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// $G $F.go && $L $F.$A && ./$A.out

// Copyright 2009 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.

package main

type Number *Number

// -------------------------------------
// Peano primitives

func zero() *Number {
        return nil
}

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

func add1(x *Number) *Number {
        e := new(Number)
        *e = x
        return e
}

func sub1(x *Number) *Number {
        return *x
}

func add(x, y *Number) *Number {
        if is_zero(y) {
                return x
        }

        return add(add1(x), sub1(y))
}

func mul(x, y *Number) *Number {
        if is_zero(x) || is_zero(y) {
                return zero()
        }

        return add(mul(x, sub1(y)), x)
}

func fact(n *Number) *Number {
        if is_zero(n) {
                return add1(zero())
        }

        return mul(fact(sub1(n)), n)
}

// -------------------------------------
// Helpers to generate/count Peano integers

func gen(n int) *Number {
        if n > 0 {
                return add1(gen(n - 1))
        }

        return zero()
}

func count(x *Number) int {
        if is_zero(x) {
                return 0
        }

        return count(sub1(x)) + 1
}

func check(x *Number, expected int) {
        var c = count(x)
        if c != expected {
                print("error: found ", c, "; expected ", expected, "\n")
                panic("fail")
        }
}

// -------------------------------------
// Test basic functionality

func init() {
        check(zero(), 0)
        check(add1(zero()), 1)
        check(gen(10), 10)

        check(add(gen(3), zero()), 3)
        check(add(zero(), gen(4)), 4)
        check(add(gen(3), gen(4)), 7)

        check(mul(zero(), zero()), 0)
        check(mul(gen(3), zero()), 0)
        check(mul(zero(), gen(4)), 0)
        check(mul(gen(3), add1(zero())), 3)
        check(mul(add1(zero()), gen(4)), 4)
        check(mul(gen(3), gen(4)), 12)

        check(fact(zero()), 1)
        check(fact(add1(zero())), 1)
        check(fact(gen(5)), 120)
}

// -------------------------------------
// Factorial

var results = [...]int{
        1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800,
        39916800, 479001600,
}

func main() {
        for i := 0; i <= 9; i++ {
                if f := count(fact(gen(i))); f != results[i] {
                        println("FAIL:", i, "!:", f, "!=", results[i])
                        panic(0)
                }
        }
}