## The Type of a Recursive Combinator

The latest Cat version ( 0.9.7 at http://www.cat-language.com/download.html ) now has a linear recursion combinator "rec". The Cat type inference algorithm currently can't handle self-referential functions, but you implement recursive algorithms using the rec combinator.

Here is an example of the factorial program:

  >> define f { [dup 1 <=] [*] [pop 1] [dup --] rec }
inferred type for program 'f' as ( int ) -> ( int )
main stack: _empty_
>> 5 f
main stack: 120
>> 6 f
main stack: 120 720


The type of the rec combinator is interesting (at least I thought so):

(
(A:any*)->(A A) // argument relation
(A)->(B:any*)   // termination function
(A B)->(B)      // result relation
(A)->(bool A)   // termination condition
A               // input
)->(B)


I was wondering what people's thoughts were about the rec combinator? For example is it in fact interesting or novel to see the types explicitly stated for each component of linear recursion? Do you think there might be some educational value for students to have recursion explained in terms of arguments to a combinator?