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typechecker.erl
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typechecker.erl
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%% @private
-module(typechecker).
%% API used by gradualizer.erl
-export([type_check_forms/2]).
%% API used by the constraint solver
-export([glb/2,
lub/2]).
%% Functions used in unit tests.
-export([type_check_expr/2,
type_check_expr_in/3,
create_env/2,
subtype/3,
normalize/2,
glb/3,
type/1, type/2,
type_diff/3,
refinable/2,
compatible/3,
collect_specs_types_opaques_and_functions/1,
number_of_exported_functions/1,
bounded_type_list_to_type/2,
unfold_bounded_type/2]).
-compile([warn_missing_spec, warn_missing_spec_all,
warnings_as_errors]).
-include("typelib.hrl").
-define(verbose(Env, Fmt, Args),
case Env#env.verbose of
true -> io:format(Fmt, Args);
false -> ok
end).
-define(throw_orig_type(EXPR, ORIGTYPE, NORMTYPE),
try
EXPR
catch
throw:TypeError:ST ->
case error_evidence(TypeError) of
NORMTYPE ->
%% All error tuple sizes are > 0.
Index = size(TypeError),
Index > 0 orelse erlang:error(impossible),
Index = ?assert_type(size(TypeError), pos_integer()),
%% if the last element of the type_error tuple is the normalized type
%% replace it with the original result type
erlang:raise(throw, setelement(Index, TypeError, ORIGTYPE), ST);
_ ->
erlang:raise(throw, TypeError, ST)
end
end).
%% Checks that the location annotation of a type is set to zero and raises an
%% error if it isn't.
-define(assert_normalized_anno(Tuple),
case erl_anno:location(element(2, Tuple)) of
0 -> ok;
_ -> error({position_not_removed, Tuple})
end).
%% This is the maximum time that typechecking a single form may take.
-define(form_check_timeout_ms, 500).
-type venv() :: map().
-export_type([env/0,
venv/0,
type/0,
typed_record_field/0]).
-type expr() :: gradualizer_type:abstract_expr().
-type pattern() :: gradualizer_type:abstract_pattern().
-type type() :: gradualizer_type:abstract_type().
-type form() :: erl_parse:abstract_form().
-type forms() :: [form()].
%% Pattern macros
-define(type(T), {type, _, T, []}).
-define(type(T, A), {type, _, T, A}).
-define(top(), {remote_type, _, [{atom,_,gradualizer}
,{atom,_,top},[]]}).
-define(record_field(Name), {record_field, _, {atom, _, Name}, _}).
-define(record_field_expr(Expr), {record_field, _, _, Expr}).
-define(typed_record_field(Name), {typed_record_field, ?record_field(Name), _}).
-define(typed_record_field(Name, Type), {typed_record_field, ?record_field(Name), Type}).
-define(type_field_type(Name, Type), {type, _, field_type, [{atom, _, Name}, Type]}).
-define(any_assoc, ?type(map_field_assoc, [?type(any), ?type(any)])).
-define(user_type(), {user_type, _, _, _}).
-define(user_type(Name, Args, Anno), {user_type, Anno, Name, Args}).
%% Data collected from epp parse tree
-record(parsedata, {
module :: atom(),
export_all = false :: boolean(),
exports = [] :: [{atom(), integer()}],
imports = [] :: [{module(), atom(), integer()}],
specs = [] :: list(),
types = [] :: list(),
opaques = [] :: list(),
records = [] :: list(),
functions = [] :: list()
}).
-type af_field_name() :: gradualizer_type:af_field_name().
-type record_field() :: gradualizer_type:af_record_field(expr()).
-type typed_record_field() :: {typed_record_field, record_field(), type()}.
%% The environment passed around during typechecking.
%% TODO: See https://github.com/josefs/Gradualizer/issues/364 for details.
%% Making the type def and record def have the same number of fields fixes a broken Gradualizer
%% diagnostic, which seems to assume the record only has the
%% fields annotated in the type, not all the fields from the definition.
-include("typechecker.hrl").
-type env() :: #env{}.
-include_lib("stdlib/include/assert.hrl").
-include("constraints.hrl").
-include("gradualizer.hrl").
-type constraints() :: constraints:t().
-type compatible() :: {true, constraints:t()} | false.
-type anno() :: erl_anno:anno().
-type binary_op() :: gradualizer_type:binary_op().
-type bounded_function() :: gradualizer_type:af_constrained_function_type().
-type unary_op() :: gradualizer_type:unary_op().
%% TODO: Some of these don't seem to be thrown at all, e.g. expected_fun_type
-type type_error() :: arith_error | badkey | call_arity | call_intersect | check_clauses | cons_pat
| cyclic_type_vars | expected_fun_type | int_error | list | mismatch
| no_type_match_intersection | non_number_argument_to_minus
| non_number_argument_to_plus | op_type_too_precise | operator_pattern | pattern
| receive_after | record_pattern | rel_error | relop | unary_error
| unreachable_clauses.
-type undef() :: record | user_type | remote_type | record_field.
-type error() :: {type_error, type_error()}
| {type_error, type_error(), anno()}
| {type_error, expr(), type() | [type()], type()}
| {type_error, type_error(), anno() | type(), type() | expr()}
| {type_error, cyclic_type_vars, anno(), bounded_function(), list()}
| {type_error, type_error(), anno(), atom() | pattern(), type()}
| {type_error, type_error(), unary_op() | binary_op(), anno(), type()}
| {type_error, type_error(), binary_op(), anno(), type(), type()}
| {type_error, call_arity, anno(), atom(), arity(), arity()}
| {undef, undef(), anno(), {atom(), atom() | non_neg_integer()} | mfa() | expr()}
| {undef, undef(), expr()}
| {not_exported, remote_type, anno(), mfa()}
| {bad_type_annotation, gradualizer_type:af_string()}
| {illegal_map_type, type()}
| {argument_length_mismatch, anno(), arity(), arity()}
| {nonexhaustive, anno(), [expr()]}
| {illegal_pattern, pattern()}
| {internal_error, missing_type_spec, atom(), arity()}
| {call_undef, anno(), module(), atom(), arity()}.
%% `typechecker' returns these errors as results of its analysis.
%% Two types are compatible if one is a subtype of the other, or both.
-spec compatible(type(), type(), env()) -> compatible().
compatible(Ty1, Ty2, Env) ->
case {subtype(Ty1, Ty2, Env), subtype(Ty2, Ty1, Env)} of
{{true, C1}, {true, C2}} ->
{true, constraints:combine(C1,C2)};
{false, T={true, _C2}} ->
T;
{T={true, _C1}, false} ->
T;
{false, false} ->
false
end.
%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Subtyping compatibility
%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% The first argument is a "compatible subtype" of the second.
-spec subtype(type(), type(), env()) -> compatible().
subtype(Ty1, Ty2, Env) ->
try compat(Ty1, Ty2, maps:new(), Env) of
{_Memoization, Constraints} ->
{true, Constraints}
catch
nomatch ->
false
end.
%% Check if at least one of the types in a list is a subtype of a type.
%% Used when checking intersection types.
%%
%% When working on function intersections, `any_subtype/3' combines input parameter constraints
%% from multiple clauses into a single union type constraint.
-spec any_subtype([type()], type(), env()) -> compatible().
any_subtype(Tys, Ty, Env) ->
any_subtype(Tys, Ty, constraints:empty(), Env, false).
-spec any_subtype([type()], type(), constraints:t(), env(), boolean()) -> compatible().
any_subtype([], _Ty, Cs, _Env, true) ->
{true, Cs};
any_subtype([], _Ty, _Cs, _Env, false) ->
false;
any_subtype([Ty1|Tys], Ty, Cs, Env, AnySubtype) ->
case subtype(Ty1, Ty, Env) of
{true, Cs1} ->
Cs2 = constraints:combine_with(Cs, Cs1,
fun constraints:append_values/3,
fun (_Var, UBounds1, UBounds2) ->
%% TODO: should we be more careful here and make
%% sure Var is Ty1's argument?
[lub(UBounds1 ++ UBounds2, Env)]
end),
any_subtype(Tys, Ty, Cs2, Env, true);
false ->
any_subtype(Tys, Ty, Cs, Env, AnySubtype)
end.
-type acc(Seen) :: {Seen, constraints:t()}.
-type compat_acc() :: acc(map()).
% This function throws an exception in case of a type error
%% The functions compat and compat_ty are mutually recursive.
%% The main entry point is compat and all recursive calls should go via compat.
%% The function compat_ty is just a convenience function to be able to
%% pattern match on types in a nice way.
-spec compat(type(), type(), map(), env()) -> compat_acc().
compat(T1, T2, Seen, Env) ->
?assert_normalized_anno(T1),
?assert_normalized_anno(T2),
Ty1 = fixpoint_normalize(T1, Env),
Ty2 = fixpoint_normalize(T2, Env),
case compat_seen({T1, T2}, Seen) of
true ->
ret(Seen);
false ->
compat_ty(Ty1, Ty2, maps:put({T1, T2}, true, Seen), Env)
end.
-spec fixpoint_normalize(type(), env()) -> type().
fixpoint_normalize(Ty, Env) ->
NormTy = normalize(Ty, Env),
case NormTy of
Ty -> Ty;
_ -> fixpoint_normalize(NormTy, Env)
end.
-spec compat_seen({type(), type()}, #{ {type(), type()} := true }) -> boolean().
compat_seen({T1, T2}, Seen) ->
maps:get({T1, T2}, Seen, false).
-spec compat_ty(type(), type(), map(), env()) -> compat_acc().
%% any() and term() are used as the unknown type in the gradual type system
compat_ty({type, _, any, []}, _, Seen, _Env) ->
ret(Seen);
compat_ty(_, {type, _, any ,[]}, Seen, _Env) ->
ret(Seen);
% gradualizer:top() is the top of the subtyping hierarchy
compat_ty(_, ?top(), Seen, _Env) ->
ret(Seen);
%% None is the bottom of the subtyping relation
compat_ty({type, _, none, []}, _, Seen, _Env) ->
ret(Seen);
%% Every type is subtype of itself
compat_ty(T, T, Seen, _Env) ->
ret(Seen);
%% Variables
compat_ty({var, _, Var}, Ty, Seen, _Env) ->
{Seen, constraints:upper(Var, Ty)};
compat_ty(Ty, {var, _, Var}, Seen, _Env) ->
{Seen, constraints:lower(Var, Ty)};
% TODO: There are several kinds of fun types.
% Add support for them all eventually
compat_ty({type, _, 'fun', [_, Res1]},
{type, _, 'fun', [{type, _, any}, Res2]},
Seen, Env) ->
%% We can assert the below,
%% as we know Res2 is not {type, _, any}, which is explicitely matched on above.
Res2 = ?assert_type(Res2, type()),
compat(Res1, Res2, Seen, Env);
compat_ty({type, _, 'fun', [{type, _, product, Args1}, Res1]},
{type, _, 'fun', [{type, _, product, Args2}, Res2]},
Seen, Env) ->
{Ap, Cs} = compat_tys(Args2, Args1, Seen, Env),
{Aps, Css} = compat(Res1, Res2, Ap, Env),
{Aps, constraints:combine(Cs, Css)};
%% Unions
compat_ty({type, _, union, Tys1}, {type, _, union, Tys2}, Seen, Env) ->
lists:foldl(fun (Ty1, {Seen1, C1}) ->
{Seen2, C2} = any_type(Ty1, Tys2, Seen1, Env),
{Seen2, constraints:combine(C1, C2)}
end, {Seen, constraints:empty()}, Tys1);
compat_ty(Ty1, {type, _, union, Tys2}, Seen, Env) ->
any_type(Ty1, Tys2, Seen, Env);
compat_ty({type, _, union, Tys1}, Ty2, Seen, Env) ->
all_type(Tys1, Ty2, Seen, Env);
% Integer types
compat_ty(Ty1, Ty2, Seen, _Env) when ?is_int_type(Ty1), ?is_int_type(Ty2) ->
case gradualizer_int:is_int_subtype(Ty1, Ty2) of
true -> ret(Seen);
false -> throw(nomatch)
end;
%% Atoms
compat_ty({atom, _, _Atom}, {type, _, atom, []}, Seen, _Env) ->
ret(Seen);
%% Binary, bitstring
%%
%% <<_:M, _:_*N>> means
%% a bitstring with bit size M + K*N (for any K)
%%
%% <<_:M1, _:_*N1>> is subtype of <<_:M2, _:_*N2>> if
%% for all K, there is an L such that
%% M1 + K*N1 == M2 + L*N2
%%
%% M1 M1+N1 M1+2*N1
%% T1 .............|.......|.......|...
%% T2 .....|...|...|...|...|...|...|...
%% M2 M2+L*N2
%%
compat_ty({type, _, binary, [{integer, _, M1}, {integer, _, N1}]},
{type, _, binary, [{integer, _, M2}, {integer, _, N2}]},
Seen, _Env)
when N2 > 0, M1 >= M2,
N1 rem N2 == 0,
(M1 - M2) rem N2 == 0 ->
ret(Seen);
%% Records with the same name, defined in different modules
%% TODO: Record equivallend on tuple form
compat_ty({type, P1, record, [{atom, _, Name}]},
{type, P2, record, [{atom, _, Name}]}, Seen, Env) ->
Fields1 = get_maybe_remote_record_fields(Name, P1, Env),
Fields2 = get_maybe_remote_record_fields(Name, P2, Env),
compat_record_fields(Fields1, Fields2, Seen, Env);
%% Records that have been refined on one side or the other
compat_ty({type, Anno1, record, [{atom, _, Name}|Fields1]},
{type, Anno2, record, [{atom, _, Name}|Fields2]}, Seen, Env) ->
AllFields1 = case Fields1 of [] -> get_record_fields_types(Name, Anno1, Env); _ -> Fields1 end,
AllFields2 = case Fields2 of [] -> get_record_fields_types(Name, Anno2, Env); _ -> Fields2 end,
compat_record_tys(AllFields1, AllFields2, Seen, Env);
compat_ty({type, _, record, _}, {type, _, tuple, any}, Seen, _Env) ->
ret(Seen);
%% Lists
compat_ty(Ty1, Ty2, Seen, Env) when ?is_list_type(Ty1), ?is_list_type(Ty2) ->
{Empty1, Elem1, Term1} = list_view(Ty1),
{Empty2, Elem2, Term2} = list_view(Ty2),
case {Empty1, Empty2} of
{E, E} -> ok;
{_, any} -> ok;
_ -> throw(nomatch)
end,
compat_tys([Elem1, Term1], [Elem2, Term2], Seen, Env);
%% Tuples
compat_ty({type, _, tuple, any}, {type, _, tuple, _Args}, Seen, _Env) ->
ret(Seen);
compat_ty({type, _, tuple, _Args}, {type, _, tuple, any}, Seen, _Env) ->
ret(Seen);
compat_ty({type, _, tuple, Args1}, {type, _, tuple, Args2}, Seen, Env) ->
compat_tys(Args1, Args2, Seen, Env);
%% Maps
compat_ty({type, _, map, [?any_assoc]}, {type, _, map, _Assocs}, Seen, _Env) ->
ret(Seen);
compat_ty({type, _, map, _Assocs}, {type, _, map, [?any_assoc]}, Seen, _Env) ->
ret(Seen);
compat_ty({type, _, map, Assocs1}, {type, _, map, Assocs2}, Seen, Env) ->
%% Please see: https://github.com/josefs/Gradualizer/wiki/Map-types#subtyping-rule-long-version
%% for the below rule definitions:
%% 2. For all mandatory associations K2 := V2 in M2,
%% there is a mandatory association K1 := V1 in M1...
IsMandatory = fun
({type, _, map_field_exact, _}) -> true;
(_) -> false
end,
MandatoryAssocs1 = lists:filter(IsMandatory, Assocs1),
MandatoryAssocs2 = lists:filter(IsMandatory, Assocs2),
{Seen3, Cs3} = lists:foldl(fun ({type, _, map_field_exact, _} = Assoc2, {Seen2, Cs2}) ->
%% This nested loop will only throw nomatch, if there's at least
%% one assoc in MandatoryAssocs1;
%% if that's not the case, let's throw now.
length(MandatoryAssocs1) == 0 andalso throw(nomatch),
case lists:foldl(fun
(_Assoc1, {Seen1, Cs1}) -> {Seen1, Cs1};
(Assoc1, nomatch) ->
try
compat(Assoc1, Assoc2, Seen2, Env)
catch
nomatch -> nomatch
end
end, nomatch, MandatoryAssocs1)
of
nomatch -> throw(nomatch);
{Seen1, Cs1} -> {Seen1, constraints:combine(Cs1, Cs2)}
end
end, ret(Seen), MandatoryAssocs2),
%% 1. For all associations K1 <Assoc1> V1 in M1,
%% there exists an association K2 <Assoc2> V2 in M2...
lists:foldl(fun (Assoc1, {As, Cs1}) ->
{Ax, Cs2} = any_type(Assoc1, Assocs2, As, Env),
{Ax, constraints:combine(Cs1, Cs2)}
end, {Seen3, Cs3}, Assocs1);
compat_ty({type, _, AssocTag1, [Key1, Val1]},
{type, _, AssocTag2, [Key2, Val2]}, Seen, Env)
when AssocTag1 == map_field_assoc, AssocTag2 == map_field_assoc;
AssocTag1 == map_field_exact, AssocTag2 == map_field_exact;
AssocTag1 == map_field_exact, AssocTag2 == map_field_assoc ->
%% For M1 <: M2, mandatory fields in M2 must be mandatory fields in M1
{Seen1, Cs1} = compat(Key1, Key2, Seen, Env),
{Seen2, Cs2} = compat(Val1, Val2, Seen1, Env),
{Seen2, constraints:combine(Cs1, Cs2)};
%% Opaque user types
compat_ty({user_type, Anno, Name, Args}, {user_type, Anno, Name, Args}, Seen, _Env) ->
ret(Seen);
compat_ty({user_type, Anno, Name, Args1}, {user_type, Anno, Name, Args2}, Seen, Env)
when length(Args1) == length(Args2) ->
lists:foldl(fun ({Arg1, Arg2}, {Seen1, Cs1}) ->
{Seen2, Cs2} = compat(Arg1, Arg2, Seen1, Env),
{Seen2, constraints:combine(Cs1, Cs2)}
end, ret(Seen), lists:zip(Args1, Args2));
compat_ty(_Ty1, _Ty2, _, _) ->
throw(nomatch).
-spec compat_tys([type()], [type()], map(), env()) -> compat_acc().
compat_tys([], [], Seen, _Env) ->
ret(Seen);
compat_tys([Ty1|Tys1], [Ty2|Tys2], Seen, Env) ->
{Seen1, Cs} = compat(Ty1 ,Ty2, Seen, Env),
{Seen2, Css} = compat_tys(Tys1, Tys2, Seen1, Env),
{Seen2, constraints:combine(Cs, Css)};
compat_tys(_Tys1, _Tys2, _, _) ->
throw(nomatch).
-spec compat_record_tys([type()], [type()], map(), env()) -> compat_acc().
compat_record_tys([], [], Seen, _Env) ->
ret(Seen);
compat_record_tys([?type_field_type(Name, Field1)|Fields1], [?type_field_type(Name, Field2)|Fields2], Seen, Env) ->
{Seen1, Cs1} = compat(Field1, Field2, Seen, Env),
{Seen2, Cs2} = compat_record_tys(Fields1, Fields2, Seen1, Env),
{Seen2, constraints:combine(Cs1, Cs2)};
compat_record_tys(_, _, _, _) ->
%% Mismatching number of fields
throw(nomatch).
%% Two records are compatible if they have the same name (defined in different
%% modules) and they have the same number of fields and the field types match.
-spec compat_record_fields([_], [_], map(), env()) -> compat_acc().
compat_record_fields([], [], Seen, _Env) ->
ret(Seen);
compat_record_fields([{typed_record_field, _NameAndDefaultValue1, T1} | Fs1],
[{typed_record_field, _NameAndDefaultValue2, T2} | Fs2],
Seen, Env) ->
{Seen1, Cs1} = compat(T1, T2, Seen, Env),
{Seen2, Cs2} = compat_record_fields(Fs1, Fs2, Seen1, Env),
{Seen2, constraints:combine(Cs1, Cs2)};
compat_record_fields(_, _, _, _) ->
%% Mismatching number of fields
throw(nomatch).
%% Returns a successful matching of two types. Convenience function for when
%% there were no type variables involved.
-spec ret(Seen) -> acc(Seen) when
Seen :: map() | type().
ret(Seen) ->
{Seen, constraints:empty()}.
-spec any_type(type(), [type()], map(), env()) -> compat_acc().
any_type(_Ty, [], _Seen, _Env) ->
throw(nomatch);
any_type(Ty, [Ty1|Tys], Seen, Env) ->
try
%% TODO: Don't drop the constraint here.
%% This requires a radically different representation of constraints
%% which allows to represent unions of constraints
{Ret, _Cs} = compat(Ty, Ty1, Seen, Env),
{Ret, constraints:empty()}
catch
nomatch ->
any_type(Ty, Tys, Seen, Env)
end.
%% @doc All types in `Tys' must be compatible with `Ty'.
%% Returns all the gather memoizations and constraints.
%% Does not return (throws `nomatch') if any of the types is not compatible.
-spec all_type([type()], type(), map(), env()) -> compat_acc().
all_type(Tys, Ty, Seen, Env) ->
all_type(Tys, Ty, Seen, [], Env).
-spec all_type([type()], type(), map(), [constraints:t()], env()) -> compat_acc().
all_type([], _Ty, Seen, Css, _Env) ->
{Seen, constraints:combine(Css)};
all_type([Ty1|Tys], Ty, AIn, Css, Env) ->
{AOut, Cs} = compat(Ty1, Ty, AIn, Env),
all_type(Tys, Ty, AOut, [Cs|Css], Env).
%% Looks up the fields of a record by name and, if present, by the module where
%% it belongs if a filename is included in the Anno.
-spec get_maybe_remote_record_fields(RecName :: atom(),
Anno :: erl_anno:anno(),
Env :: env()) ->
[{typed_record_field, _, type()}].
get_maybe_remote_record_fields(RecName, Anno, Env) ->
case typelib:get_module_from_annotation(Anno) of
{ok, Module} ->
%% A record type in another module, from an expanded remote type
case gradualizer_db:get_record_type(Module, RecName) of
{ok, TypedRecordFields} ->
TypedRecordFields;
not_found ->
throw(undef(record, Anno, {Module, RecName}))
end;
none ->
%% Local record type
get_record_fields(RecName, Anno, Env)
end.
%% Looks up a record in the supplied type environment and returns its typed
%% fields.
-spec get_record_fields(RecName, Anno, Env) -> [typed_record_field()] when
RecName :: atom(),
Anno :: erl_anno:anno(),
Env :: env().
get_record_fields(RecName, _Anno, #env{tenv = #{records := REnv}}) ->
maps:get(RecName, REnv). % It must exist. Otherwise it's a compile error.
%% Greatest lower bound
%% --------------------
%%
%% * Computes the maximal (in the subtyping hierarchy) type that is a subtype
%% of two given types.
-type glb_acc() :: acc(type()).
-spec glb(type(), type(), env()) -> glb_acc().
glb(T1, T2, Env) ->
glb(T1, T2, #{}, Env).
-spec glb([type()], env()) -> glb_acc().
glb(Ts, Env) ->
lists:foldl(fun (T, {TyAcc, Cs1}) ->
{Ty, Cs2} = glb(T, TyAcc, Env),
{Ty, constraints:combine(Cs1, Cs2)}
end,
{top(), constraints:empty()},
Ts).
-spec glb(type(), type(), map(), env()) -> glb_acc().
glb(T1, T2, A, Env) ->
case stop_glb_recursion(T1, T2, A) of
%% If we hit a recursive case we approximate with none(). Conceivably
%% you could do some fixed point iteration here, but let's wait for an
%% actual use case.
true -> {type(none), constraints:empty()};
false ->
Module = maps:get(module, Env#env.tenv),
case gradualizer_cache:get_glb(Module, T1, T2) of
false ->
Ty1 = normalize(T1, Env),
Ty2 = normalize(T2, Env),
{Ty, Cs} = glb_ty(Ty1, Ty2, A#{ {T1, T2} => 0 }, Env),
NormTy = normalize(Ty, Env),
gradualizer_cache:store_glb(Module, T1, T2, {NormTy, Cs}),
{NormTy, Cs};
TyCs ->
%% these two types have already been seen and calculated
TyCs
end
end.
%% A standalone function is easier to debug / trace.
-spec stop_glb_recursion(type(), type(), #{ {type(), type()} := any() }) -> boolean().
stop_glb_recursion(T1, T2, A) ->
maps:is_key({T1, T2}, A).
-spec glb_ty(type(), type(), map(), env()) -> glb_acc().
%% none() is the bottom of the hierarchy
glb_ty({type, _, none, []} = Ty1, _Ty2, _A, _Env) ->
ret(Ty1);
glb_ty(_Ty1, {type, _, none, []} = Ty2, _A, _Env) ->
ret(Ty2);
%% We don't know anything if either type is any()
glb_ty({type, _, any, []} = Ty1, _Ty2, _A, _Env) ->
ret(Ty1);
glb_ty(_Ty1, {type, _, any, []} = Ty2, _A, _Env) ->
ret(Ty2);
%% gradualizer:top() is the top of the hierarchy
glb_ty(?top(), Ty2, _A, _Env) ->
ret(Ty2);
glb_ty(Ty1, ?top(), _A, _Env) ->
ret(Ty1);
%% glb is idempotent
glb_ty(Ty, Ty, _A, _Env) ->
ret(Ty);
%% Type variables. TODO: can we get here with constrained type variables?
glb_ty(Var = {var, _, VarName}, Ty2, _A, _Env) ->
V = gradualizer_tyvar:new(VarName, ?MODULE, ?LINE),
{{var, erl_anno:new(0), V},
constraints:add_var(V,
constraints:combine(constraints:upper(V, Var),
constraints:upper(V, Ty2)))};
glb_ty(Ty1, Var = {var, _, VarName}, _A, _Env) ->
V = gradualizer_tyvar:new(VarName, ?MODULE, ?LINE),
{{var, erl_anno:new(0), V},
constraints:add_var(V,
constraints:combine(constraints:upper(V, Var),
constraints:upper(V, Ty1)))};
%% Union types: glb distributes over unions
glb_ty({type, Ann, union, Ty1s}, Ty2, A, Env) ->
{Tys, Css} = lists:unzip([ glb(Ty1, Ty2, A, Env) || Ty1 <- Ty1s ]),
{{type, Ann, union, Tys}, constraints:combine(Css)};
glb_ty(Ty1, {type, Ann, union, Ty2s}, A, Env) ->
{Tys, Css} = lists:unzip([glb(Ty1, Ty2, A, Env) || Ty2 <- Ty2s ]),
{{type, Ann, union, Tys}, constraints:combine(Css)};
%% Atom types
glb_ty(Ty1 = {atom, _, _}, {type, _, atom, []}, _A, _Env) ->
ret(Ty1);
glb_ty({type, _, atom, []}, Ty2 = {atom, _, _}, _A, _Env) ->
ret(Ty2);
%% Number types
glb_ty(Ty1, Ty2, _A, _Env) when ?is_int_type(Ty1), ?is_int_type(Ty2) ->
Glb = gradualizer_int:int_type_glb(Ty1, Ty2),
ret(Glb);
%% List types
glb_ty(Ty1, Ty2, A, Env) when ?is_list_type(Ty1), ?is_list_type(Ty2) ->
{Empty1, Elem1, Term1} = list_view(Ty1),
{Empty2, Elem2, Term2} = list_view(Ty2),
Empty =
case {Empty1, Empty2} of
{E, E} -> E;
{any, E} -> E;
{E, any} -> E;
{empty, nonempty} -> none;
{nonempty, empty} -> none
end,
{Elem, Cs1} = glb(Elem1, Elem2, A, Env),
{Term, Cs2} = glb(Term1, Term2, A, Env),
{from_list_view({Empty, Elem, Term}), constraints:combine(Cs1, Cs2)};
%% Tuple types
glb_ty(Ty1 = {type, _, tuple, Tys1}, Ty2 = {type, _, tuple, Tys2}, A, Env) ->
case {Tys1, Tys2} of
{any, _} -> ret(Ty2);
{_, any} -> ret(Ty1);
_ when length(Tys1) /= length(Tys2) -> ret(type(none));
_ ->
{Tys, Css} = lists:unzip(lists:zipwith(fun(T1, T2) ->
glb(T1, T2, A, Env)
end,
Tys1, Tys2)),
TupleType = case lists:any(fun(?type(none)) -> true; (_) -> false end, Tys) of
true ->
type(none);
false ->
type(tuple, Tys)
end,
{TupleType, constraints:combine(Css)}
end;
%% Record types. Either exactly the same record (handled above) or tuple().
glb_ty(Ty1 = {type, _, record, _}, {type, _, tuple, any}, _A, _Env) ->
ret(Ty1);
glb_ty({type, _, tuple, any}, Ty2 = {type, _, record, _}, _A, _Env) ->
ret(Ty2);
glb_ty({type, _, record, _}, {type, _, record, _}, _A, _Env) ->
ret(type(none));
%% Map types. These are a bit tricky.
%% For now going with a very crude approximation.
glb_ty(Ty1 = {type, _, map, Assocs1}, Ty2 = {type, _, map, Assocs2}, A, Env) ->
case {Assocs1, Assocs2} of
%% TODO: add a test case
{[?any_assoc], _} -> ret(Ty2);
{_, [?any_assoc]} -> ret(Ty1);
_ ->
%% TODO: Too simplistic!
%% We're not capable of handling overlapping keys without intersection
%% and negation types!
case {has_overlapping_keys(Ty1, Env), has_overlapping_keys(Ty2, Env)} of
{false, false} ->
{NewAssocs0, Css} = lists:unzip([ glb(As1, As2, A, Env) || As1 <- Assocs1,
As2 <- Assocs2 ]),
NewAssocs = lists:filter(fun(?type(none)) -> false; (_) -> true end, NewAssocs0),
case NewAssocs of
[] ->
ret(type(none));
[_|_] ->
{type(map, NewAssocs), constraints:combine(Css)}
end;
_ ->
ret(type(none))
end
end;
glb_ty(?type(AssocTag1, [Key1, Val1]), ?type(AssocTag2, [Key2, Val2]), A, Env)
when AssocTag1 == map_field_assoc, AssocTag2 == map_field_assoc;
AssocTag1 == map_field_exact, AssocTag2 == map_field_exact;
AssocTag1 == map_field_exact, AssocTag2 == map_field_assoc;
AssocTag1 == map_field_assoc, AssocTag2 == map_field_exact ->
AssocTag = case {AssocTag1, AssocTag2} of
{map_field_exact, map_field_exact} -> map_field_exact;
{map_field_exact, map_field_assoc} -> map_field_exact;
{map_field_assoc, map_field_exact} -> map_field_exact;
{map_field_assoc, map_field_assoc} -> map_field_assoc
end,
{Key, Cs1} = case {Key1, AssocTag, Key2} of
{?type(any), map_field_assoc, ?type(any)} -> ret(type(any));
{_, map_field_exact, ?type(any)} -> ret(Key1);
{?type(any), map_field_exact, _} -> ret(Key2);
{_, _, _} -> glb(Key1, Key2, A, Env)
%{_, _, _} -> ret(type(none))
end,
{Val, Cs2} = case {Val1, AssocTag, Val2} of
{?type(any), map_field_assoc, ?type(any)} -> ret(type(any));
{_, map_field_exact, ?type(any)} -> ret(Val1);
{?type(any), map_field_exact, _} -> ret(Val2);
{_, _, _} -> glb(Val1, Val2, A, Env)
%{_, _, _} -> ret(type(none))
end,
case lists:any(fun(?type(none)) -> true; (_) -> false end, [Key, Val]) of
true ->
ret(type(none));
false ->
{type(AssocTag, [Key, Val]), constraints:combine(Cs1, Cs2)}
end;
%% Binary types. For now approximate this by returning the smallest type if
%% they are comparable, otherwise none(). See the corresponding case in
%% compat_ty for the subtyping rule.
glb_ty(Ty1 = {type, _, binary, _},
Ty2 = {type, _, binary, _}, _A, Env) ->
case subtype(Ty1, Ty2, Env) of
{true, _} -> ret(Ty1); %% Will never produce constraints
false ->
case subtype(Ty2, Ty1, Env) of
{true, _} -> ret(Ty2);
false -> ret(type(none))
end
end;
%% Function types. Would require lub on arguments for proper implementation.
%% For now pick biggest arguments when comparable and none() otherwise.
glb_ty({type, _, 'fun', [{type, _, product, Args1}, Res1]},
{type, _, 'fun', [{type, _, product, Args2}, Res2]}, A, Env) ->
NoConstraints = constraints:empty(),
{Res, Cs} = glb(Res1, Res2, A, Env),
Subtype =
fun(Ts1, Ts2) ->
try compat_tys(Ts1, Ts2, maps:new(), Env) of
{_, NoConstraints} -> true;
_ -> false
catch throw:nomatch -> false end
end,
case Subtype(Args1, Args2) of
true -> {type('fun', [type(product, Args2), Res]), Cs};
false ->
case Subtype(Args2, Args1) of
true -> {type('fun', [type(product, Args1), Res]), Cs};
false -> {type(none), Cs}
end
end;
glb_ty({type, _, 'fun', [{type, _, any} = Any, Res1]},
{type, _, 'fun', [{type, _, any}, Res2]}, A, Env) ->
{Res, Cs} = glb(Res1, Res2, A, Env),
{type('fun', [Any, Res]), Cs};
glb_ty({type, _, 'fun', [{type, _, any}, Res1]},
{type, _, 'fun', [{type, _, product, _} = TArgs2, _]} = T2, A, Env) ->
glb(type('fun', [TArgs2, Res1]), T2, A, Env);
glb_ty({type, _, 'fun', [{type, _, product, _} = TArgs1, _]} = T1,
{type, _, 'fun', [{type, _, any}, Res2]}, A, Env) ->
glb(T1, type('fun', [TArgs1, Res2]), A, Env);
%% normalize only does the top layer
glb_ty({type, _, Name, Args1}, {type, _, Name, Args2}, A, Env)
when length(Args1) == length(Args2) ->
{Args, Css} = lists:unzip([ glb(Arg1, Arg2, A, Env) || {Arg1, Arg2} <- lists:zip(Args1, Args2) ]),
{type(Name, Args), constraints:combine(Css)};
%% Incompatible
glb_ty(_Ty1, _Ty2, _A, _Env) -> {type(none), constraints:empty()}.
-spec has_overlapping_keys(type(), env()) -> boolean().
has_overlapping_keys({type, _, map, Assocs}, Env) ->
Cart = [ case {subtype(As1, As2, Env), subtype(As2, As1, Env)} of
{false, false} ->
false;
{_R1, _R2} ->
true
end
|| As1 <- ?assert_type(Assocs, list()),
As2 <- ?assert_type(Assocs, list()),
As1 /= As2 ],
lists:any(fun(X) -> X end, Cart).
-spec lub([type()], env()) -> type().
lub(Tys, Env) ->
normalize(type(union, Tys), Env).
%% Normalize
%% ---------
%%
%% * Expand user-defined and remote types on head level (except opaque types)
%% * Replace built-in type synonyms
%% * Flatten unions and merge overlapping types (e.g. ranges) in unions
-spec normalize(type(), env()) -> type().
normalize(Ty, Env) ->
normalize_rec(Ty, Env).
%% The third argument is a set of user types that we've already unfolded.
%% It's important that we don't keep unfolding such types because it will
%% lead to infinite recursion.
-spec normalize_rec(type(), env()) -> type().
normalize_rec({type, _, union, Tys}, Env) ->
UnionSizeLimit = Env#env.union_size_limit,
Types = flatten_unions(Tys, Env),
case merge_union_types(Types, Env) of
[] -> type(none);
[T] -> T;
%% Performance hack: Unions larger than this value are replaced by any().
Ts when length(Ts) > UnionSizeLimit -> type(any);
Ts -> type(union, Ts)
end;
normalize_rec({user_type, _, Name, Args} = Type, Env) ->
case gradualizer_lib:get_type_definition(Type, Env, []) of
{ok, T} ->
normalize_rec(T, Env);
opaque ->
Type;
not_found ->
P = position_info_from_spec(Env#env.current_spec),
throw(undef(user_type, P, {Name, arity(length(Args))}))
end;
normalize_rec(T = ?top(), _Env) ->
%% Don't normalize gradualizer:top().
T;
normalize_rec({remote_type, _, [{atom, _, M}, {atom, _, N}, Args]}, Env) ->
%% It's safe as we explicitly match out `Module :: af_atom()' and `TypeName :: af_atom()'.
Args = ?assert_type(Args, [type()]),
P = position_info_from_spec(Env#env.current_spec),
case gradualizer_db:get_exported_type(M, N, Args) of
{ok, T} ->
normalize_rec(T, Env);
opaque ->
NormalizedArgs = lists:map(fun (Ty) -> normalize_rec(Ty, Env) end, Args),
Ty = {user_type, 0, N, NormalizedArgs},
typelib:annotate_user_type(M, ?assert_type(Ty, type()));
not_exported ->
throw(not_exported(remote_type, P, {M, N, arity(length(Args))}));
not_found ->
throw(undef(remote_type, P, {M, N, arity(length(Args))}))
end;
normalize_rec({op, _, _, _Arg} = Op, _Env) ->
erl_eval:partial_eval(Op);
normalize_rec({op, _, _, _Arg1, _Arg2} = Op, _Env) ->
erl_eval:partial_eval(Op);
normalize_rec({type, Ann, range, [T1, T2]}, Env) ->
{type, Ann, range, [normalize_rec(T1, Env),
normalize_rec(T2, Env)]};
normalize_rec(Type, _Env) ->
expand_builtin_aliases(Type).
%% Replace built-in type aliases
-spec expand_builtin_aliases(type()) -> type().
expand_builtin_aliases({var, Ann, '_'}) ->
{type, Ann, any, []};
expand_builtin_aliases({type, Ann, term, []}) ->
{type, Ann, any, []};
expand_builtin_aliases({type, Ann, binary, []}) ->
{type, Ann, binary, [{integer, Ann, 0}, {integer, Ann, 8}]};
expand_builtin_aliases({type, Ann, nonempty_binary, []}) ->
{type, Ann, binary, [{integer, Ann, 8}, {integer, Ann, 8}]};
expand_builtin_aliases({type, Ann, bitstring, []}) ->
{type, Ann, binary, [{integer, Ann, 0}, {integer, Ann, 1}]};
expand_builtin_aliases({type, Ann, nonempty_bitstring, []}) ->
{type, Ann, binary, [{integer, Ann, 1}, {integer, Ann, 1}]};
expand_builtin_aliases({type, Ann, boolean, []}) ->
{type, Ann, union, [{atom, Ann, false}, {atom, Ann, true}]};
expand_builtin_aliases({type, Ann, bool, []}) ->
{type, Ann, union, [{atom, Ann, false}, {atom, Ann, true}]};
expand_builtin_aliases({type, Ann, byte, []}) ->
{type, Ann, range, [{integer, Ann, 0}, {integer, Ann, 255}]};
expand_builtin_aliases({type, Ann, char, []}) ->
{type, Ann, range, [{integer, Ann, 0}, {integer, Ann, 16#10ffff}]};
expand_builtin_aliases({type, Ann, number, []}) ->
{type, Ann, union, [{type, Ann, integer, []}, {type, Ann, float, []}]};
expand_builtin_aliases({type, Ann, list, []}) ->
{type, Ann, list, [{type, Ann, any, []}]};
expand_builtin_aliases({type, Ann, maybe_improper_list, []}) ->
{type, Ann, maybe_improper_list, [{type, Ann, any, []},
{type, Ann, any, []}]};
expand_builtin_aliases({type, Ann, nonempty_list, []}) ->
{type, Ann, nonempty_list, [{type, Ann, any, []}]};
expand_builtin_aliases({type, Ann, string, []}) ->
{type, Ann, list, [{type, Ann, char, []}]};
expand_builtin_aliases({type, Ann, nonempty_string, []}) ->
{type, Ann, nonempty_list, [{type, Ann, char, []}]};
expand_builtin_aliases({type, Ann, iodata, []}) ->
{type, Ann, union, [{type, Ann, iolist, []}, {type, Ann, binary, []}]};
expand_builtin_aliases({type, Ann, iolist, []}) ->
%% recursive type
Union = [{type, Ann, byte, []},
{type, Ann, binary, []},
{type, Ann, iolist, []}],
Tail = [{type, Ann, nil, []},
{type, Ann, binary, []}],
{type, Ann, maybe_improper_list, [{type, Ann, union, Union},
{type, Ann, union, Tail}]};
expand_builtin_aliases({type, Ann, map, any}) ->
{type, Ann, map, [{type, Ann, map_field_assoc, [{type, Ann, any, []},
{type, Ann, any, []}]}]};
expand_builtin_aliases({type, Ann, function, []}) ->
{type, Ann, 'fun', [{type, Ann, any}, {type, Ann, any, []}]};
expand_builtin_aliases({type, Ann, 'fun', []}) ->
%% `fun()' is not a built-in alias per the erlang docs
%% but it is equivalent with `fun((...) -> any())'
{type, Ann, 'fun', [{type, Ann, any}, {type, Ann, any, []}]};
expand_builtin_aliases({type, Ann, module, []}) ->
{type, Ann, atom, []};
expand_builtin_aliases({type, Ann, mfa, []}) ->
{type, Ann, tuple, [{type, Ann, module, []},
{type, Ann, atom, []},
{type, Ann, arity, []}]};
expand_builtin_aliases({type, Ann, arity, []}) ->
{type, Ann, range, [{integer, Ann, 0}, {integer, Ann, 255}]};
expand_builtin_aliases({type, Ann, identifier, []}) ->
{type, Ann, union, [{type, Ann, pid, []},
{type, Ann, port, []},
{type, Ann, reference, []}]};
expand_builtin_aliases({type, Ann, node, []}) ->
{type, Ann, atom, []};
expand_builtin_aliases({type, Ann, timeout, []}) ->
{type, Ann, union, [{atom, Ann, infinity},
{type, Ann, non_neg_integer, []}]};
expand_builtin_aliases({type, Ann, no_return, []}) ->
{type, Ann, none, []};
%% TODO: This is a kludge by which lists of types slip through calls to normalize().
%% Specifically, lists of Types representing bounded fun clauses.
expand_builtin_aliases(Type) ->
Type.
%% Flattens nested unions
%%
%% Mutually recursive with normalize/2
%%
%% * Normalize each element
%% * TODO: Detect user-defined and remote types expanding to themselves
%% or to unions containing themselves (using memoization?)
%% * Remove subtypes of other types in the same union; keeping any() separate
%% * Merge integer types, including singleton integers and ranges
%% 1, 1..5, integer(), non_neg_integer(), pos_integer(), neg_integer()
-spec flatten_unions([type()], env()) -> [type()].
flatten_unions(Tys, Env) ->
lists:flatmap(fun (Ty) -> flatten_union(Ty, Env) end, Tys).
-spec flatten_union(type(), env()) -> [type()].
flatten_union({user_type, _, _, _} = Ty, _Env) ->
[Ty];
flatten_union({type, _, none, []}, _Env) ->
[];
flatten_union({type, _, no_return, []}, _Env) ->
%% This is an alias for `none()' which should've been removed by `expand_builtin_aliases',
%% but there's no guarantee the latter has been called by now.
%% If it wasn't, `fixpoint_normalize' might alternate between a union with `none()'
%% and without it and never stop.
%% Caught thanks to `prop_compatible' test.
[];
flatten_union({type, _, union, Tys}, Env) ->
flatten_unions(Tys, Env);
flatten_union(Ty, Env) ->
[normalize_rec(Ty, Env)].