Exponentials.swift

//Exercises from https://www.pointfree.co/episodes/ep9-algebraic-data-types-exponents

import UIKit

enum Either<A,B> {
    case left(A)
    case right(B)
}

struct Pair<A,B> {
    let a: A
    let b: B
}


// a^(b+c)= a^b*a^c
//Either<B,C> -> A = (B->A,C->A)
func to<A,B,C>(_ f: @escaping (Either<B,C>) -> A) -> ((B) -> A, (C) -> A) {
    let fromBtoA = { b in
        f(.left(b))
    }
    let fromCtoA = { c in
        f(.right(c))
    }
    return (fromBtoA, fromCtoA)
}

func from<A,B,C>(_ f: ((B) -> A,(C) -> A)) -> (Either<B,C>) -> A {
    return { either in
        switch either {
        case let .left(b):
            return f.0(b)
        case let .right(c):
            return f.1(c)
        }
    }
}

//Example
let eitherToA: (Either<Int,Int>) -> String = { either in
    switch either {
    case let .left(b):
        return "Left value \(b)"
    case let .right(c):
        return "Right value \(c)"
    }
}

to(eitherToA)
from(to(eitherToA))

//(a*b)^c = a^c*b^c
//(a,b) <- c = (a <- c,b<-c)
//c -> (a,b) = (c -> a, c ->b)
// c -> Pair<A,B> = Pair<C->A,C->B>

func to<A,B,C>(_ f: @escaping (C) -> Pair<A,B>) -> Pair<(C)->A,(C)->B> {
    let toA = { c in f(c).a }
    let toB = { c in f(c).b }
    return Pair(a: toA, b: toB)
}

func from<A,B,C>(_ f: Pair<(C)->A,(C)->B>) -> (C) -> Pair<A,B> {
    return { c in
        Pair(a: f.a(c),b: f.b(c))
    }
}


//Example

let valueToPair: (Int) -> Pair<Int,Int> = { number in
    return Pair(a: number/2, b: number % 2)
}

to(valueToPair)
from(to(valueToPair))