> IIUC, my add function would be declared as : > val add : 'a sized_int * 'a sized_int -> 'a sized_int > then, with > val x : size16 sized_int > val y : size16 sized_int > the type infered for z in > let z = add (x,y) > will be > z : size16 sized_int > > Am i right ?
Yes, this is right. You can already experiment in ocaml, as Denis Berthod suggested, by adding abstract types by hand instead of having constants in the initial environment. > You're perfectly right Christophe, > I now realize that i've opened some kind of Pandora box. > Supporting function declaration > concat : int<n> -> int<m> -> int<n+m> (or multiplication) > would be great (even with only addition on sizes), but a too long term goal > for me > (esp. taking into account that i'm by no means a specialist in type theory !). I think your low-cost approach is reasonable. If you wish to go further, you could look into Dependent ML, which explored using types dependent on integers and other kind of data restricted to decidable constraint domains (presburger arithmetic, etc.), integrating a domain-specific solver in the type system. http://www.cs.bu.edu/~hwxi/DML/DML.html Hongwei Xi is now working on ATS, which reuses those ideas and goes further, aiming at statically safe low-level programming, but in a more complex framework http://www.ats-lang.org/ Also related is the currently ongoing design of the Habit language, which also uses restricted arithmetic operations at the type level. http://hasp.cs.pdx.edu/ On Tue, Sep 27, 2011 at 10:23 AM, Jocelyn Sérot <jocelyn.se...@ubpmes.univ-bpclermont.fr> wrote: > > Le 26 sept. 11 à 18:44, Gabriel Scherer a écrit : > >>> Phantom types could be a solution but we must declare a new type for >>> each possible size, which is cumbersome / annoying. >> >> If you define the type system yourself, you can easily add a family of >> type constants `size<n>` (with `n` an integer literal) to the default >> environment of the type checker. Then you can define a parametrized >> type `type 's sized_int` (or float, etc.) and instantiate it with any >> of the size<n>. > > Yes. Good point. Thanks for the idea. > IIUC, my add function would be declared as : > > val add : 'a sized_int * 'a sized_int -> 'a sized_int > > then, with > > val x : size16 sized_int > val y : size16 sized_int > > the type infered for z in > > let z = add (x,y) > > will be > > z : size16 sized_int > > Am i right ? > >> >> One issue with this minimal -- in term of modifications -- mechanism >> is that you can represent meaningless types such as `float size_int` : >> `float` is not a size. The canonical way to handle this is to add >> a kind system on top of your type system, that would classify the >> types into different kinds. Usual types would have kind `★`, and sizes >> would have kind `Size`. You would then restrict the `'a` type variable in >> `sized_int` to be of kind `Size`: >> >> type ('a : Size) sized_int >> >> http://en.wikipedia.org/wiki/Kind_(type_theory) >> >> Remark: There is another useful way to combine kinds and sizes, which >> is to use "sized kinds" to classify types whose memory representation >> has a given size in your implementation. For example you would have >> a kind `★` for types of one machine word, `★2` for two machine >> words... This allows to keep parametric polymorphism in presence of >> non-uniform representations, but it is restricted, less general, as >> a given polymorphic definition would not quantify over all types, but >> on all types of a given kind – unless you introduce kind polymorphism, >> etc. It may be useful for typing low-level programs, but it doesn't >> look like what you're looking for here. > > Thanks for the pointer. I'll have a look at this. > But i'm afraid that this would require a too profound change in the > implementation of the type system.. > > Jocelyn > >> >> >> On Mon, Sep 26, 2011 at 5:55 PM, Jocelyn Sérot >> <jocelyn.se...@ubpmes.univ-bpclermont.fr> wrote: >>> >>> Thanks to all for your answers. >>> Phantom types could be a solution but we must declare a new type for each >>> possible size, which is cumbersome / annoying. >>> Moreover, since i'm writing a DSL, the fact that they do not require a >>> modification to the existing type system is not really an advantage. >>> My language has its own type system (largely inspired from OCaml's) so >>> what >>> I was looking for was more a way to modify the type representation to >>> support the requested behavior. >>> To those familiar with Caml compiler source code, i was wondering if i >>> could >>> hack the following definitions (from types. ml) >>> type typ = >>> | TyVar of typ_var >>> | TyTerm of string * typ list >>> and typ_var = >>> { mutable level: int; >>> mutable value: tyvar_value } >>> and tyvar_value = >>> | Unknown >>> | Known of typ >>> by adding a notion of "size variable" (sorry if this sounds imprecise, >>> this >>> is still a but hazy in my mind..) >>> type typ = >>> | TyVar of typ_var >>> | TyTerm of string * typ list * typ_size >>> and typ_sz = >>> { mutable value: tysz_value } >>> and tyvar_value = >>> | Unknown >>> | Known of int >>> and update the unification engine accordingly.. >>> Well, the easiest answer is maybe just to try :-S >>> I'm just a bit surprised that no one seems to have proposed such an >>> extension yet. >>> Jocelyn >>> Le 26 sept. 11 à 14:45, Yaron Minsky a écrit : >>> >>> 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.bert...@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> ... >>>>> >>>>> >>>>> >>>> >>>> >>>> -- >>>> Caml-list mailing list. 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