[Haskell-cafe] Generalized list-comprehension

[Ron de Bruijn]

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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