Typeclasses in Swift

algebra.swift

// Playground - noun: a place where people can play

import Cocoa

var str = "Hello, playground"

// Here's take 1. First, I defined the algebra like I would in
// Scala, as separate protocols:
protocol Semigroup {
    typealias T
    func plus(a: T, _ b: T) -> T
}

// And the monoid extension:
protocol Monoid: Semigroup {
    func zero() -> T
}

// The problem here is you end up with these separate instances
// that implement the typeclasses. Because Swift has no implicit
// resolution, you have to go through some gymnastics to build on the
// typeclass.
class IntMonoid: Monoid {
    typealias T = Int
    func plus(a: Int, _ b: Int) -> Int {
        return a + b
    }
    func zero() -> Int {
        return 0
    }
}

// I wrote this protocol that the types themselves could extend;
// the idea was that they could use the Monoid implementations to
// implement the functions. This is a sad but of duplication.
//
// This protocol allows you to call plus directly on an instance.
protocol Addable {
    func zero() -> Self
    func plus(x: Self) -> Self
}

// And an example of how to implement Addable for Int:

extension Int: Addable {
    var monoid: IntMonoid { return IntMonoid() }
    func zero() -> Int {
        return monoid.zero()
    }
    func plus(x: Int) -> Int {
        return monoid.plus(self, x);
    }
}

// It works!!
1.plus(15)


// I can't quite get this to work (the error is "missing argument
// for parameter #1 in call"), but it doesn't matter. It's clearly
// too much duplication.
/**
// This is commented out because it screws up the playground.
func sum1<T : Addable>(array: T[]) -> T {
    return array.reduce(T.zero(), combine: { $0.plus($1) })
}
**/

// For take 2, I took the approach from this post:
// http://slashmesays.tumblr.com/post/87833542239/type-classes-in-swift

protocol Semigroup2 {
    class func plus(a: Self, _ b: Self) -> Self
}

// And the monoid extension:
protocol Monoid2: Semigroup2 {
    class func zero() -> Self
}

// This allows you to extend Int directly:
extension Int: Monoid2 {
    static func zero() -> Int {
        return 0
    }
    static func plus(a: Int, _ b: Int) -> Int {
        return a + b
    }
}

// Addition is now a class method.
Int.plus(1, 2)

// And you can write global aliases for these things that LOOK
// like they're doing implicit resolution. This works because the 
// generic type is aliased to the resolved, specific type within
// the body of the function:
func plus<T: Semigroup2>(a: T, b: T) -> T {
    return T.plus(a, b)
}

// This works, now:
plus(1, 2)


// And you can build on top of the lower level functions:
func sum2<T : Monoid2>(array: T[]) -> T {
    return array.reduce(T.zero(), combine: { plus($0, $1)})
}

// This works great for integers, and for anything else
// that implements the typeclass:
sum2([1, 2, 3])