How do I get polymorphic partial application?

How do I get polymorphic partial application?

[Till Varoquaux]

Humm... I have a small issue here: I need to get the result of the
partial application of a polymorphic function. Since variable are
generalized in Let it is generally advised to use eta expansions,
(i.e transform to a total application).
sometimes eta expansions just won't do the trick, consider:

let cntTag start=
 let cnt=ref start in
 fun v -> ((incr cnt;!cnt),v)

the partial application is not fully polymorphic

let tag1 = cntTag 1

has type

val tag1 : '_a -> int * '_a = <fun>

the eta expanded equivalent doesn't have the same semantic (it
actually seems even less useful):

let tag1 x= cntTag 1 x

Is there an elegant solution to that problem?
Cheers,
Till

-- 
http://till-varoquaux.blogspot.com/

Re: [Caml-list] How do I get polymorphic partial application?

[Philippe Wang]

Till Varoquaux wrote:
> Humm... I have a small issue here: I need to get the result of the
> partial application of a polymorphic function. Since variable are
> generalized in Let it is generally advised to use eta expansions,
> (i.e transform to a total application).
> sometimes eta expansions just won't do the trick, consider:
>
> let cntTag start=
> let cnt=ref start in
> fun v -> ((incr cnt;!cnt),v)
>
> the partial application is not fully polymorphic
>
> let tag1 = cntTag 1
>
> has type
>
> val tag1 : '_a -> int * '_a = <fun>
>
> the eta expanded equivalent doesn't have the same semantic (it
> actually seems even less useful):
>
> let tag1 x= cntTag 1 x
>
> Is there an elegant solution to that problem?
> Cheers,
> Till
>
Hi,

I think you should not try to "hide" that ugly side effect...

If you do something like

let rec f a = incr x ; a
and x = ref 42          
and start s = x := s ;;

then you don't need to ask yourself how to bypass the type checker...

Still, you can hide things in a module...

module X :
sig 
  val f : 'a -> int * 'a
  val start : int -> unit
end = struct
  let rec f a = incr x ; !x, a
  and x = ref 42    
  and start s = x := s
end
(* include X *)

(only Obj.magic can do exactly what you're asking for -- except the 
"elegant" part)

-- 
Philippe Wang
   mail[at]philippewang.info

Re: [Caml-list] How do I get polymorphic partial application?

[Lukasz Stafiniak]

On 6/23/07, Philippe Wang <lists@philippewang.info> wrote:
> Till Varoquaux wrote:
> > Humm... I have a small issue here: I need to get the result of the
> > partial application of a polymorphic function. Since variable are
> > generalized in Let it is generally advised to use eta expansions,
> > (i.e transform to a total application).
> > sometimes eta expansions just won't do the trick, consider:
>
> I think you should not try to "hide" that ugly side effect...
>
Could someone give an example where this "eta-thing" forbids a crash?
I don't remember any example even in Xavier Leroy papers.

Re: [Caml-list] How do I get polymorphic partial application?

[Till Varoquaux]

As said previously, in a HM type ineference system type variables are
generalized only in "let", that is:

let id x = x (*starting with an identity function*)
let id'= id id (*this is a partial application; it has type '_a ->'_a*)
let _=
  print_string (id' "a");
  print_int (id' 4)

won't work (since id' has type '_a->'_a).

Replacing the definition of id' with the eta expanded version (let id'
x = (id id) x)  will however work. It is not 100% equivalent since
every application of the new id' goes twice through id whilst the old
was a reference to id....

I hope this answers your question.
Cheers,
Till
On 6/23/07, Lukasz Stafiniak <lukstafi@gmail.com> wrote:
> On 6/23/07, Philippe Wang <lists@philippewang.info> wrote:
> > Till Varoquaux wrote:
> > > Humm... I have a small issue here: I need to get the result of the
> > > partial application of a polymorphic function. Since variable are
> > > generalized in Let it is generally advised to use eta expansions,
> > > (i.e transform to a total application).
> > > sometimes eta expansions just won't do the trick, consider:
> >
> > I think you should not try to "hide" that ugly side effect...
> >
> Could someone give an example where this "eta-thing" forbids a crash?
> I don't remember any example even in Xavier Leroy papers.
>
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>


-- 
http://till-varoquaux.blogspot.com/

Re: [Caml-list] How do I get polymorphic partial application?

[Lukasz Stafiniak]

On 6/24/07, Till Varoquaux <till.varoquaux@gmail.com> wrote:
> As said previously, in a HM type ineference system type variables are
> generalized only in "let", that is:
>
> let id x = x (*starting with an identity function*)
> let id'= id id (*this is a partial application; it has type '_a ->'_a*)
> let _=
>   print_string (id' "a");
>   print_int (id' 4)
>
> won't work (since id' has type '_a->'_a).
>
> Replacing the definition of id' with the eta expanded version (let id'
> x = (id id) x)  will however work. It is not 100% equivalent since
> every application of the new id' goes twice through id whilst the old
> was a reference to id....
>
> I hope this answers your question.
> Cheers,
> Till

No, it is related to the so called "value restriction" made Caml-ish
way, in a pure functional (no references) HM types can be generalized.
And I restate my question: can someone give an example, where if the
top-level let-definition types were generalized, this would lead to a
crash?

Re: [Caml-list] How do I get polymorphic partial application?

[Philippe Wang]

Lukasz Stafiniak wrote:
> On 6/23/07, Philippe Wang <lists@philippewang.info> wrote:
>> Till Varoquaux wrote:
>> > Humm... I have a small issue here: I need to get the result of the
>> > partial application of a polymorphic function. Since variable are
>> > generalized in Let it is generally advised to use eta expansions,
>> > (i.e transform to a total application).
>> > sometimes eta expansions just won't do the trick, consider:
>>
>> I think you should not try to "hide" that ugly side effect...
>>
> Could someone give an example where this "eta-thing" forbids a crash?
> I don't remember any example even in Xavier Leroy papers.

If I understand what you mean, this could explain it :

let foo () =
   let container = ref [] in
     fun x -> container := x :: !container; !container

val foo : unit -> 'a -> 'a list

(* first : doesn't work *)
let plop = foo ()
let l1 = plop 42
let l2 = plop "42"  (* crash  -- but wouldn't crash with most *dynamic* 
typing systems *)

let plop2 = fun () -> foo ()
let l1' = plop2 () 42
let l2' = plop2 () "42"  (* no crash *)

but plop and plop2 don't share the same semantics...

--
  Philippe Wang
    mail[at]philippewang.info

Re: [Caml-list] How do I get polymorphic partial application?

[Lukasz Stafiniak]

On 6/24/07, Philippe Wang <lists@philippewang.info> wrote:
>
> If I understand what you mean, this could explain it :
>
Uuups, I skipped your answer. Thanks and sorry for the noise!

Re: How do I get polymorphic partial application?

[Zheng Li]

"Till Varoquaux" <till.varoquaux@gmail.com> writes:
> Humm... I have a small issue here: I need to get the result of the
> partial application of a polymorphic function. Since variable are
> generalized in Let it is generally advised to use eta expansions,
> (i.e transform to a total application).
> sometimes eta expansions just won't do the trick, consider:
Well, there are cases eta expansions won't help. somehow you must modify your
code.

> let cntTag start=
> let cnt=ref start in
> fun v -> ((incr cnt;!cnt),v)
> the partial application is not fully polymorphic
> let tag1 = cntTag 1
> has type
> val tag1 : '_a -> int * '_a = <fun>

I suppose you still want to create different instance with parametrized
counter. You can do it in this way:

# type tag_func = {func: 'a. 'a -> int * 'a} ;;
# let cnTag s = let r = ref s in {func = fun x -> incr r; !r, x} ;;

(* either explicit use tag1.func here *)
# let tag1 = cnTag 1 ;;

# tag1.func 10;;
- : int * int = (2, 10)
# tag1.func "asdf";;
- : int * string = (3, "asdf")

(* or one extra step *)
# let tag1 = cnTag 1 ;;
# let tag1 x = tag1.func x ;;

# tag1 10;;
- : int * int = (2, 10)
# tag1 "asdf";;
- : int * string = (3, "asdf")

HTH.

-- 
Zheng Li
http://www.pps.jussieu.fr/~li

Re: How do I get polymorphic partial application?

[Zheng Li]

"Till Varoquaux" <till.varoquaux@gmail.com> writes:
> Humm... I have a small issue here: I need to get the result of the
> partial application of a polymorphic function. Since variable are
> generalized in Let it is generally advised to use eta expansions,
> (i.e transform to a total application).
> sometimes eta expansions just won't do the trick, consider:
Well, there are cases eta expansions won't help. somehow you must modify your
code.

> let cntTag start=
> let cnt=ref start in
> fun v -> ((incr cnt;!cnt),v)
> the partial application is not fully polymorphic
> let tag1 = cntTag 1
> has type
> val tag1 : '_a -> int * '_a = <fun>

I suppose you still want to create different instance with parametrized
counter. You can do it in this way:

# type tag_func = {func: 'a. 'a -> int * 'a} ;;
# let cnTag s = let r = ref s in {func = fun x -> incr r; !r, x} ;;

(* either explicit use tag1.func here *)
# let tag1 = cnTag 1 ;;

# tag1.func 10;;
- : int * int = (2, 10)
# tag1.func "asdf";;
- : int * string = (3, "asdf")

(* or one extra step *)
# let tag1 = cnTag 1 ;;
# let tag1 x = tag1.func x ;;

# tag1 10;;
- : int * int = (2, 10)
# tag1 "asdf";;
- : int * string = (3, "asdf")

HTH.

-- 
Zheng Li
http://www.pps.jussieu.fr/~li