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[Caml-list] polymorphic variant typing question
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Date: -- (:)
From: Damien <Damien.Pous@e...>
Subject: Re: [Caml-list] polymorphic variant typing question
On 11 Sep 2004 17:49:25 +1000 skaller wrote:

> Consider this:
> [...]
> What this does is extend the regular expression
> type to allow a group combinator, but then reduce it
> by using left/right bracket codes. This typing
> compiles.
> 
> Question: how can I replace the last two lines of
> the match with something which just handles 'all the
> rest of the cases'?
>
> Do I have to factor the original regexp_t into invariant
> and variant parts??
I think yes...

I often use the following scheme :

<<
(* invariant type *)
type t  = [ `A | `B ]

(*** first level ***)
type 'x v1 = [ t | `C of 'x ]
type t1 = 'x v1 as 'x

(* open recursion with r *)
let r1 r = function
  | #t as x -> x
  | `C x -> `C (r x)

(* close the recursion for use at the first level *)
let rec f1: t1 -> t1 = fun x -> r1 f1 x



(*** second level ***)
type 'x v2 = [ 'x v1 | `D of 'x ]
type t2 = 'x v2 as 'x

(* open recursion (use the previous open recursion) *)
let r2 r = function
(*  | `C x -> `D (r x)   (* possible overriding of the `C case *) *)
  | #v1 as x1 -> r1 r x1
  | `D x -> `D (r x)

(* close the recursion at the second level *)
let rec f2: t2 -> t2 = fun x -> r2 f2 x



(* second to first level (similar to your groupify function) *)
let r21 r = function
  | #v1 as x1 -> r1 r x1 (* first level recursion *)
  | `D x -> `C (r x) (* convert GROUPS into brackets here... *)
let rec f21: t2 -> t1 = fun x -> r21 f21 x
>>

You may be interested by this paper from Jacques Garrigue :
<http://wwwfun.kurims.kyoto-u.ac.jp/~garrigue/papers/variant-reuse.pdf>

Hope this helps,
damien


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