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89 lines
1.5 KiB
89 lines
1.5 KiB
4 months ago
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// Peano integers are represented by a linked
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// list whose nodes contain no data
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// (the nodes are the data).
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// http://en.wikipedia.org/wiki/Peano_axioms
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// This program demonstrates that Go's automatic
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// stack management can handle heavily recursive
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// computations.
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package main
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import "fmt"
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// Number is a pointer to a Number
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type Number *Number
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// The arithmetic value of a Number is the
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// count of the nodes comprising the list.
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// (See the count function below.)
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// -------------------------------------
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// Peano primitives
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func zero() *Number {
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return nil
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}
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func isZero(x *Number) bool {
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return x == nil
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}
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func add1(x *Number) *Number {
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e := new(Number)
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*e = x
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return e
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}
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func sub1(x *Number) *Number {
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return *x
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}
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func add(x, y *Number) *Number {
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if isZero(y) {
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return x
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}
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return add(add1(x), sub1(y))
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}
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func mul(x, y *Number) *Number {
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if isZero(x) || isZero(y) {
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return zero()
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}
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return add(mul(x, sub1(y)), x)
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}
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func fact(n *Number) *Number {
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if isZero(n) {
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return add1(zero())
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}
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return mul(fact(sub1(n)), n)
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}
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// -------------------------------------
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// Helpers to generate/count Peano integers
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func gen(n int) *Number {
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if n > 0 {
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return add1(gen(n - 1))
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}
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return zero()
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}
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func count(x *Number) int {
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if isZero(x) {
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return 0
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}
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return count(sub1(x)) + 1
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}
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// -------------------------------------
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// Print i! for i in [0,9]
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func main() {
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for i := 0; i <= 9; i++ {
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f := count(fact(gen(i)))
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fmt.Println(i, "! =", f)
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}
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}
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