Re: [Caml-list] Dependent types ?

[Yaron Minsky <yminsky@gmail.com>]

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As written, the behavior of the types might not be what you expect, since
addition of two 16 bit ints may result in an int that requires 17 bits.

When using phantom types, you need to be especially careful that the types
mean what you think they mean.
On Sep 26, 2011 8:13 AM, "Denis Berthod" <denis.berthod@gmail.com> wrote:
> 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> ...
>>
>>
>>
>
>
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