text: """Type inference constraints."""
  
  from typing import Iterable, List, Optional, Sequence
  from typing_extensions import Final
  
  from mypy.types import (
      CallableType, Type, TypeVisitor, UnboundType, AnyType, NoneType, TypeVarType, Instance,
      TupleType, TypedDictType, UnionType, Overloaded, ErasedType, PartialType, DeletedType,
      UninhabitedType, TypeType, TypeVarId, TypeQuery, is_named_instance, TypeOfAny, LiteralType,
  )
  from mypy.maptype import map_instance_to_supertype
  import mypy.subtypes
  import mypy.sametypes
  import mypy.typeops
  from mypy.erasetype import erase_typevars
  from mypy.nodes import COVARIANT, CONTRAVARIANT
  from mypy.argmap import ArgTypeExpander
  
  SUBTYPE_OF = 0  # type: Final[int]
  SUPERTYPE_OF = 1  # type: Final[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]
      mapper = ArgTypeExpander()
  
      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 = mapper.expand_actual_type(actual_arg_type, arg_kinds[actual],
                                                      callee.arg_names[i], callee.arg_kinds[i])
              c = infer_constraints(callee.arg_types[i], actual_type, SUPERTYPE_OF)
              constraints.extend(c)
  
      return constraints
  
  
  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 mypy.sametypes.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: NoneType) -> 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 []
  
      def visit_literal_type(self, template: LiteralType) -> 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, Overloaded)) and template.type.is_protocol:
              if template.type.protocol_members == ['__call__']:
                  # Special case: a generic callback protocol
                  if not any(mypy.sametypes.is_same_type(template, t)
                             for t in template.type.inferring):
                      template.type.inferring.append(template)
                      call = mypy.subtypes.find_member('__call__', template, actual)
                      assert call is not None
                      if mypy.subtypes.is_subtype(actual, erase_typevars(call)):
                          subres = infer_constraints(call, actual, self.direction)
                          res.extend(subres)
                      template.type.inferring.pop()
                      return res
          if isinstance(actual, CallableType) and actual.fallback is not None:
              actual = actual.fallback
          if isinstance(actual, Overloaded) and actual.fallback is not None:
              actual = actual.fallback
          if isinstance(actual, TypedDictType):
              actual = actual.as_anonymous().fallback
          if isinstance(actual, Instance):
              instance = actual
              erased = erase_typevars(template)
              assert isinstance(erased, Instance)
              # 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)
                  tvars = mapped.type.defn.type_vars
                  for i in range(len(instance.args)):
                      # The constraints for generic type parameters depend on variance.
                      # Include constraints from both directions if invariant.
                      if tvars[i].variance != CONTRAVARIANT:
                          res.extend(infer_constraints(
                              mapped.args[i], instance.args[i], self.direction))
                      if tvars[i].variance != COVARIANT:
                          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)
                  tvars = template.type.defn.type_vars
                  for j in range(len(template.args)):
                      # The constraints for generic type parameters depend on variance.
                      # Include constraints from both directions if invariant.
                      if tvars[j].variance != CONTRAVARIANT:
                          res.extend(infer_constraints(
                              template.args[j], mapped.args[j], self.direction))
                      if tvars[j].variance != COVARIANT:
                          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.
                      # Note that we use is_protocol_implementation instead of is_subtype
                      # because some type may be considered a subtype of a protocol
                      # due to _promote, but still not implement the protocol.
                      not any(mypy.sametypes.is_same_type(template, t)
                              for t in template.type.inferring) and
                      mypy.subtypes.is_protocol_implementation(instance, erased)):
                  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(mypy.sametypes.is_same_type(instance, i)
                            for i in instance.type.inferring) and
                    mypy.subtypes.is_protocol_implementation(erased, 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 self.direction == SUPERTYPE_OF:
              return infer_constraints(template,
                                       mypy.typeops.tuple_fallback(actual),
                                       self.direction)
          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_compatible(item, template,
                                                  is_compat=mypy.subtypes.is_subtype,
                                                  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]
  