from typing import TypeVar, Generic, Union, Optional
from dataclasses import dataclass
from enum import Enum, auto

carrier = TypeVar('carrier')
item = TypeVar('item')

@dataclass
class List(Generic[item]):
    def cata(self,a):
        return a.cata(self)

@dataclass
class Nil(List[item]):
    pass

@dataclass
class Cons(List[item]):
    head: item
    tail: List[item]

class op(Enum):
    Add = auto()
    Sub = auto()
    Mul = auto()

    def carrier(self) -> item:
        match self:
            case op.Add:
                return 0
            case op.Sub:
                return 0
            case op.Mul:
                return 1

    def eval(self, a: item, b:item) -> item:
        match self:
            case op.Add:
                return a + b
            case op.Sub:
                return a - b
            case op.Mul:
                return a * b

@dataclass
class Functor(Generic[item, carrier]):
    method: op
    cons: list[item, carrier]

def ieval(xs, carrier: Optional[item] = None) -> item:
    match xs:
        case Nil():
            return carrier
        case Functor(m, Cons(h, t)):
            return m.eval(
                ieval(h, m.carrier()), ieval(t, m.carrier())
            )
        case i:
            return i

def test_eval_add():
    x = Functor(
        op.Add,
        Cons(
            1,
            Functor(
                op.Add,
                    Cons(
                        2,
                        3
                    )
                )
            )
    )
    assert ieval(x) == 6


if __name__ == "__main__":
    test_eval_add()