from typing import Dict, Iterable, List, Mapping, Set


class Type3ClassMethod:
    __slots__ = ('type3_class', 'name', 'signature', )

    type3_class: 'Type3Class'
    name: str
    signature: str

    def __init__(self, type3_class: 'Type3Class', name: str, signature: str) -> None:
        self.type3_class = type3_class
        self.name = name
        self.signature = signature

    @property
    def signature_parts(self) -> List[str]:
        return self.signature.split(' -> ')

    @property
    def type_vars(self) -> Set[str]:
        return {
            x
            for x in self.signature_parts
            if 1 == len(x)
            and x == x.lower()
        }

    def __repr__(self) -> str:
        return f'Type3ClassMethod({repr(self.type3_class)}, {repr(self.name)}, {repr(self.signature)})'

class Type3Class:
    __slots__ = ('name', 'args', 'methods', 'operators', )

    name: str
    args: List[str]
    methods: Dict[str, Type3ClassMethod]
    operators: Dict[str, Type3ClassMethod]

    def __init__(self, name: str, args: Iterable[str], methods: Mapping[str, str], operators: Mapping[str, str]) -> None:
        self.name = name
        self.args = [*args]
        self.methods = {
            k: Type3ClassMethod(self, k, v)
            for k, v in methods.items()
        }
        self.operators = {
            k: Type3ClassMethod(self, k, v)
            for k, v in operators.items()
        }

    def __repr__(self) -> str:
        return self.name

Num = Type3Class('Num', ['a'], methods={}, operators={
    '+': 'a -> a -> a',
    '-': 'a -> a -> a',
    '*': 'a -> a -> a',
})