Re: [Haskell-cafe] There can be only one fix? Pondering Bekic's lemma

On 3/19/07, Nicolas Frisby wrote:

Nope, but I believe the two are equipotent. This usage of "believe" is one of those "I think I remember reading it somewhere" usages.

On 3/19/07, Henning Thielemann wrote:

...

On Sat, 17 Mar 2007, Nicolas Frisby wrote:

...

Bekic's lemma [1], allows us to transform nested fixed points into a single fixed point, such as:

fix (\x -> fix (\y -> f (x, y))) = fix f where f :: (a, a) -> a

The 'fix' on the right hand side is not the standard one (e.g. Control.Monad.Fix), is it?

Yes, it is the standard "fix". The Bekic lemma actually reads: fix (\x -> fix (\y -> f (x, y))) = fix (\x -> f (x, x)) which should explain the confusion here. -Levent.