foldMfilterM.swift

// Equivalent to foldM

extension Sliceable where
  SubSlice : Sliceable,
  SubSlice.Generator.Element == Generator.Element,
  SubSlice.SubSlice == SubSlice {
  func flatReduce
    <U, S : SequenceType where S.Generator.Element == U>
    (initial: U, @noescape combine: (U, Generator.Element) -> S) -> [U] {
      return first.map {
        combine(initial, $0).flatMap {
          dropFirst(self).flatReduce($0, combine: combine)
        }
      } ?? [initial]
    }
  func flatReduce<U>(initial: U, @noescape combine: (U, Generator.Element) -> U?) -> U? {
    return first.map {
      combine(initial, $0).flatMap {
        dropFirst(self).flatReduce($0, combine: combine)
      }
    } ?? initial
  }
}

// Equivalent to filterM

extension Sliceable where
  SubSlice : Sliceable,
  SubSlice.Generator.Element == Generator.Element,
  SubSlice.SubSlice == SubSlice {
  func flatFilter
    <S : SequenceType where S.Generator.Element == Bool>
    (isElement: Generator.Element -> S) -> [[Generator.Element]] {
      return first.map {
        element in
        let answers = isElement(element)
        return dropFirst(self).flatFilter(isElement).flatMap {
          rest in
          answers.map {
            ($0 ? [element] : []) + rest
          }
        }
      } ?? [[]]
  }
  func flatFilter(isElement: Generator.Element -> Bool?) -> [Generator.Element]? {
    return first.map {
      element in
      let answers = isElement(element)
      return dropFirst(self).flatFilter(isElement).flatMap {
        rest in
        answers.map {
          ($0 ? [element] : []) + rest
        }
      }
    } ?? []
  }
}

[1, 2, 3].flatFilter {_ in [true, false]} // [[1, 2, 3], [2, 3], [1, 3], [3], [1, 2], [2], [1], []]