| // $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 { |
| print("error: found ", c, "; expected ", expected, "\n") |
| panic("fail") |
| } |
| } |
| |
| |
| // ------------------------------------- |
| // 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 <= 9; i++ { |
| print(i, "! = ", count(fact(gen(i))), "\n") |
| } |
| } |