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Swiftly towards the monoid
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| // erm… this Num protocol is useless, but let's overlook this bit for now, shall we? | |
| protocol Num: IntegerLiteralConvertible, IntegerArithmeticType {} | |
| extension Int: Num {} | |
| protocol Monoid { | |
| typealias t | |
| static func mempty() -> t | |
| static func mappend(a: t, _ b: t) -> t | |
| static func mconcat(a: [t]) -> t | |
| } | |
| extension Monoid { | |
| static func mconcat(a: [t]) -> t { | |
| return a.reduce(mempty(), combine: mappend) | |
| } | |
| } | |
| extension Array: Monoid { | |
| static func mempty() -> [Element] { | |
| return [] | |
| } | |
| static func mappend(a: [Element], _ b: [Element]) -> [Element] { | |
| return a + b | |
| } | |
| } | |
| struct Sum<T: Num> { | |
| let value: T | |
| init(_ v: T) { value = v } | |
| } | |
| extension Sum: Monoid { | |
| static func mempty() -> Sum<T> { | |
| return Sum(0) | |
| } | |
| static func mappend(a: Sum<T>, _ b: Sum<T>) -> Sum<T> { | |
| return Sum(a.value + b.value) | |
| } | |
| } | |
| struct Product<T: Num> { | |
| let value: T | |
| init(_ v: T) { value = v } | |
| } | |
| extension Product: Monoid { | |
| static func mempty() -> Product<T> { | |
| return Product(1) | |
| } | |
| static func mappend(a: Product<T>, _ b: Product<T>) -> Product<T> { | |
| return Product(a.value * b.value) | |
| } | |
| } | |
| let a1: [Int] = .mempty() // [] | |
| let a2: [Int] = .mappend([1,2],[3,4,5]) // [1,2,3,4,5] | |
| let a3: [Int] = .mconcat([[1,2],[3],[4,5]]) // [1,2,3,4,5] | |
| let s1: Sum<Int> = .mempty() | |
| s1.value // 0 | |
| let s2: Sum = .mappend(Sum(1), Sum(2)) | |
| s2.value // 3 | |
| let s3: Sum = .mconcat([1,2,3,4,5].map(Sum.init)) | |
| s3.value // 15 | |
| let p1: Product<Int> = .mempty() | |
| p1.value // 1 | |
| let p2: Product = .mappend(Product(2), Product(3)) | |
| p2.value // 6 | |
| let p3: Product = .mconcat([1,2,3,4,5].map(Product.init)) | |
| p3.value // 120 |
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Inspired by/stolen from https://twitter.com/RuiAAPeres/status/626010701086236672