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[Caml-list] A G'Caml question
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Date: 2001-06-25 (17:12)
From: Jun Furuse <Jun.Furuse@i...>
Subject: "Re: [Caml-list] A G'Caml question" + additional info

Thanks your comment about the exntesion. It is natural idea to extend
generic values and it must be definitively required. This extension
of generic values cannot be handled by the normal redefinition which
is available in G'Caml. They essentially requires its own syntax and
typing, which are still not be implemented...

Let me explain details using your example:

> # generic rec print = case 
>   | int -> unit => print_int
>   | string -> unit => print_string
>   | $a list -> unit => 
>       function [] -> ()
>       |   x :: xs -> print x; print xs
>   ;;            
> # generic rec print = case float -> unit => print_float | $a -> unit =>
> print;;
> # print 1.0;;
> 1- : unit = ()
> # print 1 (* infinite loop! *)
> Well, that should be expected, since we try and print an int, which isn't
> a float, so we try (from $a -> unit => print) to print, ad
> infinitum. 

Yes, as you pointed out, your second definition of print will not
work, because its definition is completely independent from the first;
it uses the same name print, but it points to the new print. 
We can have the same thing even in the normal let rec expressions:

   let f () = print_string "hello";;
   let rec f () = f ()

The second f does not call the first f, but itself (and loops forever).

> # let print' = print ;;
> # generic rec print = case 
>   | float -> unit => print_float 
>   | $a -> unit => print'
>   ;;
> # print [1.0;2.0;3.0];; 
> This generic full instance is used with type float list -> unit
>  which is not its valid instance of ...

This does not work neither. Since what print recursively calls
is the original print, not the newly defined print. Therefore
we cannot use the interesting mixed case of float list -> unit...

> Is there some trick to build up recursive generics by parts? One thing 
> to do is to break the recursive generic into a non-recursive generic
> and a recursive function which applies the generic to the elements, 
> but that feels like cheating. Maybe open recursion for generics would 
> be desirable, so that I can add a new case and have the recursive call in 
> an existing case call the new one? Yes, it's a half baked idea, but maybe 
> a better cook can finish baking...

As we have seen, redefinitions cannot achieve what you (and I) want. 
We will need some special construction for the extension. We will have
the new "include" phrase to import the type case definitions of the
other generic values. For example:

	generic print' = case
	| include print
	| float -> unit => print_float

This newly defined print' will be semantically equivalent to the 
following generic definition:
	generic print' = case
	| int -> unit => print_int
	| string -> unit => print_float
	| $a list -> unit =>
	     function [] -> ()
		    | x :: xs -> print' x; print' xs  
	| float -> unit => print_float

Note that the recursive occurrences of print in the original
definition are now replaced by print', in order to point 
the newly defined generic value. In this sense, the include phrase is
not the pure inclusion of the source. Thus, the new print' can print
float lists:

      # print' [1.2; 3.4; 5.6];; : unit = ()

Thus, the generic values are "open" to the others who include them,
but it is not the open recursion you mentioned; print and print' are
different values and independent each other. 

  We do not want to introduce the full open recursion to generic
values. You could add new type cases easily using the open recursion
and it should be helpful in some cases. But it can also introduce
heavy semantic confusion to our programs, since in the open recursion
the semantics of generic values could not be fixed until all modules 
are linked together. 


Several people have courageously tried some module programming using
G'Caml and reported troubles. I am sorry but you cannot write .mli
files with extensional polymorphic values. At the time of the
implementation, we had not had clear idea to store generic constraints
in signatures... Please only use the toplevel.

I explained briefly the limitations of the current implementation at

However, none of them are theoretical. 
They can be fixed when I will get some more time for coding!


Jun P. Furuse
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