On Wed, Dec 12, 2001 at 11:31:53PM +0100, Diego Olivier Fernandez Pons wrote:

One wants write the following function 

# let rec app f  = function 
    [] -> f 
  | x::l -> app (f x) l    ;;

but caml reply :

This expression has type 'a but is here used with type 'b -> 'a


Thanks to OOP in caml ;-) , we can use cyclics types (-rectypes option)
and now :

# let rec app f  = function 
    [] -> f 
  | x::l -> app (f x) l    ;;
val app : ('b -> 'a as 'a) -> 'b list -> 'a = <fun>


So what about the first argument of app. I need a function with 'a -> 'b
as type, it must be a function with no termination. Ok, the result may
be raised by an exception.
For instance :

exception Int of int

# let sum2 x y = raise (Int (x+y))
  let sum3 x y z = raise (Int (x+y+z)) ;;
val sum2 : int -> int -> 'a = <fun>
val sum3 : int -> int -> int -> 'a = <fun>

To end, the apply function will catch the result :

# let  apply  f l = try app f l ; 0 with Int x -> x ;;
Warning: this function application is partial,
maybe some arguments are missing.
val apply : ('b -> 'a as 'a) -> 'b list -> int = <fun>

We are more intelligent than the type checker and we ommit the warning ...

and now let's try :

# apply sum2 [1;2] ;;
- : int = 3

# apply sum3 [1;2;3] ;;
- : int = 6


Bruno Pagano
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