Re: [Caml-list] Dependent types ?

[Denis Berthod <denis.berthod@gmail.com>]

Hello,

I think that achieving something very near from what you whant is 
relatively easy using phantom types.
That avoid the boxing/unboxing in records.

type i16
type i32

module SizedInt:
     sig
       type 'a integer
       val  int16: int -> i16 integer
       val  int32: int -> i32 integer
       val  add: 'a integer -> 'a integer -> 'a integer
     end
  =
     struct
         type 'a integer = int

         let int16 x = x
         let int32 x = x

        let add x y = x + y
     end

then

open SizedInt

let bar =
    let x = int16 42 in
    foo x

must have type i16 integer -> i16 integer

Regards,

Denis Berthod


Le 26/09/2011 13:42, Jocelyn Sérot a écrit :
> Hello,
>
> I've recently come across a problem while writing a domain specific 
> language for hardware synthesis 
> (http://wwwlasmea.univ-bpclermont.fr/Personnel/Jocelyn.Serot/caph.html).
> The idea is to extend the type system to accept "size" annotations for 
> int types (it could equally apply to floats).
> The target language (VHDL in this case) accept "generic" functions, 
> operating on ints with variable bit width and I'd like to reflect this 
> in the source language.
>
> For instance, I'd like to be able to declare :
>
> val foo : int * int -> int
>
> (where the type int is not annotated, i.e. "generic")
>
> so that, when applied to, let say :
>
> val x : int<16>
> val y : int<16>
>
> (where <16> is a size annotation),
>
> like in
>
> let z = foo (x,y)
>
> then the compiler will infer type int<16> for z
>
> In fact, the exact type signature for foo would be :
>
> val foo : int<s> * int <s> -> int<s>
>
> where "s" would be a "size variable" (playing a role similar to a type 
> variable in, for ex : val map : 'a list -> ('a ->'b) -> 'b list).
>
> In a sense, it has to do with the theory of sized types (Hughes and 
> Paretto, .. ) and dependent types (DML for ex), but my goal is far 
> less ambitious.
> In particular, i dont want to do _computations_ (1) on the size (and, 
> a fortiori, don't want to prove anything on the programs).
> So sized types / dependent types seems a big machinery for a 
> relatively small goal.
> My intuition is that this is just a variant of polymorphism in which 
> the variables ranged over are not types but integers.
> Before testing this intuition by trying to implement it, I'd like to 
> know s/o has already tackled this problem.
> Any pointer - including "well, this is trivial" ! ;-) - will be 
> appreciated.
>
> Best wishes
>
> Jocelyn
>
> (1) i.e. i dont bother supporting declarations like : val mul : int<n> 
> * int<n> -> int <2*n> ...
>
>
>