diff options
Diffstat (limited to 'lib/compiler/src/beam_types.erl')
| -rw-r--r-- | lib/compiler/src/beam_types.erl | 778 |
1 files changed, 778 insertions, 0 deletions
diff --git a/lib/compiler/src/beam_types.erl b/lib/compiler/src/beam_types.erl new file mode 100644 index 0000000000..821ccd31bb --- /dev/null +++ b/lib/compiler/src/beam_types.erl @@ -0,0 +1,778 @@ +%% +%% %CopyrightBegin% +%% +%% Copyright Ericsson AB 2019. All Rights Reserved. +%% +%% Licensed under the Apache License, Version 2.0 (the "License"); +%% you may not use this file except in compliance with the License. +%% You may obtain a copy of the License at +%% +%% http://www.apache.org/licenses/LICENSE-2.0 +%% +%% Unless required by applicable law or agreed to in writing, software +%% distributed under the License is distributed on an "AS IS" BASIS, +%% WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +%% See the License for the specific language governing permissions and +%% limitations under the License. +%% +%% %CopyrightEnd% +%% + +-module(beam_types). + +-include("beam_types.hrl"). + +-import(lists, [foldl/3, reverse/1, reverse/2]). + +-export([meet/1, meet/2, join/1, join/2, subtract/2]). + +-export([get_singleton_value/1, + is_singleton_type/1, + is_boolean_type/1, + normalize/1]). + +-export([get_element_type/2, set_element_type/3]). + +-export([make_type_from_value/1]). + +-export([make_atom/1, + make_boolean/0, + make_integer/1, + make_integer/2]). + +-define(IS_LIST_TYPE(N), + N =:= list orelse + N =:= cons orelse + N =:= nil). + +-define(IS_NUMBER_TYPE(N), + N =:= number orelse + N =:= float orelse + is_record(N, t_integer)). + +-define(TUPLE_SET_LIMIT, 20). + +%% Folds meet/2 over a list. + +-spec meet([type()]) -> type(). + +meet([T1, T2 | Ts]) -> + meet([meet(T1, T2) | Ts]); +meet([T]) -> T. + +%% Return the "meet" of Type1 and Type2, which is more general than Type1 and +%% Type2. This is identical to glb/2 but can operate on and produce unions. +%% +%% A = #t_union{list=nil, number=[number], other=[#t_map{}]} +%% B = #t_union{number=[#t_integer{}], other=[#t_map{}]} +%% +%% meet(A, B) -> +%% #t_union{number=[#t_integer{}], other=[#t_map{}]} +%% +%% The meet of two different types result in 'none', which is the bottom +%% element for our type lattice: +%% +%% meet(#t_integer{}, #t_map{}) -> none + +-spec meet(type(), type()) -> type(). + +meet(T, T) -> + verified_type(T); +meet(any, T) -> + verified_type(T); +meet(T, any) -> + verified_type(T); +meet(#t_union{}=A, B) -> + meet_unions(A, B); +meet(A, #t_union{}=B) -> + meet_unions(B, A); +meet(A, B) -> + glb(A, B). + +meet_unions(#t_union{atom=AtomA,list=ListA,number=NumberA, + tuple_set=TSetA,other=OtherA}, + #t_union{atom=AtomB,list=ListB,number=NumberB, + tuple_set=TSetB,other=OtherB}) -> + Union = #t_union{atom=glb(AtomA, AtomB), + list=glb(ListA, ListB), + number=glb(NumberA, NumberB), + tuple_set=meet_tuple_sets(TSetA, TSetB), + other=glb(OtherA, OtherB)}, + shrink_union(Union); +meet_unions(#t_union{atom=AtomA}, #t_atom{}=B) -> + case glb(AtomA, B) of + none -> none; + Atom -> Atom + end; +meet_unions(#t_union{number=NumberA}, B) when ?IS_NUMBER_TYPE(B) -> + case glb(NumberA, B) of + none -> none; + Number -> Number + end; +meet_unions(#t_union{list=ListA}, B) when ?IS_LIST_TYPE(B) -> + case glb(ListA, B) of + none -> none; + List -> List + end; +meet_unions(#t_union{tuple_set=Tuples}, #t_tuple{}=B) -> + Set = meet_tuple_sets(Tuples, new_tuple_set(B)), + shrink_union(#t_union{tuple_set=Set}); +meet_unions(#t_union{other=OtherA}, OtherB) -> + case glb(OtherA, OtherB) of + none -> none; + Other -> Other + end. + +meet_tuple_sets(none, _) -> + none; +meet_tuple_sets(_, none) -> + none; +meet_tuple_sets(#t_tuple{}=A, #t_tuple{}=B) -> + new_tuple_set(glb(A, B)); +meet_tuple_sets(#t_tuple{}=Tuple, Records) -> + mts_tuple(Records, Tuple, []); +meet_tuple_sets(Records, #t_tuple{}=Tuple) -> + meet_tuple_sets(Tuple, Records); +meet_tuple_sets(RecordsA, RecordsB) -> + mts_records(RecordsA, RecordsB). + +mts_tuple([{Key, Type} | Records], Tuple, Acc) -> + case glb(Type, Tuple) of + none -> mts_tuple(Records, Tuple, Acc); + T -> mts_tuple(Records, Tuple, [{Key, T} | Acc]) + end; +mts_tuple([], _Tuple, [_|_]=Acc) -> + reverse(Acc); +mts_tuple([], _Tuple, []) -> + none. + +mts_records(RecordsA, RecordsB) -> + mts_records(RecordsA, RecordsB, []). + +mts_records([{Key, A} | RsA], [{Key, B} | RsB], Acc) -> + case glb(A, B) of + none -> mts_records(RsA, RsB, Acc); + T -> mts_records(RsA, RsB, [{Key, T} | Acc]) + end; +mts_records([{KeyA, _} | _ ]=RsA, [{KeyB, _} | RsB], Acc) when KeyA > KeyB -> + mts_records(RsA, RsB, Acc); +mts_records([{KeyA, _} | RsA], [{KeyB, _} | _] = RsB, Acc) when KeyA < KeyB -> + mts_records(RsA, RsB, Acc); +mts_records(_RsA, [], [_|_]=Acc) -> + reverse(Acc); +mts_records([], _RsB, [_|_]=Acc) -> + reverse(Acc); +mts_records(_RsA, _RsB, []) -> + none. + +%% Folds join/2 over a list. + +-spec join([type()]) -> type(). + +join([T1, T2| Ts]) -> + join([join(T1, T2) | Ts]); +join([T]) -> T. + +%% Return the "join" of Type1 and Type2, which is more general than Type1 and +%% Type2. This is identical to lub/2 but can operate on and produce unions. +%% +%% join(#t_integer{}, #t_map{}) -> #t_union{number=[#t_integer{}], +%% other=[#t_map{}]} + +-spec join(type(), type()) -> type(). + +join(T, T) -> T; +join(_T, any) -> any; +join(any, _T) -> any; +join(T, none) -> T; +join(none, T) -> T; + +join(#t_union{}=A, B) -> + join_unions(A, B); +join(A, #t_union{}=B) -> + join_unions(B, A); + +%% Union creation... +join(#t_atom{}=A, #t_atom{}=B) -> + lub(A, B); +join(#t_atom{}=A, B) when ?IS_LIST_TYPE(B) -> + #t_union{atom=A,list=B}; +join(#t_atom{}=A, B) when ?IS_NUMBER_TYPE(B) -> + #t_union{atom=A,number=B}; +join(#t_atom{}=A, #t_tuple{}=B) -> + #t_union{atom=A,tuple_set=new_tuple_set(B)}; +join(#t_atom{}=A, B) -> + #t_union{atom=A,other=B}; +join(A, #t_atom{}=B) -> + join(B, A); + +join(A, B) when ?IS_LIST_TYPE(A), ?IS_LIST_TYPE(B) -> + lub(A, B); +join(A, B) when ?IS_LIST_TYPE(A), ?IS_NUMBER_TYPE(B) -> + #t_union{list=A,number=B}; +join(A, #t_tuple{}=B) when ?IS_LIST_TYPE(A) -> + #t_union{list=A,tuple_set=new_tuple_set(B)}; +join(A, B) when ?IS_LIST_TYPE(A) -> + #t_union{list=A,other=B}; +join(A, B) when ?IS_LIST_TYPE(B) -> + join(B, A); + +join(A, B) when ?IS_NUMBER_TYPE(A), ?IS_NUMBER_TYPE(B) -> + lub(A, B); +join(A, #t_tuple{}=B) when ?IS_NUMBER_TYPE(A) -> + #t_union{number=A,tuple_set=new_tuple_set(B)}; +join(A, B) when ?IS_NUMBER_TYPE(A) -> + #t_union{number=A,other=B}; +join(A, B) when ?IS_NUMBER_TYPE(B) -> + join(B, A); + +join(#t_tuple{}=A, #t_tuple{}=B) -> + case {record_key(A), record_key(B)} of + {Same, Same} -> + lub(A, B); + {none, _Key} -> + lub(A, B); + {_Key, none} -> + lub(A, B); + {KeyA, KeyB} when KeyA < KeyB -> + #t_union{tuple_set=[{KeyA, A}, {KeyB, B}]}; + {KeyA, KeyB} when KeyA > KeyB -> + #t_union{tuple_set=[{KeyB, B}, {KeyA, A}]} + end; +join(#t_tuple{}=A, B) -> + %% All other combinations have been tried already, so B must be 'other' + #t_union{tuple_set=new_tuple_set(A),other=B}; +join(A, #t_tuple{}=B) -> + join(B, A); + +join(A, B) -> + lub(A, B). + +join_unions(#t_union{atom=AtomA,list=ListA,number=NumberA, + tuple_set=TSetA,other=OtherA}, + #t_union{atom=AtomB,list=ListB,number=NumberB, + tuple_set=TSetB,other=OtherB}) -> + Union = #t_union{atom=lub(AtomA, AtomB), + list=lub(ListA, ListB), + number=lub(NumberA, NumberB), + tuple_set=join_tuple_sets(TSetA, TSetB), + other=lub(OtherA, OtherB)}, + shrink_union(Union); +join_unions(#t_union{atom=AtomA}=A, #t_atom{}=B) -> + A#t_union{atom=lub(AtomA, B)}; +join_unions(#t_union{list=ListA}=A, B) when ?IS_LIST_TYPE(B) -> + A#t_union{list=lub(ListA, B)}; +join_unions(#t_union{number=NumberA}=A, B) when ?IS_NUMBER_TYPE(B) -> + A#t_union{number=lub(NumberA, B)}; +join_unions(#t_union{tuple_set=TSetA}=A, #t_tuple{}=B) -> + Set = join_tuple_sets(TSetA, new_tuple_set(B)), + shrink_union(A#t_union{tuple_set=Set}); +join_unions(#t_union{other=OtherA}=A, B) -> + case lub(OtherA, B) of + any -> any; + T -> A#t_union{other=T} + end. + +join_tuple_sets(A, none) -> + A; +join_tuple_sets(none, B) -> + B; +join_tuple_sets(#t_tuple{}=A, #t_tuple{}=B) -> + lub(A, B); +join_tuple_sets(#t_tuple{}=Tuple, Records) -> + jts_tuple(Records, Tuple); +join_tuple_sets(Records, #t_tuple{}=Tuple) -> + join_tuple_sets(Tuple, Records); +join_tuple_sets(RecordsA, RecordsB) -> + jts_records(RecordsA, RecordsB). + +jts_tuple([{_Key, Tuple} | Records], Acc) -> + jts_tuple(Records, lub(Tuple, Acc)); +jts_tuple([], Acc) -> + Acc. + +jts_records(RsA, RsB) -> + jts_records(RsA, RsB, 0, []). + +jts_records(RsA, RsB, N, Acc) when N > ?TUPLE_SET_LIMIT -> + A = normalize_tuple_set(RsA, none), + B = normalize_tuple_set(RsB, A), + #t_tuple{} = normalize_tuple_set(Acc, B); +jts_records([{Key, A} | RsA], [{Key, B} | RsB], N, Acc) -> + jts_records(RsA, RsB, N + 1, [{Key, lub(A, B)} | Acc]); +jts_records([{KeyA, _} | _]=RsA, [{KeyB, B} | RsB], N, Acc) when KeyA > KeyB -> + jts_records(RsA, RsB, N + 1, [{KeyB, B} | Acc]); +jts_records([{KeyA, A} | RsA], [{KeyB, _} | _] = RsB, N, Acc) when KeyA < KeyB -> + jts_records(RsA, RsB, N + 1, [{KeyA, A} | Acc]); +jts_records([], RsB, _N, Acc) -> + reverse(Acc, RsB); +jts_records(RsA, [], _N, Acc) -> + reverse(Acc, RsA). + +%% Subtract Type2 from Type1. Example: +%% subtract(list, cons) -> nil + +-spec subtract(type(), type()) -> type(). + +subtract(#t_atom{elements=[_|_]=Set0}, #t_atom{elements=[_|_]=Set1}) -> + case ordsets:subtract(Set0, Set1) of + [] -> none; + [_|_]=Set -> #t_atom{elements=Set} + end; +subtract(number, float) -> #t_integer{}; +subtract(number, #t_integer{elements=any}) -> float; +subtract(list, cons) -> nil; +subtract(list, nil) -> cons; + +subtract(#t_union{atom=Atom}=A, #t_atom{}=B)-> + shrink_union(A#t_union{atom=subtract(Atom, B)}); +subtract(#t_union{number=Number}=A, B) when ?IS_NUMBER_TYPE(B) -> + shrink_union(A#t_union{number=subtract(Number, B)}); +subtract(#t_union{list=List}=A, B) when ?IS_LIST_TYPE(B) -> + shrink_union(A#t_union{list=subtract(List, B)}); +subtract(#t_union{tuple_set=[_|_]=Records0}=A, #t_tuple{}=B) -> + %% Filter out all records that are strictly more specific than B. + NewSet = case [{Key, T} || {Key, T} <- Records0, meet(T, B) =/= T] of + [_|_]=Records -> Records; + [] -> none + end, + shrink_union(A#t_union{tuple_set=NewSet}); +subtract(#t_union{tuple_set=#t_tuple{}=Tuple}=A, #t_tuple{}=B) -> + %% Exclude Tuple if it's strictly more specific than B. + case meet(Tuple, B) of + Tuple -> shrink_union(A#t_union{tuple_set=none}); + _ -> A + end; + +subtract(T, _) -> T. + +%%% +%%% Type operators +%%% + +-spec get_singleton_value(Type) -> Result when + Type :: type(), + Result :: {ok, term()} | error. +get_singleton_value(#t_atom{elements=[Atom]}) -> + {ok, Atom}; +get_singleton_value(#t_integer{elements={Int,Int}}) -> + {ok, Int}; +get_singleton_value(nil) -> + {ok, []}; +get_singleton_value(_) -> + error. + +-spec is_boolean_type(type()) -> boolean(). +is_boolean_type(#t_atom{elements=[F,T]}) -> + F =:= false andalso T =:= true; +is_boolean_type(#t_atom{elements=[B]}) -> + is_boolean(B); +is_boolean_type(#t_union{}=T) -> + is_boolean_type(normalize(T)); +is_boolean_type(_) -> + false. + +-spec is_singleton_type(type()) -> boolean(). +is_singleton_type(Type) -> + get_singleton_value(Type) =/= error. + +-spec set_element_type(Key, Type, Elements) -> Elements when + Key :: term(), + Type :: type(), + Elements :: elements(). +set_element_type(_Key, none, Es) -> + Es; +set_element_type(Key, any, Es) -> + maps:remove(Key, Es); +set_element_type(Key, Type, Es) -> + Es#{ Key => Type }. + +-spec get_element_type(Key, Elements) -> type() when + Key :: term(), + Elements :: elements(). +get_element_type(Index, Es) -> + case Es of + #{ Index := T } -> T; + #{} -> any + end. + +-spec normalize(type()) -> normal_type(). +normalize(#t_union{atom=Atom,list=List,number=Number, + tuple_set=Tuples,other=Other}) -> + A = lub(Atom, List), + B = lub(A, Number), + C = lub(B, Other), + normalize_tuple_set(Tuples, C); +normalize(T) -> + verified_normal_type(T). + +normalize_tuple_set([{_, A} | Records], B) -> + normalize_tuple_set(Records, lub(A, B)); +normalize_tuple_set([], B) -> + B; +normalize_tuple_set(A, B) -> + lub(A, B). + +%%% +%%% Type constructors +%%% + +-spec make_type_from_value(term()) -> type(). +make_type_from_value(Value) -> + mtfv_1(Value). + +mtfv_1([]) -> nil; +mtfv_1([_|_]) -> cons; +mtfv_1(A) when is_atom(A) -> #t_atom{elements=[A]}; +mtfv_1(B) when is_binary(B) -> #t_bitstring{unit=8}; +mtfv_1(B) when is_bitstring(B) -> #t_bitstring{}; +mtfv_1(F) when is_float(F) -> float; +mtfv_1(F) when is_function(F) -> + {arity, Arity} = erlang:fun_info(F, arity), + #t_fun{arity=Arity}; +mtfv_1(I) when is_integer(I) -> make_integer(I); +mtfv_1(M) when is_map(M) -> #t_map{}; +mtfv_1(T) when is_tuple(T) -> + {Es,_} = foldl(fun(Val, {Es0, Index}) -> + Type = mtfv_1(Val), + Es = set_element_type(Index, Type, Es0), + {Es, Index + 1} + end, {#{}, 1}, tuple_to_list(T)), + #t_tuple{exact=true,size=tuple_size(T),elements=Es}; +mtfv_1(_Term) -> + any. + +-spec make_atom(atom()) -> type(). +make_atom(Atom) when is_atom(Atom) -> + #t_atom{elements=[Atom]}. + +-spec make_boolean() -> type(). +make_boolean() -> + #t_atom{elements=[false,true]}. + +-spec make_integer(integer()) -> type(). +make_integer(Int) when is_integer(Int) -> + make_integer(Int, Int). + +-spec make_integer(Min, Max) -> type() when + Min :: integer(), + Max :: integer(). +make_integer(Min, Max) when is_integer(Min), is_integer(Max), Min =< Max -> + #t_integer{elements={Min,Max}}. + +%%% +%%% Helpers +%%% + +%% Return the greatest lower bound of the types Type1 and Type2. The GLB is a +%% more specific type than Type1 and Type2, and is always a normal type. +%% +%% glb(#t_integer{elements=any}, #t_integer{elements={0,3}}) -> +%% #t_integer{elements={0,3}} +%% +%% The GLB of two different types result in 'none', which is the bottom +%% element for our type lattice: +%% +%% glb(#t_integer{}, #t_map{}) -> none + +-spec glb(normal_type(), normal_type()) -> normal_type(). + +glb(T, T) -> + verified_normal_type(T); +glb(any, T) -> + verified_normal_type(T); +glb(T, any) -> + verified_normal_type(T); +glb(#t_atom{elements=[_|_]=Set1}, #t_atom{elements=[_|_]=Set2}) -> + case ordsets:intersection(Set1, Set2) of + [] -> + none; + [_|_]=Set -> + #t_atom{elements=Set} + end; +glb(#t_atom{elements=[_|_]}=T, #t_atom{elements=any}) -> + T; +glb(#t_atom{elements=any}, #t_atom{elements=[_|_]}=T) -> + T; +glb(#t_bs_context{slots=SlotCountA,valid=ValidSlotsA}, + #t_bs_context{slots=SlotCountB,valid=ValidSlotsB}) -> + CommonSlotMask = (1 bsl min(SlotCountA, SlotCountB)) - 1, + CommonSlotsA = ValidSlotsA band CommonSlotMask, + CommonSlotsB = ValidSlotsB band CommonSlotMask, + if + CommonSlotsA =:= CommonSlotsB -> + #t_bs_context{slots=max(SlotCountA, SlotCountB), + valid=ValidSlotsA bor ValidSlotsB}; + CommonSlotsA =/= CommonSlotsB -> + none + end; +glb(#t_fun{arity=any}, #t_fun{}=T) -> + T; +glb(#t_fun{}=T, #t_fun{arity=any}) -> + T; +glb(#t_integer{elements={_,_}}=T, #t_integer{elements=any}) -> + T; +glb(#t_integer{elements=any}, #t_integer{elements={_,_}}=T) -> + T; +glb(#t_integer{elements={MinA,MaxA}}, #t_integer{elements={MinB,MaxB}}) + when MinA >= MinB, MinA =< MaxB; + MinB >= MinA, MinB =< MaxA -> + true = MinA =< MaxA andalso MinB =< MaxB, %Assertion. + #t_integer{elements={max(MinA, MinB),min(MaxA, MaxB)}}; +glb(#t_integer{}=T, number) -> T; +glb(float=T, number) -> T; +glb(number, #t_integer{}=T) -> T; +glb(number, float=T) -> T; +glb(list, cons) -> cons; +glb(list, nil) -> nil; +glb(cons, list) -> cons; +glb(nil, list) -> nil; +glb(#t_tuple{}=T1, #t_tuple{}=T2) -> + glb_tuples(T1, T2); +glb(#t_bitstring{unit=U1}, #t_bitstring{unit=U2}) -> + #t_bitstring{unit=U1 * U2 div gcd(U1, U2)}; +glb(_, _) -> + %% Inconsistent types. There will be an exception at runtime. + none. + +glb_tuples(#t_tuple{size=Sz1,exact=true}, + #t_tuple{size=Sz2,exact=true}) when Sz1 =/= Sz2 -> + none; +glb_tuples(#t_tuple{size=Sz1,exact=Ex1,elements=Es1}, + #t_tuple{size=Sz2,exact=Ex2,elements=Es2}) -> + Size = max(Sz1, Sz2), + Exact = Ex1 or Ex2, + case glb_elements(Es1, Es2) of + none -> + none; + Es -> + #t_tuple{size=Size,exact=Exact,elements=Es} + end. + +glb_elements(Es1, Es2) -> + Keys = maps:keys(Es1) ++ maps:keys(Es2), + glb_elements_1(Keys, Es1, Es2, #{}). + +glb_elements_1([Key | Keys], Es1, Es2, Acc) -> + case {Es1, Es2} of + {#{ Key := Type1 }, #{ Key := Type2 }} -> + %% Note the use of meet/2; elements don't need to be normal types. + case meet(Type1, Type2) of + none -> none; + Type -> glb_elements_1(Keys, Es1, Es2, Acc#{ Key => Type }) + end; + {#{ Key := Type1 }, _} -> + glb_elements_1(Keys, Es1, Es2, Acc#{ Key => Type1 }); + {_, #{ Key := Type2 }} -> + glb_elements_1(Keys, Es1, Es2, Acc#{ Key => Type2 }) + end; +glb_elements_1([], _Es1, _Es2, Acc) -> + Acc. + +%% Return the least upper bound of the types Type1 and Type2. The LUB is a more +%% general type than Type1 and Type2, and is always a normal type. +%% +%% For example: +%% +%% lub(#t_integer{elements=any}, #t_integer=elements={0,3}}) -> +%% #t_integer{} +%% +%% The LUB for two different types result in 'any' (not a union type!), which +%% is the top element for our type lattice: +%% +%% lub(#t_integer{}, #t_map{}) -> any + +-spec lub(normal_type(), normal_type()) -> normal_type(). + +lub(T, T) -> + verified_normal_type(T); +lub(none, T) -> + verified_normal_type(T); +lub(T, none) -> + verified_normal_type(T); +lub(any, _) -> + any; +lub(_, any) -> + any; +lub(#t_atom{elements=[_|_]=Set1}, #t_atom{elements=[_|_]=Set2}) -> + Set = ordsets:union(Set1, Set2), + case ordsets:size(Set) of + Size when Size =< ?ATOM_SET_SIZE -> + #t_atom{elements=Set}; + _Size -> + #t_atom{elements=any} + end; +lub(#t_atom{elements=any}=T, #t_atom{elements=[_|_]}) -> T; +lub(#t_atom{elements=[_|_]}, #t_atom{elements=any}=T) -> T; +lub(#t_bitstring{unit=U1}, #t_bitstring{unit=U2}) -> + #t_bitstring{unit=gcd(U1, U2)}; +lub(#t_fun{}, #t_fun{}) -> + #t_fun{}; +lub(#t_integer{elements={MinA,MaxA}}, + #t_integer{elements={MinB,MaxB}}) -> + #t_integer{elements={min(MinA,MinB),max(MaxA,MaxB)}}; +lub(#t_bs_context{slots=SlotsA,valid=ValidA}, + #t_bs_context{slots=SlotsB,valid=ValidB}) -> + #t_bs_context{slots=min(SlotsA, SlotsB), + valid=ValidA band ValidB}; +lub(#t_integer{}, #t_integer{}) -> #t_integer{}; +lub(list, cons) -> list; +lub(cons, list) -> list; +lub(nil, cons) -> list; +lub(cons, nil) -> list; +lub(nil, list) -> list; +lub(list, nil) -> list; +lub(#t_integer{}, float) -> number; +lub(float, #t_integer{}) -> number; +lub(#t_integer{}, number) -> number; +lub(number, #t_integer{}) -> number; +lub(float, number) -> number; +lub(number, float) -> number; +lub(#t_tuple{size=Sz,exact=ExactA,elements=EsA}, + #t_tuple{size=Sz,exact=ExactB,elements=EsB}) -> + Exact = ExactA and ExactB, + Es = lub_tuple_elements(Sz, EsA, EsB), + #t_tuple{size=Sz,exact=Exact,elements=Es}; +lub(#t_tuple{size=SzA,elements=EsA}, #t_tuple{size=SzB,elements=EsB}) -> + Sz = min(SzA, SzB), + Es = lub_tuple_elements(Sz, EsA, EsB), + #t_tuple{size=Sz,elements=Es}; +lub(_T1, _T2) -> + %%io:format("~p ~p\n", [_T1,_T2]), + any. + +lub_tuple_elements(MinSize, EsA, EsB) -> + Es0 = lub_elements(EsA, EsB), + maps:filter(fun(Index, _Type) -> Index =< MinSize end, Es0). + +lub_elements(Es1, Es2) -> + Keys = if + map_size(Es1) =< map_size(Es2) -> maps:keys(Es1); + map_size(Es1) > map_size(Es2) -> maps:keys(Es2) + end, + lub_elements_1(Keys, Es1, Es2, #{}). + +lub_elements_1([Key | Keys], Es1, Es2, Acc0) -> + case {Es1, Es2} of + {#{ Key := Type1 }, #{ Key := Type2 }} -> + %% Note the use of join/2; elements don't need to be normal types. + Acc = set_element_type(Key, join(Type1, Type2), Acc0), + lub_elements_1(Keys, Es1, Es2, Acc); + {#{}, #{}} -> + lub_elements_1(Keys, Es1, Es2, Acc0) + end; +lub_elements_1([], _Es1, _Es2, Acc) -> + Acc. + +%% + +gcd(A, B) -> + case A rem B of + 0 -> B; + X -> gcd(B, X) + end. + +%% + +record_key(#t_tuple{exact=true,size=Size,elements=#{ 1 := Tag }}) -> + case is_singleton_type(Tag) of + true -> {Size, Tag}; + false -> none + end; +record_key(_) -> + none. + +new_tuple_set(T) -> + case record_key(T) of + none -> T; + Key -> [{Key, T}] + end. + +%% + +shrink_union(#t_union{other=any}) -> + any; +shrink_union(#t_union{atom=Atom,list=none,number=none, + tuple_set=none,other=none}) -> + Atom; +shrink_union(#t_union{atom=none,list=List,number=none, + tuple_set=none,other=none}) -> + List; +shrink_union(#t_union{atom=none,list=none,number=Number, + tuple_set=none,other=none}) -> + Number; +shrink_union(#t_union{atom=none,list=none,number=none, + tuple_set=#t_tuple{}=Tuple,other=none}) -> + Tuple; +shrink_union(#t_union{atom=none,list=none,number=none, + tuple_set=[{_Key, Record}],other=none}) -> + #t_tuple{} = Record; %Assertion. +shrink_union(#t_union{atom=none,list=none,number=none, + tuple_set=none,other=Other}) -> + Other; +shrink_union(#t_union{}=T) -> + T. + +%% Verifies that the given type is well-formed. + +-spec verified_type(T) -> T when + T :: type(). + +verified_type(#t_union{atom=Atom, + list=List, + number=Number, + tuple_set=TSet, + other=Other}=T) -> + _ = verified_normal_type(Atom), + _ = verified_normal_type(List), + _ = verified_normal_type(Number), + _ = verify_tuple_set(TSet), + _ = verified_normal_type(Other), + T; +verified_type(T) -> + verified_normal_type(T). + +verify_tuple_set([_|_]=T) -> + _ = [verified_normal_type(Rec) || {_, Rec} <- T], + T; +verify_tuple_set(#t_tuple{}=T) -> + none = record_key(T), %Assertion. + T; +verify_tuple_set(none=T) -> + T. + +-spec verified_normal_type(T) -> T when + T :: normal_type(). + +verified_normal_type(any=T) -> T; +verified_normal_type(none=T) -> T; +verified_normal_type(#t_atom{elements=any}=T) -> T; +verified_normal_type(#t_atom{elements=[_|_]}=T) -> T; +verified_normal_type(#t_bitstring{unit=U}=T) + when is_integer(U), U >= 1 -> + T; +verified_normal_type(#t_bs_context{}=T) -> T; +verified_normal_type(#t_fun{arity=Arity}=T) + when Arity =:= any; is_integer(Arity) -> + T; +verified_normal_type(float=T) -> T; +verified_normal_type(#t_integer{elements=any}=T) -> T; +verified_normal_type(#t_integer{elements={Min,Max}}=T) + when is_integer(Min), is_integer(Max), Min =< Max -> + T; +verified_normal_type(list=T) -> T; +verified_normal_type(#t_map{}=T) -> T; +verified_normal_type(nil=T) -> T; +verified_normal_type(cons=T) -> T; +verified_normal_type(number=T) -> T; +verified_normal_type(#t_tuple{size=Size,elements=Es}=T) -> + %% All known elements must have a valid index and type (which may be a + %% union). 'any' is prohibited since it's implicit and should never be + %% present in the map, and a 'none' element ought to have reduced the + %% entire tuple to 'none'. + maps:fold(fun(Index, Element, _) when is_integer(Index), + 1 =< Index, Index =< Size, + Element =/= any, Element =/= none -> + verified_type(Element) + end, [], Es), + T. |