coll.scala

trait Collections {
  type CC[+X]         // the overarching container type (in scala: any covariant collection, e.g. List, Vector)
  type Min[+X]        // the minimum type constructor which can be reconstituted to CC[X] (in scala: GenTraversableOnce)
  type Opt[+X]        // the container type for optional results (in scala: Option)
  type CCPair[+X]     // some representation of a divided CC[A] (at simplest, (CC[A], CC[A]))
  type ~>[-V1, +V2]   // some means of composing operations (at simplest, Function1)

  type Iso[A]            = CC[A] ~> CC[A]       // e.g. filter, take, drop, reverse, etc.
  type Map[-A, +B]       = CC[A] ~> CC[B]       // e.g. map, collect
  type FlatMap[-A, +B]   = CC[A] ~> Min[B]      // e.g. flatMap
  type Grouped[A, DD[X]] = CC[A] ~> CC[DD[A]]   // e.g. sliding
  type Fold[-A, +R]      = CC[A] ~> R           // e.g. fold, but also subsumes all operations on CC[A]
  type Flatten[A]        = CC[Min[A]] ~> CC[A]  // e.g. flatten
  type Build[A]          = Min[A] ~> CC[A]      // for use in e.g. sliding, flatMap
  type Pure[A]           = A ~> CC[A]           // we may not need

  trait Relations[A] {
    type MapTo[+B]  = Map[A, B]       // an alias incorporating the known A
    type FoldTo[+R] = Fold[A, R]      // another one
    type This       = CC[A]           // the CC[A] under consideration
    type Twosome    = CCPair[A]       // a (CC[A], CC[A]) representation
    type Self       = Iso[A]          // a.k.a. CC[A] => CC[A], e.g. tail, filter, reverse
    type Select     = FoldTo[A]       // a.k.a. CC[A] => A, e.g. head, reduce, max
    type Find       = FoldTo[Opt[A]]  // a.k.a. CC[A] => Opt[A], e.g. find
    type Split      = FoldTo[Twosome] // a.k.a. CC[A] => (CC[A], CC[A]), e.g. partition, span
  }
}