Fixed-point combinator in Python

fix.py

from functools import partial


def fix1(f, x):
    return f(partial(fix1, f), x)


fact = lambda f, n: 1 if n <= 1 else n * f(n - 1)


def fix(f):
    return f(lambda: fix(f))


fact0 = lambda f: lambda n: 1 if n <= 1 else n * f()(n - 1)


attrs = lambda f: {
    "foo": lambda: "foo",
    "bar": lambda: "bar",
    "foobar": lambda: f()["foo"]() + f()["bar"](),
    "foobarfoobar": lambda: f()["foobar"]() + f()["foobar"](),
}

from typing import Callable, Dict, TypeVar

K = TypeVar("K")
V = TypeVar("V")


def evals(f: Callable[[V], Dict[K, Callable[[], V]]]) -> Dict[K, V]:
    return {k: f() for k, f in fix(f).items()}


from functools import cache

import time


@cache
def expensive():
    time.sleep(2)
    return 42


r = lambda f: {
    "foo": lambda: expensive(),
    "bar": lambda: f()["foo"]() + expensive(),
    "baz": lambda: f()["bar"]() + expensive(),
    "qux": lambda: f()["baz"]() + expensive(),
}