Luhn Algorithm for Credit Card Validation using lazy() in Swift

LuhnAlgorithm.swift

// See @SwiftLDN's tweet for a short description of the Luhn algorithm:
//   https://twitter.com/SwiftLDN/status/529412592834338817
// or Wikipedia for a longer one.
//   http://en.wikipedia.org/wiki/Luhn_algorithm
//
// Only meant to show extending Swift's lazy() for infotainment purposes,
// not necessarily recommending best or even good practices!
//
// Alternative, saner, solutions here:
//   https://gist.github.com/alskipp/55b28891412ae0cf0d51
// and here:
//   https://github.com/robrix/credit-card-validation


// mapSome is my Swift version of Haskell's mapMaybe, which
// is a map that takes a transform function that returns an
// optional, and returns a collection of only those values
// that weren't nil

// first we need a lazy view that holds the original
// sequence and the transform function
struct MapSomeSequenceView<Base: SequenceType, T> {
    private let _base: Base
    private let _transform: (Base.Generator.Element) -> T?
}

// extend it to implement SequenceType
extension MapSomeSequenceView: SequenceType {
    typealias Generator = GeneratorOf<T>
    
    func generate() -> Generator {
        var g = _base.generate()
        // GeneratorOf is a helper that takes a
        // closure and calls it to generate each
        // element
        return GeneratorOf {
            while let element = g.next() {
                if let some = self._transform(element) {
                    return some
                }
            }
            return nil
        }
    }
}

// now extend a lazy collection to return that view
// from a call to mapSome.  In pracice, when doing this, 
// you should do it for all the lazy wrappers
// (i.e. random-access, forward and sequence)
extension LazyBidirectionalCollection {
    // I might be missing a trick with this super-ugly return type, is there a better way?
    func mapSome<U>(transform: (S.Generator.Element) -> U?) -> LazySequence<MapSomeSequenceView<LazyBidirectionalCollection<S>,U>> {
        return lazy(MapSomeSequenceView(_base: self, _transform: transform))
    }
}

// curried function - call with 1 argument to get a function
// that tells you if i is a multiple of a given number
// e.g. 
//  let isEven = isMultipleOf(2)
//  isEven(4) // true
func isMultipleOf<T: IntegerType>(of: T)->T->Bool {
    return { $0 % of == 0 }
}

// extend LazySequence to map only every nth element, with all
// other elements untransformed.
extension LazySequence {
    func mapEveryN(n: Int, _ transform: (S.Generator.Element) -> S.Generator.Element) -> LazySequence<MapSequenceView<EnumerateSequence<LazySequence<S>>,S.Generator.Element>> {
        let isNth = isMultipleOf(n)
        return lazy(enumerate(self)).map { (pair: (index: Int, elem: S.Generator.Element)) -> S.Generator.Element in
            isNth(pair.index+1)
                ? transform(pair.elem)
                : pair.elem
        }
    }
}

infix operator |> {
    associativity left
}

func |><T,U>(t: T, f: (T)->U) -> U {
    return f(t)
}

infix operator • {
    associativity left
}

func • <T, U, V> (g: U -> V, f: T -> U) -> T -> V {
    return { x in g(f(x)) }
}

// function to free a method from the shackles
// of it's owner
func freeMemberFunc<T,U>(f: T->()->U)->T->U {
    return { (t: T)->U in f(t)() }
}

// stringToInt can now be pipelined or composed
let stringToInt = freeMemberFunc(String.toInt)
// if only Character also had a toInt method
let charToString = { (c: Character) -> String in String(c) }
let charToInt = stringToInt • charToString

func sum<S: SequenceType where S.Generator.Element: IntegerType>(nums: S)->S.Generator.Element {
    return reduce(nums, 0) { $0.0 + $0.1 }
}

let double = { $0*2 }

let combineDoubleDigits = { 
    (10...18).contains($0) ? $0-9 : $0 
}

let ccnum = "4012 8888 8888 1881"

let checksum = { (cc: String) -> Bool in
    lazy(cc).reverse().mapSome(charToInt).mapEveryN(2, combineDoubleDigits • double)
        |> sum
        |> isMultipleOf(10)
}

println( checksum(ccnum) ? "👍" : "👎" )

Bikeshedding… but as a name, mapOptional would be more in line with the idea of mapMaybe.

True, mapOptional would mirror the name mapMaybe but I prefer mapSome since it seems more descriptive of what it actually does. (I'd probably prefer mapJust in Haskell, tho it's less good)