Untyped Lambda Calculus, Chruch Numerals, Y Combinator in Golang

lambda_test.go

package main

import (
	"testing"

	"github.com/stretchr/testify/assert"
)

type V func(v V) V

var Y V = func(f V) V {
	return (func(x V) V { return func(n V) V { return f(x(x))(n) } })(func(x V) V { return func(n V) V { return f(x(x))(n) } })
}

var tru V = func(x V) V { return func(y V) V { return x } }
var fals V = func(x V) V { return func(y V) V { return y } }

var zero V = func(f V) V { return func(x V) V { return x } }
var one V = func(f V) V { return func(x V) V { return f(x) } }
var two V = func(f V) V { return func(x V) V { return f(f(x)) } }
var plus V = func(m V) V {
	return func(n V) V { return func(f V) V { return func(x V) V { return m(f)(n(f)(x)) } } }
}
var mult V = func(m V) V { return func(n V) V { return func(f V) V { return func(x V) V { return m(n(f))(x) } } } }
var pred V = func(n V) V {
	return func(f V) V {
		return func(x V) V {
			return n(func(g V) V { return func(h V) V { return h(g(f)) } })(func(u V) V { return x })(func(u V) V { return u })
		}
	}
}
var isZero V = func(n V) V { return n(func(_ V) V { return fals })(tru) }

var fact V = Y(func(f V) V {
	return func(n V) V {
		return isZero(n)(func(x V) V { return one })(func(x V) V { return (mult(n)(f(pred(n)))) })(zero)
	}
})
var fib V = Y(func(f V) V {
	return func(n V) V {
		return isZero(pred(n))(func(_ V) V { return n })(func(_ V) V { return plus(f(pred(n)))(f(pred(pred(n)))) })(zero)
	}
})

func (f V) toInt() int {
	n := 0
	f(func(v V) V { n++; return v })(func(v V) V { return v })
	return n
}

func (f V) toBool() bool {
	var res bool
	f(func(v V) V { res = true; return v })(func(v V) V { res = false; return v })(func(v V) V { return v })
	return res
}

func Test(t *testing.T) {
	three := plus(two)(one)
	six := mult(two)(three)
	sevenTwenty := fact(six)
	eight := fib(six)
	assert.Equal(t, 3, three.toInt())
	assert.Equal(t, 6, six.toInt())
	assert.Equal(t, true, isZero(zero).toBool())
	assert.Equal(t, false, isZero(one).toBool())
	assert.Equal(t, 720, sevenTwenty.toInt())
	assert.Equal(t, 2, pred(three).toInt())
	assert.Equal(t, false, isZero(pred(two)).toBool())
	assert.Equal(t, 8, eight.toInt())
}