under in go

under.go

package main

import (
	"fmt"
	"math"
)

//Setup some types for functions we want to pass around
type unaryFloat func(float64) float64
type binaryFloat func(float64, float64) float64

//A wrapper around + that will let us pass it around
func passableAdd(x, y float64) float64 {
	return x + y
}

//This is the magical under function.
//Call some function on each value (verb)
//Combine these new values in another function (fn)
//Undo the verb (obverse)
func under(verb, obverse unaryFloat, fn binaryFloat, x, y float64) float64 {
	return obverse(fn(verb(x), verb(y)))
}

//We want to make functions that call math.Pow to an exponent that we specify.
//square = makePower(2)
//cubing = makePower(3)
func makePower(exp float64) func(float64) float64 {
	f := func(x float64) float64 {
		return math.Pow(x, exp)
	}
	return f
}

//My favourite demonstration of under. Pythagoras theorem
func pythag(x, y float64) float64 {
	sq := makePower(2)
	return under(sq, math.Sqrt, passableAdd, x, y)
}

func main() {
	fmt.Println(pythag(3, 4))
}