-- NOTE: this is unfinished and untested

import prelude
import bintree

Collection : Type -> Type
Collection C = 
  sig 
	-- types
	Elem : Type
	-- Add stuff
	zero : C
        plus : C -> C -> C
	-- Collection-specific stuff
        size : C -> Integer
	add : Elem -> C -> C
	elem : Elem -> C -> Bool
        map : (Elem -> Elem) -> C -> C
        filter : (Elem -> Bool) -> C -> C
        fromList : List Elem -> C
        toList : C -> List Elem


--
-- Collection String instance
--

collection_String : Collection String
collection_String =
  rec
	Elem = Char
	zero = ""
	plus = prim_add_String
	size = prim_length_String
	-- ...


--
-- Collection List instance
--

collection_List : (A : Type) -> Collection (List A)
collection_List A = 
  rec
	Elem = A
	zero = Nil A
	plus = append A
	size = length A
	add  = Cons A
	-- ...

--
-- Collection Vector instance
--

collection_Vector : (A : Type) -> (n : Nat) -> Collection (Vector A n)
collection_Vector A n = 
  rec
	Elem = A
	zero = Empty A
	plus = appendV A n n -- FIXME: this only works for vectors of the same length!
	-- ...


--
-- Collection BinTree instance
--

collection_BinTree : (A : Type) -> Ord A -> Collection (BinTree A)
collection_BinTree A o = 
  rec
	Elem = A
	zero = Nil A
	plus = merge A o
	size = sizeBT A
	add  = insert A o
	-- ...