Overloads

In Python, it is common for callable objects to be polymorphic, meaning they accept different types of arguments. It is also common for such callables to return different types depending on the arguments passed to them. Overloads provide a way to describe the accepted input signatures and corresponding return types.

Overload definitions

The @overload decorator allows describing functions and methods that support multiple different combinations of argument types. This pattern is used frequently in builtin modules and types. For example, the __getitem__() method of the bytes type can be described as follows:

from typing import overload

class bytes:
    ...
    @overload
    def __getitem__(self, i: int) -> int: ...
    @overload
    def __getitem__(self, s: slice) -> bytes: ...

This description is more precise than would be possible using unions, which cannot express the relationship between the argument and return types:

class bytes:
    ...
    def __getitem__(self, a: int | slice) -> int | bytes: ...

Another example where @overload comes in handy is the type of the builtin map() function, which takes a different number of arguments depending on the type of the callable:

from typing import TypeVar, overload
from collections.abc import Callable, Iterable, Iterator

T1 = TypeVar('T1')
T2 = TypeVar('T2')
S = TypeVar('S')

@overload
def map(func: Callable[[T1], S], iter1: Iterable[T1]) -> Iterator[S]: ...
@overload
def map(func: Callable[[T1, T2], S],
        iter1: Iterable[T1], iter2: Iterable[T2]) -> Iterator[S]: ...
# ... and we could add more items to support more than two iterables

Note that we could also easily add items to support map(None, ...):

@overload
def map(func: None, iter1: Iterable[T1]) -> Iterable[T1]: ...
@overload
def map(func: None,
        iter1: Iterable[T1],
        iter2: Iterable[T2]) -> Iterable[tuple[T1, T2]]: ...

Uses of the @overload decorator as shown above are suitable for stub files. In regular modules, a series of @overload-decorated definitions must be followed by exactly one non-@overload-decorated definition (for the same function/method). The @overload-decorated definitions are for the benefit of the type checker only, since they will be overwritten by the non-@overload-decorated definition, while the latter is used at runtime but should be ignored by a type checker. At runtime, calling an @overload-decorated function directly will raise NotImplementedError. Here’s an example of a non-stub overload that can’t easily be expressed using a union or a type variable:

@overload
def utf8(value: None) -> None:
    pass
@overload
def utf8(value: bytes) -> bytes:
    pass
@overload
def utf8(value: unicode) -> bytes:
    pass
def utf8(value):
    <actual implementation>

A constrained TypeVar type can sometimes be used instead of using the @overload decorator. For example, the definitions of concat1 and concat2 in this stub file are equivalent:

from typing import TypeVar

AnyStr = TypeVar('AnyStr', str, bytes)

def concat1(x: AnyStr, y: AnyStr) -> AnyStr: ...

@overload
def concat2(x: str, y: str) -> str: ...
@overload
def concat2(x: bytes, y: bytes) -> bytes: ...

Some functions, such as map or bytes.__getitem__ above, can’t be represented precisely using type variables. We recommend that @overload is only used in cases where a type variable is not sufficient.

Another important difference between type variables such as AnyStr and using @overload is that the prior can also be used to define constraints for generic class type parameters. For example, the type parameter of the generic class typing.IO is constrained (only IO[str], IO[bytes] and IO[Any] are valid):

class IO(Generic[AnyStr]): ...

Invalid overload definitions

Type checkers should enforce the following rules for overload definitions.

At least two @overload-decorated definitions must be present. If only one is present, an error should be reported.

The @overload-decorated definitions must be followed by an overload implementation, which does not include an @overload decorator. Type checkers should report an error or warning if an implementation is missing. Overload definitions within stub files, protocols, and on abstract methods within abstract base classes are exempt from this check.

If one overload signature is decorated with @staticmethod or @classmethod, all overload signatures must be similarly decorated. The implementation, if present, must also have a consistent decorator. Type checkers should report an error if these conditions are not met.

If a @final or @override decorator is supplied for a function with overloads, the decorator should be applied only to the overload implementation if it is present. If an overload implementation isn’t present (for example, in a stub file), the @final or @override decorator should be applied only to the first overload. Type checkers should enforce these rules and generate an error when they are violated. If a @final or @override decorator follows these rules, a type checker should treat the decorator as if it is present on all overloads.

Overloads are allowed to use a mixture of async def and def statements within the same overload definition. Type checkers should convert async def statements to a non-async signature (wrapping the return type in a Coroutine) before testing for implementation consistency.

Implementation consistency

If an overload implementation is defined, type checkers should validate that it is consistent with all of its associated overload signatures. The implementation should accept all potential sets of arguments that are accepted by the overloads and should produce all potential return types produced by the overloads. In typing terms, this means the input signature of the implementation should be assignable to the input signatures of all overloads, and the return type of all overloads should be assignable to the return type of the implementation.

If the implementation is inconsistent with its overloads, a type checker should report an error:

@overload
def func(x: str, /) -> str: ...
@overload
def func(x: int) -> int: ...

# This implementation is inconsistent with the second overload
# because it does not accept a keyword argument ``x`` and the
# the overload's return type ``int`` is not assignable to the
# implementation's return type ``str``.
def func(x: int | str, /) -> str:
  return str(x)

When a type checker checks the implementation for consistency with overloads, it should first apply any transforms that change the effective type of the implementation including the presence of a yield statement in the implementation body, the use of async def, and the presence of additional decorators.

Overload call evaluation

When a type checker evaluates the call of an overloaded function, it attempts to “match” the supplied arguments with one or more overloads. This section describes the algorithm that type checkers should use for overload matching.

Only the overloads (the @overload-decorated signatures) should be considered for matching purposes. The implementation, if provided, should be ignored for purposes of overload matching.

Step 1: Examine the argument list to determine the number of positional and keyword arguments. Use this information to eliminate any overload candidates that are not plausible based on their input signatures.

• If no candidate overloads remain, generate an error and stop.

• If only one candidate overload remains, it is the winning match. Evaluate it as if it were a non-overloaded function call and stop.

• If two or more candidate overloads remain, proceed to step 2.

Step 2: Evaluate each remaining overload as a regular (non-overloaded) call to determine whether it is compatible with the supplied argument list. Unlike step 1, this step considers the types of the parameters and arguments. During this step, do not generate any user-visible errors. Simply record which of the overloads result in evaluation errors.

• If all overloads result in errors, proceed to step 3.

• If only one overload evaluates without error, it is the winning match. Evaluate it as if it were a non-overloaded function call and stop.

• If two or more candidate overloads remain, proceed to step 4.

Step 3: If step 2 produces errors for all overloads, perform “argument type expansion”. Union types can be expanded into their constituent subtypes. For example, the type int | str can be expanded into int and str.

Type expansion should be performed one argument at a time from left to right. Each expansion results in sets of effective argument types. For example, if there are two arguments whose types evaluate to int | str and int | bytes, expanding the first argument type results in two sets of argument types: (int, int | bytes) and (str, int | bytes). If type expansion for the second argument is required, four sets of argument types are produced: (int, int), (int, bytes), (str, int), and (str, bytes).

After each argument’s expansion, return to step 2 and evaluate all expanded argument lists.

• If all argument lists evaluate successfully, combine their respective return types by union to determine the final return type for the call, and stop.

• If argument expansion has been applied to all arguments and one or more of the expanded argument lists cannot be evaluated successfully, generate an error and stop.

For additional details about argument type expansion, see argument-type-expansion below.

Step 4: If the argument list is compatible with two or more overloads, determine whether one or more of the overloads has a variadic parameter (either *args or **kwargs) that maps to a corresponding argument that supplies an indeterminate number of positional or keyword arguments. If so, eliminate overloads that do not have a variadic parameter.

• If this results in only one remaining candidate overload, it is the winning match. Evaluate it as if it were a non-overloaded function call and stop.

• If two or more candidate overloads remain, proceed to step 5.

Step 5: For all arguments, determine whether all possible materializations of the argument’s type are assignable to the corresponding parameter type for each of the remaining overloads. If so, eliminate all of the subsequent remaining overloads.

Consider the following example:

@overload
def example(x: list[int]) -> int: ...
@overload
def example(x: list[Any]) -> str: ...
@overload
def example(x: Any) -> Any: ...

def test(a: list[Any]):
    # All materializations of list[Any] will match either the first or
    # second overload, so the third overload can be eliminated.
    example(a)

This rule eliminates overloads that will never be chosen even if the caller eliminates types that include Any.

If the call involves more than one argument, all possible materializations of every argument type must be assignable to its corresponding parameter type. If this condition exists, all subsequent remaining overloads should be eliminated.

Once this filtering process is applied for all arguments, examine the return types of the remaining overloads. If these return types include type variables, they should be replaced with their solved types. If the resulting return types for all remaining overloads are equivalent, proceed to step 6.

If the return types are not equivalent, overload matching is ambiguous. In this case, assume a return type of Any and stop.

Step 6: Choose the first remaining candidate overload as the winning match. Evaluate it as if it were a non-overloaded function call and stop.

Example 1:

@overload
def example1(x: int, y: str) -> int: ...
@overload
def example1(x: str) -> str: ...

example1()  # Error in step 1: no plausible overloads
example1(1, "")  # Step 1 eliminates second overload
example1("")  # Step 1 eliminates first overload

example1("", "")  # Error in step 2: no compatible overloads
example1(1)  # Error in step 2: no compatible overloads

Example 2:

@overload
def example2(x: int, y: str, z: int) -> str: ...
@overload
def example2(x: int, y: int, z: int) -> int: ...

def test(values: list[str | int]):
    # In this example, argument type expansion is
    # performed on the first two arguments. Expansion
    # of the third is unnecessary.
    r1 = example2(1, values[0], 1)
    reveal_type(r1)  # Should reveal str | int

    # Here, the types of all three arguments are expanded
    # without success.
    example2(values[0], values[1], values[2])  # Error in step 3

Example 3:

@overload
def example3(x: int, /) -> tuple[int]: ...
@overload
def example3(x: int, y: int, /) -> tuple[int, int]: ...
@overload
def example3(*args: int) -> tuple[int, ...]: ...

def test(val: list[int]):
    # Step 1 eliminates second overload. Step 4 and
    # step 5 do not apply. Step 6 picks the first
    # overload.
    r1 = example3(1)
    reveal_type(r1)  # Should reveal tuple[int]

    # Step 1 eliminates first overload. Step 4 and
    # step 5 do not apply. Step 6 picks the second
    # overload.
    r2 = example3(1, 2)
    reveal_type(r2)  # Should reveal tuple[int, int]

    # Step 1 doesn't eliminate any overloads. Step 4
    # picks the third overload.
    r3 = example3(*val)
    reveal_type(r3)  # Should reveal tuple[int, ...]

Example 4:

@overload
def example4(x: list[int], y: int) -> int: ...
@overload
def example4(x: list[str], y: str) -> int: ...
@overload
def example4(x: int, y: int) -> list[int]: ...

def test(v1: list[Any], v2: Any):
    # Step 2 eliminates the third overload. Step 5
    # determines that first and second overloads
    # both apply and are ambiguous due to Any, but
    # return types are consistent.
    r1 = example4(v1, v2)
    reveal_type(r1)  # Reveals int

    # Step 2 eliminates the second overload. Step 5
    # determines that first and third overloads
    # both apply and are ambiguous due to Any, and
    # the return types are inconsistent.
    r2 = example4(v2, 1)
    reveal_type(r2)  # Should reveal Any

Argument type expansion

When performing argument type expansion, a type that is equivalent to a union of a finite set of subtypes should be expanded into its constituent subtypes. This includes the following cases.

1. Explicit unions: Each subtype of the union should be considered as a separate argument type. For example, the type int | str should be expanded into int and str.

2. bool should be expanded into Literal[True] and Literal[False].

3. Enum types (other than those that derive from enum.Flag) should be expanded into their literal members.

4. type[A | B] should be expanded into type[A] and type[B].

5. Tuples of known length that contain expandable types should be expanded into all possible combinations of their element types. For example, the type tuple[int | str, bool] should be expanded into (int, Literal[True]), (int, Literal[False]), (str, Literal[True]), and (str, Literal[False]).

The above list may not be exhaustive, and additional cases may be added in the future as the type system evolves.