Tyng-Ruey Chuang <trc@iis.sinica.edu.tw> writes:

> Jean-Christophe FILLIATRE wrote:
> > Actually, there  is a  type-able way of  writing this  function, which
> > consists in duplicating it into two functions, like this:
> > 
> > ======================================================================
> > type ('a,'b,'c) t =
> >   | A of 'a * 'b * 'c
> >   | B of ('b, 'a, 'c) t
> > 
> > let rec gamma = function
> >   | A _ -> 0
> >   | B x -> 1 + gamma' x
> > 
> > and gamma' = function
> >   | A _ -> 0
> >   | B x -> 1 + gamma x
> > ======================================================================
> > 
> > which gives the expected types:
> > 
> > ======================================================================
> > val gamma : ('a, 'b, 'c) t -> int = <fun>
> > val gamma' : ('a, 'b, 'c) t -> int = <fun>
> > ======================================================================
> 
> Interesting! But then size of the duplicated code grows exponentially.

Actually, you can share a little more: 

        let gamma_body gamma = function 
           | A _ -> 0
           | B x -> 1 + gamma x

        let rec gamma  x = gamma_body gamma' x 
            and gamma' x = gamma_body gamma  x;;
        ;;

and a for three parameters: 

        type ('a, 'b, 'c) sigma = 
          | I of 'a * 'b * 'c 
          | T of ('b, 'a, 'c) sigma
          | P of ('b, 'c, 'a) sigma

        let body gT gP = function
           | I _ -> 0
           | T x -> 1 + gT x
           | P x -> 1 + gP x

        let rec abc s = body bac bca s
            and acb s = body cab cba s
            and bac s = body abc acb s
            and bca s = body cba cab s
            and cab s = body acb abc s
            and cba s = body bca bac s
        ;;

Didier
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