@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
EqForOrd(R)|<: Eq()|.
    `==`(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 = Add and Sub and Mul

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

AddForInt = Patch Int
AddForInt|<: Add(Int)|.
    AddO = Int
    `_+_`(self: Self, other: Int): Int = magic("Add.`_+_`")

# TODO: Mul and Div
NumForInterval M, N, O, P: Int = Patch M..N
NumForInterval(M, N, O, P)|<: Add(O..P)|.
    Output = M+O..N+P
    __add__(self: Self, other: O..P) = magic("NumForInterval.`_+_`")
NumForInterval(M, N, O, P)|<: Sub(O..P)|.
    Output = M-P..N-O
    __sub__(self: Self, other: O..P) = magic("NumForInterval.`_-_`")

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

discard _x = None

discard 1

# if: |T, U|(Bool, T, U) -> T or U
cond|T: Type|(c: Bool, then: T, else: T): T =
    if c:
        do then
        do else

assert cond(False, 1, 2) == 2
# assert cond(True, 1, 3) == "a"
# assert "a" == cond(True, 1, 3)