Fixed point combinator for mutually recursive functions?

Question

Is there a fixed point combinator for creating tuples of mutually recursive functions? I.e. I\'m looking for something like the Y-Combinator but which takes multiple \"recu

Answer 1

The following web page describes the fix-point combinators for mutual recursion (polyvariadic fixpoint combinators) in detail. It derives the simplest so far combinator. http://okmij.org/ftp/Computation/fixed-point-combinators.html#Poly-variadic

For ease of reference, here is the simplest polyvariadic combinator in Haskell (one-liner)

fix_poly:: [[a]->a] -> [a]
fix_poly fl = fix (\self -> map ($ self) fl)
  where fix f = f (fix f)

and here it is in Scheme, a strict language

 (define (Y* . l)
   ((lambda (u) (u u))
    (lambda (p)
       (map (lambda (li) (lambda x (apply (apply li (p p)) x))) l))))

Please see the web page for examples and more discussion.