OCaml Functors Sort - ocaml

Question

I am a beginner in OCaml and I'm trying to understand functors, I'm developing a "general sort function" with functors that can takes array, list, string and return an ordered list, array, string.
Can someone help me with this?
I've done this
module type Comparable= sig
type t
val compare : t -> t -> int
val fold_left : ('a -> 'b -> 'a) -> 'a -> 'b list -> 'a
end;;
module Make_sort(S: Comparable)= struct
type t= S.t
type et= S.t list
let order t= function
|[] -> 0
|a::b -> S.fold_left (S.compare (a t)(b t)) ;;
end;;

Answer 1

First of all, I think that your intuition is correct but there is small confusion between the value level and the type level, ie: S.compare (a t)(b t) this expression is not valid (a and b) must be functions, this why I think that you try to give the sense of 'a t.
But, I understand what you try to do, so here is a small primer on functor (function from module to module), using a small subset of your example.
First, in order to sort we need to define how to order
Exactly as you did, we can start with a signature (COMPARABLE) which handle the "notion of comparison". For example:
module type COMPARABLE = sig
(** something which is comparable. *)
type t
(** [compare x y] returns 1 if x > y, 0 if x = 0 and -1 if x < 0 *)
val compare : t -> t -> int
end
With this signature, it is easy to define module which are comparable, for example, for Int:
module Int_comparable :
COMPARABLE with type t = int =
struct
type t = int
let compare x y =
if x > y then 1
else if x = 0 then 0
else -1
end
Note that module are candidate for a signature only if the module match the signature so de anotation : COMPARABLE with type t = int is not very necessary. And, since Int (the module from the stdlib) already implement compare and a type t, it is not necessary to define it. You can just pass Int when you need a comparable.
Now, we can define somethign "sortable"
In this very small example, something which is comparable seems to be sortable. In other words, if I have a COMPARABLE, I can sort. This relation (If I have X, I can have Y) seems quite suitable for using a functor (so, I give you a COMPARABLE and you give me something sortable). Here is a proposition:
module Sortable (C : COMPARABLE) : sig
(** if something is comparable, it is sortable. *)
type t = C.t
(** [max_of x y] returns the greater between x and y. *)
val max_of : t -> t -> t
(** [min_of x y] returns the lower between x and y. *)
val min_of : t -> t -> t
(** [sort x y] returns an ordered tuple [(max_of x y, min_of x y)]. *)
val sort : t -> t -> (t * t)
end = struct
type t = C.t
let max_of x y =
let value = C.compare x y in
if value > 0 then x
else y
let min_of x y =
let value = C.compare x y in
if value < 0 then x
else y
let sort x y =
if (C.compare x y) >= 0 then (y, x) else (x, y)
end
It is probably possible to add more helpers in the module, but I'll keep the implementation as simple as possible. So now, if I want have sortable capabilities for Int.t I can just use the module Int (from stdlib: https://caml.inria.fr/pub/docs/manual-ocaml/libref/Int.html) which has a type t and compare like this
module Sortable_int = Sortable (Int)
Now, you have the basis. For traversing using Sort, you can implement a signature (Foldable for example) and I think you have all the bricks in your hands to generalize the logic of sorting collections (modulo a little algorithmic!)