List Monad in Python

list-monad.py

"""A List Monad."""
from __future__ import annotations
from itertools import chain

from typing import Any as b
from typing import Callable as Function
from typing import Iterable as Functor
from typing import List
from typing import TypeVar

a = TypeVar("T")
concat = chain.from_iterable

class FunctorList(List[a]):

  def fmap(fa, f: (a, b)) -> f[b]:
      return FunctorList(map(f, fa))

class ApplicativeList(FunctorList):

    def pure(a) -> m[a]:
        return ApplicativeList(a)

    def apply(fs, xs) -> f[b]:
      return ApplicativeList([f(x) for f in xs for x in fs])

class MonadList(ApplicativeList):

    def ret(a) -> m[a]:
        return MonadList(a)

    def __rshift__(xs, f: (a, m[b])) -> m[b]:
        return MonadList(concat (map(f, xs)))

print(
  "FunctorList\n",
  FunctorList([1, 2, 3])
    .fmap(lambda x: x + 1)
    .fmap(lambda x: str(x))
    .fmap(lambda x: x + "0")
)

print(
  "ApplicativeList\n",
  ApplicativeList([1, 2, 3])
    .apply([(lambda x: x + 1)])
    .apply([(lambda x: str(x))])
    .apply([(lambda x: x + "0")])
)

print(
  "MonadList\n",
  MonadList([1, 2, 3])
    >> (lambda x: [x + 1])
    >> (lambda x: [str(x)])
    >> (lambda x: [x + "0"])
)