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

2007-03-21 Thread Nicolas Frisby
Whooops. Thanks for the correction. On 3/20/07, Levent Erkok [EMAIL PROTECTED] wrote: On 3/19/07, Nicolas Frisby [EMAIL PROTECTED] 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

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

2007-03-20 Thread Levent Erkok
On 3/19/07, Nicolas Frisby [EMAIL PROTECTED] 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 [EMAIL PROTECTED] wrote: On Sat, 17 Mar 2007, Nicolas Frisby wrote: Bekic's

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

2007-03-19 Thread Henning Thielemann
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

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

2007-03-19 Thread Nicolas Frisby
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 [EMAIL PROTECTED] wrote: On Sat, 17 Mar 2007, Nicolas Frisby wrote: Bekic's lemma [1], allows us to transform nested fixed points

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

2007-03-19 Thread Albert Y. C. Lai
Nicolas Frisby wrote: My question is: Given products and a fixed point combinator, can any pure expression be transformed into a corresponding expression that has just a single use of fix? If yes, has there been any usage of such a transformation, or is it just crazy? Yes. One use is

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

2007-03-18 Thread Lennart Augustsson
Using a single fix sounds possible. First transform your program (by lambda lifting) to a program with only global definitions, and then tuple them up and and use fix. The c with a hacek, č, is Unicode character 010D. -- Lennart On Mar 18, 2007, at 03:01 , Nicolas Frisby wrote:

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

2007-03-17 Thread Nicolas Frisby
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 This depends on having true products, though I'm not exactly sure what that means. Mutual recursion can also be described with