t_contains_opaque(?nil) -> false; -t_contains_opaque(?number(_Set, _Tag)) -> false; -t_contains_opaque(?opaque(_)) -> true; -t_contains_opaque(?product(Types)) -> list_contains_opaque(Types); -t_contains_opaque(?tuple(?any, _, _)) -> false; -t_contains_opaque(?tuple(Types, _, _)) -> list_contains_opaque(Types); -t_contains_opaque(?tuple_set(_Set) = T) -> - list_contains_opaque(t_tuple_subtypes(T)); -t_contains_opaque(?union(List)) -> list_contains_opaque(List); -t_contains_opaque(?var(_Id)) -> false. - --spec list_contains_opaque([erl_type()]) -> boolean(). - -list_contains_opaque(List) -> - lists:any(fun t_contains_opaque/1, List). +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(?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. @@ -506,9 +517,12 @@ t_find_opaque_mismatch(T1, T2) -> t_find_opaque_mismatch(?any, _Type, _TopType) -> error; t_find_opaque_mismatch(?none, _Type, _TopType) -> error; -t_find_opaque_mismatch(?list(T1, _, _), ?list(T2, _, _), TopType) -> - t_find_opaque_mismatch(T1, T2, TopType); +t_find_opaque_mismatch(?list(T1, Tl1, _), ?list(T2, Tl2, _), TopType) -> + t_find_opaque_mismatch_ordlists([T1, Tl1], [T2, Tl2], TopType); t_find_opaque_mismatch(_T1, ?opaque(_) = T2, TopType) -> {ok, TopType, T2}; +t_find_opaque_mismatch(?opaque(_) = T1, _T2, TopType) -> + %% The generated message is somewhat misleading: + {ok, TopType, T1}; t_find_opaque_mismatch(?product(T1), ?product(T2), TopType) -> t_find_opaque_mismatch_ordlists(T1, T2, TopType); t_find_opaque_mismatch(?tuple(T1, Arity, _), ?tuple(T2, Arity, _), TopType) -> @@ -538,6 +552,166 @@ t_find_opaque_mismatch_list([H|T]) -> 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. +%% XXX. Returns one element even if both oparands contain opaque types. +%% XXX. Slow since t_inf() is called but the results are ignored. +t_find_unknown_opaque(_T1, _T2, 'universe') -> []; +t_find_unknown_opaque(T1, T2, Opaques) -> + try t_inf(T1, T2, {match, Opaques}) of + _ -> [] + catch throw:N when is_integer(N) -> [N] + 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(?none=Type, _, _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, + NewOpaqueTypes, All) -> + IsOpaque = is_opaque_type2(Opaque, Opaques), + I = t_inf(Type, S), + case not IsOpaque orelse t_is_none(I = t_inf(Type, S)) of + true -> decoration(OpaqueTypes, Type, Opaques, NewOpaqueTypes, All); + false -> + NewOpaque = Opaque#opaque{struct = decorate(I, S, Opaques)}, + NewAll = All orelse t_is_equal(I, Type), + decoration(OpaqueTypes, Type, Opaques, [NewOpaque|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,_,_R] = U1, + [_,_,_,_,_,_,_,_,Opaque,_] = U2, + List = [A,B,F,I,L,N,T,M], + DecList = [Dec || + E <- List, + 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(dict()) -> [erl_type()]. t_opaque_from_records(RecDict) -> @@ -559,44 +733,6 @@ t_opaque_from_records(RecDict) -> end, OpaqueRecDict), [OpaqueType || {_Key, OpaqueType} <- dict:to_list(OpaqueTypeDict)]. --spec t_opaque_match_atom(erl_type(), [erl_type()]) -> [erl_type()]. - -t_opaque_match_atom(?atom(_) = Atom, Opaques) -> - case t_atom_vals(Atom) of - unknown -> []; - _ -> [O || O <- Opaques, t_inf(Atom, O, opaque) =/= ?none, - t_opaque_atom_vals(t_opaque_structure(O)) =/= unknown] - end; -t_opaque_match_atom(_, _) -> []. - --spec t_opaque_atom_vals(erl_type()) -> 'unknown' | [atom(),...]. - -t_opaque_atom_vals(OpaqueStruct) -> - case OpaqueStruct of - ?atom(_) -> t_atom_vals(OpaqueStruct); - ?union([Atom,_,_,_,_,_,_,_,_,_]) -> t_atom_vals(Atom); - _ -> unknown - end. - --spec t_opaque_match_record(erl_type(), [erl_type()]) -> [erl_type()]. - -t_opaque_match_record(?tuple([?atom(_) = Tag|_Fields], _, _) = Rec, Opaques) -> - [O || O <- Opaques, t_inf(Rec, O, opaque) =/= ?none, - lists:member(Tag, t_opaque_tuple_tags(t_opaque_structure(O)))]; -t_opaque_match_record(_, _) -> []. - --spec t_opaque_tuple_tags(erl_type()) -> [erl_type()]. - -t_opaque_tuple_tags(OpaqueStruct) -> - case OpaqueStruct of - ?tuple([?atom(_) = Tag|_Fields], _, _) -> [Tag]; - ?tuple_set(_) = TupleSet -> - Tuples = t_tuple_subtypes(TupleSet), - lists:flatten([t_opaque_tuple_tags(T) || T <- Tuples]); - ?union([_,_,_,_,_,_,Tuples,_,_,_]) -> t_opaque_tuple_tags(Tuples); - _ -> [] - end. - %% 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(). @@ -605,9 +741,10 @@ 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), Term, Size); + ?list(t_struct_from_opaque(Types, Opaques), + t_struct_from_opaque(Term, Opaques), Size); t_struct_from_opaque(?opaque(_) = T, Opaques) -> - case lists:member(T, Opaques) of + case is_opaque_type(T, Opaques) of true -> t_opaque_structure(T); false -> T end; @@ -627,24 +764,10 @@ t_struct_from_opaque(Type, _Opaques) -> Type. list_struct_from_opaque(Types, Opaques) -> [t_struct_from_opaque(Type, Opaques) || Type <- Types]. --spec t_unopaque_on_mismatch(erl_type(), erl_type(), [erl_type()]) -> erl_type(). - -t_unopaque_on_mismatch(GenType, Type, Opaques) -> - case t_inf(GenType, Type) of - ?none -> - Unopaqued = t_unopaque(Type, Opaques), - %% XXX: Unions might be a problem, must investigate. - case t_inf(GenType, Unopaqued) of - ?none -> Type; - _ -> Unopaqued - end; - _ -> Type - end. - -spec module_builtin_opaques(module()) -> [erl_type()]. module_builtin_opaques(Module) -> - [O || O <- all_opaque_builtins(), t_opaque_module(O) =:= Module]. + [O || O <- all_opaque_builtins(), lists:member(Module, t_opaque_modules(O))]. %%----------------------------------------------------------------------------- %% Remote types: these types are used for preprocessing; @@ -657,8 +780,11 @@ t_remote(Mod, Name, Args) -> -spec t_is_remote(erl_type()) -> boolean(). -t_is_remote(?remote(_)) -> true; -t_is_remote(_) -> false. +t_is_remote(Type) -> + do_opaque(Type, 'universe', fun is_remote/1). + +is_remote(?remote(_)) -> true; +is_remote(_) -> false. -spec t_solve_remote(erl_type(), set(), dict()) -> erl_type(). @@ -827,40 +953,75 @@ t_atoms(List) when is_list(List) -> -spec t_atom_vals(erl_type()) -> 'unknown' | [atom(),...]. -t_atom_vals(?atom(?any)) -> unknown; -t_atom_vals(?atom(Set)) -> set_to_list(Set); -t_atom_vals(Other) -> +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), - t_atom_vals(Atm). + atom_vals(Atm). -spec t_is_atom(erl_type()) -> boolean(). -t_is_atom(?atom(_)) -> true; -t_is_atom(_) -> false. +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_atom(atom(), erl_type()) -> boolean(). +-spec t_is_any_atom(atom(), erl_type()) -> boolean(). -t_is_atom(Atom, ?atom(?any)) when is_atom(Atom) -> false; -t_is_atom(Atom, ?atom(Set)) when is_atom(Atom) -> set_is_singleton(Atom, Set); -t_is_atom(Atom, _) when is_atom(Atom) -> false. +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])). --spec t_is_boolean(erl_type()) -> boolean(). - -t_is_boolean(?atom(?any)) -> false; -t_is_boolean(?atom(Set)) -> +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; -t_is_boolean(_) -> false. +is_boolean(_) -> false. %%----------------------------------------------------------------------------- %% Binaries @@ -873,9 +1034,17 @@ t_binary() -> -spec t_is_binary(erl_type()) -> boolean(). -t_is_binary(?bitstr(U, B)) -> +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); -t_is_binary(_) -> false. +is_binary(_) -> false. %%----------------------------------------------------------------------------- %% Bitstrings @@ -922,19 +1091,27 @@ t_bitstr_concat_1([], Acc) -> t_bitstr_concat(T1, T2) -> T1p = t_inf(t_bitstr(), T1), T2p = t_inf(t_bitstr(), T2), - bitstr_concat(T1p, T2p). + 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(T1p, T2p). + bitstr_match(t_unopaque(T1p), t_unopaque(T2p)). -spec t_is_bitstr(erl_type()) -> boolean(). -t_is_bitstr(?bitstr(_, _)) -> true; -t_is_bitstr(_) -> false. +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 @@ -1045,27 +1222,59 @@ t_fun(Arity, Range) when is_integer(Arity), 0 =< Arity, Arity =< 255 -> -spec t_fun_args(erl_type()) -> 'unknown' | [erl_type()]. -t_fun_args(?function(?any, _)) -> +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; -t_fun_args(?function(?product(Domain), _)) when is_list(Domain) -> +fun_args(?function(?product(Domain), _)) when is_list(Domain) -> Domain. -spec t_fun_arity(erl_type()) -> 'unknown' | non_neg_integer(). -t_fun_arity(?function(?any, _)) -> +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; -t_fun_arity(?function(?product(Domain), _)) -> +fun_arity(?function(?product(Domain), _)) -> length(Domain). -spec t_fun_range(erl_type()) -> erl_type(). -t_fun_range(?function(_, Range)) -> +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(?function(_, _)) -> true; -t_is_fun(_) -> false. +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. @@ -1092,9 +1301,17 @@ t_port() -> -spec t_is_port(erl_type()) -> boolean(). -t_is_port(?identifier(?any)) -> false; -t_is_port(?identifier(Set)) -> set_is_singleton(?port_qual, Set); -t_is_port(_) -> false. +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. %%------------------------------------ @@ -1105,9 +1322,17 @@ t_pid() -> -spec t_is_pid(erl_type()) -> boolean(). -t_is_pid(?identifier(?any)) -> false; -t_is_pid(?identifier(Set)) -> set_is_singleton(?pid_qual, Set); -t_is_pid(_) -> false. +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. %%------------------------------------ @@ -1118,9 +1343,17 @@ t_reference() -> -spec t_is_reference(erl_type()) -> boolean(). -t_is_reference(?identifier(?any)) -> false; -t_is_reference(?identifier(Set)) -> set_is_singleton(?reference_qual, Set); -t_is_reference(_) -> false. +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. @@ -1138,21 +1371,39 @@ t_number(X) when is_integer(X) -> -spec t_is_number(erl_type()) -> boolean(). -t_is_number(?number(_, _)) -> true; -t_is_number(_) -> false. +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(?int_set(?any)) -> unknown; -t_number_vals(?int_set(Set)) -> set_to_list(Set); -t_number_vals(?number(_, _)) -> unknown; -t_number_vals(Other) -> +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(?any)) -> unknown; +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 - t_number_vals(Inf). + number_vals(Inf). %%------------------------------------ @@ -1163,8 +1414,16 @@ t_float() -> -spec t_is_float(erl_type()) -> boolean(). -t_is_float(?float) -> true; -t_is_float(_) -> false. +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. %%------------------------------------ @@ -1185,8 +1444,16 @@ t_integers(List) when is_list(List) -> -spec t_is_integer(erl_type()) -> boolean(). -t_is_integer(?integer(_)) -> true; -t_is_integer(_) -> false. +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. %%------------------------------------ @@ -1250,7 +1517,7 @@ t_cons(Hd, ?nil) -> t_cons(Hd, ?list(Contents, Termination, _)) -> ?nonempty_list(t_sup(Contents, Hd), Termination); t_cons(Hd, Tail) -> - case t_inf(Tail, t_maybe_improper_list()) of + 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. @@ -1262,18 +1529,45 @@ t_cons(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(?nonempty_list(_, _)) -> true; -t_is_cons(_) -> false. +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(?nonempty_list(Contents, _Termination)) -> Contents. +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(?nonempty_list(_Contents, Termination) = T) -> +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(). @@ -1283,8 +1577,16 @@ t_nil() -> -spec t_is_nil(erl_type()) -> boolean(). -t_is_nil(?nil) -> true; -t_is_nil(_) -> false. +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(). @@ -1300,8 +1602,16 @@ t_list(Contents) -> -spec t_list_elements(erl_type()) -> erl_type(). -t_list_elements(?list(Contents, _, _)) -> Contents; -t_list_elements(?nil) -> ?none. +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()) -> erl_type(). @@ -1356,9 +1666,17 @@ t_maybe_improper_list(Content, Termination) -> -spec t_is_maybe_improper_list(erl_type()) -> boolean(). -t_is_maybe_improper_list(?list(_, _, _)) -> true; -t_is_maybe_improper_list(?nil) -> true; -t_is_maybe_improper_list(_) -> false. +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(). @@ -1405,32 +1723,77 @@ t_tuple(List) -> -spec get_tuple_tags([erl_type()]) -> [erl_type(),...]. -get_tuple_tags([?atom(?any)|_]) -> [?any]; -get_tuple_tags([?atom(Set)|_]) -> +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; -get_tuple_tags(_) -> [?any]. +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(?tuple(Args, _, _)) when is_list(Args) -> Args. +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(?tuple(_, Size, _)) when is_integer(Size) -> Size. +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(?tuple(?any, ?any, ?any)) -> unknown; -t_tuple_sizes(?tuple(_, Size, _)) when is_integer(Size) -> [Size]; -t_tuple_sizes(?tuple_set(List)) -> [Size || {Size, _} <- List]. +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)) -> @@ -1438,9 +1801,17 @@ t_tuple_subtypes(?tuple_set(List)) -> -spec t_is_tuple(erl_type()) -> boolean(). -t_is_tuple(?tuple(_, _, _)) -> true; -t_is_tuple(?tuple_set(_)) -> true; -t_is_tuple(_) -> false. +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 @@ -1451,6 +1822,7 @@ t_is_tuple(_) -> false. t_bitstrlist() -> t_iolist(1, t_bitstr()). +%% XXX. To be removed. -spec t_constant() -> erl_type(). t_constant() -> @@ -1555,7 +1927,8 @@ t_timeout() -> t_array() -> t_opaque(array, array, [], t_tuple([t_atom('array'), - t_non_neg_integer(), t_non_neg_integer(), + t_sup([t_atom('undefined'), t_non_neg_integer()]), + t_sup([t_atom('undefined'), t_non_neg_integer()]), t_any(), t_any()])). -spec t_dict() -> erl_type(). @@ -1566,7 +1939,8 @@ t_dict() -> t_non_neg_integer(), t_non_neg_integer(), t_non_neg_integer(), t_non_neg_integer(), t_non_neg_integer(), t_non_neg_integer(), - t_tuple(), t_tuple()])). + t_sup([t_atom('undefined'), t_tuple()]), + t_sup([t_atom('undefined'), t_tuple()])])). -spec t_digraph() -> erl_type(). @@ -1601,7 +1975,9 @@ t_set() -> t_opaque(sets, set, [], t_tuple([t_atom('set'), t_non_neg_integer(), t_non_neg_integer(), t_pos_integer(), t_non_neg_integer(), t_non_neg_integer(), - t_non_neg_integer(), t_tuple(), t_tuple()])). + t_non_neg_integer(), + t_sup([t_atom('undefined'), t_tuple()]), + t_sup([t_atom('undefined'), t_tuple()])])). -spec t_tid() -> erl_type(). @@ -1673,8 +2049,11 @@ 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(?opaque(_)=T) -> +%% %% "Polymorphic opaque types not supported yet" +%% t_has_var(t_opaque_structure(T)); %% t_has_var(?union(_) = U) -> -%% exit(lists:flatten(io_lib:format("Union happens in t_has_var/1 ~p\n",[U]))); +%% exit(flat_format("Union happens in t_has_var/1 ~p\n",[U])); t_has_var(_) -> false. -spec t_has_var_list([erl_type()]) -> boolean(). @@ -1705,6 +2084,9 @@ t_collect_vars(?tuple(Types, _, _), Acc) -> t_collect_vars(?tuple_set(_) = TS, Acc) -> lists:foldl(fun(T, TmpAcc) -> t_collect_vars(T, TmpAcc) end, Acc, t_tuple_subtypes(TS)); +%% t_collect_vars(?opaque(_)=T, Acc) -> +%% %% "Polymorphic opaque types not supported yet" +%% t_collect_vars(t_opaque_structure(T), Acc); t_collect_vars(_, Acc) -> Acc. @@ -1827,15 +2209,31 @@ t_is_bitwidth(_) -> false. -spec number_min(erl_type()) -> rng_elem(). -number_min(?int_range(From, _)) -> From; -number_min(?int_set(Set)) -> set_min(Set); -number_min(?number(?any, _Tag)) -> neg_inf. +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(?int_range(_, To)) -> To; -number_max(?int_set(Set)) -> set_max(Set); -number_max(?number(?any, _Tag)) -> pos_inf. +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(). %% @@ -1917,7 +2315,7 @@ t_sup(?function(Domain1, Range1), ?function(Domain2, Range2)) -> t_sup(?identifier(Set1), ?identifier(Set2)) -> ?identifier(set_union(Set1, Set2)); t_sup(?opaque(Set1), ?opaque(Set2)) -> - ?opaque(set_union_no_limit(Set1, 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; @@ -2005,6 +2403,27 @@ t_sup(T1, T2) -> ?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}, T} || + #opaque{mod = Mod, name = Name}=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]) -> @@ -2132,19 +2551,26 @@ t_elements(?number(_, _) = T) -> ?int_set(Set) -> [t_integer(I) || I <- Set] end; -t_elements(?opaque(_) = T) -> [T]; +t_elements(?opaque(_) = T) -> + do_elements(T); t_elements(?tuple(_, _, _) = T) -> [T]; t_elements(?tuple_set(_) = TS) -> case t_tuple_subtypes(TS) of unknown -> []; Elems -> Elems end; -t_elements(?union(List)) -> - lists:append([t_elements(T) || T <- List]); +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 %% @@ -2162,74 +2588,77 @@ t_inf([]) -> ?none. -spec t_inf(erl_type(), erl_type()) -> erl_type(). t_inf(T1, T2) -> - t_inf(T1, T2, structured). - --type t_inf_mode() :: 'opaque' | 'structured'. --spec t_inf(erl_type(), erl_type(), t_inf_mode()) -> erl_type(). - -t_inf(?var(_), ?var(_), _Mode) -> ?any; -t_inf(?var(_), T, _Mode) -> subst_all_vars_to_any(T); -t_inf(T, ?var(_), _Mode) -> subst_all_vars_to_any(T); -t_inf(?any, T, _Mode) -> subst_all_vars_to_any(T); -t_inf(T, ?any, _Mode) -> subst_all_vars_to_any(T); -t_inf(?none, _, _Mode) -> ?none; -t_inf(_, ?none, _Mode) -> ?none; -t_inf(?unit, _, _Mode) -> ?unit; % ?unit cases should appear below ?none -t_inf(_, ?unit, _Mode) -> ?unit; -t_inf(T, T, _Mode) -> subst_all_vars_to_any(T); + t_inf(T1, T2, 'universe'). + +%% 'match' should be used from t_find_unknown_opaque() only +-type t_inf_opaques() :: 'universe' + | [erl_type()] | {'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), _Mode) -> +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), _Mode) -> +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), _Mode) -> +t_inf(?bitstr(U1, B1), ?bitstr(U1, B1), _Opaques) -> t_bitstr(U1, B1); -t_inf(?bitstr(U1, B1), ?bitstr(U2, B2), _Mode) when U2 > U1 -> +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), _Mode) -> +t_inf(?bitstr(U1, B1), ?bitstr(U2, B2), _Opaques) -> inf_bitstr(U1, B1, U2, B2); -t_inf(?function(Domain1, Range1), ?function(Domain2, Range2), Mode) -> - case t_inf(Domain1, Domain2, Mode) of +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, Mode)) + Domain -> ?function(Domain, t_inf(Range1, Range2, Opaques)) end; -t_inf(?identifier(Set1), ?identifier(Set2), _Mode) -> +t_inf(?identifier(Set1), ?identifier(Set2), _Opaques) -> case set_intersection(Set1, Set2) of ?none -> ?none; Set -> ?identifier(Set) end; -t_inf(?matchstate(Pres1, Slots1), ?matchstate(Pres2, Slots2), _Mode) -> +t_inf(?matchstate(Pres1, Slots1), ?matchstate(Pres2, Slots2), _Opaques) -> ?matchstate(t_inf(Pres1, Pres2), t_inf(Slots1, Slots2)); -t_inf(?nil, ?nil, _Mode) -> ?nil; -t_inf(?nil, ?nonempty_list(_, _), _Mode) -> +t_inf(?nil, ?nil, _Opaques) -> ?nil; +t_inf(?nil, ?nonempty_list(_, _), _Opaques) -> ?none; -t_inf(?nonempty_list(_, _), ?nil, _Mode) -> +t_inf(?nonempty_list(_, _), ?nil, _Opaques) -> ?none; -t_inf(?nil, ?list(_Contents, Termination, _), Mode) -> - t_inf(?nil, Termination, Mode); -t_inf(?list(_Contents, Termination, _), ?nil, Mode) -> - t_inf(?nil, Termination, Mode); +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), Mode) -> - case t_inf(Termination1, Termination2, Mode) of + ?list(Contents2, Termination2, Size2), Opaques) -> + case t_inf(Termination1, Termination2, Opaques) of ?none -> ?none; Termination -> - case t_inf(Contents1, Contents2, Mode) of - ?none -> + 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 -> + Contents -> Size = case {Size1, Size2} of {?unknown_qual, ?unknown_qual} -> ?unknown_qual; @@ -2240,7 +2669,7 @@ t_inf(?list(Contents1, Termination1, Size1), ?list(Contents, Termination, Size) end end; -t_inf(?number(_, _) = T1, ?number(_, _) = T2, _Mode) -> +t_inf(?number(_, _) = T1, ?number(_, _) = T2, _Opaques) -> case {T1, T2} of {T, T} -> T; {_, ?number(?any, ?unknown_qual)} -> T1; @@ -2249,16 +2678,16 @@ t_inf(?number(_, _) = T1, ?number(_, _) = T2, _Mode) -> {?integer(_), ?float} -> ?none; {?integer(?any), ?integer(_)} -> T2; {?integer(_), ?integer(?any)} -> T1; - {?int_set(Set1), ?int_set(Set2)} -> + {?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)} -> + {?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 = + Ans2 = case set_filter(fun(X) -> in_range(X, Range) end, Set) of ?none -> ?none; NewSet -> ?int_set(NewSet) @@ -2271,193 +2700,253 @@ t_inf(?number(_, _) = T1, ?number(_, _) = T2, _Mode) -> NewSet -> ?int_set(NewSet) end end; -t_inf(?product(Types1), ?product(Types2), Mode) -> +t_inf(?product(Types1), ?product(Types2), Opaques) -> L1 = length(Types1), L2 = length(Types2), - if L1 =:= L2 -> ?product(t_inf_lists(Types1, Types2, Mode)); + if L1 =:= L2 -> ?product(t_inf_lists(Types1, Types2, Opaques)); true -> ?none end; -t_inf(?product(_), _, _Mode) -> +t_inf(?product(_), _, _Opaques) -> ?none; -t_inf(_, ?product(_), _Mode) -> +t_inf(_, ?product(_), _Opaques) -> ?none; -t_inf(?tuple(?any, ?any, ?any), ?tuple(_, _, _) = T, _Mode) -> +t_inf(?tuple(?any, ?any, ?any), ?tuple(_, _, _) = T, _Opaques) -> subst_all_vars_to_any(T); -t_inf(?tuple(_, _, _) = T, ?tuple(?any, ?any, ?any), _Mode) -> +t_inf(?tuple(_, _, _) = T, ?tuple(?any, ?any, ?any), _Opaques) -> subst_all_vars_to_any(T); -t_inf(?tuple(?any, ?any, ?any), ?tuple_set(_) = T, _Mode) -> +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), _Mode) -> +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), Mode) -> - case t_inf_lists_strict(Elements1, Elements2, Mode) of +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), Mode) -> - inf_tuple_sets(List1, List2, Mode); -t_inf(?tuple_set(List), ?tuple(_, Arity, _) = T, Mode) -> - inf_tuple_sets(List, [{Arity, [T]}], Mode); -t_inf(?tuple(_, Arity, _) = T, ?tuple_set(List), Mode) -> - inf_tuple_sets(List, [{Arity, [T]}], Mode); +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, Mode) -> +t_inf(?union(U1), T, Opaques) -> ?union(U2) = force_union(T), - inf_union(U1, U2, Mode); -t_inf(T, ?union(U2), Mode) -> + inf_union(U1, U2, Opaques); +t_inf(T, ?union(U2), Opaques) -> ?union(U1) = force_union(T), - inf_union(U1, U2, Mode); + 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(?opaque(Set1) = T1, ?opaque(Set2) = T2, Mode) -> - case set_intersection(Set1, Set2) of - ?none -> - case Mode =:= opaque of - true -> - Struct1 = t_opaque_structure(T1), - case t_inf(Struct1, T2) of - ?none -> - Struct2 = t_opaque_structure(T2), - case t_inf(Struct2, T1) of - ?none -> ?none; - _ -> T2 - end; - _ -> T1 - end; - false -> ?none - end; - NewSet -> ?opaque(NewSet) - end; -t_inf(?opaque(_) = T1, T2, opaque) -> - case t_inf(t_opaque_structure(T1), T2, structured) of - ?none -> ?none; - _Type -> T1 - end; -t_inf(T1, ?opaque(_) = T2, opaque) -> - case t_inf(T1, t_opaque_structure(T2), structured) of - ?none -> ?none; - _Type -> T2 - end; 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); +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} = T1, + #opaque{mod = Mod2, name = Name2} = T2, + case {Mod1, Name1} =:= {Mod2, Name2} of + true -> [comb(Mod1, Name1, S, T1)]; + false -> [comb(Mod1, Name1, S, T1), comb(Mod2, Name2, S, T2)] + end. + +comb(Mod, Name, S, T) -> + case is_same_name(Mod, Name, S) of + true -> S; + false -> T#opaque{struct = S} + end. + +is_same_name(Mod, Name, ?opaque([#opaque{mod = Mod, name = Name}])) -> true; +is_same_name(_Mod, _Name, _Opaque) -> false. + +%% Combining two lists this way can be very time consuming... +inf_opaque(Set1, Set2, Opaques) -> + List1 = inf_look_up(Set1, 1, Opaques), + List2 = inf_look_up(Set2, 2, Opaques), + List0 = [combine(Inf, T1, T2) || + {Is1, ModName1, T1} <- List1, + {Is2, ModName2, T2} <- List2, + not t_is_none(Inf = inf_opaque_types(Is1, ModName1, T1, + Is2, ModName2, T2, + Opaques))], + List = lists:sort(lists:append(List0)), + sup_opaque(List). + +%% Optimization: do just one lookup. +inf_look_up(Set, Pos, Opaques) -> + [{Opaques =:= 'universe' orelse inf_is_opaque_type2(T, Pos, Opaques), + {M, N}, T} || + #opaque{mod = M, name = N} = T <- set_to_list(Set)]. + +inf_is_opaque_type2(T, Pos, {match, Opaques}) -> + is_opaque_type2(T, Opaques) orelse throw(Pos); +inf_is_opaque_type2(T, _Pos, Opaques) -> + is_opaque_type2(T, Opaques). + +inf_opaque_types(IsOpaque1, ModName1, T1, IsOpaque2, ModName2, T2, Opaques) -> + #opaque{struct = S1}=T1, + #opaque{struct = S2}=T2, + case Opaques =:= 'universe' orelse ModName1 =:= ModName2 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} -> t_none() + end + end. + -spec t_inf_lists([erl_type()], [erl_type()]) -> [erl_type()]. t_inf_lists(L1, L2) -> - t_inf_lists(L1, L2, structured). + t_inf_lists(L1, L2, 'universe'). --spec t_inf_lists([erl_type()], [erl_type()], t_inf_mode()) -> [erl_type()]. +-spec t_inf_lists([erl_type()], [erl_type()], t_inf_opaques()) -> [erl_type()]. -t_inf_lists(L1, L2, Mode) -> - t_inf_lists(L1, L2, [], Mode). +t_inf_lists(L1, L2, Opaques) -> + t_inf_lists(L1, L2, [], Opaques). --spec t_inf_lists([erl_type()], [erl_type()], [erl_type()], t_inf_mode()) -> [erl_type()]. +-spec t_inf_lists([erl_type()], [erl_type()], [erl_type()], [erl_type()]) -> [erl_type()]. -t_inf_lists([T1|Left1], [T2|Left2], Acc, Mode) -> - t_inf_lists(Left1, Left2, [t_inf(T1, T2, Mode)|Acc], Mode); -t_inf_lists([], [], Acc, _Mode) -> +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()], t_inf_mode()) -> 'bottom' | [erl_type()]. +-spec t_inf_lists_strict([erl_type()], [erl_type()], [erl_type()]) -> 'bottom' | [erl_type()]. -t_inf_lists_strict(L1, L2, Mode) -> - t_inf_lists_strict(L1, L2, [], Mode). +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()], t_inf_mode()) -> 'bottom' | [erl_type()]. +-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, Mode) -> - case t_inf(T1, T2, Mode) of +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], Mode) + T -> t_inf_lists_strict(Left1, Left2, [T|Acc], Opaques) end; -t_inf_lists_strict([], [], Acc, _Mode) -> +t_inf_lists_strict([], [], Acc, _Opaques) -> lists:reverse(Acc). --spec t_inf_lists_masked([erl_type()], [erl_type()], [t_inf_mode()]) -> [erl_type()]. - -t_inf_lists_masked(List1, List2, Mask) -> - List = lists:zip3(List1, List2, Mask), - [t_inf(T1, T2, Mode) || {T1, T2, Mode} <- List]. - -inf_tuple_sets(L1, L2, Mode) -> - case inf_tuple_sets(L1, L2, [], Mode) of +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, Mode) -> - case inf_tuples_in_sets(Tuples1, Tuples2, Mode) of - [] -> inf_tuple_sets(Ts1, Ts2, Acc, Mode); +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], Mode); - NewTuples -> inf_tuple_sets(Ts1, Ts2, [{Arity, NewTuples}|Acc], Mode) + 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, Mode) -> - if Arity1 < Arity2 -> inf_tuple_sets(Ts1, L2, Acc, Mode); - Arity1 > Arity2 -> inf_tuple_sets(L1, Ts2, Acc, Mode) +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, _Mode) -> lists:reverse(Acc); -inf_tuple_sets(_, [], Acc, _Mode) -> lists:reverse(Acc). - -inf_tuples_in_sets([?tuple(Elements1, _, ?any)], L2, Mode) -> - NewList = [t_inf_lists_strict(Elements1, Elements2, Mode) +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)], Mode) -> - NewList = [t_inf_lists_strict(Elements1, Elements2, Mode) +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, Mode) -> - inf_tuples_in_sets(L1, L2, [], Mode). +inf_tuples_in_sets(L1, L2, Opaques) -> + inf_tuples_in_sets2(L1, L2, [], Opaques). -inf_tuples_in_sets([?tuple(Elements1, Arity, Tag)|Ts1], - [?tuple(Elements2, Arity, Tag)|Ts2], Acc, Mode) -> - case t_inf_lists_strict(Elements1, Elements2, Mode) of - bottom -> inf_tuples_in_sets(Ts1, Ts2, Acc, Mode); +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_sets(Ts1, Ts2, [?tuple(NewElements, Arity, Tag)|Acc], Mode) + 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_sets([?tuple(_, _, Tag1)|Ts1] = L1, - [?tuple(_, _, Tag2)|Ts2] = L2, Acc, Mode) -> - if Tag1 < Tag2 -> inf_tuples_in_sets(Ts1, L2, Acc, Mode); - Tag1 > Tag2 -> inf_tuples_in_sets(L1, Ts2, Acc, Mode) +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,_,_R] = Union2, + List = [A,B,F,I,L,N,T,M], + inf_union_collect(List, Opaque, InfFun, [], []) + end, + O1 = OpaqueFun(U1, U2, fun(E, Opaque) -> t_inf(Opaque, E, Opaques) end), + O2 = OpaqueFun(U2, U1, fun(E, Opaque) -> t_inf(E, Opaque, Opaques) end), + Union = inf_union(U1, U2, 0, [], Opaques), + t_sup([O1, O2, Union]). + +inf_union_collect([], _Opaque, _InfFun, InfList, ThrowList) -> + case t_sup(InfList) of + ?none when ThrowList =/= [] -> throw(hd(lists:flatten(ThrowList))); + Sup -> Sup end; -inf_tuples_in_sets([], _, Acc, _Mode) -> lists:reverse(Acc); -inf_tuples_in_sets(_, [], Acc, _Mode) -> lists:reverse(Acc). - -inf_union(U1, U2, opaque) -> -%%--------------------------------------------------------------------- -%% Under Testing -%%---------------------------------------------------------------------- -%% OpaqueFun = -%% fun(Union1, Union2) -> -%% [_,_,_,_,_,_,_,_,Opaque,_] = Union1, -%% [A,B,F,I,L,N,T,M,_,_R] = Union2, -%% List = [A,B,F,I,L,N,T,M], -%% case [T || T <- List, t_inf(T, Opaque, opaque) =/= ?none] of -%% [] -> ?none; -%% _ -> Opaque -%% end -%% end, -%% O1 = OpaqueFun(U1, U2), -%% O2 = OpaqueFun(U2, U1), -%% Union = inf_union(U1, U2, 0, [], opaque), -%% t_sup([O1, O2, Union]); - inf_union(U1, U2, 0, [], opaque); -inf_union(U1, U2, OtherMode) -> - inf_union(U1, U2, 0, [], OtherMode). - -inf_union([?none|Left1], [?none|Left2], N, Acc, Mode) -> - inf_union(Left1, Left2, N, [?none|Acc], Mode); -inf_union([T1|Left1], [T2|Left2], N, Acc, Mode) -> - case t_inf(T1, T2, Mode) of - ?none -> inf_union(Left1, Left2, N, [?none|Acc], Mode); - T -> inf_union(Left1, Left2, N+1, [T|Acc], Mode) +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:N when is_integer(N) -> + inf_union_collect(L, Opaque, InfFun, InfList, [N|ThrowList]) + end. + +inf_union([?none|Left1], [?none|Left2], N, Acc, Opaques) -> + inf_union(Left1, Left2, N, [?none|Acc], Opaques); +inf_union([T1|Left1], [T2|Left2], N, Acc, Opaques) -> + case t_inf(T1, T2, Opaques) of + ?none -> inf_union(Left1, Left2, N, [?none|Acc], Opaques); + T -> inf_union(Left1, Left2, N+1, [T|Acc], Opaques) end; -inf_union([], [], N, Acc, _Mode) -> +inf_union([], [], N, Acc, _Opaques) -> if N =:= 0 -> ?none; N =:= 1 -> [Type] = [T || T <- Acc, T =/= ?none], @@ -2536,6 +3025,11 @@ t_subst_dict(?tuple(Elements, _Arity, _Tag), Dict) -> t_tuple([t_subst_dict(E, Dict) || E <- Elements]); t_subst_dict(?tuple_set(_) = TS, Dict) -> t_sup([t_subst_dict(T, Dict) || T <- t_tuple_subtypes(TS)]); +%% t_subst_dict(?opaque(Es), Dict) -> +%% %% "Polymorphic opaque types not supported yet" +%% List = [Opaque#opaque{struct = t_subst_dict(S, Dict)} || +%% Opaque = #opaque{struct = S} <- set_to_list(Es)], +%% ?opaque(ordsets:from_list(List)); t_subst_dict(T, _Dict) -> T. @@ -2578,6 +3072,11 @@ t_subst_aux(?tuple(Elements, _Arity, _Tag), VarMap) -> t_tuple([t_subst_aux(E, VarMap) || E <- Elements]); t_subst_aux(?tuple_set(_) = TS, VarMap) -> t_sup([t_subst_aux(T, VarMap) || T <- t_tuple_subtypes(TS)]); +%% t_subst_aux(?opaque(Es), VarMap) -> +%% %% "Polymorphic opaque types not supported yet" +%% List = [Opaque#opaque{struct = t_subst_aux(S, VarMap)} || +%% Opaque = #opaque{struct = S} <- set_to_list(Es)], +%% ?opaque(ordsets:from_list(List)); t_subst_aux(T, _VarMap) -> T. @@ -2590,112 +3089,147 @@ t_subst_aux(T, _VarMap) -> -spec t_unify(erl_type(), erl_type()) -> t_unify_ret(). t_unify(T1, T2) -> - t_unify(T1, T2, []). - --spec t_unify(erl_type(), erl_type(), [erl_type()]) -> t_unify_ret(). - -t_unify(T1, T2, Opaques) -> - {T, VarMap} = t_unify(T1, T2, [], Opaques), + {T, VarMap} = t_unify(T1, T2, []), {t_subst_kv(T, VarMap), lists:keysort(1, VarMap)}. -t_unify(?var(Id) = T, ?var(Id), VarMap, _Opaques) -> +t_unify(?var(Id) = T, ?var(Id), VarMap) -> {T, VarMap}; -t_unify(?var(Id1) = T, ?var(Id2), VarMap, Opaques) -> +t_unify(?var(Id1) = T, ?var(Id2), VarMap) -> case lists:keyfind(Id1, 1, VarMap) of false -> case lists:keyfind(Id2, 1, VarMap) of false -> {T, [{Id2, T} | VarMap]}; - {Id2, Type} -> t_unify(T, Type, VarMap, Opaques) + {Id2, Type} -> t_unify(T, Type, VarMap) end; {Id1, Type1} -> case lists:keyfind(Id2, 1, VarMap) of false -> {Type1, [{Id2, T} | VarMap]}; - {Id2, Type2} -> t_unify(Type1, Type2, VarMap, Opaques) + {Id2, Type2} -> t_unify(Type1, Type2, VarMap) end end; -t_unify(?var(Id), Type, VarMap, Opaques) -> +t_unify(?var(Id), Type, VarMap) -> case lists:keyfind(Id, 1, VarMap) of false -> {Type, [{Id, Type} | VarMap]}; - {Id, VarType} -> t_unify(VarType, Type, VarMap, Opaques) + {Id, VarType} -> t_unify(VarType, Type, VarMap) end; -t_unify(Type, ?var(Id), VarMap, Opaques) -> +t_unify(Type, ?var(Id), VarMap) -> case lists:keyfind(Id, 1, VarMap) of false -> {Type, [{Id, Type} | VarMap]}; - {Id, VarType} -> t_unify(VarType, Type, VarMap, Opaques) + {Id, VarType} -> t_unify(VarType, Type, VarMap) end; -t_unify(?function(Domain1, Range1), ?function(Domain2, Range2), VarMap, Opaques) -> - {Domain, VarMap1} = t_unify(Domain1, Domain2, VarMap, Opaques), - {Range, VarMap2} = t_unify(Range1, Range2, VarMap1, Opaques), +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, Opaques) -> - {Contents, VarMap1} = t_unify(Contents1, Contents2, VarMap, Opaques), - {Termination, VarMap2} = t_unify(Termination1, Termination2, VarMap1, Opaques), + ?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, Opaques) -> - {Types, VarMap1} = unify_lists(Types1, Types2, VarMap, Opaques), +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, _Opaques) -> +t_unify(?tuple(?any, ?any, ?any) = T, ?tuple(?any, ?any, ?any), VarMap) -> {T, VarMap}; t_unify(?tuple(Elements1, Arity, _), - ?tuple(Elements2, Arity, _), VarMap, Opaques) when Arity =/= ?any -> - {NewElements, VarMap1} = unify_lists(Elements1, Elements2, VarMap, Opaques), + ?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, Opaques) when Arity =/= ?any -> - unify_tuple_set_and_tuple(T1, T2, VarMap, Opaques); + ?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, Opaques) when Arity =/= ?any -> - unify_tuple_set_and_tuple(T2, T1, VarMap, Opaques); -t_unify(?tuple_set(List1), ?tuple_set(List2), VarMap, Opaques) -> - {Tuples, NewVarMap} = - unify_lists(lists:append([T || {_Arity, T} <- List1]), - lists:append([T || {_Arity, T} <- List2]), VarMap, Opaques), - {t_sup(Tuples), NewVarMap}; -t_unify(?opaque(Elements) = T, ?opaque(Elements), VarMap, _Opaques) -> - {T, VarMap}; -t_unify(?opaque(_) = T1, ?opaque(_) = T2, _VarMap, _Opaques) -> - throw({mismatch, T1, T2}); -t_unify(Type, ?opaque(_) = OpType, VarMap, Opaques) -> - t_unify_with_opaque(Type, OpType, VarMap, Opaques); -t_unify(?opaque(_) = OpType, Type, VarMap, Opaques) -> - t_unify_with_opaque(Type, OpType, VarMap, Opaques); -t_unify(T, T, VarMap, _Opaques) -> + ?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(?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(T1, T2, _, _) -> +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}). -t_unify_with_opaque(Type, OpType, VarMap, Opaques) -> - case lists:member(OpType, Opaques) of +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,R] = List, + if O =:= ?none -> no; true -> - Struct = t_opaque_structure(OpType), - try t_unify(Type, Struct, VarMap, Opaques) of - {_T, VarMap1} -> {OpType, VarMap1} - catch - throw:{mismatch, _T1, _T2} -> - case t_inf(OpType, Type, opaque) of - ?none -> throw({mismatch, Type, OpType}); - _ -> {OpType, VarMap} - end - end; - false -> - throw({mismatch, Type, OpType}) + S = t_opaque_structure(O), + {yes, t_sup([A,B,F,I,L,N,T,M,S,R])} end. -unify_tuple_set_and_tuple(?tuple_set([{Arity, List}]), - ?tuple(Elements2, Arity, _), VarMap, Opaques) -> +-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}, Opaques) -> + F1 = fun(?opaque(Es)) -> + F2 = fun(#opaque{mod = Mod, name = Name}) -> + Mod1 =:= Mod andalso Name1 =:= Name + end, + lists:any(F2, Es) + end, + lists:any(F1, Opaques). + +%% 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(sup_tuple_elements(List), Elements2, VarMap, Opaques), + {NewElements, VarMap1} = + unify_lists(Elements2, sup_tuple_elements(List), VarMap), {t_tuple(NewElements), VarMap1}. -unify_lists(L1, L2, VarMap, Opaques) -> - unify_lists(L1, L2, VarMap, [], Opaques). +unify_lists(L1, L2, VarMap) -> + unify_lists(L1, L2, VarMap, []). -unify_lists([T1|Left1], [T2|Left2], VarMap, Acc, Opaques) -> - {NewT, NewVarMap} = t_unify(T1, T2, VarMap, Opaques), - unify_lists(Left1, Left2, NewVarMap, [NewT|Acc], Opaques); -unify_lists([], [], VarMap, Acc, _Opaques) -> +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) -> @@ -2837,11 +3371,12 @@ t_subtract(?identifier(Set1), ?identifier(Set2)) -> ?none -> ?none; Set -> ?identifier(Set) end; -t_subtract(?opaque(Set1), ?opaque(Set2)) -> - case set_subtract(Set1, Set2) of - ?none -> ?none; - Set -> ?opaque(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 @@ -2976,6 +3511,17 @@ t_subtract(T1, T2) -> ?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) -> @@ -2991,7 +3537,18 @@ t_subtract_lists([], [], Acc) -> -spec subtract_union([erl_type(),...], [erl_type(),...]) -> erl_type(). subtract_union(U1, U2) -> - subtract_union(U1, U2, 0, []). + [A1,B1,F1,I1,L1,N1,T1,M1,O1,R1] = U1, + [A2,B2,F2,I2,L2,N2,T2,M2,O2,R2] = U2, + List1 = [A1,B1,F1,I1,L1,N1,T1,M1,?none,R1], + List2 = [A2,B2,F2,I2,L2,N2,T2,M2,?none,R2], + 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(). @@ -3052,10 +3609,24 @@ t_is_equal(_, _) -> false. t_is_subtype(T1, T2) -> Inf = t_inf(T1, T2), - t_is_equal(T1, Inf). + 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)). @@ -3067,12 +3638,12 @@ t_unopaque(T) -> -spec t_unopaque(erl_type(), 'universe' | [erl_type()]) -> erl_type(). t_unopaque(?opaque(_) = T, Opaques) -> - case Opaques =:= universe orelse lists:member(T, Opaques) of + case Opaques =:= 'universe' orelse is_opaque_type(T, Opaques) of true -> t_unopaque(t_opaque_structure(T), Opaques); false -> T % XXX: needs revision for parametric opaque data types end; t_unopaque(?list(ElemT, Termination, Sz), Opaques) -> - ?list(t_unopaque(ElemT, Opaques), Termination, Sz); + ?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], @@ -3081,14 +3652,19 @@ 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,R]), Opaques) -> UL = t_unopaque(L, Opaques), UT = t_unopaque(T, Opaques), - UO = case O of - ?none -> []; - ?opaque(Os) -> [t_unopaque(S, Opaques) || #opaque{struct = S} <- Os] - end, - t_sup([?union([A,B,F,I,UL,N,UT,M,?none,R])|UO]); + UF = t_unopaque(F, 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,M,OF,R])|UO]); t_unopaque(T, _) -> T. @@ -3134,6 +3710,12 @@ 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(T, _K) -> T. %%============================================================================ @@ -3167,7 +3749,7 @@ t_abstract_records(?union(Types), RecDict) -> t_abstract_records(?tuple(?any, ?any, ?any) = T, _RecDict) -> T; t_abstract_records(?tuple(Elements, Arity, ?atom(_) = Tag), RecDict) -> - [TagAtom] = t_atom_vals(Tag), + [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, T} <- Fields]]) @@ -3176,6 +3758,8 @@ 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. @@ -3198,6 +3782,14 @@ 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, T) -> Fun(T). @@ -3239,11 +3831,11 @@ t_to_string(?bitstr(8, 0), _RecDict) -> t_to_string(?bitstr(1, 0), _RecDict) -> "bitstring()"; t_to_string(?bitstr(0, B), _RecDict) -> - lists:flatten(io_lib:format("<<_:~w>>", [B])); + flat_format("<<_:~w>>", [B]); t_to_string(?bitstr(U, 0), _RecDict) -> - lists:flatten(io_lib:format("<<_:_*~w>>", [U])); + flat_format("<<_:_*~w>>", [U]); t_to_string(?bitstr(U, B), _RecDict) -> - lists:flatten(io_lib:format("<<_:~w,_:_*~w>>", [B, U])); + flat_format("<<_:~w,_:_*~w>>", [B, U]); t_to_string(?function(?any, ?any), _RecDict) -> "fun()"; t_to_string(?function(?any, Range), RecDict) -> @@ -3255,18 +3847,16 @@ t_to_string(?identifier(Set), _RecDict) -> case Set of ?any -> "identifier()"; _ -> - string:join([io_lib:format("~w()", [T]) || T <- set_to_list(Set)], " | ") + string:join([flat_format("~w()", [T]) || T <- set_to_list(Set)], " | ") end; -t_to_string(?opaque(Set), _RecDict) -> - string:join([case is_opaque_builtin(Mod, Name) of - true -> io_lib:format("~w()", [Name]); - false -> io_lib:format("~w:~w()", [Mod, Name]) - end - || #opaque{mod = Mod, name = Name} <- set_to_list(Set)], +t_to_string(?opaque(Set), RecDict) -> + string:join([opaque_type(Mod, Name, S, RecDict) || + #opaque{mod = Mod, name = Name, struct = S} + <- set_to_list(Set)], " | "); t_to_string(?matchstate(Pres, Slots), RecDict) -> - io_lib:format("ms(~s,~s)", [t_to_string(Pres, RecDict), - t_to_string(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) -> @@ -3282,7 +3872,9 @@ t_to_string(?nonempty_list(Contents, Termination), RecDict) -> case Contents =:= ?any of true -> ok; false -> - erlang:error({illegal_list, ?nonempty_list(Contents, Termination)}) + %% XXX. See comment below. + %% erlang:error({illegal_list, ?nonempty_list(Contents, Termination)}) + ok end, "nonempty_maybe_improper_list()"; _ -> @@ -3305,11 +3897,14 @@ t_to_string(?list(Contents, Termination, ?unknown_qual), RecDict) -> 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 -> - L = ?list(Contents, Termination, ?unknown_qual), - erlang:error({illegal_list, L}) + ok + %% L = ?list(Contents, Termination, ?unknown_qual), + %% erlang:error({illegal_list, L}) end, "maybe_improper_list()"; _ -> @@ -3330,7 +3925,7 @@ 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) -> - lists:flatten(io_lib:format("~w..~w", [From, To])); + 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()"; @@ -3338,10 +3933,10 @@ t_to_string(?product(List), RecDict) -> "<" ++ comma_sequence(List, RecDict) ++ ">"; t_to_string(?remote(Set), RecDict) -> string:join([case Args =:= [] of - true -> io_lib:format("~w:~w()", [Mod, Name]); + true -> flat_format("~w:~w()", [Mod, Name]); false -> ArgString = comma_sequence(Args, RecDict), - io_lib:format("~w:~w(~s)", [Mod, Name, ArgString]) + flat_format("~w:~w(~s)", [Mod, Name, ArgString]) end || #remote{mod = Mod, name = Name, args = Args} <- set_to_list(Set)], @@ -3350,7 +3945,7 @@ 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] = t_atom_vals(Tag), + [TagAtom] = atom_vals(Tag), case lookup_record(TagAtom, Arity-1, RecDict) of error -> "{" ++ comma_sequence(Elements, RecDict) ++ "}"; {ok, FieldNames} -> @@ -3361,9 +3956,9 @@ t_to_string(?tuple_set(_) = 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) -> - io_lib:format("~s", [atom_to_list(Id)]); + flat_format("~s", [atom_to_list(Id)]); t_to_string(?var(Id), _RecDict) when is_integer(Id) -> - io_lib:format("var(~w)", [Id]). + flat_format("var(~w)", [Id]). record_to_string(Tag, [_|Fields], FieldNames, RecDict) -> FieldStrings = record_fields_to_string(Fields, FieldNames, RecDict, []), @@ -3371,7 +3966,7 @@ record_to_string(Tag, [_|Fields], FieldNames, RecDict) -> record_fields_to_string([F|Fs], [{FName, _DefType}|FDefs], RecDict, Acc) -> NewAcc = - case t_is_any(F) orelse t_is_atom('undefined', F) of + case t_is_equal(F, t_any()) orelse t_is_any_atom('undefined', F) of true -> Acc; false -> StrFV = atom_to_string(FName) ++ "::" ++ t_to_string(F, RecDict), @@ -3389,13 +3984,14 @@ record_fields_to_string([], [], _RecDict, Acc) -> -spec record_field_diffs_to_string(erl_type(), dict()) -> string(). record_field_diffs_to_string(?tuple([_|Fs], Arity, Tag), RecDict) -> - [TagAtom] = t_atom_vals(Tag), + [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, DefType}|FDefs], RecDict, Acc) -> + %% Don't care about opaqueness for now. NewAcc = case not t_is_none(t_inf(F, DefType)) of true -> Acc; @@ -3418,6 +4014,24 @@ union_sequence(Types, RecDict) -> List = [t_to_string(T, RecDict) || T <- Types], string:join(List, " | "). +-ifdef(DEBUG). +opaque_type(Mod, Name, S, RecDict) -> + opaque_name(Mod, Name, t_to_string(S, RecDict)). +-else. +opaque_type(Mod, Name, _S, _RecDict) -> + opaque_name(Mod, Name, ""). +-endif. + +opaque_name(Mod, Name, Extra) -> + S = mod_name(Mod, Name), + flat_format("~s(~s)", [S, Extra]). + +mod_name(Mod, Name) -> + case is_opaque_builtin(Mod, Name) of + true -> flat_format("~w", [Name]); + false -> flat_format("~w:~w", [Mod, Name]) + end. + %%============================================================================= %% %% Build a type from parse forms. @@ -3437,246 +4051,197 @@ t_from_form(Form, RecDict) -> -spec t_from_form(parse_form(), dict(), dict()) -> erl_type(). t_from_form(Form, RecDict, VarDict) -> - {T, _R} = t_from_form(Form, [], false, RecDict, VarDict), + {T, _R} = t_from_form(Form, [], RecDict, VarDict), T. -type type_names() :: [{'type' | 'opaque' | 'record', atom()}]. --spec t_from_form(parse_form(), type_names(), boolean(), dict(), dict()) -> +-spec t_from_form(parse_form(), type_names(), dict(), dict()) -> {erl_type(), type_names()}. -t_from_form({var, _L, '_'}, _TypeNames, _InOpaque, _RecDict, _VarDict) -> +t_from_form({var, _L, '_'}, _TypeNames, _RecDict, _VarDict) -> {t_any(), []}; -t_from_form({var, _L, Name}, _TypeNames, _InOpaque, _RecDict, VarDict) -> +t_from_form({var, _L, Name}, _TypeNames, _RecDict, VarDict) -> case dict:find(Name, VarDict) of error -> {t_var(Name), []}; {ok, Val} -> {Val, []} end; -t_from_form({ann_type, _L, [_Var, Type]}, TypeNames, InOpaque, RecDict, - VarDict) -> - t_from_form(Type, TypeNames, InOpaque, RecDict, VarDict); -t_from_form({paren_type, _L, [Type]}, TypeNames, InOpaque, RecDict, - VarDict) -> - t_from_form(Type, TypeNames, InOpaque, RecDict, VarDict); +t_from_form({ann_type, _L, [_Var, Type]}, TypeNames, RecDict, VarDict) -> + t_from_form(Type, TypeNames, RecDict, VarDict); +t_from_form({paren_type, _L, [Type]}, TypeNames, RecDict, VarDict) -> + t_from_form(Type, TypeNames, RecDict, VarDict); t_from_form({remote_type, _L, [{atom, _, Module}, {atom, _, Type}, Args]}, - TypeNames, InOpaque, RecDict, VarDict) -> - {L, R} = list_from_form(Args, TypeNames, InOpaque, RecDict, VarDict), + TypeNames, RecDict, VarDict) -> + {L, R} = list_from_form(Args, TypeNames, RecDict, VarDict), {t_remote(Module, Type, L), R}; -t_from_form({atom, _L, Atom}, _TypeNames, _InOpaque, _RecDict, _VarDict) -> +t_from_form({atom, _L, Atom}, _TypeNames, _RecDict, _VarDict) -> {t_atom(Atom), []}; -t_from_form({integer, _L, Int}, _TypeNames, _InOpaque, _RecDict, _VarDict) -> +t_from_form({integer, _L, Int}, _TypeNames, _RecDict, _VarDict) -> {t_integer(Int), []}; -t_from_form({op, _L, _Op, _Arg} = Op, _TypeNames, _InOpaque, _RecDict, - _VarDict) -> +t_from_form({op, _L, _Op, _Arg} = Op, _TypeNames, _RecDict, _VarDict) -> case erl_eval:partial_eval(Op) of {integer, _, Val} -> {t_integer(Val), []}; _ -> throw({error, io_lib:format("Unable to evaluate type ~w\n", [Op])}) end; -t_from_form({op, _L, _Op, _Arg1, _Arg2} = Op, _TypeNames, _InOpaque, +t_from_form({op, _L, _Op, _Arg1, _Arg2} = Op, _TypeNames, _RecDict, _VarDict) -> case erl_eval:partial_eval(Op) of {integer, _, Val} -> {t_integer(Val), []}; _ -> throw({error, io_lib:format("Unable to evaluate type ~w\n", [Op])}) end; -t_from_form({type, _L, any, []}, _TypeNames, _InOpaque, _RecDict, - _VarDict) -> +t_from_form({type, _L, any, []}, _TypeNames, _RecDict, _VarDict) -> {t_any(), []}; -t_from_form({type, _L, arity, []}, _TypeNames, _InOpaque, _RecDict, - _VarDict) -> +t_from_form({type, _L, arity, []}, _TypeNames, _RecDict, _VarDict) -> {t_arity(), []}; -t_from_form({type, _L, array, []}, _TypeNames, _InOpaque, _RecDict, - _VarDict) -> +t_from_form({type, _L, array, []}, _TypeNames, _RecDict, _VarDict) -> {t_array(), []}; -t_from_form({type, _L, atom, []}, _TypeNames, _InOpaque, _RecDict, - _VarDict) -> +t_from_form({type, _L, atom, []}, _TypeNames, _RecDict, _VarDict) -> {t_atom(), []}; -t_from_form({type, _L, binary, []}, _TypeNames, _InOpaque, _RecDict, - _VarDict) -> +t_from_form({type, _L, binary, []}, _TypeNames, _RecDict, _VarDict) -> {t_binary(), []}; t_from_form({type, _L, binary, [Base, Unit]} = Type, - _TypeNames, _InOpaque, _RecDict, _VarDict) -> + _TypeNames, _RecDict, _VarDict) -> 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), []}; _ -> throw({error, io_lib:format("Unable to evaluate type ~w\n", [Type])}) end; -t_from_form({type, _L, bitstring, []}, _TypeNames, _InOpaque, _RecDict, - _VarDict) -> +t_from_form({type, _L, bitstring, []}, _TypeNames, _RecDict, _VarDict) -> {t_bitstr(), []}; -t_from_form({type, _L, bool, []}, _TypeNames, _InOpaque, _RecDict, - _VarDict) -> +t_from_form({type, _L, bool, []}, _TypeNames, _RecDict, _VarDict) -> {t_boolean(), []}; % XXX: Temporarily -t_from_form({type, _L, boolean, []}, _TypeNames, _InOpaque, _RecDict, - _VarDict) -> +t_from_form({type, _L, boolean, []}, _TypeNames, _RecDict, _VarDict) -> {t_boolean(), []}; -t_from_form({type, _L, byte, []}, _TypeNames, _InOpaque, _RecDict, - _VarDict) -> +t_from_form({type, _L, byte, []}, _TypeNames, _RecDict, _VarDict) -> {t_byte(), []}; -t_from_form({type, _L, char, []}, _TypeNames, _InOpaque, _RecDict, - _VarDict) -> +t_from_form({type, _L, char, []}, _TypeNames, _RecDict, _VarDict) -> {t_char(), []}; -t_from_form({type, _L, dict, []}, _TypeNames, _InOpaque, _RecDict, - _VarDict) -> +t_from_form({type, _L, dict, []}, _TypeNames, _RecDict, _VarDict) -> {t_dict(), []}; -t_from_form({type, _L, digraph, []}, _TypeNames, _InOpaque, _RecDict, - _VarDict) -> +t_from_form({type, _L, digraph, []}, _TypeNames, _RecDict, _VarDict) -> {t_digraph(), []}; -t_from_form({type, _L, float, []}, _TypeNames, _InOpaque, _RecDict, - _VarDict) -> +t_from_form({type, _L, float, []}, _TypeNames, _RecDict, _VarDict) -> {t_float(), []}; -t_from_form({type, _L, function, []}, _TypeNames, _InOpaque, _RecDict, - _VarDict) -> +t_from_form({type, _L, function, []}, _TypeNames, _RecDict, _VarDict) -> {t_fun(), []}; -t_from_form({type, _L, 'fun', []}, _TypeNames, _InOpaque, _RecDict, - _VarDict) -> +t_from_form({type, _L, 'fun', []}, _TypeNames, _RecDict, _VarDict) -> {t_fun(), []}; t_from_form({type, _L, 'fun', [{type, _, any}, Range]}, TypeNames, - InOpaque, RecDict, VarDict) -> - {T, R} = t_from_form(Range, TypeNames, InOpaque, RecDict, VarDict), + RecDict, VarDict) -> + {T, R} = t_from_form(Range, TypeNames, RecDict, VarDict), {t_fun(T), R}; t_from_form({type, _L, 'fun', [{type, _, product, Domain}, Range]}, - TypeNames, InOpaque, RecDict, VarDict) -> - {L, R1} = list_from_form(Domain, TypeNames, InOpaque, RecDict, VarDict), - {T, R2} = t_from_form(Range, TypeNames, InOpaque, RecDict, VarDict), + TypeNames, RecDict, VarDict) -> + {L, R1} = list_from_form(Domain, TypeNames, RecDict, VarDict), + {T, R2} = t_from_form(Range, TypeNames, RecDict, VarDict), {t_fun(L, T), R1 ++ R2}; -t_from_form({type, _L, gb_set, []}, _TypeNames, _InOpaque, _RecDict, - _VarDict) -> +t_from_form({type, _L, gb_set, []}, _TypeNames, _RecDict, _VarDict) -> {t_gb_set(), []}; -t_from_form({type, _L, gb_tree, []}, _TypeNames, _InOpaque, _RecDict, - _VarDict) -> +t_from_form({type, _L, gb_tree, []}, _TypeNames, _RecDict, _VarDict) -> {t_gb_tree(), []}; -t_from_form({type, _L, identifier, []}, _TypeNames, _InOpaque, _RecDict, - _VarDict) -> +t_from_form({type, _L, identifier, []}, _TypeNames, _RecDict, _VarDict) -> {t_identifier(), []}; -t_from_form({type, _L, integer, []}, _TypeNames, _InOpaque, _RecDict, - _VarDict) -> +t_from_form({type, _L, integer, []}, _TypeNames, _RecDict, _VarDict) -> {t_integer(), []}; -t_from_form({type, _L, iodata, []}, _TypeNames, _InOpaque, _RecDict, - _VarDict) -> +t_from_form({type, _L, iodata, []}, _TypeNames, _RecDict, _VarDict) -> {t_iodata(), []}; -t_from_form({type, _L, iolist, []}, _TypeNames, _InOpaque, _RecDict, - _VarDict) -> +t_from_form({type, _L, iolist, []}, _TypeNames, _RecDict, _VarDict) -> {t_iolist(), []}; -t_from_form({type, _L, list, []}, _TypeNames, _InOpaque, _RecDict, - _VarDict) -> +t_from_form({type, _L, list, []}, _TypeNames, _RecDict, _VarDict) -> {t_list(), []}; -t_from_form({type, _L, list, [Type]}, TypeNames, InOpaque, RecDict, - VarDict) -> - {T, R} = t_from_form(Type, TypeNames, InOpaque, RecDict, VarDict), +t_from_form({type, _L, list, [Type]}, TypeNames, RecDict, VarDict) -> + {T, R} = t_from_form(Type, TypeNames, RecDict, VarDict), {t_list(T), R}; -t_from_form({type, _L, mfa, []}, _TypeNames, _InOpaque, _RecDict, - _VarDict) -> +t_from_form({type, _L, mfa, []}, _TypeNames, _RecDict, _VarDict) -> {t_mfa(), []}; -t_from_form({type, _L, module, []}, _TypeNames, _InOpaque, _RecDict, - _VarDict) -> +t_from_form({type, _L, module, []}, _TypeNames, _RecDict, _VarDict) -> {t_module(), []}; -t_from_form({type, _L, nil, []}, _TypeNames, _InOpaque, _RecDict, - _VarDict) -> +t_from_form({type, _L, nil, []}, _TypeNames, _RecDict, _VarDict) -> {t_nil(), []}; -t_from_form({type, _L, neg_integer, []}, _TypeNames, _InOpaque, _RecDict, - _VarDict) -> +t_from_form({type, _L, neg_integer, []}, _TypeNames, _RecDict, _VarDict) -> {t_neg_integer(), []}; -t_from_form({type, _L, non_neg_integer, []}, _TypeNames, _InOpaque, _RecDict, +t_from_form({type, _L, non_neg_integer, []}, _TypeNames, _RecDict, _VarDict) -> {t_non_neg_integer(), []}; -t_from_form({type, _L, no_return, []}, _TypeNames, _InOpaque, _RecDict, - _VarDict) -> +t_from_form({type, _L, no_return, []}, _TypeNames, _RecDict, _VarDict) -> {t_unit(), []}; -t_from_form({type, _L, node, []}, _TypeNames, _InOpaque, _RecDict, - _VarDict) -> +t_from_form({type, _L, node, []}, _TypeNames, _RecDict, _VarDict) -> {t_node(), []}; -t_from_form({type, _L, none, []}, _TypeNames, _InOpaque, _RecDict, - _VarDict) -> +t_from_form({type, _L, none, []}, _TypeNames, _RecDict, _VarDict) -> {t_none(), []}; -t_from_form({type, _L, nonempty_list, []}, _TypeNames, _InOpaque, _RecDict, - _VarDict) -> +t_from_form({type, _L, nonempty_list, []}, _TypeNames, _RecDict, _VarDict) -> {t_nonempty_list(), []}; -t_from_form({type, _L, nonempty_list, [Type]}, TypeNames, InOpaque, RecDict, - VarDict) -> - {T, R} = t_from_form(Type, TypeNames, InOpaque, RecDict, VarDict), +t_from_form({type, _L, nonempty_list, [Type]}, TypeNames, RecDict, VarDict) -> + {T, R} = t_from_form(Type, TypeNames, RecDict, VarDict), {t_nonempty_list(T), R}; t_from_form({type, _L, nonempty_improper_list, [Cont, Term]}, TypeNames, - InOpaque, RecDict, VarDict) -> - {T1, R1} = t_from_form(Cont, TypeNames, InOpaque, RecDict, VarDict), - {T2, R2} = t_from_form(Term, TypeNames, InOpaque, RecDict, VarDict), + RecDict, VarDict) -> + {T1, R1} = t_from_form(Cont, TypeNames, RecDict, VarDict), + {T2, R2} = t_from_form(Term, TypeNames, RecDict, VarDict), {t_cons(T1, T2), R1 ++ R2}; t_from_form({type, _L, nonempty_maybe_improper_list, []}, _TypeNames, - _InOpaque, _RecDict, _VarDict) -> + _RecDict, _VarDict) -> {t_cons(?any, ?any), []}; t_from_form({type, _L, nonempty_maybe_improper_list, [Cont, Term]}, - TypeNames, InOpaque, RecDict, VarDict) -> - {T1, R1} = t_from_form(Cont, TypeNames, InOpaque, RecDict, VarDict), - {T2, R2} = t_from_form(Term, TypeNames, InOpaque, RecDict, VarDict), + TypeNames, RecDict, VarDict) -> + {T1, R1} = t_from_form(Cont, TypeNames, RecDict, VarDict), + {T2, R2} = t_from_form(Term, TypeNames, RecDict, VarDict), {t_cons(T1, T2), R1 ++ R2}; -t_from_form({type, _L, nonempty_string, []}, _TypeNames, _InOpaque, _RecDict, +t_from_form({type, _L, nonempty_string, []}, _TypeNames, _RecDict, _VarDict) -> {t_nonempty_string(), []}; -t_from_form({type, _L, number, []}, _TypeNames, _InOpaque, _RecDict, - _VarDict) -> +t_from_form({type, _L, number, []}, _TypeNames, _RecDict, _VarDict) -> {t_number(), []}; -t_from_form({type, _L, pid, []}, _TypeNames, _InOpaque, _RecDict, - _VarDict) -> +t_from_form({type, _L, pid, []}, _TypeNames, _RecDict, _VarDict) -> {t_pid(), []}; -t_from_form({type, _L, port, []}, _TypeNames, _InOpaque, _RecDict, - _VarDict) -> +t_from_form({type, _L, port, []}, _TypeNames, _RecDict, _VarDict) -> {t_port(), []}; -t_from_form({type, _L, pos_integer, []}, _TypeNames, _InOpaque, _RecDict, - _VarDict) -> +t_from_form({type, _L, pos_integer, []}, _TypeNames, _RecDict, _VarDict) -> {t_pos_integer(), []}; -t_from_form({type, _L, maybe_improper_list, []}, _TypeNames, _InOpaque, +t_from_form({type, _L, maybe_improper_list, []}, _TypeNames, _RecDict, _VarDict) -> {t_maybe_improper_list(), []}; t_from_form({type, _L, maybe_improper_list, [Content, Termination]}, - TypeNames, InOpaque, RecDict, VarDict) -> - {T1, R1} = t_from_form(Content, TypeNames, InOpaque, RecDict, VarDict), - {T2, R2} = t_from_form(Termination, TypeNames, InOpaque, RecDict, VarDict), + TypeNames, RecDict, VarDict) -> + {T1, R1} = t_from_form(Content, TypeNames, RecDict, VarDict), + {T2, R2} = t_from_form(Termination, TypeNames, RecDict, VarDict), {t_maybe_improper_list(T1, T2), R1 ++ R2}; -t_from_form({type, _L, product, Elements}, TypeNames, InOpaque, RecDict, - VarDict) -> - {L, R} = list_from_form(Elements, TypeNames, InOpaque, RecDict, VarDict), +t_from_form({type, _L, product, Elements}, TypeNames, RecDict, VarDict) -> + {L, R} = list_from_form(Elements, TypeNames, RecDict, VarDict), {t_product(L), R}; -t_from_form({type, _L, queue, []}, _TypeNames, _InOpaque, _RecDict, - _VarDict) -> +t_from_form({type, _L, queue, []}, _TypeNames, _RecDict, _VarDict) -> {t_queue(), []}; t_from_form({type, _L, range, [From, To]} = Type, - _TypeNames, _InOpaque, _RecDict, _VarDict) -> + _TypeNames, _RecDict, _VarDict) -> case {erl_eval:partial_eval(From), erl_eval:partial_eval(To)} of {{integer, _, FromVal}, {integer, _, ToVal}} -> {t_from_range(FromVal, ToVal), []}; _ -> throw({error, io_lib:format("Unable to evaluate type ~w\n", [Type])}) end; -t_from_form({type, _L, record, [Name|Fields]}, TypeNames, InOpaque, RecDict, - VarDict) -> - record_from_form(Name, Fields, TypeNames, InOpaque, RecDict, VarDict); -t_from_form({type, _L, reference, []}, _TypeNames, _InOpaque, _RecDict, - _VarDict) -> +t_from_form({type, _L, record, [Name|Fields]}, TypeNames, RecDict, VarDict) -> + record_from_form(Name, Fields, TypeNames, RecDict, VarDict); +t_from_form({type, _L, reference, []}, _TypeNames, _RecDict, _VarDict) -> {t_reference(), []}; -t_from_form({type, _L, set, []}, _TypeNames, _InOpaque, _RecDict, - _VarDict) -> +t_from_form({type, _L, set, []}, _TypeNames, _RecDict, _VarDict) -> {t_set(), []}; -t_from_form({type, _L, string, []}, _TypeNames, _InOpaque, _RecDict, - _VarDict) -> +t_from_form({type, _L, string, []}, _TypeNames, _RecDict, _VarDict) -> {t_string(), []}; -t_from_form({type, _L, term, []}, _TypeNames, _InOpaque, _RecDict, - _VarDict) -> +t_from_form({type, _L, term, []}, _TypeNames, _RecDict, _VarDict) -> {t_any(), []}; -t_from_form({type, _L, tid, []}, _TypeNames, _InOpaque, _RecDict, - _VarDict) -> +t_from_form({type, _L, tid, []}, _TypeNames, _RecDict, _VarDict) -> {t_tid(), []}; -t_from_form({type, _L, timeout, []}, _TypeNames, _InOpaque, _RecDict, - _VarDict) -> +t_from_form({type, _L, timeout, []}, _TypeNames, _RecDict, _VarDict) -> {t_timeout(), []}; -t_from_form({type, _L, tuple, any}, _TypeNames, _InOpaque, _RecDict, - _VarDict) -> +t_from_form({type, _L, tuple, any}, _TypeNames, _RecDict, _VarDict) -> {t_tuple(), []}; -t_from_form({type, _L, tuple, Args}, TypeNames, InOpaque, RecDict, VarDict) -> - {L, R} = list_from_form(Args, TypeNames, InOpaque, RecDict, VarDict), +t_from_form({type, _L, tuple, Args}, TypeNames, RecDict, VarDict) -> + {L, R} = list_from_form(Args, TypeNames, RecDict, VarDict), {t_tuple(L), R}; -t_from_form({type, _L, union, Args}, TypeNames, InOpaque, RecDict, VarDict) -> - {L, R} = list_from_form(Args, TypeNames, InOpaque, RecDict, VarDict), +t_from_form({type, _L, union, Args}, TypeNames, RecDict, VarDict) -> + {L, R} = list_from_form(Args, TypeNames, RecDict, VarDict), {t_sup(L), R}; -t_from_form({type, _L, Name, Args}, TypeNames, InOpaque, RecDict, VarDict) -> +t_from_form({type, _L, Name, Args}, TypeNames, RecDict, VarDict) -> ArgsLen = length(Args), case lookup_type(Name, ArgsLen, RecDict) of {type, {_Module, Type, ArgNames}} -> @@ -3685,13 +4250,12 @@ t_from_form({type, _L, Name, Args}, TypeNames, InOpaque, RecDict, VarDict) -> List = lists:zipwith( fun(ArgName, ArgType) -> {Ttemp, _R} = t_from_form(ArgType, TypeNames, - InOpaque, RecDict, - VarDict), + RecDict, VarDict), {ArgName, Ttemp} end, ArgNames, Args), TmpVarDict = dict:from_list(List), - {T, R} = t_from_form(Type, [{type, Name}|TypeNames], InOpaque, + {T, R} = t_from_form(Type, [{type, Name}|TypeNames], RecDict, TmpVarDict), case lists:member({type, Name}, R) of true -> {t_limit(T, ?REC_TYPE_LIMIT), R}; @@ -3706,13 +4270,12 @@ t_from_form({type, _L, Name, Args}, TypeNames, InOpaque, RecDict, VarDict) -> List = lists:zipwith( fun(ArgName, ArgType) -> {Ttemp, _R} = t_from_form(ArgType, TypeNames, - InOpaque, RecDict, - VarDict), + RecDict, VarDict), {ArgName, Ttemp} end, ArgNames, Args), TmpVarDict = dict:from_list(List), - {T, R} = t_from_form(Type, [{opaque, Name}|TypeNames], true, + {T, R} = t_from_form(Type, [{opaque, Name}|TypeNames], RecDict, TmpVarDict), case lists:member({opaque, Name}, R) of true -> {t_limit(T, ?REC_TYPE_LIMIT), R}; @@ -3720,27 +4283,21 @@ t_from_form({type, _L, Name, Args}, TypeNames, InOpaque, RecDict, VarDict) -> end; false -> {t_any(), [{opaque, Name}]} end, - Tret = - case InOpaque of - true -> Rep; - false -> - t_from_form({opaque, -1, Name, {Module, Args, Rep}}, - RecDict, VarDict) - end, + Tret = t_from_form({opaque, -1, Name, {Module, Args, Rep}}, + RecDict, VarDict), {Tret, Rret}; error -> Msg = io_lib:format("Unable to find type ~w/~w\n", [Name, ArgsLen]), throw({error, Msg}) end; -t_from_form({opaque, _L, Name, {Mod, Args, Rep}}, _TypeNames, _InOpaque, +t_from_form({opaque, _L, Name, {Mod, Args, Rep}}, _TypeNames, _RecDict, _VarDict) -> case Args of [] -> {t_opaque(Mod, Name, Args, Rep), []}; _ -> throw({error, "Polymorphic opaque types not supported yet"}) end. -record_from_form({atom, _, Name}, ModFields, TypeNames, InOpaque, RecDict, - VarDict) -> +record_from_form({atom, _, Name}, ModFields, TypeNames, RecDict, VarDict) -> case can_unfold_more({record, Name}, TypeNames) of true -> case lookup_record(Name, RecDict) of @@ -3751,11 +4308,11 @@ record_from_form({atom, _, Name}, ModFields, TypeNames, InOpaque, RecDict, {DeclFields1, R1} = case lists:all(fun(Elem) -> Elem end, AreTyped) of true -> {DeclFields, []}; - false -> fields_from_form(DeclFields, TypeNames1, InOpaque, + false -> fields_from_form(DeclFields, TypeNames1, RecDict, dict:new()) end, {GetModRec, R2} = get_mod_record(ModFields, DeclFields1, - TypeNames1, InOpaque, + TypeNames1, RecDict, VarDict), case GetModRec of {error, FieldName} -> @@ -3772,13 +4329,11 @@ record_from_form({atom, _, Name}, ModFields, TypeNames, InOpaque, RecDict, false -> {t_any(), []} end. -get_mod_record([], DeclFields, _TypeNames, _InOpaque, _RecDict, - _VarDict) -> +get_mod_record([], DeclFields, _TypeNames, _RecDict, _VarDict) -> {{ok, DeclFields}, []}; -get_mod_record(ModFields, DeclFields, TypeNames, InOpaque, RecDict, - VarDict) -> +get_mod_record(ModFields, DeclFields, TypeNames, RecDict, VarDict) -> DeclFieldsDict = orddict:from_list(DeclFields), - {ModFieldsDict, R} = build_field_dict(ModFields, TypeNames, InOpaque, + {ModFieldsDict, R} = build_field_dict(ModFields, TypeNames, RecDict, VarDict), case get_mod_record(DeclFieldsDict, ModFieldsDict, []) of {error, _FieldName} = Error -> {Error, R}; @@ -3788,17 +4343,16 @@ get_mod_record(ModFields, DeclFields, TypeNames, InOpaque, RecDict, R} end. -build_field_dict(FieldTypes, TypeNames, InOpaque, RecDict, VarDict) -> - build_field_dict(FieldTypes, TypeNames, InOpaque, RecDict, VarDict, []). +build_field_dict(FieldTypes, TypeNames, RecDict, VarDict) -> + build_field_dict(FieldTypes, TypeNames, RecDict, VarDict, []). build_field_dict([{type, _, field_type, [{atom, _, Name}, Type]}|Left], - TypeNames, InOpaque, RecDict, VarDict, Acc) -> - {T, R1} = t_from_form(Type, TypeNames, InOpaque, RecDict, VarDict), + TypeNames, RecDict, VarDict, Acc) -> + {T, R1} = t_from_form(Type, TypeNames, RecDict, VarDict), NewAcc = [{Name, T}|Acc], - {D, R2} = build_field_dict(Left, TypeNames, InOpaque, RecDict, VarDict, - NewAcc), + {D, R2} = build_field_dict(Left, TypeNames, RecDict, VarDict, NewAcc), {D, R1 ++ R2}; -build_field_dict([], _TypeNames, _InOpaque, _RecDict, _VarDict, Acc) -> +build_field_dict([], _TypeNames, _RecDict, _VarDict, Acc) -> {orddict:from_list(Acc), []}. get_mod_record([{FieldName, DeclType}|Left1], @@ -3817,19 +4371,19 @@ get_mod_record(DeclFields, [], Acc) -> get_mod_record(_, [{FieldName2, _ModType}|_], _Acc) -> {error, FieldName2}. -fields_from_form([], _TypeNames, _InOpaque, _RecDict, _VarDict) -> +fields_from_form([], _TypeNames, _RecDict, _VarDict) -> {[], []}; -fields_from_form([{Name, Type}|Tail], TypeNames, InOpaque, RecDict, +fields_from_form([{Name, Type}|Tail], TypeNames, RecDict, VarDict) -> - {T, R1} = t_from_form(Type, TypeNames, InOpaque, RecDict, VarDict), - {F, R2} = fields_from_form(Tail, TypeNames, InOpaque, RecDict, VarDict), + {T, R1} = t_from_form(Type, TypeNames, RecDict, VarDict), + {F, R2} = fields_from_form(Tail, TypeNames, RecDict, VarDict), {[{Name, T}|F], R1 ++ R2}. -list_from_form([], _TypeNames, _InOpaque, _RecDict, _VarDict) -> +list_from_form([], _TypeNames, _RecDict, _VarDict) -> {[], []}; -list_from_form([H|Tail], TypeNames, InOpaque, RecDict, VarDict) -> - {T, R1} = t_from_form(H, TypeNames, InOpaque, RecDict, VarDict), - {L, R2} = list_from_form(Tail, TypeNames, InOpaque, RecDict, VarDict), +list_from_form([H|Tail], TypeNames, RecDict, VarDict) -> + {T, R1} = t_from_form(H, TypeNames, RecDict, VarDict), + {L, R2} = list_from_form(Tail, TypeNames, RecDict, VarDict), {[T|L], R1 ++ R2}. -spec t_form_to_string(parse_form()) -> string(). @@ -3852,10 +4406,10 @@ t_form_to_string({op, _L, _Op, _Arg1, _Arg2} = Op) -> 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]}) -> - io_lib:format("(~s)", [t_form_to_string(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), ",") ++ ")", - io_lib:format("~w:~w", [Mod, Name]) ++ ArgString; + 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) -> @@ -3866,9 +4420,9 @@ t_form_to_string({type, _L, binary, [Base, Unit]} = Type) -> {0, 0} -> "<<>>"; {8, 0} -> "binary()"; {1, 0} -> "bitstring()"; - {0, B} -> lists:flatten(io_lib:format("<<_:~w>>", [B])); - {U, 0} -> lists:flatten(io_lib:format("<<_:_*~w>>", [U])); - {U, B} -> lists:flatten(io_lib:format("<<_:~w,_:_*~w>>", [B, U])) + {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; @@ -3894,16 +4448,16 @@ t_form_to_string({type, _L, product, 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}} -> - io_lib:format("~w..~w", [FromVal, ToVal]); - _ -> io_lib:format("Badly formed type ~w",[Type]) + flat_format("~w..~w", [FromVal, ToVal]); + _ -> flat_format("Badly formed type ~w",[Type]) end; t_form_to_string({type, _L, record, [{atom, _, Name}]}) -> - io_lib:format("#~w{}", [Name]); + flat_format("#~w{}", [Name]); t_form_to_string({type, _L, record, [{atom, _, Name}|Fields]}) -> FieldString = string:join(t_form_to_string_list(Fields), ","), - io_lib:format("#~w{~s}", [Name, FieldString]); + flat_format("#~w{~s}", [Name, FieldString]); t_form_to_string({type, _L, field_type, [{atom, _, Name}, Type]}) -> - io_lib:format("~w::~s", [Name, t_form_to_string(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()"; @@ -3916,8 +4470,8 @@ t_form_to_string({type, _L, Name, []} = T) -> catch throw:{error, _} -> atom_to_string(Name) ++ "()" end; t_form_to_string({type, _L, Name, List}) -> - io_lib:format("~w(~s)", - [Name, string:join(t_form_to_string_list(List), ",")]). + flat_format("~w(~s)", + [Name, string:join(t_form_to_string_list(List), ",")]). t_form_to_string_list(List) -> t_form_to_string_list(List, []). @@ -3930,7 +4484,7 @@ t_form_to_string_list([], Acc) -> -spec atom_to_string(atom()) -> string(). atom_to_string(Atom) -> - lists:flatten(io_lib:format("~w", [Atom])). + flat_format("~w", [Atom]). %%============================================================================= %% @@ -4002,6 +4556,29 @@ 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,R] = 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,R]), Opaques, Pred); + false -> Pred(Type) + end + end; +do_opaque(Type, _Opaques, Pred) -> + Pred(Type). + %% ----------------------------------- %% Set %% @@ -4068,7 +4645,7 @@ set_size(Set) -> set_to_string(Set) -> L = [case is_atom(X) of true -> io_lib:write_string(atom_to_list(X), $'); % stupid emacs ' - false -> io_lib:format("~w", [X]) + false -> flat_format("~w", [X]) end || X <- set_to_list(Set)], string:join(L, " | "). @@ -4077,6 +4654,9 @@ 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 @@ -4131,6 +4711,11 @@ handle_base(Unit, Pos) when Pos >= 0 -> 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). + %%============================================================================= %% Consistency-testing function(s) below %%============================================================================= |