"""Type inference constraints."""

from __future__ import annotations

from typing import TYPE_CHECKING, Final, Iterable, List, Sequence

import mypy.subtypes
import mypy.typeops
from mypy.argmap import ArgTypeExpander
from mypy.erasetype import erase_typevars
from mypy.maptype import map_instance_to_supertype
from mypy.nodes import (
    ARG_OPT,
    ARG_POS,
    ARG_STAR,
    ARG_STAR2,
    CONTRAVARIANT,
    COVARIANT,
    ArgKind,
    TypeInfo,
)
from mypy.types import (
    TUPLE_LIKE_INSTANCE_NAMES,
    AnyType,
    CallableType,
    DeletedType,
    ErasedType,
    Instance,
    LiteralType,
    NoneType,
    NormalizedCallableType,
    Overloaded,
    Parameters,
    ParamSpecType,
    PartialType,
    ProperType,
    TupleType,
    Type,
    TypeAliasType,
    TypedDictType,
    TypeOfAny,
    TypeQuery,
    TypeType,
    TypeVarId,
    TypeVarLikeType,
    TypeVarTupleType,
    TypeVarType,
    TypeVisitor,
    UnboundType,
    UninhabitedType,
    UnionType,
    UnpackType,
    find_unpack_in_list,
    get_proper_type,
    has_recursive_types,
    has_type_vars,
    is_named_instance,
    split_with_prefix_and_suffix,
)
from mypy.types_utils import is_union_with_any
from mypy.typestate import type_state

if TYPE_CHECKING:
    from mypy.infer import ArgumentInferContext

SUBTYPE_OF: Final = 0
SUPERTYPE_OF: Final = 1


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

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

    type_var: TypeVarId
    op = 0  # SUBTYPE_OF or SUPERTYPE_OF
    target: Type

    def __init__(self, type_var: TypeVarLikeType, op: int, target: Type) -> None:
        self.type_var = type_var.id
        self.op = op
        # TODO: should we add "assert not isinstance(target, UnpackType)"?
        # UnpackType is a synthetic type, and is never valid as a constraint target.
        self.target = target
        self.origin_type_var = type_var
        # These are additional type variables that should be solved for together with type_var.
        # TODO: A cleaner solution may be to modify the return type of infer_constraints()
        # to include these instead, but this is a rather big refactoring.
        self.extra_tvars: list[TypeVarLikeType] = []

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

    def __hash__(self) -> int:
        return hash((self.type_var, self.op, self.target))

    def __eq__(self, other: object) -> bool:
        if not isinstance(other, Constraint):
            return False
        return (self.type_var, self.op, self.target) == (other.type_var, other.op, other.target)


def infer_constraints_for_callable(
    callee: CallableType,
    arg_types: Sequence[Type | None],
    arg_kinds: list[ArgKind],
    arg_names: Sequence[str | None] | None,
    formal_to_actual: list[list[int]],
    context: ArgumentInferContext,
) -> list[Constraint]:
    """Infer type variable constraints for a callable and actual arguments.

    Return a list of constraints.
    """
    constraints: list[Constraint] = []
    mapper = ArgTypeExpander(context)

    param_spec = callee.param_spec()
    param_spec_arg_types = []
    param_spec_arg_names = []
    param_spec_arg_kinds = []

    incomplete_star_mapping = False
    for i, actuals in enumerate(formal_to_actual):
        for actual in actuals:
            if actual is None and callee.arg_kinds[i] in (ARG_STAR, ARG_STAR2):
                # We can't use arguments to infer ParamSpec constraint, if only some
                # are present in the current inference pass.
                incomplete_star_mapping = True
                break

    for i, actuals in enumerate(formal_to_actual):
        if isinstance(callee.arg_types[i], UnpackType):
            unpack_type = callee.arg_types[i]
            assert isinstance(unpack_type, UnpackType)

            # In this case we are binding all the actuals to *args,
            # and we want a constraint that the typevar tuple being unpacked
            # is equal to a type list of all the actuals.
            actual_types = []

            unpacked_type = get_proper_type(unpack_type.type)
            if isinstance(unpacked_type, TypeVarTupleType):
                tuple_instance = unpacked_type.tuple_fallback
            elif isinstance(unpacked_type, TupleType):
                tuple_instance = unpacked_type.partial_fallback
            else:
                assert False, "mypy bug: unhandled constraint inference case"

            for actual in actuals:
                actual_arg_type = arg_types[actual]
                if actual_arg_type is None:
                    continue

                expanded_actual = mapper.expand_actual_type(
                    actual_arg_type,
                    arg_kinds[actual],
                    callee.arg_names[i],
                    callee.arg_kinds[i],
                    allow_unpack=True,
                )

                if arg_kinds[actual] != ARG_STAR or isinstance(
                    get_proper_type(actual_arg_type), TupleType
                ):
                    actual_types.append(expanded_actual)
                else:
                    # If we are expanding an iterable inside * actual, append a homogeneous item instead
                    actual_types.append(
                        UnpackType(tuple_instance.copy_modified(args=[expanded_actual]))
                    )

            if isinstance(unpacked_type, TypeVarTupleType):
                constraints.append(
                    Constraint(
                        unpacked_type,
                        SUPERTYPE_OF,
                        TupleType(actual_types, unpacked_type.tuple_fallback),
                    )
                )
            elif isinstance(unpacked_type, TupleType):
                # Prefixes get converted to positional args, so technically the only case we
                # should have here is like Tuple[Unpack[Ts], Y1, Y2, Y3]. If this turns out
                # not to hold we can always handle the prefixes too.
                inner_unpack = unpacked_type.items[0]
                assert isinstance(inner_unpack, UnpackType)
                inner_unpacked_type = get_proper_type(inner_unpack.type)
                suffix_len = len(unpacked_type.items) - 1
                if isinstance(inner_unpacked_type, TypeVarTupleType):
                    # Variadic item can be either *Ts...
                    constraints.append(
                        Constraint(
                            inner_unpacked_type,
                            SUPERTYPE_OF,
                            TupleType(
                                actual_types[:-suffix_len], inner_unpacked_type.tuple_fallback
                            ),
                        )
                    )
                else:
                    # ...or it can be a homogeneous tuple.
                    assert (
                        isinstance(inner_unpacked_type, Instance)
                        and inner_unpacked_type.type.fullname == "builtins.tuple"
                    )
                    for at in actual_types[:-suffix_len]:
                        constraints.extend(
                            infer_constraints(inner_unpacked_type.args[0], at, SUPERTYPE_OF)
                        )
                # Now handle the suffix (if any).
                if suffix_len:
                    for tt, at in zip(unpacked_type.items[1:], actual_types[-suffix_len:]):
                        constraints.extend(infer_constraints(tt, at, SUPERTYPE_OF))
            else:
                assert False, "mypy bug: unhandled constraint inference case"
        else:
            for actual in actuals:
                actual_arg_type = arg_types[actual]
                if actual_arg_type is None:
                    continue

                if param_spec and callee.arg_kinds[i] in (ARG_STAR, ARG_STAR2):
                    # If actual arguments are mapped to ParamSpec type, we can't infer individual
                    # constraints, instead store them and infer single constraint at the end.
                    # It is impossible to map actual kind to formal kind, so use some heuristic.
                    # This inference is used as a fallback, so relying on heuristic should be OK.
                    if not incomplete_star_mapping:
                        param_spec_arg_types.append(
                            mapper.expand_actual_type(
                                actual_arg_type, arg_kinds[actual], None, arg_kinds[actual]
                            )
                        )
                        actual_kind = arg_kinds[actual]
                        param_spec_arg_kinds.append(
                            ARG_POS if actual_kind not in (ARG_STAR, ARG_STAR2) else actual_kind
                        )
                        param_spec_arg_names.append(arg_names[actual] if arg_names else None)
                else:
                    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)
    if (
        param_spec
        and not any(c.type_var == param_spec.id for c in constraints)
        and not incomplete_star_mapping
    ):
        # Use ParamSpec constraint from arguments only if there are no other constraints,
        # since as explained above it is quite ad-hoc.
        constraints.append(
            Constraint(
                param_spec,
                SUPERTYPE_OF,
                Parameters(
                    arg_types=param_spec_arg_types,
                    arg_kinds=param_spec_arg_kinds,
                    arg_names=param_spec_arg_names,
                    imprecise_arg_kinds=True,
                ),
            )
        )
    if any(isinstance(v, ParamSpecType) for v in callee.variables):
        # As a perf optimization filter imprecise constraints only when we can have them.
        constraints = filter_imprecise_kinds(constraints)
    return constraints


def infer_constraints(
    template: Type, actual: Type, direction: int, skip_neg_op: bool = False
) -> 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 skip_neg_op == True,
    then skip adding reverse (polymorphic) constraints (since this is already a call
    to infer such constraints).
    """
    if any(
        get_proper_type(template) == get_proper_type(t)
        and get_proper_type(actual) == get_proper_type(a)
        for (t, a) in reversed(type_state.inferring)
    ):
        return []
    if has_recursive_types(template) or isinstance(get_proper_type(template), Instance):
        # This case requires special care because it may cause infinite recursion.
        # Note that we include Instances because the may be recursive as str(Sequence[str]).
        if not has_type_vars(template):
            # Return early on an empty branch.
            return []
        type_state.inferring.append((template, actual))
        res = _infer_constraints(template, actual, direction, skip_neg_op)
        type_state.inferring.pop()
        return res
    return _infer_constraints(template, actual, direction, skip_neg_op)


def _infer_constraints(
    template: Type, actual: Type, direction: int, skip_neg_op: bool
) -> list[Constraint]:
    orig_template = template
    template = get_proper_type(template)
    actual = get_proper_type(actual)

    # Type inference shouldn't be affected by whether union types have been simplified.
    # We however keep any ErasedType items, so that the caller will see it when using
    # checkexpr.has_erased_component().
    if isinstance(template, UnionType):
        template = mypy.typeops.make_simplified_union(template.items, keep_erased=True)
    if isinstance(actual, UnionType):
        actual = mypy.typeops.make_simplified_union(actual.items, keep_erased=True)

    # Ignore Any types from the type suggestion engine to avoid them
    # causing us to infer Any in situations where a better job could
    # be done otherwise. (This can produce false positives but that
    # doesn't really matter because it is all heuristic anyway.)
    if isinstance(actual, AnyType) and actual.type_of_any == TypeOfAny.suggestion_engine:
        return []

    # 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, direction, actual)]

    if (
        isinstance(actual, TypeVarType)
        and not actual.id.is_meta_var()
        and direction == SUPERTYPE_OF
    ):
        # Unless template is also a type variable (or a union that contains one), using the upper
        # bound for inference will usually give better result for actual that is a type variable.
        if not isinstance(template, UnionType) or not any(
            isinstance(t, TypeVarType) for t in template.items
        ):
            actual = get_proper_type(actual.upper_bound)

    # 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(orig_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.
        result = any_constraints(
            [
                infer_constraints_if_possible(t_item, actual, direction)
                for t_item in template.items
            ],
            eager=False,
        )
        if result:
            return result
        elif has_recursive_types(template) and not has_recursive_types(actual):
            return handle_recursive_union(template, actual, direction)
        return []

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


def infer_constraints_if_possible(
    template: Type, actual: Type, direction: int
) -> list[Constraint] | None:
    """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
    if (
        direction == SUPERTYPE_OF
        and isinstance(template, TypeVarType)
        and not mypy.subtypes.is_subtype(actual, erase_typevars(template.upper_bound))
    ):
        # This is not caught by the above branch because of the erase_typevars() call,
        # that would return 'Any' for a type variable.
        return None
    return infer_constraints(template, actual, direction)


def select_trivial(options: Sequence[list[Constraint] | None]) -> list[list[Constraint]]:
    """Select only those lists where each item is a constraint against Any."""
    res = []
    for option in options:
        if option is None:
            continue
        if all(isinstance(get_proper_type(c.target), AnyType) for c in option):
            res.append(option)
    return res


def merge_with_any(constraint: Constraint) -> Constraint:
    """Transform a constraint target into a union with given Any type."""
    target = constraint.target
    if is_union_with_any(target):
        # Do not produce redundant unions.
        return constraint
    # TODO: if we will support multiple sources Any, use this here instead.
    any_type = AnyType(TypeOfAny.implementation_artifact)
    return Constraint(
        constraint.origin_type_var,
        constraint.op,
        UnionType.make_union([target, any_type], target.line, target.column),
    )


def handle_recursive_union(template: UnionType, actual: Type, direction: int) -> list[Constraint]:
    # This is a hack to special-case things like Union[T, Inst[T]] in recursive types. Although
    # it is quite arbitrary, it is a relatively common pattern, so we should handle it well.
    # This function may be called when inferring against such union resulted in different
    # constraints for each item. Normally we give up in such case, but here we instead split
    # the union in two parts, and try inferring sequentially.
    non_type_var_items = [t for t in template.items if not isinstance(t, TypeVarType)]
    type_var_items = [t for t in template.items if isinstance(t, TypeVarType)]
    return infer_constraints(
        UnionType.make_union(non_type_var_items), actual, direction
    ) or infer_constraints(UnionType.make_union(type_var_items), actual, direction)


def any_constraints(options: list[list[Constraint] | None], 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 not valid_options:
        return []

    if len(valid_options) == 1:
        return valid_options[0]

    if 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.
        return valid_options[0]

    if all(is_similar_constraints(valid_options[0], c) for c in valid_options[1:]):
        # All options have same structure. In this case we can merge-in trivial
        # options (i.e. those that only have Any) and try again.
        # TODO: More generally, if a given (variable, direction) pair appears in
        # every option, combine the bounds with meet/join always, not just for Any.
        trivial_options = select_trivial(valid_options)
        if trivial_options and len(trivial_options) < len(valid_options):
            merged_options = []
            for option in valid_options:
                if option in trivial_options:
                    continue
                if option is not None:
                    merged_option: list[Constraint] | None = [merge_with_any(c) for c in option]
                else:
                    merged_option = None
                merged_options.append(merged_option)
            return any_constraints(list(merged_options), eager)

    # If normal logic didn't work, try excluding trivially unsatisfiable constraint (due to
    # upper bounds) from each option, and comparing them again.
    filtered_options = [filter_satisfiable(o) for o in options]
    if filtered_options != options:
        return any_constraints(filtered_options, eager=eager)

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


def filter_satisfiable(option: list[Constraint] | None) -> list[Constraint] | None:
    """Keep only constraints that can possibly be satisfied.

    Currently, we filter out constraints where target is not a subtype of the upper bound.
    Since those can be never satisfied. We may add more cases in future if it improves type
    inference.
    """
    if not option:
        return option
    satisfiable = []
    for c in option:
        if isinstance(c.origin_type_var, TypeVarType) and c.origin_type_var.values:
            if any(
                mypy.subtypes.is_subtype(c.target, value) for value in c.origin_type_var.values
            ):
                satisfiable.append(c)
        elif mypy.subtypes.is_subtype(c.target, c.origin_type_var.upper_bound):
            satisfiable.append(c)
    if not satisfiable:
        return None
    return satisfiable


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:
    # Ignore direction when comparing constraints against Any.
    skip_op_check = isinstance(get_proper_type(c1.target), AnyType) and isinstance(
        get_proper_type(c2.target), AnyType
    )
    return (
        c1.type_var == c2.type_var
        and (c1.op == c2.op or skip_op_check)
        and mypy.subtypes.is_same_type(c1.target, c2.target)
    )


def is_similar_constraints(x: list[Constraint], y: list[Constraint]) -> bool:
    """Check that two lists of constraints have similar structure.

    This means that each list has same type variable plus direction pairs (i.e we
    ignore the target). Except for constraints where target is Any type, there
    we ignore direction as well.
    """
    return _is_similar_constraints(x, y) and _is_similar_constraints(y, x)


def _is_similar_constraints(x: list[Constraint], y: list[Constraint]) -> bool:
    """Check that every constraint in the first list has a similar one in the second.

    See docstring above for definition of similarity.
    """
    for c1 in x:
        has_similar = False
        for c2 in y:
            # Ignore direction when either constraint is against Any.
            skip_op_check = isinstance(get_proper_type(c1.target), AnyType) or isinstance(
                get_proper_type(c2.target), AnyType
            )
            if c1.type_var == c2.type_var and (c1.op == c2.op or skip_op_check):
                has_similar = True
                break
        if not has_similar:
            return False
    return True


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

    def __init__(self, actual: ProperType, direction: int, skip_neg_op: bool) -> None:
        # Direction must be SUBTYPE_OF or SUPERTYPE_OF.
        self.actual = actual
        self.direction = direction
        # Whether to skip polymorphic inference (involves inference in opposite direction)
        # this is used to prevent infinite recursion when both template and actual are
        # generic callables.
        self.skip_neg_op = skip_neg_op

    # 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)"
        )

    def visit_param_spec(self, template: ParamSpecType) -> list[Constraint]:
        # Can't infer ParamSpecs from component values (only via Callable[P, T]).
        return []

    def visit_type_var_tuple(self, template: TypeVarTupleType) -> list[Constraint]:
        raise NotImplementedError

    def visit_unpack_type(self, template: UnpackType) -> list[Constraint]:
        raise RuntimeError("Mypy bug: unpack should be handled at a higher level.")

    def visit_parameters(self, template: Parameters) -> list[Constraint]:
        # Constraining Any against C[P] turns into infer_against_any([P], Any)
        if isinstance(self.actual, AnyType):
            return self.infer_against_any(template.arg_types, self.actual)
        if type_state.infer_polymorphic and isinstance(self.actual, Parameters):
            # For polymorphic inference we need to be able to infer secondary constraints
            # in situations like [x: T] <: P <: [x: int].
            return infer_callable_arguments_constraints(template, self.actual, self.direction)
        if type_state.infer_polymorphic and isinstance(self.actual, ParamSpecType):
            # Similar for [x: T] <: Q <: Concatenate[int, P].
            return infer_callable_arguments_constraints(
                template, self.actual.prefix, self.direction
            )
        # There also may be unpatched types after a user error, simply ignore them.
        return []

    # Non-leaf types

    def visit_instance(self, template: Instance) -> list[Constraint]:
        original_actual = actual = self.actual
        res: list[Constraint] = []
        if isinstance(actual, (CallableType, Overloaded)) and template.type.is_protocol:
            if "__call__" in template.type.protocol_members:
                # Special case: a generic callback protocol
                if not any(template == t for t in template.type.inferring):
                    template.type.inferring.append(template)
                    call = mypy.subtypes.find_member(
                        "__call__", template, actual, is_operator=True
                    )
                    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()
        if isinstance(actual, CallableType) and actual.fallback is not None:
            if actual.is_type_obj() and template.type.is_protocol:
                ret_type = get_proper_type(actual.ret_type)
                if isinstance(ret_type, TupleType):
                    ret_type = mypy.typeops.tuple_fallback(ret_type)
                if isinstance(ret_type, Instance):
                    if self.direction == SUBTYPE_OF:
                        subtype = template
                    else:
                        subtype = ret_type
                    res.extend(
                        self.infer_constraints_from_protocol_members(
                            ret_type, template, subtype, template, class_obj=True
                        )
                    )
            actual = actual.fallback
        if isinstance(actual, TypeType) and template.type.is_protocol:
            if isinstance(actual.item, Instance):
                if self.direction == SUBTYPE_OF:
                    subtype = template
                else:
                    subtype = actual.item
                res.extend(
                    self.infer_constraints_from_protocol_members(
                        actual.item, template, subtype, template, class_obj=True
                    )
                )
            if self.direction == SUPERTYPE_OF:
                # Infer constraints for Type[T] via metaclass of T when it makes sense.
                a_item = actual.item
                if isinstance(a_item, TypeVarType):
                    a_item = get_proper_type(a_item.upper_bound)
                if isinstance(a_item, Instance) and a_item.type.metaclass_type:
                    res.extend(
                        self.infer_constraints_from_protocol_members(
                            a_item.type.metaclass_type, template, actual, template
                        )
                    )

        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, LiteralType):
            actual = actual.fallback
        if isinstance(actual, Instance):
            instance = actual
            erased = erase_typevars(template)
            assert isinstance(erased, Instance)  # type: ignore[misc]
            # 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

                if instance.type.has_type_var_tuple_type:
                    # Variadic types need special handling to map each type argument to
                    # the correct corresponding type variable.
                    assert instance.type.type_var_tuple_prefix is not None
                    assert instance.type.type_var_tuple_suffix is not None
                    prefix_len = instance.type.type_var_tuple_prefix
                    suffix_len = instance.type.type_var_tuple_suffix
                    tvt = instance.type.defn.type_vars[prefix_len]
                    assert isinstance(tvt, TypeVarTupleType)
                    fallback = tvt.tuple_fallback
                    i_prefix, i_middle, i_suffix = split_with_prefix_and_suffix(
                        instance.args, prefix_len, suffix_len
                    )
                    m_prefix, m_middle, m_suffix = split_with_prefix_and_suffix(
                        mapped.args, prefix_len, suffix_len
                    )
                    instance_args = i_prefix + (TupleType(list(i_middle), fallback),) + i_suffix
                    mapped_args = m_prefix + (TupleType(list(m_middle), fallback),) + m_suffix
                else:
                    mapped_args = mapped.args
                    instance_args = instance.args

                # N.B: We use zip instead of indexing because the lengths might have
                # mismatches during daemon reprocessing.
                for tvar, mapped_arg, instance_arg in zip(tvars, mapped_args, instance_args):
                    if isinstance(tvar, TypeVarType):
                        # The constraints for generic type parameters depend on variance.
                        # Include constraints from both directions if invariant.
                        if tvar.variance != CONTRAVARIANT:
                            res.extend(infer_constraints(mapped_arg, instance_arg, self.direction))
                        if tvar.variance != COVARIANT:
                            res.extend(
                                infer_constraints(mapped_arg, instance_arg, neg_op(self.direction))
                            )
                    elif isinstance(tvar, ParamSpecType) and isinstance(mapped_arg, ParamSpecType):
                        prefix = mapped_arg.prefix
                        if isinstance(instance_arg, Parameters):
                            # No such thing as variance for ParamSpecs, consider them invariant
                            # TODO: constraints between prefixes using
                            # infer_callable_arguments_constraints()
                            suffix: Type = instance_arg.copy_modified(
                                instance_arg.arg_types[len(prefix.arg_types) :],
                                instance_arg.arg_kinds[len(prefix.arg_kinds) :],
                                instance_arg.arg_names[len(prefix.arg_names) :],
                            )
                            res.append(Constraint(mapped_arg, SUBTYPE_OF, suffix))
                            res.append(Constraint(mapped_arg, SUPERTYPE_OF, suffix))
                        elif isinstance(instance_arg, ParamSpecType):
                            suffix = instance_arg.copy_modified(
                                prefix=Parameters(
                                    instance_arg.prefix.arg_types[len(prefix.arg_types) :],
                                    instance_arg.prefix.arg_kinds[len(prefix.arg_kinds) :],
                                    instance_arg.prefix.arg_names[len(prefix.arg_names) :],
                                )
                            )
                            res.append(Constraint(mapped_arg, SUBTYPE_OF, suffix))
                            res.append(Constraint(mapped_arg, SUPERTYPE_OF, suffix))
                    elif isinstance(tvar, TypeVarTupleType):
                        # Handle variadic type variables covariantly for consistency.
                        res.extend(infer_constraints(mapped_arg, instance_arg, 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
                if template.type.has_type_var_tuple_type:
                    # Variadic types need special handling to map each type argument to
                    # the correct corresponding type variable.
                    assert template.type.type_var_tuple_prefix is not None
                    assert template.type.type_var_tuple_suffix is not None
                    prefix_len = template.type.type_var_tuple_prefix
                    suffix_len = template.type.type_var_tuple_suffix
                    tvt = template.type.defn.type_vars[prefix_len]
                    assert isinstance(tvt, TypeVarTupleType)
                    fallback = tvt.tuple_fallback
                    t_prefix, t_middle, t_suffix = split_with_prefix_and_suffix(
                        template.args, prefix_len, suffix_len
                    )
                    m_prefix, m_middle, m_suffix = split_with_prefix_and_suffix(
                        mapped.args, prefix_len, suffix_len
                    )
                    template_args = t_prefix + (TupleType(list(t_middle), fallback),) + t_suffix
                    mapped_args = m_prefix + (TupleType(list(m_middle), fallback),) + m_suffix
                else:
                    mapped_args = mapped.args
                    template_args = template.args
                # N.B: We use zip instead of indexing because the lengths might have
                # mismatches during daemon reprocessing.
                for tvar, mapped_arg, template_arg in zip(tvars, mapped_args, template_args):
                    if isinstance(tvar, TypeVarType):
                        # The constraints for generic type parameters depend on variance.
                        # Include constraints from both directions if invariant.
                        if tvar.variance != CONTRAVARIANT:
                            res.extend(infer_constraints(template_arg, mapped_arg, self.direction))
                        if tvar.variance != COVARIANT:
                            res.extend(
                                infer_constraints(template_arg, mapped_arg, neg_op(self.direction))
                            )
                    elif isinstance(tvar, ParamSpecType) and isinstance(
                        template_arg, ParamSpecType
                    ):
                        prefix = template_arg.prefix
                        if isinstance(mapped_arg, Parameters):
                            # No such thing as variance for ParamSpecs, consider them invariant
                            # TODO: constraints between prefixes using
                            # infer_callable_arguments_constraints()
                            suffix = mapped_arg.copy_modified(
                                mapped_arg.arg_types[len(prefix.arg_types) :],
                                mapped_arg.arg_kinds[len(prefix.arg_kinds) :],
                                mapped_arg.arg_names[len(prefix.arg_names) :],
                            )
                            res.append(Constraint(template_arg, SUBTYPE_OF, suffix))
                            res.append(Constraint(template_arg, SUPERTYPE_OF, suffix))
                        elif isinstance(mapped_arg, ParamSpecType):
                            suffix = mapped_arg.copy_modified(
                                prefix=Parameters(
                                    mapped_arg.prefix.arg_types[len(prefix.arg_types) :],
                                    mapped_arg.prefix.arg_kinds[len(prefix.arg_kinds) :],
                                    mapped_arg.prefix.arg_names[len(prefix.arg_names) :],
                                )
                            )
                            res.append(Constraint(template_arg, SUBTYPE_OF, suffix))
                            res.append(Constraint(template_arg, SUPERTYPE_OF, suffix))
                    elif isinstance(tvar, TypeVarTupleType):
                        # Consider variadic type variables to be invariant.
                        res.extend(infer_constraints(template_arg, mapped_arg, SUBTYPE_OF))
                        res.extend(infer_constraints(template_arg, mapped_arg, SUPERTYPE_OF))
                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 to 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(template == t for t in reversed(template.type.inferring))
                and mypy.subtypes.is_protocol_implementation(instance, erased, skip=["__call__"])
            ):
                template.type.inferring.append(template)
                res.extend(
                    self.infer_constraints_from_protocol_members(
                        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(instance == i for i in reversed(instance.type.inferring))
                and mypy.subtypes.is_protocol_implementation(erased, instance, skip=["__call__"])
            ):
                instance.type.inferring.append(instance)
                res.extend(
                    self.infer_constraints_from_protocol_members(
                        instance, template, template, instance
                    )
                )
                instance.type.inferring.pop()
                return res
        if res:
            return res

        if isinstance(actual, AnyType):
            return self.infer_against_any(template.args, actual)
        if (
            isinstance(actual, TupleType)
            and is_named_instance(template, TUPLE_LIKE_INSTANCE_NAMES)
            and self.direction == SUPERTYPE_OF
        ):
            for item in actual.items:
                if isinstance(item, UnpackType):
                    unpacked = get_proper_type(item.type)
                    if isinstance(unpacked, TypeVarTupleType):
                        # Cannot infer anything for T from [T, ...] <: *Ts
                        continue
                    assert (
                        isinstance(unpacked, Instance)
                        and unpacked.type.fullname == "builtins.tuple"
                    )
                    item = unpacked.args[0]
                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)
        elif isinstance(actual, TypeVarType):
            if not actual.values and not actual.id.is_meta_var():
                return infer_constraints(template, actual.upper_bound, self.direction)
            return []
        elif isinstance(actual, ParamSpecType):
            return infer_constraints(template, actual.upper_bound, self.direction)
        elif isinstance(actual, TypeVarTupleType):
            raise NotImplementedError
        else:
            return []

    def infer_constraints_from_protocol_members(
        self,
        instance: Instance,
        template: Instance,
        subtype: Type,
        protocol: Instance,
        class_obj: bool = False,
    ) -> list[Constraint]:
        """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).
        """
        res = []
        for member in protocol.type.protocol_members:
            inst = mypy.subtypes.find_member(member, instance, subtype, class_obj=class_obj)
            temp = mypy.subtypes.find_member(member, template, subtype)
            if inst is None or temp is None:
                if member == "__call__":
                    continue
                return []  # See #11020
            # 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):
                # Settable members are invariant, add opposite constraints
                res.extend(infer_constraints(temp, inst, neg_op(self.direction)))
        return res

    def visit_callable_type(self, template: CallableType) -> list[Constraint]:
        # Normalize callables before matching against each other.
        # Note that non-normalized callables can be created in annotations
        # using e.g. callback protocols.
        # TODO: check that callables match? Ideally we should not infer constraints
        # callables that can never be subtypes of one another in given direction.
        template = template.with_unpacked_kwargs()
        extra_tvars = False
        if isinstance(self.actual, CallableType):
            res: list[Constraint] = []
            cactual = self.actual.with_unpacked_kwargs()
            param_spec = template.param_spec()

            template_ret_type, cactual_ret_type = template.ret_type, cactual.ret_type
            if template.type_guard is not None and cactual.type_guard is not None:
                template_ret_type = template.type_guard
                cactual_ret_type = cactual.type_guard

            if template.type_is is not None and cactual.type_is is not None:
                template_ret_type = template.type_is
                cactual_ret_type = cactual.type_is

            res.extend(infer_constraints(template_ret_type, cactual_ret_type, self.direction))

            if param_spec is None:
                # TODO: Erase template variables if it is generic?
                if (
                    type_state.infer_polymorphic
                    and cactual.variables
                    and not self.skip_neg_op
                    # Technically, the correct inferred type for application of e.g.
                    # Callable[..., T] -> Callable[..., T] (with literal ellipsis), to a generic
                    # like U -> U, should be Callable[..., Any], but if U is a self-type, we can
                    # allow it to leak, to be later bound to self. A bunch of existing code
                    # depends on this old behaviour.
                    and not any(tv.id.is_self() for tv in cactual.variables)
                ):
                    # If the actual callable is generic, infer constraints in the opposite
                    # direction, and indicate to the solver there are extra type variables
                    # to solve for (see more details in mypy/solve.py).
                    res.extend(
                        infer_constraints(
                            cactual, template, neg_op(self.direction), skip_neg_op=True
                        )
                    )
                    extra_tvars = True

                # We can't infer constraints from arguments if the template is Callable[..., T]
                # (with literal '...').
                if not template.is_ellipsis_args:
                    unpack_present = find_unpack_in_list(template.arg_types)
                    # When both ParamSpec and TypeVarTuple are present, things become messy
                    # quickly. For now, we only allow ParamSpec to "capture" TypeVarTuple,
                    # but not vice versa.
                    # TODO: infer more from prefixes when possible.
                    if unpack_present is not None and not cactual.param_spec():
                        # We need to re-normalize args to the form they appear in tuples,
                        # for callables we always pack the suffix inside another tuple.
                        unpack = template.arg_types[unpack_present]
                        assert isinstance(unpack, UnpackType)
                        tuple_type = get_tuple_fallback_from_unpack(unpack)
                        template_types = repack_callable_args(template, tuple_type)
                        actual_types = repack_callable_args(cactual, tuple_type)
                        # Now we can use the same general helper as for tuple types.
                        unpack_constraints = build_constraints_for_simple_unpack(
                            template_types, actual_types, neg_op(self.direction)
                        )
                        res.extend(unpack_constraints)
                    else:
                        # TODO: do we need some special-casing when unpack is present in actual
                        # callable but not in template callable?
                        res.extend(
                            infer_callable_arguments_constraints(template, cactual, self.direction)
                        )
            else:
                prefix = param_spec.prefix
                prefix_len = len(prefix.arg_types)
                cactual_ps = cactual.param_spec()

                if type_state.infer_polymorphic and cactual.variables and not self.skip_neg_op:
                    # Similar logic to the branch above.
                    res.extend(
                        infer_constraints(
                            cactual, template, neg_op(self.direction), skip_neg_op=True
                        )
                    )
                    extra_tvars = True

                # Compare prefixes as well
                cactual_prefix = cactual.copy_modified(
                    arg_types=cactual.arg_types[:prefix_len],
                    arg_kinds=cactual.arg_kinds[:prefix_len],
                    arg_names=cactual.arg_names[:prefix_len],
                )
                res.extend(
                    infer_callable_arguments_constraints(prefix, cactual_prefix, self.direction)
                )

                param_spec_target: Type | None = None
                if not cactual_ps:
                    max_prefix_len = len([k for k in cactual.arg_kinds if k in (ARG_POS, ARG_OPT)])
                    prefix_len = min(prefix_len, max_prefix_len)
                    param_spec_target = Parameters(
                        arg_types=cactual.arg_types[prefix_len:],
                        arg_kinds=cactual.arg_kinds[prefix_len:],
                        arg_names=cactual.arg_names[prefix_len:],
                        variables=cactual.variables if not type_state.infer_polymorphic else [],
                        imprecise_arg_kinds=cactual.imprecise_arg_kinds,
                    )
                else:
                    if len(param_spec.prefix.arg_types) <= len(cactual_ps.prefix.arg_types):
                        param_spec_target = cactual_ps.copy_modified(
                            prefix=Parameters(
                                arg_types=cactual_ps.prefix.arg_types[prefix_len:],
                                arg_kinds=cactual_ps.prefix.arg_kinds[prefix_len:],
                                arg_names=cactual_ps.prefix.arg_names[prefix_len:],
                                imprecise_arg_kinds=cactual_ps.prefix.imprecise_arg_kinds,
                            )
                        )
                if param_spec_target is not None:
                    res.append(Constraint(param_spec, self.direction, param_spec_target))
            if extra_tvars:
                for c in res:
                    c.extra_tvars += cactual.variables
            return res
        elif isinstance(self.actual, AnyType):
            param_spec = template.param_spec()
            any_type = AnyType(TypeOfAny.from_another_any, source_any=self.actual)
            if param_spec is None:
                # FIX what if generic
                res = self.infer_against_any(template.arg_types, self.actual)
            else:
                res = [
                    Constraint(
                        param_spec,
                        SUBTYPE_OF,
                        Parameters([any_type, any_type], [ARG_STAR, ARG_STAR2], [None, None]),
                    )
                ]
            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, is_operator=True
            )
            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 that is callable compatible. 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, item, self.direction)

    def visit_tuple_type(self, template: TupleType) -> list[Constraint]:
        actual = self.actual
        unpack_index = find_unpack_in_list(template.items)
        is_varlength_tuple = (
            isinstance(actual, Instance) and actual.type.fullname == "builtins.tuple"
        )

        if isinstance(actual, TupleType) or is_varlength_tuple:
            res: list[Constraint] = []
            if unpack_index is not None:
                if is_varlength_tuple:
                    # Variadic tuple can be only a supertype of a tuple type, but even if
                    # direction is opposite, inferring something may give better error messages.
                    unpack_type = template.items[unpack_index]
                    assert isinstance(unpack_type, UnpackType)
                    unpacked_type = get_proper_type(unpack_type.type)
                    if isinstance(unpacked_type, TypeVarTupleType):
                        res = [
                            Constraint(type_var=unpacked_type, op=self.direction, target=actual)
                        ]
                    else:
                        assert (
                            isinstance(unpacked_type, Instance)
                            and unpacked_type.type.fullname == "builtins.tuple"
                        )
                        res = infer_constraints(unpacked_type, actual, self.direction)
                    assert isinstance(actual, Instance)  # ensured by is_varlength_tuple == True
                    for i, ti in enumerate(template.items):
                        if i == unpack_index:
                            # This one we just handled above.
                            continue
                        # For Tuple[T, *Ts, S] <: tuple[X, ...] infer also T <: X and S <: X.
                        res.extend(infer_constraints(ti, actual.args[0], self.direction))
                    return res
                else:
                    assert isinstance(actual, TupleType)
                    unpack_constraints = build_constraints_for_simple_unpack(
                        template.items, actual.items, self.direction
                    )
                    actual_items: tuple[Type, ...] = ()
                    template_items: tuple[Type, ...] = ()
                    res.extend(unpack_constraints)
            elif isinstance(actual, TupleType):
                a_unpack_index = find_unpack_in_list(actual.items)
                if a_unpack_index is not None:
                    # The case where template tuple doesn't have an unpack, but actual tuple
                    # has an unpack. We can infer something if actual unpack is a variadic tuple.
                    # Tuple[T, S, U] <: tuple[X, *tuple[Y, ...], Z] => T <: X, S <: Y, U <: Z.
                    a_unpack = actual.items[a_unpack_index]
                    assert isinstance(a_unpack, UnpackType)
                    a_unpacked = get_proper_type(a_unpack.type)
                    if len(actual.items) + 1 <= len(template.items):
                        a_prefix_len = a_unpack_index
                        a_suffix_len = len(actual.items) - a_unpack_index - 1
                        t_prefix, t_middle, t_suffix = split_with_prefix_and_suffix(
                            tuple(template.items), a_prefix_len, a_suffix_len
                        )
                        actual_items = tuple(actual.items[:a_prefix_len])
                        if a_suffix_len:
                            actual_items += tuple(actual.items[-a_suffix_len:])
                        template_items = t_prefix + t_suffix
                        if isinstance(a_unpacked, Instance):
                            assert a_unpacked.type.fullname == "builtins.tuple"
                            for tm in t_middle:
                                res.extend(
                                    infer_constraints(tm, a_unpacked.args[0], self.direction)
                                )
                    else:
                        actual_items = ()
                        template_items = ()
                else:
                    actual_items = tuple(actual.items)
                    template_items = tuple(template.items)
            else:
                return res

            # Cases above will return if actual wasn't a TupleType.
            assert isinstance(actual, TupleType)
            if len(actual_items) == len(template_items):
                if (
                    actual.partial_fallback.type.is_named_tuple
                    and template.partial_fallback.type.is_named_tuple
                ):
                    # For named tuples using just the fallbacks usually gives better results.
                    return res + infer_constraints(
                        template.partial_fallback, actual.partial_fallback, self.direction
                    )
                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: 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 visit_type_alias_type(self, template: TypeAliasType) -> list[Constraint]:
        assert False, f"This should be never called, got {template}"

    def infer_against_any(self, types: Iterable[Type], any_type: AnyType) -> list[Constraint]:
        res: list[Constraint] = []
        for t in types:
            if isinstance(t, UnpackType):
                if isinstance(t.type, TypeVarTupleType):
                    res.append(Constraint(t.type, self.direction, any_type))
                else:
                    unpacked = get_proper_type(t.type)
                    assert isinstance(unpacked, Instance)
                    res.extend(infer_constraints(unpacked, any_type, self.direction))
            else:
                # Note that we ignore variance and simply always use the
                # original direction. This is because for Any targets direction is
                # irrelevant in most cases, see e.g. is_same_constraint().
                res.extend(infer_constraints(t, any_type, self.direction))
        return res

    def visit_overloaded(self, template: Overloaded) -> list[Constraint]:
        if isinstance(self.actual, CallableType):
            items = find_matching_overload_items(template, self.actual)
        else:
            items = template.items
        res: list[Constraint] = []
        for t in 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(f"Invalid operator {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,
            is_proper_subtype=False,
            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]


def find_matching_overload_items(
    overloaded: Overloaded, template: CallableType
) -> list[CallableType]:
    """Like find_matching_overload_item, but return all matches, not just the first."""
    items = overloaded.items
    res = []
    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,
            is_proper_subtype=False,
            ignore_return=True,
        ):
            res.append(item)
    if not res:
        # Falling back to all items if we can't find a match is pretty arbitrary, but
        # it maintains backward compatibility.
        res = items.copy()
    return res


def get_tuple_fallback_from_unpack(unpack: UnpackType) -> TypeInfo:
    """Get builtins.tuple type from available types to construct homogeneous tuples."""
    tp = get_proper_type(unpack.type)
    if isinstance(tp, Instance) and tp.type.fullname == "builtins.tuple":
        return tp.type
    if isinstance(tp, TypeVarTupleType):
        return tp.tuple_fallback.type
    if isinstance(tp, TupleType):
        for base in tp.partial_fallback.type.mro:
            if base.fullname == "builtins.tuple":
                return base
    assert False, "Invalid unpack type"


def repack_callable_args(callable: CallableType, tuple_type: TypeInfo) -> list[Type]:
    """Present callable with star unpack in a normalized form.

    Since positional arguments cannot follow star argument, they are packed in a suffix,
    while prefix is represented as individual positional args. We want to put all in a single
    list with unpack in the middle, and prefix/suffix on the sides (as they would appear
    in e.g. a TupleType).
    """
    if ARG_STAR not in callable.arg_kinds:
        return callable.arg_types
    star_index = callable.arg_kinds.index(ARG_STAR)
    arg_types = callable.arg_types[:star_index]
    star_type = callable.arg_types[star_index]
    suffix_types = []
    if not isinstance(star_type, UnpackType):
        # Re-normalize *args: X -> *args: *tuple[X, ...]
        star_type = UnpackType(Instance(tuple_type, [star_type]))
    else:
        tp = get_proper_type(star_type.type)
        if isinstance(tp, TupleType):
            assert isinstance(tp.items[0], UnpackType)
            star_type = tp.items[0]
            suffix_types = tp.items[1:]
    return arg_types + [star_type] + suffix_types


def build_constraints_for_simple_unpack(
    template_args: list[Type], actual_args: list[Type], direction: int
) -> list[Constraint]:
    """Infer constraints between two lists of types with variadic items.

    This function is only supposed to be called when a variadic item is present in templates.
    If there is no variadic item the actuals, we simply use split_with_prefix_and_suffix()
    and infer prefix <: prefix, suffix <: suffix, variadic <: middle. If there is a variadic
    item in the actuals we need to be more careful, only common prefix/suffix can generate
    constraints, also we can only infer constraints for variadic template item, if template
    prefix/suffix are shorter that actual ones, otherwise there may be partial overlap
    between variadic items, for example if template prefix is longer:

        templates: T1, T2, Ts, Ts, Ts, ...
        actuals:   A1, As, As, As, ...

    Note: this function can only be called for builtin variadic constructors: Tuple and Callable.
    For instances, you should first find correct type argument mapping.
    """
    template_unpack = find_unpack_in_list(template_args)
    assert template_unpack is not None
    template_prefix = template_unpack
    template_suffix = len(template_args) - template_prefix - 1

    t_unpack = None
    res = []

    actual_unpack = find_unpack_in_list(actual_args)
    if actual_unpack is None:
        t_unpack = template_args[template_unpack]
        if template_prefix + template_suffix > len(actual_args):
            # These can't be subtypes of each-other, return fast.
            assert isinstance(t_unpack, UnpackType)
            if isinstance(t_unpack.type, TypeVarTupleType):
                # Set TypeVarTuple to empty to improve error messages.
                return [
                    Constraint(
                        t_unpack.type, direction, TupleType([], t_unpack.type.tuple_fallback)
                    )
                ]
            else:
                return []
        common_prefix = template_prefix
        common_suffix = template_suffix
    else:
        actual_prefix = actual_unpack
        actual_suffix = len(actual_args) - actual_prefix - 1
        common_prefix = min(template_prefix, actual_prefix)
        common_suffix = min(template_suffix, actual_suffix)
        if actual_prefix >= template_prefix and actual_suffix >= template_suffix:
            # This is the only case where we can guarantee there will be no partial overlap
            # (note however partial overlap is OK for variadic tuples, it is handled below).
            t_unpack = template_args[template_unpack]

    # Handle constraints from prefixes/suffixes first.
    start, middle, end = split_with_prefix_and_suffix(
        tuple(actual_args), common_prefix, common_suffix
    )
    for t, a in zip(template_args[:common_prefix], start):
        res.extend(infer_constraints(t, a, direction))
    if common_suffix:
        for t, a in zip(template_args[-common_suffix:], end):
            res.extend(infer_constraints(t, a, direction))

    if t_unpack is not None:
        # Add constraint(s) for variadic item when possible.
        assert isinstance(t_unpack, UnpackType)
        tp = get_proper_type(t_unpack.type)
        if isinstance(tp, Instance) and tp.type.fullname == "builtins.tuple":
            # Homogeneous case *tuple[T, ...] <: [X, Y, Z, ...].
            for a in middle:
                # TODO: should we use union instead of join here?
                if not isinstance(a, UnpackType):
                    res.extend(infer_constraints(tp.args[0], a, direction))
                else:
                    a_tp = get_proper_type(a.type)
                    # This is the case *tuple[T, ...] <: *tuple[A, ...].
                    if isinstance(a_tp, Instance) and a_tp.type.fullname == "builtins.tuple":
                        res.extend(infer_constraints(tp.args[0], a_tp.args[0], direction))
        elif isinstance(tp, TypeVarTupleType):
            res.append(Constraint(tp, direction, TupleType(list(middle), tp.tuple_fallback)))
    elif actual_unpack is not None:
        # A special case for a variadic tuple unpack, we simply infer T <: X from
        # Tuple[..., *tuple[T, ...], ...] <: Tuple[..., *tuple[X, ...], ...].
        actual_unpack_type = actual_args[actual_unpack]
        assert isinstance(actual_unpack_type, UnpackType)
        a_unpacked = get_proper_type(actual_unpack_type.type)
        if isinstance(a_unpacked, Instance) and a_unpacked.type.fullname == "builtins.tuple":
            t_unpack = template_args[template_unpack]
            assert isinstance(t_unpack, UnpackType)
            tp = get_proper_type(t_unpack.type)
            if isinstance(tp, Instance) and tp.type.fullname == "builtins.tuple":
                res.extend(infer_constraints(tp.args[0], a_unpacked.args[0], direction))
    return res


def infer_directed_arg_constraints(left: Type, right: Type, direction: int) -> list[Constraint]:
    """Infer constraints between two arguments using direction between original callables."""
    if isinstance(left, (ParamSpecType, UnpackType)) or isinstance(
        right, (ParamSpecType, UnpackType)
    ):
        # This avoids bogus constraints like T <: P.args
        # TODO: can we infer something useful for *T vs P?
        return []
    if direction == SUBTYPE_OF:
        # We invert direction to account for argument contravariance.
        return infer_constraints(left, right, neg_op(direction))
    else:
        return infer_constraints(right, left, neg_op(direction))


def infer_callable_arguments_constraints(
    template: NormalizedCallableType | Parameters,
    actual: NormalizedCallableType | Parameters,
    direction: int,
) -> list[Constraint]:
    """Infer constraints between argument types of two callables.

    This function essentially extracts four steps from are_parameters_compatible() in
    subtypes.py that involve subtype checks between argument types. We keep the argument
    matching logic, but ignore various strictness flags present there, and checks that
    do not involve subtyping. Then in place of every subtype check we put an infer_constraints()
    call for the same types.
    """
    res = []
    if direction == SUBTYPE_OF:
        left, right = template, actual
    else:
        left, right = actual, template
    left_star = left.var_arg()
    left_star2 = left.kw_arg()
    right_star = right.var_arg()
    right_star2 = right.kw_arg()

    # Numbering of steps below matches the one in are_parameters_compatible() for convenience.
    # Phase 1a: compare star vs star arguments.
    if left_star is not None and right_star is not None:
        res.extend(infer_directed_arg_constraints(left_star.typ, right_star.typ, direction))
    if left_star2 is not None and right_star2 is not None:
        res.extend(infer_directed_arg_constraints(left_star2.typ, right_star2.typ, direction))

    # Phase 1b: compare left args with corresponding non-star right arguments.
    for right_arg in right.formal_arguments():
        left_arg = mypy.typeops.callable_corresponding_argument(left, right_arg)
        if left_arg is None:
            continue
        res.extend(infer_directed_arg_constraints(left_arg.typ, right_arg.typ, direction))

    # Phase 1c: compare left args with right *args.
    if right_star is not None:
        right_by_position = right.try_synthesizing_arg_from_vararg(None)
        assert right_by_position is not None
        i = right_star.pos
        assert i is not None
        while i < len(left.arg_kinds) and left.arg_kinds[i].is_positional():
            left_by_position = left.argument_by_position(i)
            assert left_by_position is not None
            res.extend(
                infer_directed_arg_constraints(
                    left_by_position.typ, right_by_position.typ, direction
                )
            )
            i += 1

    # Phase 1d: compare left args with right **kwargs.
    if right_star2 is not None:
        right_names = {name for name in right.arg_names if name is not None}
        left_only_names = set()
        for name, kind in zip(left.arg_names, left.arg_kinds):
            if name is None or kind.is_star() or name in right_names:
                continue
            left_only_names.add(name)

        right_by_name = right.try_synthesizing_arg_from_kwarg(None)
        assert right_by_name is not None
        for name in left_only_names:
            left_by_name = left.argument_by_name(name)
            assert left_by_name is not None
            res.extend(
                infer_directed_arg_constraints(left_by_name.typ, right_by_name.typ, direction)
            )
    return res


def filter_imprecise_kinds(cs: list[Constraint]) -> list[Constraint]:
    """For each ParamSpec remove all imprecise constraints, if at least one precise available."""
    have_precise = set()
    for c in cs:
        if not isinstance(c.origin_type_var, ParamSpecType):
            continue
        if (
            isinstance(c.target, ParamSpecType)
            or isinstance(c.target, Parameters)
            and not c.target.imprecise_arg_kinds
        ):
            have_precise.add(c.type_var)
    new_cs = []
    for c in cs:
        if not isinstance(c.origin_type_var, ParamSpecType) or c.type_var not in have_precise:
            new_cs.append(c)
        if not isinstance(c.target, Parameters) or not c.target.imprecise_arg_kinds:
            new_cs.append(c)
    return new_cs
