def typed_dict_get_callback(ctx: MethodContext) -> Type:
    """Infer a precise return type for TypedDict.get with literal first argument."""
    if (isinstance(ctx.type, TypedDictType)
            and len(ctx.arg_types) >= 1
            and len(ctx.arg_types[0]) == 1):
        key = try_getting_str_literal(ctx.args[0][0], ctx.arg_types[0][0])
        if key is None:
            return ctx.default_return_type

        value_type = ctx.type.items.get(key)
        if value_type:
            if len(ctx.arg_types) == 1:
                return UnionType.make_simplified_union([value_type, NoneTyp()])
            elif (len(ctx.arg_types) == 2 and len(ctx.arg_types[1]) == 1
                  and len(ctx.args[1]) == 1):
                default_arg = ctx.args[1][0]
                if (isinstance(default_arg, DictExpr) and len(default_arg.items) == 0
                        and isinstance(value_type, TypedDictType)):
                    # Special case '{}' as the default for a typed dict type.
                    return value_type.copy_modified(required_keys=set())
                else:
                    return UnionType.make_simplified_union([value_type, ctx.arg_types[1][0]])
        else:
            ctx.api.msg.typeddict_key_not_found(ctx.type, key, ctx.context)
            return AnyType(TypeOfAny.from_error)
    return ctx.default_return_type

def typed_dict_pop_signature_callback(ctx: MethodSigContext) -> CallableType:
    """Try to infer a better signature type for TypedDict.pop.

    This is used to get better type context for the second argument that
    depends on a TypedDict value type.
    """
    signature = ctx.default_signature
    str_type = ctx.api.named_generic_type('builtins.str', [])
    if (isinstance(ctx.type, TypedDictType)
            and len(ctx.args) == 2
            and len(ctx.args[0]) == 1
            and isinstance(ctx.args[0][0], StrExpr)
            and len(signature.arg_types) == 2
            and len(signature.variables) == 1
            and len(ctx.args[1]) == 1):
        key = ctx.args[0][0].value
        value_type = ctx.type.items.get(key)
        if value_type:
            # Tweak the signature to include the value type as context. It's
            # only needed for type inference since there's a union with a type
            # variable that accepts everything.
            tv = TypeVarType(signature.variables[0])
            typ = UnionType.make_simplified_union([value_type, tv])
            return signature.copy_modified(
                arg_types=[str_type, typ],
                ret_type=typ)
    return signature.copy_modified(arg_types=[str_type, signature.arg_types[1]])

def _autoconvertible_to_cdata(tp: Type, api: 'mypy.plugin.CheckerPluginInterface') -> Type:
    """Get a type that is compatible with all types that can be implicitly converted to the given
    CData type.

    Examples:
    * c_int -> Union[c_int, int]
    * c_char_p -> Union[c_char_p, bytes, int, NoneType]
    * MyStructure -> MyStructure
    """
    allowed_types = []
    # If tp is a union, we allow all types that are convertible to at least one of the union
    # items. This is not quite correct - strictly speaking, only types convertible to *all* of the
    # union items should be allowed. This may be worth changing in the future, but the more
    # correct algorithm could be too strict to be useful.
    for t in union_items(tp):
        # Every type can be converted from itself (obviously).
        allowed_types.append(t)
        if isinstance(t, Instance):
            unboxed = _find_simplecdata_base_arg(t, api)
            if unboxed is not None:
                # If _SimpleCData appears in tp's (direct or indirect) bases, its type argument
                # specifies the type's "unboxed" version, which can always be converted back to
                # the original "boxed" type.
                allowed_types.append(unboxed)

                if t.type.has_base('ctypes._PointerLike'):
                    # Pointer-like _SimpleCData subclasses can also be converted from
                    # an int or None.
                    allowed_types.append(api.named_generic_type('builtins.int', []))
                    allowed_types.append(NoneTyp())

    return UnionType.make_simplified_union(allowed_types)

def typed_dict_get_signature_callback(ctx: MethodSigContext) -> CallableType:
    """Try to infer a better signature type for TypedDict.get.

    This is used to get better type context for the second argument that
    depends on a TypedDict value type.
    """
    signature = ctx.default_signature
    if (isinstance(ctx.type, TypedDictType)
            and len(ctx.args) == 2
            and len(ctx.args[0]) == 1
            and isinstance(ctx.args[0][0], StrExpr)
            and len(signature.arg_types) == 2
            and len(signature.variables) == 1
            and len(ctx.args[1]) == 1):
        key = ctx.args[0][0].value
        value_type = ctx.type.items.get(key)
        ret_type = signature.ret_type
        if value_type:
            default_arg = ctx.args[1][0]
            if (isinstance(value_type, TypedDictType)
                    and isinstance(default_arg, DictExpr)
                    and len(default_arg.items) == 0):
                # Caller has empty dict {} as default for typed dict.
                value_type = value_type.copy_modified(required_keys=set())
            # Tweak the signature to include the value type as context. It's
            # only needed for type inference since there's a union with a type
            # variable that accepts everything.
            tv = TypeVarType(signature.variables[0])
            return signature.copy_modified(
                arg_types=[signature.arg_types[0],
                           UnionType.make_simplified_union([value_type, tv])],
                ret_type=ret_type)
    return signature

def join_simple(declaration: Type, s: Type, t: Type) -> Type:
    """Return a simple least upper bound given the declared type."""

    if isinstance(s, AnyType):
        return s

    if isinstance(s, NoneTyp) and not isinstance(t, Void):
        return t

    if isinstance(s, ErasedType):
        return t

    if is_subtype(s, t):
        return t

    if is_subtype(t, s):
        return s

    if isinstance(declaration, UnionType):
        return UnionType.make_simplified_union([s, t])

    value = t.accept(TypeJoinVisitor(s))

    if value is None:
        # XXX this code path probably should be avoided.
        # It seems to happen when a line (x = y) is a type error, and
        # it's not clear that assuming that x is arbitrary afterward
        # is a good idea.
        return declaration

    if declaration is None or is_subtype(value, declaration):
        return value

    return declaration

def meet_simple_away(s: Type, t: Type) -> Type:
    if isinstance(s, UnionType):
        return UnionType.make_simplified_union([x for x in s.items
                                                if not is_subtype(x, t)])
    elif not isinstance(s, AnyType) and is_subtype(s, t):
        return Void()
    else:
        return s

 def visit_union_type(self, t: UnionType) -> Type:
     if isinstance(self.s, UnionType):
         meets = []  # type: List[Type]
         for x in t.items:
             for y in self.s.items:
                 meets.append(meet_types(x, y))
     else:
         meets = [meet_types(x, self.s) for x in t.items]
     return UnionType.make_simplified_union(meets)

 def visit_none_type(self, t: NoneTyp) -> Type:
     if state.strict_optional:
         if isinstance(self.s, (NoneTyp, UninhabitedType)):
             return t
         elif isinstance(self.s, UnboundType):
             return AnyType(TypeOfAny.special_form)
         else:
             return UnionType.make_simplified_union([self.s, t])
     else:
         return self.s

def restrict_subtype_away(t: Type, s: Type) -> Type:
    """Return a supertype of (t intersect not s)

    Currently just remove elements of a union type.
    """
    if isinstance(t, UnionType):
        new_items = [item for item in t.items if not is_subtype(item, s)]
        return UnionType.make_union(new_items)
    else:
        return t

 def visit_none_type(self, t: NoneTyp) -> Type:
     if experiments.STRICT_OPTIONAL:
         if isinstance(self.s, (NoneTyp, UninhabitedType)):
             return t
         elif isinstance(self.s, UnboundType):
             return AnyType(TypeOfAny.special_form)
         else:
             return UnionType.make_simplified_union([self.s, t])
     else:
         return self.s

def generate_type_combinations(types: List[Type]) -> List[Type]:
    """Generate possible combinations of a list of types.

    mypy essentially supports two different ways to do this: joining the types
    and unioning the types. We try both.
    """
    joined_type = join_type_list(types)
    union_type = UnionType.make_simplified_union(types)
    if is_same_type(joined_type, union_type):
        return [joined_type]
    else:
        return [joined_type, union_type]

def meet_simple(s: Type, t: Type, default_right: bool = True) -> Type:
    if s == t:
        return s
    if isinstance(s, UnionType):
        return UnionType.make_simplified_union([meet_types(x, t) for x in s.items])
    elif not is_overlapping_types(s, t):
        return Void()
    else:
        if default_right:
            return t
        else:
            return s

def narrow_declared_type(declared: Type, narrowed: Type) -> Type:
    """Return the declared type narrowed down to another type."""
    if declared == narrowed:
        return declared
    if isinstance(declared, UnionType):
        return UnionType.make_simplified_union([narrow_declared_type(x, narrowed)
                                                for x in declared.relevant_items()])
    elif not is_overlapping_types(declared, narrowed, use_promotions=True):
        if experiments.STRICT_OPTIONAL:
            return UninhabitedType()
        else:
            return NoneTyp()
    elif isinstance(narrowed, UnionType):
        return UnionType.make_simplified_union([narrow_declared_type(declared, x)
                                                for x in narrowed.relevant_items()])
    elif isinstance(narrowed, AnyType):
        return narrowed
    elif isinstance(declared, (Instance, TupleType)):
        return meet_types(declared, narrowed)
    elif isinstance(declared, TypeType) and isinstance(narrowed, TypeType):
        return TypeType.make_normalized(narrow_declared_type(declared.item, narrowed.item))
    return narrowed

def narrow_declared_type(declared: Type, narrowed: Type) -> Type:
    """Return the declared type narrowed down to another type."""
    if declared == narrowed:
        return declared
    if isinstance(declared, UnionType):
        return UnionType.make_simplified_union([narrow_declared_type(x, narrowed)
                                                for x in declared.relevant_items()])
    elif not is_overlapping_types(declared, narrowed,
                                  prohibit_none_typevar_overlap=True):
        if state.strict_optional:
            return UninhabitedType()
        else:
            return NoneTyp()
    elif isinstance(narrowed, UnionType):
        return UnionType.make_simplified_union([narrow_declared_type(declared, x)
                                                for x in narrowed.relevant_items()])
    elif isinstance(narrowed, AnyType):
        return narrowed
    elif isinstance(declared, (Instance, TupleType)):
        return meet_types(declared, narrowed)
    elif isinstance(declared, TypeType) and isinstance(narrowed, TypeType):
        return TypeType.make_normalized(narrow_declared_type(declared.item, narrowed.item))
    return narrowed

def meet_simple(s: Type, t: Type, default_right: bool = True) -> Type:
    if s == t:
        return s
    if isinstance(s, UnionType):
        return UnionType.make_simplified_union([meet_types(x, t) for x in s.items])
    elif not is_overlapping_types(s, t, use_promotions=True):
        if experiments.STRICT_OPTIONAL:
            return UninhabitedType()
        else:
            return NoneTyp()
    else:
        if default_right:
            return t
        else:
            return s

 def visit_none_type(self, t: NoneTyp) -> Type:
     if experiments.STRICT_OPTIONAL:
         if isinstance(self.s, (NoneTyp, UninhabitedType)):
             return t
         elif isinstance(self.s, UnboundType):
             return AnyType()
         elif isinstance(self.s, Void) or isinstance(self.s, ErrorType):
             return ErrorType()
         else:
             return UnionType.make_simplified_union([self.s, t])
     else:
         if not isinstance(self.s, Void):
             return self.s
         else:
             return self.default(self.s)

def array_raw_callback(ctx: 'mypy.plugin.AttributeContext') -> Type:
    """Callback to provide an accurate type for ctypes.Array.raw."""
    et = _get_array_element_type(ctx.type)
    if et is not None:
        types = []  # type: List[Type]
        for tp in union_items(et):
            if (isinstance(tp, AnyType)
                    or isinstance(tp, Instance) and tp.type.fullname() == 'ctypes.c_char'):
                types.append(_get_bytes_type(ctx.api))
            else:
                ctx.api.msg.fail(
                    'ctypes.Array attribute "raw" is only available'
                    ' with element type c_char, not "{}"'
                    .format(et),
                    ctx.context)
        return UnionType.make_simplified_union(types)
    return ctx.default_attr_type

def _autounboxed_cdata(tp: Type) -> Type:
    """Get the auto-unboxed version of a CData type, if applicable.

    For *direct* _SimpleCData subclasses, the only type argument of _SimpleCData in the bases list
    is returned.
    For all other CData types, including indirect _SimpleCData subclasses, tp is returned as-is.
    """
    if isinstance(tp, UnionType):
        return UnionType.make_simplified_union([_autounboxed_cdata(t) for t in tp.items])
    elif isinstance(tp, Instance):
        for base in tp.type.bases:
            if base.type.fullname() == 'ctypes._SimpleCData':
                # If tp has _SimpleCData as a direct base class,
                # the auto-unboxed type is the single type argument of the _SimpleCData type.
                assert len(base.args) == 1
                return base.args[0]
    # If tp is not a concrete type, or if there is no _SimpleCData in the bases,
    # the type is not auto-unboxed.
    return tp

def join_simple(declaration: Optional[Type], s: Type, t: Type) -> Type:
    """Return a simple least upper bound given the declared type."""

    if (s.can_be_true, s.can_be_false) != (t.can_be_true, t.can_be_false):
        # if types are restricted in different ways, use the more general versions
        s = true_or_false(s)
        t = true_or_false(t)

    if isinstance(s, AnyType):
        return s

    if isinstance(s, ErasedType):
        return t

    if is_proper_subtype(s, t):
        return t

    if is_proper_subtype(t, s):
        return s

    if isinstance(declaration, UnionType):
        return UnionType.make_simplified_union([s, t])

    if isinstance(s, NoneTyp) and not isinstance(t, NoneTyp):
        s, t = t, s

    if isinstance(s, UninhabitedType) and not isinstance(t, UninhabitedType):
        s, t = t, s

    value = t.accept(TypeJoinVisitor(s))

    if value is None:
        # XXX this code path probably should be avoided.
        # It seems to happen when a line (x = y) is a type error, and
        # it's not clear that assuming that x is arbitrary afterward
        # is a good idea.
        return declaration

    if declaration is None or is_subtype(value, declaration):
        return value

    return declaration

def typed_dict_pop_callback(ctx: MethodContext) -> Type:
    """Type check and infer a precise return type for TypedDict.pop."""
    if (isinstance(ctx.type, TypedDictType)
            and len(ctx.arg_types) >= 1
            and len(ctx.arg_types[0]) == 1):
        key = try_getting_str_literal(ctx.args[0][0], ctx.arg_types[0][0])
        if key is None:
            ctx.api.fail(message_registry.TYPEDDICT_KEY_MUST_BE_STRING_LITERAL, ctx.context)
            return AnyType(TypeOfAny.from_error)

        if key in ctx.type.required_keys:
            ctx.api.msg.typeddict_key_cannot_be_deleted(ctx.type, key, ctx.context)
        value_type = ctx.type.items.get(key)
        if value_type:
            if len(ctx.args[1]) == 0:
                return value_type
            elif (len(ctx.arg_types) == 2 and len(ctx.arg_types[1]) == 1
                  and len(ctx.args[1]) == 1):
                return UnionType.make_simplified_union([value_type, ctx.arg_types[1][0]])
        else:
            ctx.api.msg.typeddict_key_not_found(ctx.type, key, ctx.context)
            return AnyType(TypeOfAny.from_error)
    return ctx.default_return_type