@Attach NeImpl
Eq(R |= Self) = Trait {
    .`==` = (self: Self, R) -> Bool
}

NeImpl R = Patch Eq R
NeImpl(R).
    `!=`(self, other: R): Bool = not(self == other)

@Attach EqImpl, LeImpl, LtImpl, GeImpl, GtImpl
PartialOrd(R := Self) = Trait {
    .cmp = (self: Self, R) -> Option Ordering
}
Ord = Subsume PartialOrd()

EqForOrd R = Patch Ord, Impl := Eq()
EqForOrd(R).
    `==`(self, other: R): Bool = self.cmp(other) == Ordering.Equal

LeForOrd = Patch Ord
LeForOrd.
    `<=`(self, other: Self): Bool = self.cmp(other) == Ordering.Less or self == other
LtForOrd = Patch Ord
LtForOrd.
    `<`(self, other: Self): Bool = self.cmp(other) == Ordering.Less
GeForOrd = Patch Ord
GeForOrd.
    `>=`(self, other: Self): Bool = self.cmp(other) == Ordering.Greater or self == other
GtForOrd = Patch Ord
GtForOrd.
    `>`(self, other: Self): Bool = self.cmp(other) == Ordering.Greater

Add(R := Self) = Trait {
    .Output = Type
    .`_+_` = (self: Self, R) -> Self.Output
}
Sub(R := Self) = Trait {
    .Output = Type
    .`_-_` = (self: Self, R) -> Self.Output
}
Mul(R := Self()) = Trait {
    .Output = Type
    .`*` = (self: Self, R) -> Self.Output
}
Div(R := Self) = Trait {
    .Output = Type
    .`/` = (self: Self, R) -> Self.Output or Panic
}
Num: (R |= Type) -> Type
Num = Add and Sub and Mul

Seq T = Trait {
    .__len__ = (self: Ref(Self)) -> Nat
    .get = (self: Ref(Self), Nat) -> T
}

`_+_`: |R: Type, A <: Add(R)| (A, R) -> A.AddO
`_-_`: |R: Type, S <: Add(R)| (S, R) -> S.SubO
`*`: |R, O: Type, M <: Add(R)| (M, R) -> M.MulO
`/`: |R, O: Type, D <: Add(R)| (D, R) -> D.DivO

AddForInt = Patch Int, Impl := Add()
AddForInt.AddO = Int
AddForInt.
    `_+_`: (self: Self, other: Int) -> Int = magic("Add.`_+_`")

# TODO: Mul and Div
NumForInterval M, N, O, P: Int =
    Patch M..N, Impl := Add(R := O..P) and Sub(R := O..P)
NumForInterval(M, N, O, P).
    `_+_`: (self: Self, other: O..P) -> M+O..N+P = magic("NumForInterval.`_+_`")
    `_-_`: (self: Self, other: O..P) -> M-P..N-O = magic("NumForInterval.`_-_`")

Read = Trait {
    .read = (self: Ref(Self)) -> Str
}
Read! = Trait {
    .read! = (self: Ref!(Self)) => Str
}
Write! = Trait {
    .write! = (self: Ref!(Self), Str) => ()
}