Re: [Haskell-cafe] Suggestions for improvement
On 4/10/2010, at 8:52 AM, N. Raghavendra wrote: I am reading the book `The Haskell Road to Math, Logic, One of the exercises in the first chapter asks for a function that maps a string abcd to abbccc and bang! to baannn!. answer s = concat $ zipWith replicate [1..] s I looked at the examples and said, hmm, elements are being repeated varying numbers of times. Looked up repeat, found that that was the wrong function, and saw replicate, which is the right one: replicate n x = [x . x] with n copies of x So zipWith [1..] abcd is [a, bb, ccc, ] and pasting those together is just what concat does. Had replicate, zipWith, concat not already been provided, I might have done one of two things. (a) Write them. concat (x:xs) = x ++ concat xs concat [] = [] zipWith f (x:xs) (y:ys) = f x y : zipWith f xs ys zipWith _ _ _= [] replicate (n+1) x = x : replicate n x replicate 0 _ = [] This is _still_ less code than the code I'm replying to, and gives you some reusable components as well. (b) I'd have generalised the function to f n [x1,...,xk] = [x1 n times, x2 n+1 times, ..., xk n+k-1 times] in order to get a clean recursion for f. answer s = f 1 s where f _ [] = [] -- list iteration f n (x:xs) = g n (f (n+1) xs) where g (n+1) s = x : g n s -- element replication g 0 s = s You can think of this by imagining the answer laid out in a triangle abcd bcd cd d ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
[Haskell-cafe] Suggestions for improvement
I am reading the book `The Haskell Road to Math, Logic, One of the exercises in the first chapter asks for a function that maps a string abcd to abbccc and bang! to baannn!. Since such a function f fixes the empty word, and maps wa to f(w)a^(length(w)+1) for any word w and any letter a, I came up with the following solution: -- Map abcd to abbccc and bang! to baannn!. blowup :: String - String blowup [] = [] blowup x = blowup (allButLast x) ++ lastToTheLength x -- Map abcd to abc. allButLast :: String - String allButLast [] = [] allButLast [x] = [] allButLast (x : xs) = x : allButLast xs -- Map abcd to d^4 = . lastToTheLength :: String - String lastToTheLength [] = [] lastToTheLength [x] = [x] lastToTheLength (_ : xs) = lastToTheLength xs ++ [last xs] One question I have is whether I can eliminate points in the above definition of blowup, and write something like blowup = (++) . (blowup . allButLast, lastToTheLength) thinking of (++) as a function String x String - String. Also, I can't figure out whether it is possible to get a shorter solution using fold. I have tried Hlint on my file, but it gave no suggestions. I am sure there are better ways, and would like some pointers and any general suggestions for improvement. Thanks and regards, Raghavendra. -- N. Raghavendra ra...@mri.ernet.in | http://www.retrotexts.net/ Harish-Chandra Research Institute | http://www.mri.ernet.in/ See message headers for contact and OpenPGP information. ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Suggestions for improvement
One question I have is whether I can eliminate points in the above definition of blowup, and write something like blowup = (++) . (blowup . allButLast, lastToTheLength) thinking of (++) as a function String x String - String. Actually (++) is of type String - String - String. When you want something of the type you mean (you normally write that as (String, String) - String in Haskell, then you can use (uncurry (++)). Additionally, you can't combine the functions (blowup . allButLast) and lastToTheLength into a function that returns a pair like you seem to attempt. You need a function like the following for that: comma :: (a - b) - (a - c) - a - (b,c) comma f g x = (f x, g x) Then you could say: blowup = (uncurry (++)) . comma (blowup . allButLast) lastToTheLength Ignore this if you haven't read about Applicative or type classes yet, but using the Applicative instance for arrow types (-) a, you can also write comma = liftA2 (,) or blowup = (uncurry (++)) . liftA2 (,) (blowup . allButLast) lastToTheLength Also, I can't figure out whether it is possible to get a shorter solution using fold. I have tried Hlint on my file, but it gave no suggestions. I am sure there are better ways, and would like some pointers and any general suggestions for improvement. By the way, shorter is not always better. Trying to recognize abstraction patterns in your code is never a bad thing though. Dominique ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Suggestions for improvement
On 10/3/10 1:45 PM, Dominique Devriese wrote: Additionally, you can't combine the functions (blowup . allButLast) and lastToTheLength into a function that returns a pair like you seem to attempt. You need a function like the following for that: comma :: (a - b) - (a - c) - a - (b,c) comma f g x = (f x, g x) Then you could say: blowup = (uncurry (++)) . comma (blowup . allButLast) lastToTheLength It is worth noting that such a function already exists in the standard libraries; it is the operator in Control.Arrow: blowup = uncurry (++) . (blowup . allButLast lastToTheLength) Cheers, Greg ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Suggestions for improvement
Gregory, 2010/10/3 Gregory Crosswhite gcr...@phys.washington.edu: On 10/3/10 1:45 PM, Dominique Devriese wrote: Additionally, you can't combine the functions (blowup . allButLast) and lastToTheLength into a function that returns a pair like you seem to attempt. You need a function like the following for that: comma :: (a - b) - (a - c) - a - (b,c) comma f g x = (f x, g x) Then you could say: blowup = (uncurry (++)) . comma (blowup . allButLast) lastToTheLength It is worth noting that such a function already exists in the standard libraries; it is the operator in Control.Arrow: blowup = uncurry (++) . (blowup . allButLast lastToTheLength) Or you can write it as (liftA2 (,)) as I noted a few lines further in my mail ;) Dominique ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Suggestions for improvement
On 10/3/10 2:24 PM, Dominique Devriese wrote: Or you can write it as (liftA2 (,)) as I noted a few lines further in my mail ;) Dominique I know, I just mentioned it to increase awareness of the fact that the instance methods for all the classes in Control.Arrow can equivalently be interpreted as useful pre-defined combinators for ordinary functions. Cheers, Greg ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Suggestions for improvement
I suggest to pay more attention to haskell's standard library. allButLast is called init in Data.List module. Second, do not use explicit recursion. You can capture recursion using some high-order function like map, filter, foldr and so on: lastToTheLength xs = map f xs where f = const . last $ xs And last, your type signatures are too restrictive. You can apply your functions to arbitrary lists. lastToTheLength :: [a] - [a] Standard library knowledge is very helpful in producing short and clear definitions. blowup = concat . zipWith replicate [1..] On Mon, Oct 4, 2010 at 1:24 AM, Dominique Devriese dominique.devri...@cs.kuleuven.be wrote: Gregory, 2010/10/3 Gregory Crosswhite gcr...@phys.washington.edu: On 10/3/10 1:45 PM, Dominique Devriese wrote: Additionally, you can't combine the functions (blowup . allButLast) and lastToTheLength into a function that returns a pair like you seem to attempt. You need a function like the following for that: comma :: (a - b) - (a - c) - a - (b,c) comma f g x = (f x, g x) Then you could say: blowup = (uncurry (++)) . comma (blowup . allButLast) lastToTheLength It is worth noting that such a function already exists in the standard libraries; it is the operator in Control.Arrow: blowup = uncurry (++) . (blowup . allButLast lastToTheLength) Or you can write it as (liftA2 (,)) as I noted a few lines further in my mail ;) Dominique ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe -- Victor Nazarov ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Suggestions for improvement
On 10/3/10 5:52 PM, Victor Nazarov wrote: I suggest to pay more attention to haskell's standard library. allButLast is called init in Data.List module. Second, do not use explicit recursion. You can capture recursion using some high-order function like map, filter, foldr and so on: lastToTheLength xs = map f xs where f = const . last $ xs And just to play a little Haskell golf: lastToTheLength = ap (flip map) (const . last) -- Live well, ~wren ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
