Peano integers in Go

peano.go

// Peano integers are represented by a linked
// list whose nodes contain no data
// (the nodes are the data).
// http://en.wikipedia.org/wiki/Peano_axioms

package main

import "fmt"

// Number is a pointer to a Number
type Number *Number

func zero() *Number {
	return nil
}

func isZero(x *Number) bool {
	return x == nil
}

func succ(x *Number) *Number {
	n := new(Number)
	*n = x
	return n
}

func prec(x *Number) *Number {
	return *x
}

func add(x, y *Number) *Number {
	if isZero(x) {
		return y
	}
	return add(prec(x), succ(y))
}

func gen(i int) *Number {
	if i > 0 {
		return succ(gen(i - 1))
	}
	return zero()
}

func toInt(x *Number) int {
	if isZero(x) {
		return 0
	}
	return toInt(prec(x)) + 1
}

func isEven(x *Number) bool {
	if isZero(x) {
		return true
	}
	return !isEven(prec(x))
}

func isOdd(x *Number) bool {
	return !isEven(x)
}

func main() {
	fmt.Println("4+5 =", toInt(add(gen(4), gen(5))))
	fmt.Println("isEven/isOdd 4 ?", isEven(gen(4)), isOdd(gen(4)))
	fmt.Println("isEven/isOdd 5 ?", isEven(gen(5)), isOdd(gen(5)))
	fmt.Println("isEven/isOdd 0 ?", isEven(gen(0)), isOdd(gen(0)))
}