protocolsarefornewbies.swift

import UIKit

struct Monoid<A> {
    let zero: A
    let append: (A, A) -> A
}

let additive = Monoid(zero: 0, append: +)
let multiplicative = Monoid(zero: 1, append: *)

additive.append(5, 6)

extension Array {
    func reduced(_ monoid: Monoid<Element>) -> Element {
        return self.reduce(monoid.zero, monoid.append)
    }
}

Array(1..<10).reduced(additive)

let conjuctiveBool = Monoid(zero: true, append: { $0 && $1 })
let disjunctiveBool = Monoid(zero: false, append: { $0 || $1 })

// FunctionM: (A) -> M

func functionMonoid<A, Result> (monoid: Monoid<Result>) -> Monoid<(A) -> Result> {
    return Monoid(zero: { _ in monoid.zero }, append: { lhs, rhs in { a in monoid.append(lhs(a), rhs(a)) } })
}

extension Array {
    func and_filtered(predicates: [(Element) -> Bool]) -> [Element] {
        return self.filter(predicates.reduced(functionMonoid(monoid: disjunctiveBool)))
    }
}

let isEven = { $0 % 2 == 0 }
let isLessThan10 = { $0 < 10 }

Array(0...100).and_filtered(predicates: [isEven, isLessThan10])