Re: [Haskell-cafe] Exercise in point free-style
G'day all. Quoting Donald Bruce Stewart <[EMAIL PROTECTED]>: > Get some free theorems: > lambdabot> free f :: (b -> b) -> [b] -> [b] > f . g = h . f => map f . f g = f h . map f I finally got around to fixing the name clash bug. It now reports: g . h = k . g => map g . f h = f k . map g Get your free theorems from: http://andrew.bromage.org/darcs/freetheorems/ Cheers, Andrew Bromage ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Exercise in point free-style
haskell: > Julien Oster wrote: > > >But I'm having problems with one of the functions: > > > >func3 f l = l ++ map f l > > While we're at it: The best thing I could come up for > > func2 f g l = filter f (map g l) > > is > > func2p f g = (filter f) . (map g) > > Which isn't exactly point-_free_. Is it possible to reduce that further? Similarly: lambdabot> pl func2 f g l = filter f (map g l) func2 = (. map) . (.) . filter :) ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Exercise in point free-style
haskell: > Hello, > > I was just doing Exercise 7.1 of Hal Daum?'s very good "Yet Another > Haskell Tutorial". It consists of 5 short functions which are to be > converted into point-free style (if possible). > > It's insightful and after some thinking I've been able to come up with > solutions that make me understand things better. > > But I'm having problems with one of the functions: > > func3 f l = l ++ map f l > > Looks pretty clear and simple. However, I can't come up with a solution. > Is it even possible to remove one of the variables, f or l? If so, how? The solution is to install lambdabot ;) Point free refactoring: lambdabot> pl func3 f l = l ++ map f l func3 = ap (++) . map Find the type: lambdabot> type ap (++) . map forall b. (b -> b) -> [b] -> [b] Get some free theorems: lambdabot> free f :: (b -> b) -> [b] -> [b] f . g = h . f => map f . f g = f h . map f :) -- Don ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Exercise in point free-style
Julien Oster wrote: > = ((.) (filter f)) . map g l > = (.)((.) . filter f)(map) g l -- desugaring > = (.map)((.) . filter f) g l -- sweeten up > = (.map) . (.) . filter g l-- definition of (.) By the way, I think from now on, when doing point-free-ifying, my philosophy will be: If it involves composing a composition, don't do it. I just think that this really messes up readability. Cheers, Julien ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Exercise in point free-style
Udo Stenzel wrote: Thank you all a lot for helping me, it's amazing how quickly I received these detailed answers! > func2 f g l = filter f (map g l) > func2 f g = (filter f) . (map g) -- definition of (.) > func2 f g = ((.) (filter f)) (map g) -- desugaring > func2 f = ((.) (filter f)) . map -- definition of (.) > func2 f = flip (.) map ((.) (filter f)) -- desugaring, def. of flip > func2 = flip (.) map . (.) . filter -- def. of (.), twice > func2 = (. map) . (.) . filter-- add back some sugar Aaaah. After learning from Neil's answer and from @pl that (.) is just another infix function, too (well, what else should it be, but it wasn't clear to me) I still wasn't able to come up with that solution without hurting my brain. The desugaring was the bit that was missing. Thanks, I will keep that in mind for other infix functions as well. I tried to work it out on paper again, without looking at your posting while doing it. I did almost the same thing, however, I did not use flip. Instead the last few steps read: = ((.) (filter f)) . map g l = (.)((.) . filter f)(map) g l -- desugaring = (.map)((.) . filter f) g l -- sweeten up = (.map) . (.) . filter g l -- definition of (.) I guess that's possible as well? > The general process is called "lambda elimination" and can be done > mechanically. Ask Goole for "Unlambda", the not-quite-serious > programming language; since it's missing the lambda, its manual explains > lambda elimination in some detail. I think, all that's needed is flip, > (.) and liftM2. Will do, thank you! Cheers, Julien ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Exercise in point free-style
Julien Oster wrote: > While we're at it: The best thing I could come up for > > func2 f g l = filter f (map g l) > > is > > func2p f g = (filter f) . (map g) > > Which isn't exactly point-_free_. Is it possible to reduce that further? Sure it is: func2 f g l = filter f (map g l) func2 f g = (filter f) . (map g)-- definition of (.) func2 f g = ((.) (filter f)) (map g)-- desugaring func2 f = ((.) (filter f)) . map-- definition of (.) func2 f = flip (.) map ((.) (filter f)) -- desugaring, def. of flip func2 = flip (.) map . (.) . filter -- def. of (.), twice func2 = (. map) . (.) . filter -- add back some sugar The general process is called "lambda elimination" and can be done mechanically. Ask Goole for "Unlambda", the not-quite-serious programming language; since it's missing the lambda, its manual explains lambda elimination in some detail. I think, all that's needed is flip, (.) and liftM2. Udo. -- I'm not prejudiced, I hate everyone equally. signature.asc Description: Digital signature ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Exercise in point free-style
On Friday 01 September 2006 11:44, Neil Mitchell wrote: > Hi > > > func2 f g l = filter f (map g l) > > is > > func2p f g = (filter f) . (map g) > > func2 = (. map) . (.) . filter > > Again, how anyone can come up with a solution like this, is entirely > beyond me... To answer part of the OP's question, it's always possible to rewrite a lambda term using point-free style (using a surprisingly small set of basic combinators). The price you pay is that the new term is often quite a bit larger than the old term. Rewriting complicated lambda terms as point-free terms is often of, em, dubious value. OTOH, it can be interesting for understanding arrows, which are a lot like monads in points-free style (from what little experience I have with them). BTW, the process of rewriting can be entirely automated. I assume the lambdabot is using one of the well-known algorithms, probably tweaked a bit. Goolge "combinatory logic" or "Turner's combinators" if you're curious. > Thanks > > Neil -- Rob Dockins Talk softly and drive a Sherman tank. Laugh hard, it's a long way to the bank. -- TMBG ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Exercise in point free-style
Hi func2 f g l = filter f (map g l) is func2p f g = (filter f) . (map g) func2 = (. map) . (.) . filter Again, how anyone can come up with a solution like this, is entirely beyond me... Thanks Neil ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Exercise in point free-style
Hi Julien, func3 f l = l ++ map f l func3 f = ap (++) (map f) func3 = ap (++) . map Looks pretty clear and simple. However, I can't come up with a solution. Is it even possible to remove one of the variables, f or l? If so, how? I have no idea how to do this - the solution is to log into #haskell irc and fire off @pl - which automatically converts things to point free form. I'm not sure if its possible to do without the auxiliary ap (which is defined in Monad). Thanks Neil ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Exercise in point free-style
Julien Oster wrote: But I'm having problems with one of the functions: func3 f l = l ++ map f l While we're at it: The best thing I could come up for func2 f g l = filter f (map g l) is func2p f g = (filter f) . (map g) Which isn't exactly point-_free_. Is it possible to reduce that further? Thanks, Julien ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
