[Haskell-cafe] Generalized list-comprehension

[Graham Klyne]

There was an exchange about "powerset" here some time ago, before and after 
this message:
   http://www.haskell.org/pipermail/haskell-cafe/2003-June/004507.html
I think some of the ideas suggested there might be adaptable to this 
problem:  look for sample code with sub-functions for generating 
combinations of a given length.

Alternatively, here's something to conjure with:
    concat [sequence $ replicate n [1,2,3,4] | n <- [1..4]]

(noting that the [1,2,3,4] and [1..4] can be parameterized.)

#g
--

At 07:35 31/01/04 -0800, Ron de Bruijn wrote:
>Hi there,
>
>I have written this little function:
>
>f :: (Num a, Enum a) => a -> [[a]]
>f n =  [[a]|a<-fu n] ++ [a:[b]|a<-fu n,b<-fu n] ++
>[a:b:[c]|a<-fu n,b<-fu n,c<-fu n]
>fu n = [1..n]
>
>This is an example of the function in action:
>
>*Mod> f 4
>[[1],[2],[3],[4],[1,1],[1,2],[1,3],[1,4],[2,1],[2,2],[2,3],[2,4],[3,1],[3,2],[3,
>3],[3,4],[4,1],[4,2],[4,3],[4,4],[1,1,1],[1,1,2],[1,1,3],[1,1,4],[1,2,1],[1,2,2]
>,[1,2,3],[1,2,4],[1,3,1],[1,3,2],[1,3,3],[1,3,4],[1,4,1],[1,4,2],[1,4,3],[1,4,4]
>,[2,1,1],[2,1,2],[2,1,3],[2,1,4],[2,2,1],[2,2,2],[2,2,3],[2,2,4],[2,3,1],[2,3,2]
>,[2,3,3],[2,3,4],[2,4,1],[2,4,2],[2,4,3],[2,4,4],[3,1,1],[3,1,2],[3,1,3],[3,1,4]
>,[3,2,1],[3,2,2],[3,2,3],[3,2,4],[3,3,1],[3,3,2],[3,3,3],[3,3,4],[3,4,1],[3,4,2]
>,[3,4,3],[3,4,4],[4,1,1],[4,1,2],[4,1,3],[4,1,4],[4,2,1],[4,2,2],[4,2,3],[4,2,4]
>,[4,3,1],[4,3,2],[4,3,3],[4,3,4],[4,4,1],[4,4,2],[4,4,3],[4,4,4]]
>*Mod>
>
>This is ofcourse nice and all, but I need a function
>that does this same trick, but then doesn't only
>generate listelements
>of the maximum hard-coded length of three, but to
>length m, where m is an extra parameter.
>It's important that the elements are precisely in this
>order.
>
>I tried rewriting the listcomprehension to map, concat
>and filter, but that only complicated things.
>
>There is a possibility where I can write a function
>that gives the next of a list. So the next of [1,1,1]
>would be [1,1,2], but that would be somewhat
>inefficient when the list becomes large.
>Then I just call this function with (replicate n (head
>$ fu n)) and (last $ fu n).
>Then I just apply this function next to the rest,
>until I reach a state where all elements of the list
>equal the last value of the inputlist, so I have the
>required list of length n.
>Then to simply get the complete list as in function f.
>I need to map(\x->otherFunction x) [1..], but this
>"next"-function is almost identical to what the
>built-in listcomprehension does.
>I just don't like my solution.
>
>Then I can probably use Template Haskell(which I have
>never used), but that seems overkill.
>
>So does anyone has a better solution?
>
>Greets Ron
>
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------------
Graham Klyne
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