"""Type inference constraints."""

from typing import Iterable, List, Optional, Sequence

from mypy import experiments
from mypy.types import (
    CallableType, Type, TypeVisitor, UnboundType, AnyType, NoneTyp, TypeVarType, Instance,
    TupleType, TypedDictType, UnionType, Overloaded, ErasedType, PartialType, DeletedType,
    UninhabitedType, TypeType, TypeVarId, TypeQuery, is_named_instance, TypeOfAny
)
from mypy.maptype import map_instance_to_supertype
from mypy import nodes
import mypy.subtypes
from mypy.sametypes import is_same_type
from mypy.erasetype import erase_typevars


SUBTYPE_OF = 0  # type: int
SUPERTYPE_OF = 1  # type: int


class Constraint:
    """A representation of a type constraint.

    It can be either T <: type or T :> type (T is a type variable).
    """

    type_var = None  # type: TypeVarId
    op = 0           # SUBTYPE_OF or SUPERTYPE_OF
    target = None    # type: Type

    def __init__(self, type_var: TypeVarId, op: int, target: Type) -> None:
        self.type_var = type_var
        self.op = op
        self.target = target

    def __repr__(self) -> str:
        op_str = '<:'
        if self.op == SUPERTYPE_OF:
            op_str = ':>'
        return '{} {} {}'.format(self.type_var, op_str, self.target)


def infer_constraints_for_callable(
        callee: CallableType, arg_types: Sequence[Optional[Type]], arg_kinds: List[int],
        formal_to_actual: List[List[int]]) -> List[Constraint]:
    """Infer type variable constraints for a callable and actual arguments.

    Return a list of constraints.
    """
    constraints = []  # type: List[Constraint]
    tuple_counter = [0]

    for i, actuals in enumerate(formal_to_actual):
        for actual in actuals:
            actual_arg_type = arg_types[actual]
            if actual_arg_type is None:
                continue

            actual_type = get_actual_type(actual_arg_type, arg_kinds[actual],
                                          tuple_counter)
            c = infer_constraints(callee.arg_types[i], actual_type,
                                  SUPERTYPE_OF)
            constraints.extend(c)

    return constraints


def get_actual_type(arg_type: Type, kind: int,
                    tuple_counter: List[int]) -> Type:
    """Return the type of an actual argument with the given kind.

    If the argument is a *arg, return the individual argument item.
    """

    if kind == nodes.ARG_STAR:
        if isinstance(arg_type, Instance):
            if arg_type.type.fullname() == 'builtins.list':
                # List *arg.
                return arg_type.args[0]
            elif arg_type.args:
                # TODO try to map type arguments to Iterable
                return arg_type.args[0]
            else:
                return AnyType(TypeOfAny.from_error)
        elif isinstance(arg_type, TupleType):
            # Get the next tuple item of a tuple *arg.
            tuple_counter[0] += 1
            return arg_type.items[tuple_counter[0] - 1]
        else:
            return AnyType(TypeOfAny.from_error)
    elif kind == nodes.ARG_STAR2:
        if isinstance(arg_type, Instance) and (arg_type.type.fullname() == 'builtins.dict'):
            # Dict **arg. TODO more general (Mapping)
            return arg_type.args[1]
        else:
            return AnyType(TypeOfAny.from_error)
    else:
        # No translation for other kinds.
        return arg_type


def infer_constraints(template: Type, actual: Type,
                      direction: int) -> List[Constraint]:
    """Infer type constraints.

    Match a template type, which may contain type variable references,
    recursively against a type which does not contain (the same) type
    variable references. The result is a list of type constrains of
    form 'T is a supertype/subtype of x', where T is a type variable
    present in the template and x is a type without reference to type
    variables present in the template.

    Assume T and S are type variables. Now the following results can be
    calculated (read as '(template, actual) --> result'):

      (T, X)            -->  T :> X
      (X[T], X[Y])      -->  T <: Y and T :> Y
      ((T, T), (X, Y))  -->  T :> X and T :> Y
      ((T, S), (X, Y))  -->  T :> X and S :> Y
      (X[T], Any)       -->  T <: Any and T :> Any

    The constraints are represented as Constraint objects.
    """

    # If the template is simply a type variable, emit a Constraint directly.
    # We need to handle this case before handling Unions for two reasons:
    #  1. "T <: Union[U1, U2]" is not equivalent to "T <: U1 or T <: U2",
    #     because T can itself be a union (notably, Union[U1, U2] itself).
    #  2. "T :> Union[U1, U2]" is logically equivalent to "T :> U1 and
    #     T :> U2", but they are not equivalent to the constraint solver,
    #     which never introduces new Union types (it uses join() instead).
    if isinstance(template, TypeVarType):
        return [Constraint(template.id, direction, actual)]

    # Now handle the case of either template or actual being a Union.
    # For a Union to be a subtype of another type, every item of the Union
    # must be a subtype of that type, so concatenate the constraints.
    if direction == SUBTYPE_OF and isinstance(template, UnionType):
        res = []
        for t_item in template.items:
            res.extend(infer_constraints(t_item, actual, direction))
        return res
    if direction == SUPERTYPE_OF and isinstance(actual, UnionType):
        res = []
        for a_item in actual.items:
            res.extend(infer_constraints(template, a_item, direction))
        return res

    # Now the potential subtype is known not to be a Union or a type
    # variable that we are solving for. In that case, for a Union to
    # be a supertype of the potential subtype, some item of the Union
    # must be a supertype of it.
    if direction == SUBTYPE_OF and isinstance(actual, UnionType):
        # If some of items is not a complete type, disregard that.
        items = simplify_away_incomplete_types(actual.items)
        # We infer constraints eagerly -- try to find constraints for a type
        # variable if possible. This seems to help with some real-world
        # use cases.
        return any_constraints(
            [infer_constraints_if_possible(template, a_item, direction)
             for a_item in items],
            eager=True)
    if direction == SUPERTYPE_OF and isinstance(template, UnionType):
        # When the template is a union, we are okay with leaving some
        # type variables indeterminate. This helps with some special
        # cases, though this isn't very principled.
        return any_constraints(
            [infer_constraints_if_possible(t_item, actual, direction)
             for t_item in template.items],
            eager=False)

    # Remaining cases are handled by ConstraintBuilderVisitor.
    return template.accept(ConstraintBuilderVisitor(actual, direction))


def infer_constraints_if_possible(template: Type, actual: Type,
                                  direction: int) -> Optional[List[Constraint]]:
    """Like infer_constraints, but return None if the input relation is
    known to be unsatisfiable, for example if template=List[T] and actual=int.
    (In this case infer_constraints would return [], just like it would for
    an automatically satisfied relation like template=List[T] and actual=object.)
    """
    if (direction == SUBTYPE_OF and
            not mypy.subtypes.is_subtype(erase_typevars(template), actual)):
        return None
    if (direction == SUPERTYPE_OF and
            not mypy.subtypes.is_subtype(actual, erase_typevars(template))):
        return None
    return infer_constraints(template, actual, direction)


def any_constraints(options: List[Optional[List[Constraint]]], eager: bool) -> List[Constraint]:
    """Deduce what we can from a collection of constraint lists.

    It's a given that at least one of the lists must be satisfied. A
    None element in the list of options represents an unsatisfiable
    constraint and is ignored.  Ignore empty constraint lists if eager
    is true -- they are always trivially satisfiable.
    """
    if eager:
        valid_options = [option for option in options if option]
    else:
        valid_options = [option for option in options if option is not None]
    if len(valid_options) == 1:
        return valid_options[0]
    elif (len(valid_options) > 1 and
          all(is_same_constraints(valid_options[0], c)
              for c in valid_options[1:])):
        # Multiple sets of constraints that are all the same. Just pick any one of them.
        # TODO: More generally, if a given (variable, direction) pair appears in
        #       every option, combine the bounds with meet/join.
        return valid_options[0]

    # Otherwise, there are either no valid options or multiple, inconsistent valid
    # options. Give up and deduce nothing.
    return []


def is_same_constraints(x: List[Constraint], y: List[Constraint]) -> bool:
    for c1 in x:
        if not any(is_same_constraint(c1, c2) for c2 in y):
            return False
    for c1 in y:
        if not any(is_same_constraint(c1, c2) for c2 in x):
            return False
    return True


def is_same_constraint(c1: Constraint, c2: Constraint) -> bool:
    return (c1.type_var == c2.type_var
            and c1.op == c2.op
            and is_same_type(c1.target, c2.target))


def simplify_away_incomplete_types(types: List[Type]) -> List[Type]:
    complete = [typ for typ in types if is_complete_type(typ)]
    if complete:
        return complete
    else:
        return types


def is_complete_type(typ: Type) -> bool:
    """Is a type complete?

    A complete doesn't have uninhabited type components or (when not in strict
    optional mode) None components.
    """
    return typ.accept(CompleteTypeVisitor())


class CompleteTypeVisitor(TypeQuery[bool]):
    def __init__(self) -> None:
        super().__init__(all)

    def visit_uninhabited_type(self, t: UninhabitedType) -> bool:
        return False


class ConstraintBuilderVisitor(TypeVisitor[List[Constraint]]):
    """Visitor class for inferring type constraints."""

    # The type that is compared against a template
    # TODO: The value may be None. Is that actually correct?
    actual = None  # type: Type

    def __init__(self, actual: Type, direction: int) -> None:
        # Direction must be SUBTYPE_OF or SUPERTYPE_OF.
        self.actual = actual
        self.direction = direction

    # Trivial leaf types

    def visit_unbound_type(self, template: UnboundType) -> List[Constraint]:
        return []

    def visit_any(self, template: AnyType) -> List[Constraint]:
        return []

    def visit_none_type(self, template: NoneTyp) -> List[Constraint]:
        return []

    def visit_uninhabited_type(self, template: UninhabitedType) -> List[Constraint]:
        return []

    def visit_erased_type(self, template: ErasedType) -> List[Constraint]:
        return []

    def visit_deleted_type(self, template: DeletedType) -> List[Constraint]:
        return []

    # Errors

    def visit_partial_type(self, template: PartialType) -> List[Constraint]:
        # We can't do anything useful with a partial type here.
        assert False, "Internal error"

    # Non-trivial leaf type

    def visit_type_var(self, template: TypeVarType) -> List[Constraint]:
        assert False, ("Unexpected TypeVarType in ConstraintBuilderVisitor"
                       " (should have been handled in infer_constraints)")

    # Non-leaf types

    def visit_instance(self, template: Instance) -> List[Constraint]:
        original_actual = actual = self.actual
        res = []  # type: List[Constraint]
        if isinstance(actual, CallableType) and actual.fallback is not None:
            actual = actual.fallback
        if isinstance(actual, TypedDictType):
            actual = actual.as_anonymous().fallback
        if isinstance(actual, Instance):
            instance = actual
            # We always try nominal inference if possible,
            # it is much faster than the structural one.
            if (self.direction == SUBTYPE_OF and
                    template.type.has_base(instance.type.fullname())):
                mapped = map_instance_to_supertype(template, instance.type)
                for i in range(len(instance.args)):
                    # The constraints for generic type parameters are
                    # invariant. Include constraints from both directions
                    # to achieve the effect.
                    res.extend(infer_constraints(
                        mapped.args[i], instance.args[i], self.direction))
                    res.extend(infer_constraints(
                        mapped.args[i], instance.args[i], neg_op(self.direction)))
                return res
            elif (self.direction == SUPERTYPE_OF and
                    instance.type.has_base(template.type.fullname())):
                mapped = map_instance_to_supertype(instance, template.type)
                for j in range(len(template.args)):
                    # The constraints for generic type parameters are
                    # invariant.
                    res.extend(infer_constraints(
                        template.args[j], mapped.args[j], self.direction))
                    res.extend(infer_constraints(
                        template.args[j], mapped.args[j], neg_op(self.direction)))
                return res
            if (template.type.is_protocol and self.direction == SUPERTYPE_OF and
                    # We avoid infinite recursion for structural subtypes by checking
                    # whether this type already appeared in the inference chain.
                    # This is a conservative way break the inference cycles.
                    # It never produces any "false" constraints but gives up soon
                    # on purely structural inference cycles, see #3829.
                    not any(is_same_type(template, t) for t in template.type.inferring) and
                    mypy.subtypes.is_subtype(instance, erase_typevars(template))):
                template.type.inferring.append(template)
                self.infer_constraints_from_protocol_members(res, instance, template,
                                                             original_actual, template)
                template.type.inferring.pop()
                return res
            elif (instance.type.is_protocol and self.direction == SUBTYPE_OF and
                  # We avoid infinite recursion for structural subtypes also here.
                  not any(is_same_type(instance, i) for i in instance.type.inferring) and
                  mypy.subtypes.is_subtype(erase_typevars(template), instance)):
                instance.type.inferring.append(instance)
                self.infer_constraints_from_protocol_members(res, instance, template,
                                                             template, instance)
                instance.type.inferring.pop()
                return res
        if isinstance(actual, AnyType):
            # IDEA: Include both ways, i.e. add negation as well?
            return self.infer_against_any(template.args, actual)
        if (isinstance(actual, TupleType) and
            (is_named_instance(template, 'typing.Iterable') or
             is_named_instance(template, 'typing.Container') or
             is_named_instance(template, 'typing.Sequence') or
             is_named_instance(template, 'typing.Reversible'))
                and self.direction == SUPERTYPE_OF):
            for item in actual.items:
                cb = infer_constraints(template.args[0], item, SUPERTYPE_OF)
                res.extend(cb)
            return res
        elif (isinstance(actual, TupleType) and template.type.is_protocol and
              self.direction == SUPERTYPE_OF):
            if mypy.subtypes.is_subtype(actual.fallback, erase_typevars(template)):
                res.extend(infer_constraints(template, actual.fallback, self.direction))
                return res
            return []
        else:
            return []

    def infer_constraints_from_protocol_members(self, res: List[Constraint],
                                                instance: Instance, template: Instance,
                                                subtype: Type, protocol: Instance) -> None:
        """Infer constraints for situations where either 'template' or 'instance' is a protocol.

        The 'protocol' is the one of two that is an instance of protocol type, 'subtype'
        is the type used to bind self during inference. Currently, we just infer constrains for
        every protocol member type (both ways for settable members).
        """
        for member in protocol.type.protocol_members:
            inst = mypy.subtypes.find_member(member, instance, subtype)
            temp = mypy.subtypes.find_member(member, template, subtype)
            assert inst is not None and temp is not None
            # The above is safe since at this point we know that 'instance' is a subtype
            # of (erased) 'template', therefore it defines all protocol members
            res.extend(infer_constraints(temp, inst, self.direction))
            if (mypy.subtypes.IS_SETTABLE in
                    mypy.subtypes.get_member_flags(member, protocol.type)):
                # Settable members are invariant, add opposite constraints
                res.extend(infer_constraints(temp, inst, neg_op(self.direction)))

    def visit_callable_type(self, template: CallableType) -> List[Constraint]:
        if isinstance(self.actual, CallableType):
            cactual = self.actual
            # FIX verify argument counts
            # FIX what if one of the functions is generic
            res = []  # type: List[Constraint]

            # We can't infer constraints from arguments if the template is Callable[..., T] (with
            # literal '...').
            if not template.is_ellipsis_args:
                # The lengths should match, but don't crash (it will error elsewhere).
                for t, a in zip(template.arg_types, cactual.arg_types):
                    # Negate direction due to function argument type contravariance.
                    res.extend(infer_constraints(t, a, neg_op(self.direction)))
            res.extend(infer_constraints(template.ret_type, cactual.ret_type,
                                         self.direction))
            return res
        elif isinstance(self.actual, AnyType):
            # FIX what if generic
            res = self.infer_against_any(template.arg_types, self.actual)
            any_type = AnyType(TypeOfAny.from_another_any, source_any=self.actual)
            res.extend(infer_constraints(template.ret_type, any_type, self.direction))
            return res
        elif isinstance(self.actual, Overloaded):
            return self.infer_against_overloaded(self.actual, template)
        elif isinstance(self.actual, TypeType):
            return infer_constraints(template.ret_type, self.actual.item, self.direction)
        elif isinstance(self.actual, Instance):
            # Instances with __call__ method defined are considered structural
            # subtypes of Callable with a compatible signature.
            call = mypy.subtypes.find_member('__call__', self.actual, self.actual)
            if call:
                return infer_constraints(template, call, self.direction)
            else:
                return []
        else:
            return []

    def infer_against_overloaded(self, overloaded: Overloaded,
                                 template: CallableType) -> List[Constraint]:
        # Create constraints by matching an overloaded type against a template.
        # This is tricky to do in general. We cheat by only matching against
        # the first overload item, and by only matching the return type. This
        # seems to work somewhat well, but we should really use a more
        # reliable technique.
        item = find_matching_overload_item(overloaded, template)
        return infer_constraints(template.ret_type, item.ret_type,
                                 self.direction)

    def visit_tuple_type(self, template: TupleType) -> List[Constraint]:
        actual = self.actual
        if isinstance(actual, TupleType) and len(actual.items) == len(template.items):
            res = []  # type: List[Constraint]
            for i in range(len(template.items)):
                res.extend(infer_constraints(template.items[i],
                                             actual.items[i],
                                             self.direction))
            return res
        elif isinstance(actual, AnyType):
            return self.infer_against_any(template.items, actual)
        else:
            return []

    def visit_typeddict_type(self, template: TypedDictType) -> List[Constraint]:
        actual = self.actual
        if isinstance(actual, TypedDictType):
            res = []  # type: List[Constraint]
            # NOTE: Non-matching keys are ignored. Compatibility is checked
            #       elsewhere so this shouldn't be unsafe.
            for (item_name, template_item_type, actual_item_type) in template.zip(actual):
                res.extend(infer_constraints(template_item_type,
                                             actual_item_type,
                                             self.direction))
            return res
        elif isinstance(actual, AnyType):
            return self.infer_against_any(template.items.values(), actual)
        else:
            return []

    def visit_union_type(self, template: UnionType) -> List[Constraint]:
        assert False, ("Unexpected UnionType in ConstraintBuilderVisitor"
                       " (should have been handled in infer_constraints)")

    def infer_against_any(self, types: Iterable[Type], any_type: AnyType) -> List[Constraint]:
        res = []  # type: List[Constraint]
        for t in types:
            res.extend(infer_constraints(t, any_type, self.direction))
        return res

    def visit_overloaded(self, template: Overloaded) -> List[Constraint]:
        res = []  # type: List[Constraint]
        for t in template.items():
            res.extend(infer_constraints(t, self.actual, self.direction))
        return res

    def visit_type_type(self, template: TypeType) -> List[Constraint]:
        if isinstance(self.actual, CallableType):
            return infer_constraints(template.item, self.actual.ret_type, self.direction)
        elif isinstance(self.actual, Overloaded):
            return infer_constraints(template.item, self.actual.items()[0].ret_type,
                                     self.direction)
        elif isinstance(self.actual, TypeType):
            return infer_constraints(template.item, self.actual.item, self.direction)
        else:
            return []


def neg_op(op: int) -> int:
    """Map SubtypeOf to SupertypeOf and vice versa."""

    if op == SUBTYPE_OF:
        return SUPERTYPE_OF
    elif op == SUPERTYPE_OF:
        return SUBTYPE_OF
    else:
        raise ValueError('Invalid operator {}'.format(op))


def find_matching_overload_item(overloaded: Overloaded, template: CallableType) -> CallableType:
    """Disambiguate overload item against a template."""
    items = overloaded.items()
    for item in items:
        # Return type may be indeterminate in the template, so ignore it when performing a
        # subtype check.
        if mypy.subtypes.is_callable_subtype(item, template, ignore_return=True):
            return item
    # Fall back to the first item if we can't find a match. This is totally arbitrary --
    # maybe we should just bail out at this point.
    return items[0]

mypy/constraints.py
"""Type inference constraints."""

from typing import Iterable, List, Optional, Sequence

from mypy import experiments
from mypy.types import (
    CallableType, Type, TypeVisitor, UnboundType, AnyType, NoneTyp, TypeVarType, Instance,
    TupleType, TypedDictType, UnionType, Overloaded, ErasedType, PartialType, DeletedType,
    UninhabitedType, TypeType, TypeVarId, TypeQuery, is_named_instance, TypeOfAny
)
from mypy.maptype import map_instance_to_supertype
from mypy import nodes
import mypy.subtypes
from mypy.sametypes import is_same_type
from mypy.erasetype import erase_typevars


SUBTYPE_OF = 0  # type: int
SUPERTYPE_OF = 1  # type: int


class Constraint:
    """A representation of a type constraint.

    It can be either T <: type or T :> type (T is a type variable).
    """

    type_var = None  # type: TypeVarId
    op = 0           # SUBTYPE_OF or SUPERTYPE_OF
    target = None    # type: Type

    def __init__(self, type_var: TypeVarId, op: int, target: Type) -> None:
        self.type_var = type_var
        self.op = op
        self.target = target

    def __repr__(self) -> str:
        op_str = '<:'
        if self.op == SUPERTYPE_OF:
            op_str = ':>'
        return '{} {} {}'.format(self.type_var, op_str, self.target)


def infer_constraints_for_callable(
        callee: CallableType, arg_types: Sequence[Optional[Type]], arg_kinds: List[int],
        formal_to_actual: List[List[int]]) -> List[Constraint]:
    """Infer type variable constraints for a callable and actual arguments.

    Return a list of constraints.
    """
    constraints = []  # type: List[Constraint]
    tuple_counter = [0]

    for i, actuals in enumerate(formal_to_actual):
        for actual in actuals:
            actual_arg_type = arg_types[actual]
            if actual_arg_type is None:
                continue

            actual_type = get_actual_type(actual_arg_type, arg_kinds[actual],
                                          tuple_counter)
            c = infer_constraints(callee.arg_types[i], actual_type,
                                  SUPERTYPE_OF)
            constraints.extend(c)

    return constraints


def get_actual_type(arg_type: Type, kind: int,
                    tuple_counter: List[int]) -> Type:
    """Return the type of an actual argument with the given kind.

    If the argument is a *arg, return the individual argument item.
    """

    if kind == nodes.ARG_STAR:
        if isinstance(arg_type, Instance):
            if arg_type.type.fullname() == 'builtins.list':
                # List *arg.
                return arg_type.args[0]
            elif arg_type.args:
                # TODO try to map type arguments to Iterable
                return arg_type.args[0]
            else:
                return AnyType(TypeOfAny.from_error)
        elif isinstance(arg_type, TupleType):
            # Get the next tuple item of a tuple *arg.
            tuple_counter[0] += 1
            return arg_type.items[tuple_counter[0] - 1]
        else:
            return AnyType(TypeOfAny.from_error)
    elif kind == nodes.ARG_STAR2:
        if isinstance(arg_type, Instance) and (arg_type.type.fullname() == 'builtins.dict'):
            # Dict **arg. TODO more general (Mapping)
            return arg_type.args[1]
        else:
            return AnyType(TypeOfAny.from_error)
    else:
        # No translation for other kinds.
        return arg_type


def infer_constraints(template: Type, actual: Type,
                      direction: int) -> List[Constraint]:
    """Infer type constraints.

    Match a template type, which may contain type variable references,
    recursively against a type which does not contain (the same) type
    variable references. The result is a list of type constrains of
    form 'T is a supertype/subtype of x', where T is a type variable
    present in the template and x is a type without reference to type
    variables present in the template.

    Assume T and S are type variables. Now the following results can be
    calculated (read as '(template, actual) --> result'):

      (T, X)            -->  T :> X
      (X[T], X[Y])      -->  T <: Y and T :> Y
      ((T, T), (X, Y))  -->  T :> X and T :> Y
      ((T, S), (X, Y))  -->  T :> X and S :> Y
      (X[T], Any)       -->  T <: Any and T :> Any

    The constraints are represented as Constraint objects.
    """

    # If the template is simply a type variable, emit a Constraint directly.
    # We need to handle this case before handling Unions for two reasons:
    #  1. "T <: Union[U1, U2]" is not equivalent to "T <: U1 or T <: U2",
    #     because T can itself be a union (notably, Union[U1, U2] itself).
    #  2. "T :> Union[U1, U2]" is logically equivalent to "T :> U1 and
    #     T :> U2", but they are not equivalent to the constraint solver,
    #     which never introduces new Union types (it uses join() instead).
    if isinstance(template, TypeVarType):
        return [Constraint(template.id, direction, actual)]

    # Now handle the case of either template or actual being a Union.
    # For a Union to be a subtype of another type, every item of the Union
    # must be a subtype of that type, so concatenate the constraints.
    if direction == SUBTYPE_OF and isinstance(template, UnionType):
        res = []
        for t_item in template.items:
            res.extend(infer_constraints(t_item, actual, direction))
        return res
    if direction == SUPERTYPE_OF and isinstance(actual, UnionType):
        res = []
        for a_item in actual.items:
            res.extend(infer_constraints(template, a_item, direction))
        return res

    # Now the potential subtype is known not to be a Union or a type
    # variable that we are solving for. In that case, for a Union to
    # be a supertype of the potential subtype, some item of the Union
    # must be a supertype of it.
    if direction == SUBTYPE_OF and isinstance(actual, UnionType):
        # If some of items is not a complete type, disregard that.
        items = simplify_away_incomplete_types(actual.items)
        # We infer constraints eagerly -- try to find constraints for a type
        # variable if possible. This seems to help with some real-world
        # use cases.
        return any_constraints(
            [infer_constraints_if_possible(template, a_item, direction)
             for a_item in items],
            eager=True)
    if direction == SUPERTYPE_OF and isinstance(template, UnionType):
        # When the template is a union, we are okay with leaving some
        # type variables indeterminate. This helps with some special
        # cases, though this isn't very principled.
        return any_constraints(
            [infer_constraints_if_possible(t_item, actual, direction)
             for t_item in template.items],
            eager=False)

    # Remaining cases are handled by ConstraintBuilderVisitor.
    return template.accept(ConstraintBuilderVisitor(actual, direction))


def infer_constraints_if_possible(template: Type, actual: Type,
                                  direction: int) -> Optional[List[Constraint]]:
    """Like infer_constraints, but return None if the input relation is
    known to be unsatisfiable, for example if template=List[T] and actual=int.
    (In this case infer_constraints would return [], just like it would for
    an automatically satisfied relation like template=List[T] and actual=object.)
    """
    if (direction == SUBTYPE_OF and
            not mypy.subtypes.is_subtype(erase_typevars(template), actual)):
        return None
    if (direction == SUPERTYPE_OF and
            not mypy.subtypes.is_subtype(actual, erase_typevars(template))):
        return None
    return infer_constraints(template, actual, direction)


def any_constraints(options: List[Optional[List[Constraint]]], eager: bool) -> List[Constraint]:
    """Deduce what we can from a collection of constraint lists.

    It's a given that at least one of the lists must be satisfied. A
    None element in the list of options represents an unsatisfiable
    constraint and is ignored.  Ignore empty constraint lists if eager
    is true -- they are always trivially satisfiable.
    """
    if eager:
        valid_options = [option for option in options if option]
    else:
        valid_options = [option for option in options if option is not None]
    if len(valid_options) == 1:
        return valid_options[0]
    elif (len(valid_options) > 1 and
          all(is_same_constraints(valid_options[0], c)
              for c in valid_options[1:])):
        # Multiple sets of constraints that are all the same. Just pick any one of them.
        # TODO: More generally, if a given (variable, direction) pair appears in
        #       every option, combine the bounds with meet/join.
        return valid_options[0]

    # Otherwise, there are either no valid options or multiple, inconsistent valid
    # options. Give up and deduce nothing.
    return []


def is_same_constraints(x: List[Constraint], y: List[Constraint]) -> bool:
    for c1 in x:
        if not any(is_same_constraint(c1, c2) for c2 in y):
            return False
    for c1 in y:
        if not any(is_same_constraint(c1, c2) for c2 in x):
            return False
    return True


def is_same_constraint(c1: Constraint, c2: Constraint) -> bool:
    return (c1.type_var == c2.type_var
            and c1.op == c2.op
            and is_same_type(c1.target, c2.target))


def simplify_away_incomplete_types(types: List[Type]) -> List[Type]:
    complete = [typ for typ in types if is_complete_type(typ)]
    if complete:
        return complete
    else:
        return types


def is_complete_type(typ: Type) -> bool:
    """Is a type complete?

    A complete doesn't have uninhabited type components or (when not in strict
    optional mode) None components.
    """
    return typ.accept(CompleteTypeVisitor())


class CompleteTypeVisitor(TypeQuery[bool]):
    def __init__(self) -> None:
        super().__init__(all)

    def visit_uninhabited_type(self, t: UninhabitedType) -> bool:
        return False


class ConstraintBuilderVisitor(TypeVisitor[List[Constraint]]):
    """Visitor class for inferring type constraints."""

    # The type that is compared against a template
    # TODO: The value may be None. Is that actually correct?
    actual = None  # type: Type

    def __init__(self, actual: Type, direction: int) -> None:
        # Direction must be SUBTYPE_OF or SUPERTYPE_OF.
        self.actual = actual
        self.direction = direction

    # Trivial leaf types

    def visit_unbound_type(self, template: UnboundType) -> List[Constraint]:
        return []

    def visit_any(self, template: AnyType) -> List[Constraint]:
        return []

    def visit_none_type(self, template: NoneTyp) -> List[Constraint]:
        return []

    def visit_uninhabited_type(self, template: UninhabitedType) -> List[Constraint]:
        return []

    def visit_erased_type(self, template: ErasedType) -> List[Constraint]:
        return []

    def visit_deleted_type(self, template: DeletedType) -> List[Constraint]:
        return []

    # Errors

    def visit_partial_type(self, template: PartialType) -> List[Constraint]:
        # We can't do anything useful with a partial type here.
        assert False, "Internal error"

    # Non-trivial leaf type

    def visit_type_var(self, template: TypeVarType) -> List[Constraint]:
        assert False, ("Unexpected TypeVarType in ConstraintBuilderVisitor"
                       " (should have been handled in infer_constraints)")

    # Non-leaf types

    def visit_instance(self, template: Instance) -> List[Constraint]:
        original_actual = actual = self.actual
        res = []  # type: List[Constraint]
        if isinstance(actual, CallableType) and actual.fallback is not None:
            actual = actual.fallback
        if isinstance(actual, TypedDictType):
            actual = actual.as_anonymous().fallback
        if isinstance(actual, Instance):
            instance = actual
            # We always try nominal inference if possible,
            # it is much faster than the structural one.
            if (self.direction == SUBTYPE_OF and
                    template.type.has_base(instance.type.fullname())):
                mapped = map_instance_to_supertype(template, instance.type)
                for i in range(len(instance.args)):
                    # The constraints for generic type parameters are
                    # invariant. Include constraints from both directions
                    # to achieve the effect.
                    res.extend(infer_constraints(
                        mapped.args[i], instance.args[i], self.direction))
                    res.extend(infer_constraints(
                        mapped.args[i], instance.args[i], neg_op(self.direction)))
                return res
            elif (self.direction == SUPERTYPE_OF and
                    instance.type.has_base(template.type.fullname())):
                mapped = map_instance_to_supertype(instance, template.type)
                for j in range(len(template.args)):
                    # The constraints for generic type parameters are
                    # invariant.
                    res.extend(infer_constraints(
                        template.args[j], mapped.args[j], self.direction))
                    res.extend(infer_constraints(
                        template.args[j], mapped.args[j], neg_op(self.direction)))
                return res
            if (template.type.is_protocol and self.direction == SUPERTYPE_OF and
                    # We avoid infinite recursion for structural subtypes by checking
                    # whether this type already appeared in the inference chain.
                    # This is a conservative way break the inference cycles.
                    # It never produces any "false" constraints but gives up soon
                    # on purely structural inference cycles, see #3829.
                    not any(is_same_type(template, t) for t in template.type.inferring) and
                    mypy.subtypes.is_subtype(instance, erase_typevars(template))):
                template.type.inferring.append(template)
                self.infer_constraints_from_protocol_members(res, instance, template,
                                                             original_actual, template)
                template.type.inferring.pop()
                return res
            elif (instance.type.is_protocol and self.direction == SUBTYPE_OF and
                  # We avoid infinite recursion for structural subtypes also here.
                  not any(is_same_type(instance, i) for i in instance.type.inferring) and
                  mypy.subtypes.is_subtype(erase_typevars(template), instance)):
                instance.type.inferring.append(instance)
                self.infer_constraints_from_protocol_members(res, instance, template,
                                                             template, instance)
                instance.type.inferring.pop()
                return res
        if isinstance(actual, AnyType):
            # IDEA: Include both ways, i.e. add negation as well?
            return self.infer_against_any(template.args, actual)
        if (isinstance(actual, TupleType) and
            (is_named_instance(template, 'typing.Iterable') or
             is_named_instance(template, 'typing.Container') or
             is_named_instance(template, 'typing.Sequence') or
             is_named_instance(template, 'typing.Reversible'))
                and self.direction == SUPERTYPE_OF):
            for item in actual.items:
                cb = infer_constraints(template.args[0], item, SUPERTYPE_OF)
                res.extend(cb)
            return res
        elif (isinstance(actual, TupleType) and template.type.is_protocol and
              self.direction == SUPERTYPE_OF):
            if mypy.subtypes.is_subtype(actual.fallback, erase_typevars(template)):
                res.extend(infer_constraints(template, actual.fallback, self.direction))
                return res
            return []
        else:
            return []

    def infer_constraints_from_protocol_members(self, res: List[Constraint],
                                                instance: Instance, template: Instance,
                                                subtype: Type, protocol: Instance) -> None:
        """Infer constraints for situations where either 'template' or 'instance' is a protocol.

        The 'protocol' is the one of two that is an instance of protocol type, 'subtype'
        is the type used to bind self during inference. Currently, we just infer constrains for
        every protocol member type (both ways for settable members).
        """
        for member in protocol.type.protocol_members:
            inst = mypy.subtypes.find_member(member, instance, subtype)
            temp = mypy.subtypes.find_member(member, template, subtype)
            assert inst is not None and temp is not None
            # The above is safe since at this point we know that 'instance' is a subtype
            # of (erased) 'template', therefore it defines all protocol members
            res.extend(infer_constraints(temp, inst, self.direction))
            if (mypy.subtypes.IS_SETTABLE in
                    mypy.subtypes.get_member_flags(member, protocol.type)):
                # Settable members are invariant, add opposite constraints
                res.extend(infer_constraints(temp, inst, neg_op(self.direction)))

    def visit_callable_type(self, template: CallableType) -> List[Constraint]:
        if isinstance(self.actual, CallableType):
            cactual = self.actual
            # FIX verify argument counts
            # FIX what if one of the functions is generic
            res = []  # type: List[Constraint]

            # We can't infer constraints from arguments if the template is Callable[..., T] (with
            # literal '...').
            if not template.is_ellipsis_args:
                # The lengths should match, but don't crash (it will error elsewhere).
                for t, a in zip(template.arg_types, cactual.arg_types):
                    # Negate direction due to function argument type contravariance.
                    res.extend(infer_constraints(t, a, neg_op(self.direction)))
            res.extend(infer_constraints(template.ret_type, cactual.ret_type,
                                         self.direction))
            return res
        elif isinstance(self.actual, AnyType):
            # FIX what if generic
            res = self.infer_against_any(template.arg_types, self.actual)
            any_type = AnyType(TypeOfAny.from_another_any, source_any=self.actual)
            res.extend(infer_constraints(template.ret_type, any_type, self.direction))
            return res
        elif isinstance(self.actual, Overloaded):
            return self.infer_against_overloaded(self.actual, template)
        elif isinstance(self.actual, TypeType):
            return infer_constraints(template.ret_type, self.actual.item, self.direction)
        elif isinstance(self.actual, Instance):
            # Instances with __call__ method defined are considered structural
            # subtypes of Callable with a compatible signature.
            call = mypy.subtypes.find_member('__call__', self.actual, self.actual)
            if call:
                return infer_constraints(template, call, self.direction)
            else:
                return []
        else:
            return []

    def infer_against_overloaded(self, overloaded: Overloaded,
                                 template: CallableType) -> List[Constraint]:
        # Create constraints by matching an overloaded type against a template.
        # This is tricky to do in general. We cheat by only matching against
        # the first overload item, and by only matching the return type. This
        # seems to work somewhat well, but we should really use a more
        # reliable technique.
        item = find_matching_overload_item(overloaded, template)
        return infer_constraints(template.ret_type, item.ret_type,
                                 self.direction)

    def visit_tuple_type(self, template: TupleType) -> List[Constraint]:
        actual = self.actual
        if isinstance(actual, TupleType) and len(actual.items) == len(template.items):
            res = []  # type: List[Constraint]
            for i in range(len(template.items)):
                res.extend(infer_constraints(template.items[i],
                                             actual.items[i],
                                             self.direction))
            return res
        elif isinstance(actual, AnyType):
            return self.infer_against_any(template.items, actual)
        else:
            return []

    def visit_typeddict_type(self, template: TypedDictType) -> List[Constraint]:
        actual = self.actual
        if isinstance(actual, TypedDictType):
            res = []  # type: List[Constraint]
            # NOTE: Non-matching keys are ignored. Compatibility is checked
            #       elsewhere so this shouldn't be unsafe.
            for (item_name, template_item_type, actual_item_type) in template.zip(actual):
                res.extend(infer_constraints(template_item_type,
                                             actual_item_type,
                                             self.direction))
            return res
        elif isinstance(actual, AnyType):
            return self.infer_against_any(template.items.values(), actual)
        else:
            return []

    def visit_union_type(self, template: UnionType) -> List[Constraint]:
        assert False, ("Unexpected UnionType in ConstraintBuilderVisitor"
                       " (should have been handled in infer_constraints)")

    def infer_against_any(self, types: Iterable[Type], any_type: AnyType) -> List[Constraint]:
        res = []  # type: List[Constraint]
        for t in types:
            res.extend(infer_constraints(t, any_type, self.direction))
        return res

    def visit_overloaded(self, template: Overloaded) -> List[Constraint]:
        res = []  # type: List[Constraint]
        for t in template.items():
            res.extend(infer_constraints(t, self.actual, self.direction))
        return res

    def visit_type_type(self, template: TypeType) -> List[Constraint]:
        if isinstance(self.actual, CallableType):
            return infer_constraints(template.item, self.actual.ret_type, self.direction)
        elif isinstance(self.actual, Overloaded):
            return infer_constraints(template.item, self.actual.items()[0].ret_type,
                                     self.direction)
        elif isinstance(self.actual, TypeType):
            return infer_constraints(template.item, self.actual.item, self.direction)
        elif isinstance(self.actual, AnyType):
            return infer_constraints(template.item, self.actual, self.direction)
        else:
            return []


def neg_op(op: int) -> int:
    """Map SubtypeOf to SupertypeOf and vice versa."""

    if op == SUBTYPE_OF:
        return SUPERTYPE_OF
    elif op == SUPERTYPE_OF:
        return SUBTYPE_OF
    else:
        raise ValueError('Invalid operator {}'.format(op))


def find_matching_overload_item(overloaded: Overloaded, template: CallableType) -> CallableType:
    """Disambiguate overload item against a template."""
    items = overloaded.items()
    for item in items:
        # Return type may be indeterminate in the template, so ignore it when performing a
        # subtype check.
        if mypy.subtypes.is_callable_subtype(item, template, ignore_return=True):
            return item
    # Fall back to the first item if we can't find a match. This is totally arbitrary --
    # maybe we should just bail out at this point.
    return items[0]

mypy/constraints.py
diff --git a/mypy/constraints.py b/mypy/constraints.py
index 4e7c2ecba269..0a79483b235b 100644
--- a/mypy/constraints.py
+++ b/mypy/constraints.py
@@ -506,6 +506,8 @@ def visit_type_type(self, template: TypeType) -> List[Constraint]:
                                      self.direction)
         elif isinstance(self.actual, TypeType):
             return infer_constraints(template.item, self.actual.item, self.direction)
+        elif isinstance(self.actual, AnyType):
+            return infer_constraints(template.item, self.actual, self.direction)
         else:
             return []
 
diff --git a/test-data/unit/check-generics.test b/test-data/unit/check-generics.test
index 6e8fcd43e6e4..b4a5050c431a 100644
--- a/test-data/unit/check-generics.test
+++ b/test-data/unit/check-generics.test
@@ -1747,3 +1747,13 @@ class D:
     def __or__(self, x: G[X]) -> G[X]: pass
     def __ior__(self, x: G[S2]) -> G[S2]: pass \
         # E: Signatures of "__ior__" and "__or__" are incompatible
+
+[case testConstraintInferenceForAnyAgainstTypeT]
+from typing import Type, Any, TypeVar
+
+T = TypeVar('T')
+
+def f(c: Type[T]) -> T: ...
+
+x: Any
+reveal_type(f(x))  # E: Revealed type is 'Any'

No constraint inferred for Any vs. Type[T]
I'd expect the revealed type to be `Any` instead of `<nothing>` for this example:

```py
from typing import Type, Any, TypeVar

T = TypeVar('T')

def f(c: Type[T]) -> T: ...

x: Any
reveal_type(f(x))  # <nothing>
```

It looks like constraint inference doesn't work correctly when matching `Any` against `Type[T]`.
