When you say permuations, I think of reorderings of a list, for example: permutations [1,2,3] = [ [1,2,3], [1,3,2], [2,1,3], [2,3,1], [3,1,2], [3,2,1] ] Here's an implementation: -- split [1,2,3] => [ -- ( 1, [2,3] ), -- ( 2, [1,3] ), -- ( 3, [1,2] ) ] split :: [a] -> [(a, [a])] split [] = error "split: empty list" split [a] = [(a, [])] split (a:as) = (a, as) : map prefix (split as) where prefix (x, xs) = (x, a : xs) permutations :: [a] -> [[a]] permutations [] = return [] permutations xs = do (first, rest) <- split xs rest' <- permutations rest return (first : rest') The problem you solved can be solved much more elegantly: pms : [a] -> Int -> [[a]] pms xs n = foldM combine [] (replicate n xs) where combine rest as = liftM (:rest) as or, for the unreadable version: pms xs n = foldM (map . flip (:)) [] $ replicate n xs (note that, in the list monad, liftM = map). -- ryan

Hello again Ryan, I have found out where to import those stuff from and tested your more elegant suggestion and my original performance. -- print ((length ∘ pmsO [0,1]) 24) 9~ seconds -- print ((length ∘ pmsE [0,1]) 24) 23~ seconds -- print ((length ∘ pmsU [0,1]) 24) 23~ seconds -- O: original, E: elegant, U: unreadable I prefer performance over elegance (and for me using monads almost feels like adding an unnecessary dependency to the definition of pms. Though I know I may be dead wrong on that. I just don't quite understand monads yet.) I would love to have you and/or others suggest more performant versions of pms (and maybe also come up with a better name for it). mnt :: [a] → [[a]] → [[a]] mnt [] _ = [] mnt _ [] = [] mnt (x:xs) yss = map (x:) yss ++ mnt xs yss pms :: [a] → Int → [[a]] pms [] _ = [[]] pms _ 0 = [[]] pms xxs n = mnt xxs (pms xxs (n - 1)) I generalized 'pms' from the 'bools' function on page 108 of Programming in Haskell (Hutton, 2007) -- Cetin Sert On 26/01/2008, Cetin Sert wrote:

Thank you very much ^_^.

What would be a mathematically correct and understandable name for what we call 'pms' here?

And in what module do foldM, combine, replicate, rest, liftM and so on reside? How can I import them? o_O

-- Cetin Sert

On 26/01/2008, Ryan Ingram wrote:

...

When you say permuations, I think of reorderings of a list, for example:

permutations [1,2,3] = [ [1,2,3], [1,3,2], [2,1,3], [2,3,1], [3,1,2], [3,2,1] ]

Here's an implementation:

-- split [1,2,3] => [ -- ( 1, [2,3] ), -- ( 2, [1,3] ), -- ( 3, [1,2] ) ] split :: [a] -> [(a, [a])] split [] = error "split: empty list" split [a] = [(a, [])] split (a:as) = (a, as) : map prefix (split as) where prefix (x, xs) = (x, a : xs)

permutations :: [a] -> [[a]] permutations [] = return [] permutations xs = do (first, rest) <- split xs rest' <- permutations rest return (first : rest')

The problem you solved can be solved much more elegantly:

pms : [a] -> Int -> [[a]] pms xs n = foldM combine [] (replicate n xs) where combine rest as = liftM (:rest) as

or, for the unreadable version: pms xs n = foldM (map . flip (:)) [] $ replicate n xs

(note that, in the list monad, liftM = map).

-- ryan

Thanks Jed, replicateM is almost as performant as pms on my pc (+ 2~ seconds). That's a killer suggestion... thank you very much ^_^ --Cetin Sert On 27/01/2008, Jed Brown wrote:

...

The problem you solved can be solved much more elegantly:

pms : [a] -> Int -> [[a]] pms xs n = foldM combine [] (replicate n xs) where combine rest as = liftM (:rest) as

or, for the unreadable version: pms xs n = foldM (map . flip (:)) [] $ replicate n xs

or, if you don't mind getting the elements in a different order:

replicateM 3 [True,False]

Jed

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