def __lt__(self, other):
return match(other, {
Nat.O: lambda: False,
Nat.S:
lambda no:
match(self, {
Nat.O: lambda: True,
Nat.S: lambda ns: ns < no,
}),
})
def __sub__(self, other):
return match(self, {
Nat.O: lambda: self,
Nat.S:
lambda ns:
match(other, {
Nat.O: lambda: self,
Nat.S: lambda no: ns - no,
}),
})
def add(self, data):
return match(self, {
BTree.leaf: lambda: BTree.branch(BTree.leaf(), BTree.leaf(), data),
BTree.branch: lambda l, r, d:
BTree.branch(l.add(data), r, d) if data <= d \
else BTree.branch(l, r.add(data), d)
})
def __add__(self, other):
return match(self, {
Nat.O: lambda: other,
Nat.S: lambda n: n + Nat.S(other)
})
def to_int(self):
return match(self, {
Nat.O: lambda: 0,
Nat.S: lambda n: 1 + n.to_int()
})
def __pow__(self, other):
return match(other, {
Nat.O: lambda: Nat.S(Nat.O()), # forall x, x ** 0 = 1
Nat.S: lambda no: self * (self ** no), # x ** y = x * x ** (y - 1)
})
def __mul__(self, other):
return match(self, {
Nat.O: lambda: Nat.O(),
Nat.S: lambda ns: other + (other * ns), # x * y = y + (x - 1) * y
})
def __repr__(self):
return match(self, {
BTree.leaf: lambda: "",
BTree.branch: lambda l, r, d:
repr(l) + "/" + repr(d) + "\\" + repr(r),
})