Re: [Haskell-cafe] Future Edison directions
Brian Hulley wrote: splitWith :: (v -> Bool) -> c -> (c,c) splitWith p t | isEmpty t = (empty, empty) | p (measure t) = let (l,x,r) = splitWithInternal p mempty t in (l, pushL x r) | otherwise = (empty, empty) Sorry it should be: | otherwise = (t, empty) ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Future Edison directions
Jared Updike wrote: This page: http://jaortega.wordpress.com/2006/03/17/programmers-go-bananas/ lists some references at the bottom. Perhaps they would be useful. Thanks! That page looks really interesting and useful, Brian. ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Future Edison directions
Robert Dockins wrote: [snip] 7) Finally, I somehow feel like there should be a nice categorical formulation of these datastructure abstractions which would help to drive a refactoring of the API typeclasses in a principled way, rather than on an ad-hoc I-sort-of-think-these-go-together sort of way. For the last few months (!!!) I've been thinking about the relationship between measured sequences and plain sequences and also whether or not every sequence should by indexable by Int. I'm wondering if something like the following might be a possible factoring of the ops relating to indexing/measurements: -- from http://www.soi.city.ac.uk/~ross/papers/FingerTree.html class Monoid v => Measured v a where measure :: a -> v instance Measured () a where measure _ = () -- then (also based mostly on FingerTree ideas) class (Monoid v, Ord i) => IndexMeasure v i where -- no fundep index :: v -> i class BasicSeq c a | c -> a where length :: c -> Int empty :: c isEmpty :: c -> Bool atL :: c -> a atR :: c -> a pushL :: a -> c -> c viewL :: Monad m => c -> m (a, c) -- pushR, viewR class (Measured v a, Measured v c, BasicSeq c a) => Measurable c v a | c -> v where -- precondition: pred is True for v `mappend` (measure c) splitWithInternal :: (v -> Bool) -> v -> c -> (c, a, c) splitWith :: (v -> Bool) -> c -> (c,c) splitWith p t | isEmpty t = (empty, empty) | p (measure t) = let (l,x,r) = splitWithInternal p mempty t in (l, pushL x r) | otherwise = (empty, empty) splitAt :: IndexMeasure v i => i -> c -> (c,c) splitAt i = splitWith (\v -> i < index v) size :: IndexMeasure v i => c -> i size c = index (measure c) -- take, drop, takeWith, dropWith, in terms of split and splitWith atWith :: (v -> Bool) -> c -> a atWith p t = (\(_,x,_)->x) (splitWithInternal p mempty t) at :: IndexMeasure v i => i -> c -> a at i = atWith (\v -> i < index v) where splitWith p s returns (l,r) such that the measure of l `mappend` the measure of the first element of r satisfies p (FingerTree paper has explanation of this - I assume monotonic p for any useful use). The idea of the above design would be to allow multiple indexes for the same sequence (though the element type is the same in each case so possibly this could be confusing though could be prevented by using a fundep in the IndexMeasure class), as well as allowing sequences with an arbitrary measure that isn't an index (just by having no instances of IndexMeasure) eg: data TextBuffer = ... newtype Line = Line Int newtype CharPos = CharPos Int data TextBufferMeasure = ... instance IndexMeasure TextBufferMeasure Line where ... instance IndexMeasure TextBufferMeasure CharPos where ... instance Measureable TextBuffer TextBufferMeasure Char where ... Line lineCount = size textbuf CharPos charCount = size textbuf (before, after) = splitAt (CharPos 56) textbuf Of course this doesn't solve the problem of using nested sequences, but it at least allows general measurement with predicate search to coexist with simple indexing and size-with-respect-to-index where these are applicable to the relevant concrete sequence. Anyway just a very rough idea at the moment. I'm looking forward to seeing a nice categorical factoring ;-) Regards, Brian. -- Logic empowers us and Love gives us purpose. Yet still phantoms restless for eras long past, congealed in the present in unthought forms, strive mightily unseen to destroy us. http://www.metamilk.com ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Future Edison directions
This page: http://jaortega.wordpress.com/2006/03/17/programmers-go-bananas/ lists some references at the bottom. Perhaps they would be useful. Jared. On 8/1/06, Brian Hulley <[EMAIL PROTECTED]> wrote: Robert Dockins wrote: [snip other points] > 7) Finally, I somehow feel like there should be a nice categorical > formulation of these datastructure abstractions which would help to > drive a refactoring of the API typeclasses in a principled way, > rather than on an ad-hoc I-sort-of-think-these-go-together sort of > way. Unfortunately, my category-fu is quite weak, so all I have is > this vague intuition that I can't substantiate. I'm sort of familiar > with initial algebras, but I think they may be too concrete. I'm > looking for some way to classify algebras that have, eg, the property > of having folds, or of being set-like, etc. If anybody can point me > in the right direction wrt this, that would be great. I'd love to find out more about these categorical abstractions also, since Monads and Monoids (the only ones I know about) are an incredible source of power and expressiveness in Haskell programming, so I've got the feeling that I'm wasting tremendous amounts of time reinventing the wheel when other abstractions that may be equally useful are just waiting to be used... Can anyone recommend a good book or web tutorial about category theory that's not too difficult? I'm thinking about something which would have lots of diagrams and discussion about the relevance of the concepts to practical computing problems but not something loaded with complicated proofs or LaTeX symbols :-) Thanks, Brian. -- Logic empowers us and Love gives us purpose. Yet still phantoms restless for eras long past, congealed in the present in unthought forms, strive mightily unseen to destroy us. http://www.metamilk.com ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe -- http://www.updike.org/~jared/ reverse ")-:" ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Future Edison directions
Robert Dockins wrote: [snip other points] 7) Finally, I somehow feel like there should be a nice categorical formulation of these datastructure abstractions which would help to drive a refactoring of the API typeclasses in a principled way, rather than on an ad-hoc I-sort-of-think-these-go-together sort of way. Unfortunately, my category-fu is quite weak, so all I have is this vague intuition that I can't substantiate. I'm sort of familiar with initial algebras, but I think they may be too concrete. I'm looking for some way to classify algebras that have, eg, the property of having folds, or of being set-like, etc. If anybody can point me in the right direction wrt this, that would be great. I'd love to find out more about these categorical abstractions also, since Monads and Monoids (the only ones I know about) are an incredible source of power and expressiveness in Haskell programming, so I've got the feeling that I'm wasting tremendous amounts of time reinventing the wheel when other abstractions that may be equally useful are just waiting to be used... Can anyone recommend a good book or web tutorial about category theory that's not too difficult? I'm thinking about something which would have lots of diagrams and discussion about the relevance of the concepts to practical computing problems but not something loaded with complicated proofs or LaTeX symbols :-) Thanks, Brian. -- Logic empowers us and Love gives us purpose. Yet still phantoms restless for eras long past, congealed in the present in unthought forms, strive mightily unseen to destroy us. http://www.metamilk.com ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
