module Cursor

  use import seq.Seq

  type cursor 'a = private {
    ghost mutable visited : seq 'a;
  }

  predicate permitted (cursor 'a)
  axiom permitted_empty: forall c: cursor 'a. c.visited = empty -> permitted c

  predicate complete  (cursor 'a)

  val next (c: cursor 'a) : 'a
    requires { not (complete c) }
    requires { permitted c }
    writes   { c.visited }
    ensures  { c.visited = snoc (old c).visited result }
    ensures  { permitted c }

  val has_next (c: cursor 'a) : bool
    requires { permitted c }
    ensures  { result <-> not (complete c) }

end

module ListCursor

  use import seq.Seq
  use import seq.OfList
  use import list.List
  use import int.Int

  type cursor 'a = private {
    ghost mutable visited    : seq 'a;
    ghost         collection : list 'a;
  }

  predicate permitted (c: cursor 'a) =
    length c.visited <= length c.collection /\
    forall i. 0 <= i < length c.visited -> c.visited[i] = c.collection[i]

  predicate complete  (c: cursor 'a) =
    length c.visited = length c.collection

  val create (l: list 'a) : cursor 'a
    ensures { permitted result }
    ensures { result.visited = empty }
    ensures { result.collection = l }

  clone import Cursor as C with
    type cursor = cursor,
    predicate permitted = permitted,
    predicate complete  = complete,
    goal permitted_empty

end

module ArrayCursor

  use import array.Array
  use import array.ToSeq
  use import seq.Seq
  use import seq.OfList
  use import int.Int

  type cursor 'a = private {
    ghost mutable visited    : seq 'a;
    ghost         collection : seq 'a;
  }

  predicate permitted (c: cursor 'a) =
    length c.visited <= length c.collection /\
    forall i. 0 <= i < length c.visited -> c.visited[i] = c.collection[i]

  predicate complete  (c: cursor 'a) =
    length c.visited = length c.collection

  val create (a: array 'a) : cursor 'a
    ensures { permitted result }
    ensures { result.visited = empty }
    ensures { result.collection = to_seq a }

  clone import Cursor as C with
    type cursor = cursor,
    predicate permitted = permitted,
    predicate complete  = complete,
    goal permitted_empty

end