Re: [Haskell-cafe] Maybe use advice
Is it necessary (helpful) to use 'rewrite'? Nearly every time I've tried it, in the end 'transform' has been a better choice. Then you wouldn't need the 'Just's at all, and it should work fine. John From: Lyndon Maydwell maydw...@gmail.com (missed including cafe) f :: [Modification] - Maybe [Modification] and f _ = Just $ f ... are incompatible I managed to get the behaviour I'm after with the use of Either, but this really is messy: -- Sets of changes o (Modifier (Changes []) i) = Just $ i o (Modifier (Changes [c]) i) = Just $ Modifier c i o (Modifier (Changes l) i) = g (f (Left l)) where g (Right l) = Just $ Modifier (Changes l) i g (Left l) = Nothing f (Left (Scale x y : Scale x' y' : l)) = f $ Right $ Scale (x*x') (y*y') : h (f $ Left l) f (Left (Translate x y : Translate x' y' : l)) = f $ Right $ Translate (x+x') (y+y') : h (f $ Left l) f (Left (Rotatex : Rotatex': l)) = f $ Right $ Rotate(x+x'): h (f $ Left l) f x = x h (Left l) = l h (Right l) = l On Tue, Jun 7, 2011 at 3:11 AM, Maciej Marcin Piechotka uzytkown...@gmail.com wrote: On Mon, 2011-06-06 at 23:38 +0800, Lyndon Maydwell wrote: I'm writing an optimisation routine using Uniplate. Unfortunately, a sub-function I'm writing is getting caught in an infinite loop because it doesn't return Nothing when there are no optimisations left. I'd like a way to move the last Just into f, but this makes recursion very messy. I was wondering if there was a nice way to use something like the Monad or Applicative instance to help here. -- Sets of changes o (Modifier (Changes []) ?i) = Just $ i o (Modifier (Changes [c]) i) = Just $ Modifier c i o (Modifier (Changes l) ? i) = Just $ Modifier (Changes (f l)) i ? where ? ? f (Scale ? ? x y : Scale ? ? x' y' : l) = f $ Scale ? ? (x*x') (y*y') : f l ? ? f (Translate x y : Translate x' y' : l) = f $ Translate (x+x') (y+y') : f l ? ? f (Rotate ? ?x ? : Rotate ? ?x' ? ?: l) = f $ Rotate ? ?(x+x') ? ? ? ?: f l ? ? f l = l Any ideas? Something like: ... f (Rotate ? ?x ? : Rotate ? ?x' ? ?: l) ? ?= Just $ f (Rotate (x+x') : fromMaybe l (f l)) f l = Nothing -- As far as I understend Regards ___ ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Maybe use advice
The fixpoint nature of rewrite catches some cases that transform might not if I'm interpreting it correctly. (Changes [Translate 1 1, Scale 1 1, Translate 1 1]) could be rewritten as (Translate 2 2), but I'm not sure that it could be translated as such if it matches against (Changes [Translate _ _, Translate _ _]) first. I have the code on github at https://github.com/sordina/Diagrams-AST/blob/master/src/Graphics/Rendering/Diagrams/AST/Optimize.hs if you're interested. At the moment I'm not worrying about speed as I really just wrote this optimisation function as a demo of why an AST interface to Diagrams might be useful. On Tue, Jun 7, 2011 at 5:06 PM, John Lato jwl...@gmail.com wrote: Is it necessary (helpful) to use 'rewrite'? Nearly every time I've tried it, in the end 'transform' has been a better choice. Then you wouldn't need the 'Just's at all, and it should work fine. John From: Lyndon Maydwell maydw...@gmail.com (missed including cafe) f :: [Modification] - Maybe [Modification] and f _ = Just $ f ... are incompatible I managed to get the behaviour I'm after with the use of Either, but this really is messy: -- Sets of changes o (Modifier (Changes []) i) = Just $ i o (Modifier (Changes [c]) i) = Just $ Modifier c i o (Modifier (Changes l) i) = g (f (Left l)) where g (Right l) = Just $ Modifier (Changes l) i g (Left l) = Nothing f (Left (Scale x y : Scale x' y' : l)) = f $ Right $ Scale (x*x') (y*y') : h (f $ Left l) f (Left (Translate x y : Translate x' y' : l)) = f $ Right $ Translate (x+x') (y+y') : h (f $ Left l) f (Left (Rotate x : Rotate x' : l)) = f $ Right $ Rotate (x+x') : h (f $ Left l) f x = x h (Left l) = l h (Right l) = l On Tue, Jun 7, 2011 at 3:11 AM, Maciej Marcin Piechotka uzytkown...@gmail.com wrote: On Mon, 2011-06-06 at 23:38 +0800, Lyndon Maydwell wrote: I'm writing an optimisation routine using Uniplate. Unfortunately, a sub-function I'm writing is getting caught in an infinite loop because it doesn't return Nothing when there are no optimisations left. I'd like a way to move the last Just into f, but this makes recursion very messy. I was wondering if there was a nice way to use something like the Monad or Applicative instance to help here. -- Sets of changes o (Modifier (Changes []) ?i) = Just $ i o (Modifier (Changes [c]) i) = Just $ Modifier c i o (Modifier (Changes l) ? i) = Just $ Modifier (Changes (f l)) i ? where ? ? f (Scale ? ? x y : Scale ? ? x' y' : l) = f $ Scale ? ? (x*x') (y*y') : f l ? ? f (Translate x y : Translate x' y' : l) = f $ Translate (x+x') (y+y') : f l ? ? f (Rotate ? ?x ? : Rotate ? ?x' ? ?: l) = f $ Rotate ? ?(x+x') ? ? ? ?: f l ? ? f l = l Any ideas? Something like: ... f (Rotate ? ?x ? : Rotate ? ?x' ? ?: l) ? ?= Just $ f (Rotate (x+x') : fromMaybe l (f l)) f l = Nothing -- As far as I understend Regards ___ ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Maybe use advice
If I'm interpreting your code properly, it's not currently catching that case anyway. The problem is that you've got two sets of modifiers that both should be optimized, explicit Modifier constructors in the Image, and a list contained in Changes. Since 'Changes' is just a list of Modifiers, and not an Image, neither rewrite nor transform will descend on it. You get around this by explicitly calling rewrite on the modifiers in 'deBlank', but then the rules from 'optimize' aren't applied. You can't really use the biplate functions either because they only match on a single element at a time. What you really want to do is be able to express each rule exactly once, which isn't possible in the current form of your code. One solution is to move a lot of the reductions of the form 'Modifier x' from 'optimize' into 'deBlank'. Then you would have something like this: deBlank :: [Modifier] - [Modifier] deBlank = db db (Scale 1 1 : l) = db l db (Rotate x : Rotate x' : l) = db (Rotate (x+x') : l) db (Scale x y : Scale x' y' : l) = db (Scale (x*x') (y*y') : l) db (Translate x y : Translate x' y' : l) = db (Translate (x+x') (y+y') : l) db xs = xs I actually don't think uniplate gets you anything in this particular function. Now deBlank will produce a list of modifiers which is as reduced as possible (at least by the rules you've provided), and you can use it within a two-pass optimize: optimize = transform o2 . transform o o (Modifier _ Blank) = Blank o (Modifier (Scale 0 _) _i) = Blank -- similar cases omitted o (Modifier m2 (Modifier m1 i)) = Modifier (m1 `mappend` m2) i o i@(Modifier (Changes _c) _i) = i o (Modifier m i) = Modifier (Changes [m]) i o i = i o2 (Modifier (Changes c) i) = case deBlank c of [] - i [x] - Modifier x i xs - Modifier (Changes c) i o2 i = i Transformations like Scale 0 _ have remained in the Image traversal, however all other modifications are combined into a single Changes list, which is then reduced by deBlank in the second pass. Note that in the first pass, even single modifications are encapsulated in a Changes; this makes the logic of the second pass much simpler because then all the reductions of multiple modifiers are located in the 'deBlank' function instead of split between there and 'o'. This presumes there's an appropriate Monoid instance for Modifiers, but if it doesn't exist it can be written easily enough. On second thought, I think it would be good to break it up even more, and keep the reductions of the form o (Modifier _ Blank) = Blank o (Modifier (Scale 0 _) _i) = Blank as a third pass, because it's possible some of them could get lost in this form. Then the first pass would just combine terms, the second would apply 'deBlank' and reduce, then the third would be as above. There are two alternatives which may be simpler: 1) Expand Changes c into explicit modifications and do all your reductions on the resulting Image. 2) Implement a general matrix transform for Diagrams and rewrite everything in terms of that. This would be useful for shear transforms anyway, which I believe are currently inexpressible in Diagrams. John Lato On Tue, Jun 7, 2011 at 10:12 AM, Lyndon Maydwell maydw...@gmail.com wrote: The fixpoint nature of rewrite catches some cases that transform might not if I'm interpreting it correctly. (Changes [Translate 1 1, Scale 1 1, Translate 1 1]) could be rewritten as (Translate 2 2), but I'm not sure that it could be translated as such if it matches against (Changes [Translate _ _, Translate _ _]) first. I have the code on github at https://github.com/sordina/Diagrams-AST/blob/master/src/Graphics/Rendering/Diagrams/AST/Optimize.hs if you're interested. At the moment I'm not worrying about speed as I really just wrote this optimisation function as a demo of why an AST interface to Diagrams might be useful. On Tue, Jun 7, 2011 at 5:06 PM, John Lato jwl...@gmail.com wrote: Is it necessary (helpful) to use 'rewrite'? Nearly every time I've tried it, in the end 'transform' has been a better choice. Then you wouldn't need the 'Just's at all, and it should work fine. John From: Lyndon Maydwell maydw...@gmail.com (missed including cafe) f :: [Modification] - Maybe [Modification] and f _ = Just $ f ... are incompatible I managed to get the behaviour I'm after with the use of Either, but this really is messy: -- Sets of changes o (Modifier (Changes []) i) = Just $ i o (Modifier (Changes [c]) i) = Just $ Modifier c i o (Modifier (Changes l) i) = g (f (Left l)) where g (Right l) = Just $ Modifier (Changes l) i g (Left l) = Nothing f (Left (Scale x y : Scale x' y' : l)) = f $ Right $ Scale (x*x') (y*y') : h (f $ Left l) f (Left (Translate x y : Translate x' y' : l)) = f $ Right $ Translate (x+x') (y+y') : h (f $ Left l) f (Left (Rotatex : Rotatex': l)) =
Re: [Haskell-cafe] Maybe use advice
I was considering using a matrix optimisation but things are out of control enough already :) Converting all Changes constructors to nested regular constructors may be the easiest approach. It would certainly eliminate the mess of list manipulations. On Tue, Jun 7, 2011 at 6:21 PM, John Lato jwl...@gmail.com wrote: If I'm interpreting your code properly, it's not currently catching that case anyway. The problem is that you've got two sets of modifiers that both should be optimized, explicit Modifier constructors in the Image, and a list contained in Changes. Since 'Changes' is just a list of Modifiers, and not an Image, neither rewrite nor transform will descend on it. You get around this by explicitly calling rewrite on the modifiers in 'deBlank', but then the rules from 'optimize' aren't applied. You can't really use the biplate functions either because they only match on a single element at a time. What you really want to do is be able to express each rule exactly once, which isn't possible in the current form of your code. One solution is to move a lot of the reductions of the form 'Modifier x' from 'optimize' into 'deBlank'. Then you would have something like this: deBlank :: [Modifier] - [Modifier] deBlank = db db (Scale 1 1 : l) = db l db (Rotate x : Rotate x' : l) = db (Rotate (x+x') : l) db (Scale x y : Scale x' y' : l) = db (Scale (x*x') (y*y') : l) db (Translate x y : Translate x' y' : l) = db (Translate (x+x') (y+y') : l) db xs = xs I actually don't think uniplate gets you anything in this particular function. Now deBlank will produce a list of modifiers which is as reduced as possible (at least by the rules you've provided), and you can use it within a two-pass optimize: optimize = transform o2 . transform o o (Modifier _ Blank) = Blank o (Modifier (Scale 0 _) _i) = Blank -- similar cases omitted o (Modifier m2 (Modifier m1 i)) = Modifier (m1 `mappend` m2) i o i@(Modifier (Changes _c) _i) = i o (Modifier m i) = Modifier (Changes [m]) i o i = i o2 (Modifier (Changes c) i) = case deBlank c of [] - i [x] - Modifier x i xs - Modifier (Changes c) i o2 i = i Transformations like Scale 0 _ have remained in the Image traversal, however all other modifications are combined into a single Changes list, which is then reduced by deBlank in the second pass. Note that in the first pass, even single modifications are encapsulated in a Changes; this makes the logic of the second pass much simpler because then all the reductions of multiple modifiers are located in the 'deBlank' function instead of split between there and 'o'. This presumes there's an appropriate Monoid instance for Modifiers, but if it doesn't exist it can be written easily enough. On second thought, I think it would be good to break it up even more, and keep the reductions of the form o (Modifier _ Blank) = Blank o (Modifier (Scale 0 _) _i) = Blank as a third pass, because it's possible some of them could get lost in this form. Then the first pass would just combine terms, the second would apply 'deBlank' and reduce, then the third would be as above. There are two alternatives which may be simpler: 1) Expand Changes c into explicit modifications and do all your reductions on the resulting Image. 2) Implement a general matrix transform for Diagrams and rewrite everything in terms of that. This would be useful for shear transforms anyway, which I believe are currently inexpressible in Diagrams. John Lato On Tue, Jun 7, 2011 at 10:12 AM, Lyndon Maydwell maydw...@gmail.com wrote: The fixpoint nature of rewrite catches some cases that transform might not if I'm interpreting it correctly. (Changes [Translate 1 1, Scale 1 1, Translate 1 1]) could be rewritten as (Translate 2 2), but I'm not sure that it could be translated as such if it matches against (Changes [Translate _ _, Translate _ _]) first. I have the code on github at https://github.com/sordina/Diagrams-AST/blob/master/src/Graphics/Rendering/Diagrams/AST/Optimize.hs if you're interested. At the moment I'm not worrying about speed as I really just wrote this optimisation function as a demo of why an AST interface to Diagrams might be useful. On Tue, Jun 7, 2011 at 5:06 PM, John Lato jwl...@gmail.com wrote: Is it necessary (helpful) to use 'rewrite'? Nearly every time I've tried it, in the end 'transform' has been a better choice. Then you wouldn't need the 'Just's at all, and it should work fine. John From: Lyndon Maydwell maydw...@gmail.com (missed including cafe) f :: [Modification] - Maybe [Modification] and f _ = Just $ f ... are incompatible I managed to get the behaviour I'm after with the use of Either, but this really is messy: -- Sets of changes o (Modifier (Changes []) i) = Just $ i o (Modifier (Changes [c]) i) = Just $ Modifier c i o (Modifier (Changes l) i) = g (f (Left l)) where g (Right l) = Just
Re: [Haskell-cafe] Maybe use advice
On Mon, 2011-06-06 at 23:38 +0800, Lyndon Maydwell wrote: I'm writing an optimisation routine using Uniplate. Unfortunately, a sub-function I'm writing is getting caught in an infinite loop because it doesn't return Nothing when there are no optimisations left. I'd like a way to move the last Just into f, but this makes recursion very messy. I was wondering if there was a nice way to use something like the Monad or Applicative instance to help here. -- Sets of changes o (Modifier (Changes []) i) = Just $ i o (Modifier (Changes [c]) i) = Just $ Modifier c i o (Modifier (Changes l) i) = Just $ Modifier (Changes (f l)) i where f (Scale x y : Scale x' y' : l) = f $ Scale (x*x') (y*y') : f l f (Translate x y : Translate x' y' : l) = f $ Translate (x+x') (y+y') : f l f (Rotatex : Rotatex': l) = f $ Rotate(x+x'): f l f l = l Any ideas? Something like: ... f (Rotatex : Rotatex': l) = Just $ f (Rotate (x+x') : fromMaybe l (f l)) f l = Nothing -- As far as I understend Regards signature.asc Description: This is a digitally signed message part ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Maybe use advice
(missed including cafe) f :: [Modification] - Maybe [Modification] and f _ = Just $ f ... are incompatible I managed to get the behaviour I'm after with the use of Either, but this really is messy: -- Sets of changes o (Modifier (Changes []) i) = Just $ i o (Modifier (Changes [c]) i) = Just $ Modifier c i o (Modifier (Changes l) i) = g (f (Left l)) where g (Right l) = Just $ Modifier (Changes l) i g (Left l) = Nothing f (Left (Scale x y : Scale x' y' : l)) = f $ Right $ Scale (x*x') (y*y') : h (f $ Left l) f (Left (Translate x y : Translate x' y' : l)) = f $ Right $ Translate (x+x') (y+y') : h (f $ Left l) f (Left (Rotatex : Rotatex': l)) = f $ Right $ Rotate(x+x'): h (f $ Left l) f x = x h (Left l) = l h (Right l) = l On Tue, Jun 7, 2011 at 3:11 AM, Maciej Marcin Piechotka uzytkown...@gmail.com wrote: On Mon, 2011-06-06 at 23:38 +0800, Lyndon Maydwell wrote: I'm writing an optimisation routine using Uniplate. Unfortunately, a sub-function I'm writing is getting caught in an infinite loop because it doesn't return Nothing when there are no optimisations left. I'd like a way to move the last Just into f, but this makes recursion very messy. I was wondering if there was a nice way to use something like the Monad or Applicative instance to help here. -- Sets of changes o (Modifier (Changes []) i) = Just $ i o (Modifier (Changes [c]) i) = Just $ Modifier c i o (Modifier (Changes l) i) = Just $ Modifier (Changes (f l)) i where f (Scale x y : Scale x' y' : l) = f $ Scale (x*x') (y*y') : f l f (Translate x y : Translate x' y' : l) = f $ Translate (x+x') (y+y') : f l f (Rotate x : Rotate x' : l) = f $ Rotate (x+x') : f l f l = l Any ideas? Something like: ... f (Rotate x : Rotate x' : l) = Just $ f (Rotate (x+x') : fromMaybe l (f l)) f l = Nothing -- As far as I understend Regards ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Maybe use advice
On Tue, 2011-06-07 at 04:09 +0800, Lyndon Maydwell wrote: (missed including cafe) f :: [Modification] - Maybe [Modification] and f _ = Just $ f ... are incompatible My bad: f ... = let cs' = (Rotate (x+x') : fromMaybe cs (f cs)) in fromMaybe cs (f cs) Or refactoring it: g l = fromMaybe l (f l) f (Rotatex : Rotatex': cs) = g (Rotate (x+x') : g cs) Regards I managed to get the behaviour I'm after with the use of Either, but this really is messy: -- Sets of changes o (Modifier (Changes []) i) = Just $ i o (Modifier (Changes [c]) i) = Just $ Modifier c i o (Modifier (Changes l) i) = g (f (Left l)) where g (Right l) = Just $ Modifier (Changes l) i g (Left l) = Nothing f (Left (Scale x y : Scale x' y' : l)) = f $ Right $ Scale (x*x') (y*y') : h (f $ Left l) f (Left (Translate x y : Translate x' y' : l)) = f $ Right $ Translate (x+x') (y+y') : h (f $ Left l) f (Left (Rotatex : Rotatex': l)) = f $ Right $ Rotate(x+x'): h (f $ Left l) f x = x h (Left l) = l h (Right l) = l On Tue, Jun 7, 2011 at 3:11 AM, Maciej Marcin Piechotka uzytkown...@gmail.com wrote: On Mon, 2011-06-06 at 23:38 +0800, Lyndon Maydwell wrote: I'm writing an optimisation routine using Uniplate. Unfortunately, a sub-function I'm writing is getting caught in an infinite loop because it doesn't return Nothing when there are no optimisations left. I'd like a way to move the last Just into f, but this makes recursion very messy. I was wondering if there was a nice way to use something like the Monad or Applicative instance to help here. -- Sets of changes o (Modifier (Changes []) i) = Just $ i o (Modifier (Changes [c]) i) = Just $ Modifier c i o (Modifier (Changes l) i) = Just $ Modifier (Changes (f l)) i where f (Scale x y : Scale x' y' : l) = f $ Scale (x*x') (y*y') : f l f (Translate x y : Translate x' y' : l) = f $ Translate (x+x') (y+y') : f l f (Rotatex : Rotatex': l) = f $ Rotate(x+x') : f l f l = l Any ideas? Something like: ... f (Rotatex : Rotatex': l) = Just $ f (Rotate (x+x') : fromMaybe l (f l)) f l = Nothing -- As far as I understend Regards ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe signature.asc Description: This is a digitally signed message part ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Maybe use advice
Thanks Maciej! An additional Just was required in the refactored version of f: f (Rotatex : Rotatex': cs) = Just $ g (Rotate (x+x') : g cs) This is much cleaner than what I was doing. On Tue, Jun 7, 2011 at 4:14 AM, Maciej Piechotka uzytkown...@gmail.com wrote: On Tue, 2011-06-07 at 04:09 +0800, Lyndon Maydwell wrote: (missed including cafe) f :: [Modification] - Maybe [Modification] and f _ = Just $ f ... are incompatible My bad: f ... = let cs' = (Rotate (x+x') : fromMaybe cs (f cs)) in fromMaybe cs (f cs) Or refactoring it: g l = fromMaybe l (f l) f (Rotate x : Rotate x' : cs) = g (Rotate (x+x') : g cs) Regards I managed to get the behaviour I'm after with the use of Either, but this really is messy: -- Sets of changes o (Modifier (Changes []) i) = Just $ i o (Modifier (Changes [c]) i) = Just $ Modifier c i o (Modifier (Changes l) i) = g (f (Left l)) where g (Right l) = Just $ Modifier (Changes l) i g (Left l) = Nothing f (Left (Scale x y : Scale x' y' : l)) = f $ Right $ Scale (x*x') (y*y') : h (f $ Left l) f (Left (Translate x y : Translate x' y' : l)) = f $ Right $ Translate (x+x') (y+y') : h (f $ Left l) f (Left (Rotate x : Rotate x' : l)) = f $ Right $ Rotate (x+x') : h (f $ Left l) f x = x h (Left l) = l h (Right l) = l On Tue, Jun 7, 2011 at 3:11 AM, Maciej Marcin Piechotka uzytkown...@gmail.com wrote: On Mon, 2011-06-06 at 23:38 +0800, Lyndon Maydwell wrote: I'm writing an optimisation routine using Uniplate. Unfortunately, a sub-function I'm writing is getting caught in an infinite loop because it doesn't return Nothing when there are no optimisations left. I'd like a way to move the last Just into f, but this makes recursion very messy. I was wondering if there was a nice way to use something like the Monad or Applicative instance to help here. -- Sets of changes o (Modifier (Changes []) i) = Just $ i o (Modifier (Changes [c]) i) = Just $ Modifier c i o (Modifier (Changes l) i) = Just $ Modifier (Changes (f l)) i where f (Scale x y : Scale x' y' : l) = f $ Scale (x*x') (y*y') : f l f (Translate x y : Translate x' y' : l) = f $ Translate (x+x') (y+y') : f l f (Rotate x : Rotate x' : l) = f $ Rotate (x+x') : f l f l = l Any ideas? Something like: ... f (Rotate x : Rotate x' : l) = Just $ f (Rotate (x+x') : fromMaybe l (f l)) f l = Nothing -- As far as I understend Regards ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Maybe use advice
Hi Lyndon Are you just coalescing adjacent elements (if they are the same constructor)? As it seems you have a list here rather than a tree, I'd step out of Uniplate at this point and just do a list traversal with direct recursion. ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
