Sequence.Swift

extension SequenceType {
  var headTail: (Generator.Element, AnySequence<Generator.Element>)? {
    var g = self.generate()
    return g.next().map{($0, AnySequence{g})}
  }
  func scan<U>(initial: U, combine: (U, Generator.Element) -> U) -> [U] {
    var prev = initial
    return self.map{prev = combine(prev, $0); return prev}
  }
  func scan(combine: (Generator.Element, Generator.Element) -> Generator.Element) -> [Generator.Element]? {
    return self.headTail.map{$1.scan($0, combine: combine)}
  }
  func reduce(combine: (Generator.Element, Generator.Element) -> Generator.Element) -> Generator.Element? {
    return self.headTail.map{$1.reduce($0, combine: combine)}
  }
  func all(condition: Generator.Element -> Bool) -> Bool {
    return !self.contains{!condition($0)}
  }
}

protocol Lazy: SequenceType {}

extension LazySequence: Lazy {}
extension LazyBidirectionalCollection: Lazy {}
extension LazyForwardCollection: Lazy {}
extension LazyRandomAccessCollection: Lazy {}

extension Lazy {
   var headTail: (Generator.Element, LazySequence<AnySequence<Generator.Element>>)? {
    var g = self.generate()
    return g.next().map{($0, lazy(AnySequence{g}))}
  }
  func scan<U>(initial: U, combine: (U, Generator.Element) -> U) -> LazySequence<AnyGenerator<U>> {
    var (prev, g) = (initial, self.generate())
    return lazy( anyGenerator { g.next().map { prev = combine(prev, $0); return prev } } )
  }
  func scan(combine: (Generator.Element, Generator.Element) -> Generator.Element) -> LazySequence<AnyGenerator<Generator.Element>>? {
    return self.headTail.map{$1.scan($0, combine: combine)}
  }
  func reduce(combine: (Generator.Element, Generator.Element) -> Generator.Element) -> Generator.Element? {
    return self.headTail.map{$1.reduce($0, combine: combine)}
  }
}