FW: MonadFix

[Ross Paterson]

On Sun, Mar 03, 2002 at 11:38:44PM +0000, Levent Erkok wrote:
> On Monday 25 February 2002 10:42 am, Simon Marlow wrote:
> > This sounds fine to me.  It should probably go in Control.Fix.  Levent:
> > would you like to suggest a full contents for this library?
> 
> Sorry for the late reply. Modulo names, I think the attached library 
> should do it. 

I'd suggest that traceFix be renamed trace; it will be used by
Control.Arrow.  But is anyone ever going to use nthFix or paramFix?  The
former is only useful in proofs, while the latter is easily available as

paramFix :: ((a, u) -> u) -> a -> u           
paramFix f a = fix (curry f a)

How about a Control.Function module, with fix, trace and

compose :: [a -> a] -> a -> a
compose = foldr (.) id

times :: Integral n => n -> (a -> a) -> a -> a
times n f = compose (genericReplicate n f)

so then nthFix n f = times n f undefined.  Maybe some of the prelude
functions would belong in there too.