Relation between functors and polymorphism

[Christophe Raffalli <raffalli@cs.chalmers.se>]

Hi,

I have a question that arise in the following circonstances:
I modified the Hashtbl library to make it a function taking a "key structure"
containing a type "key" a function "hash : key -> int" and a function "eq :
key -> key -> bool". Then I wondered how I could use the polymorphic hash and
equality functions to recover the original polymorphic Hashtbl structure.

You can generalize the question to:

What is the relation between a functor that only depends on one type (or more)
like

module A (B : sig type t end) = struct
  type u = Some of B.t | None

  let read = function
    Some x -> x
  | None -> raise Not_found
end

and a polymorphic structure like

module A' = struct
  type 'a u = Some of 'a | None

  let read = function
    Some x -> x
  | None -> raise Not_found
end

They look isomorphic ?

---

You can easely go from A' to A (This is quite verbose but you don't have to
rewrite the types or functions definitions):

module A (B : sig type t end) = struct
  type u = B.t A'.u

  let read = (A'.read : u -> B.t)
end


But how can you reconstruct A' from A without rewriting the type or function
definitions. Is this impossible ?

----
Christophe Raffalli
Dept. of Computer Sciences
Chalmers University of Technology

URL: http://www.logique.jussieu.fr/www.raffalli