Types as function namespaces #5980

I often wish that types could also be namespaces for functions. To motivate this idea, let me start with a simple example. Say I need some functions that apply to arbitrary 2-tuples. The simplest solution is to write a module defining a Pair type along with the functions I need:

# pair.py
from typing import Tuple, TypeVar

A = TypeVar('A')
B = TypeVar('B')

Pair = Tuple[A, B]

def fst(pair: Pair[A, B]) -> A:
    a, _ = pair
    return a

def snd(pair: Pair[A, B]) -> B:
    _, b = pair
    return b

I would use my module like this:

# test.py
import pair
from pair import Pair

def f(p: Pair[int, float]) -> float:
    return pair.fst(p) + pair.snd(p)

p: Pair[int, float] = (1, 1.5)
assert f(p) == 2.5

This works and it typechecks with mypy. However, naming is a bit cumbersome with this approach. I can't use the pair identifier for Pair variables because I've already used it for my module, and I'm forced to resort to something like p instead. Also, it would be nicer if the functions fst and snd had a clearer association with the type Pair.

I'd much rather write something like this for my test:

# test.py
from pair import Pair

def f(pair: Pair[int, float]) -> float:
    return Pair.fst(pair) + Pair.snd(pair)

pair: Pair[int, float] = (1, 1.5)
assert f(pair) == 2.5

where Pair is now both a type and a namespace for associated functions.

Is it possible for mypy to support this?

I'm not making any syntax proposals here, but I'll note that the following does work at runtime:

from typing import Tuple, TypeVar

A = TypeVar('A')
B = TypeVar('B')

class Pair(Tuple[A, B]):

    def fst(pair: Pair[A, B]) -> A:
        a, _ = pair
        return a

    def snd(pair: Pair[A, B]) -> B:
        _, b = pair
        return b


def f(pair: Pair[int, float]) -> float:
    return Pair.fst(pair) + Pair.snd(pair)

pair: Pair[int, float] = (1, 1.5)
assert f(pair) == 2.5

Unfortunately, it does not typecheck with mypy, first of all because generic tuples are not allowed (#685). Second, even if generic tuples were supported, my assignment statement for pair would fail with an "Incompatible type" error because the expression has type Tuple[int, float] while the variable has type Pair[int, float], and mypy sees Pair as a subtype of Tuple due to the class definition.

I'm really curious to hear people's thoughts on this.

Thanks.