Church numerals in Go

church.go

// next up: scott encoding https://en.wikipedia.org/wiki/Mogensen%E2%80%93Scott_encoding

package main

import "fmt"

type Church[T any] func(func(T) T) func(T) T

func main() {
	churchTest[int](0, func(x int) int { return x + 1 })
	churchTest[[]int](nil, func(a []int) []int { return append(a, len(a)) })
}

func churchTest[T any](init T, succ func(T) T) {
	churchNumerals := []Church[T]{
		one[T](),
		two[T](),
		three[T](),
		four[T](),
		five[T](),
	}
	for _, church := range churchNumerals {
		fmt.Printf("%v ", church(succ)(init))
	}
	fmt.Println()
}

func zero[T any]() Church[T] {
	return func(s func(T) T) func(T) T {
		return func(x T) T {
			return x
		}
	}
}

func succ[T any](church Church[T]) Church[T] {
	return func(s func(T) T) func(T) T {
		return func(x T) T {
			return s(church(s)(x))
		}
	}
}

func one[T any]() Church[T] {
	return succ(zero[T]())
}

func two[T any]() Church[T] {
	return succ(one[T]())
}

func three[T any]() Church[T] {
	return succ(two[T]())
}

func four[T any]() Church[T] {
	return succ(three[T]())
}

func five[T any]() Church[T] {
	return succ(four[T]())
}