add new test - factorial by inc and dec

SVN=126937

test/peano.go

+// $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 struct {
+	next *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.next = x;
+	return e;
+}
+
+
+func sub1(x *Number) *Number {
+	return x.next;
+}
+
+
+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 {
+		panic "error: found ", c, "; expected ", expected, "\n";
+	}
+}
+
+
+// -------------------------------------
+// Test basic functionality
+
+func verify() {
+	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
+
+
+func main() {
+	
+	verify();
+	for i := 0; i <= 10; i++ {
+		print i, "! = ", count(fact(gen(i))), "\n";
+	}
+}
+