List monad - Haskell

Hi, I found a small exercice: counting all the tuple (x1, x2, x3, x4) whose sum is equal to 18. For that I used list comprehension:

allCombination n = [(x1, x2, x3, x4)|
  x1 <- lst,
  x2 <- lst,
  x3 <- lst,
  x4 <- lst,
  x1 + x2 + x3 + x4 == n]
  where lst = [0..n]

main = putStrLn $ show $ length (allCombination 18)

Is it possible to be more generic ? Like here I have a tuple of 4 element but would it be possible to have an arbitrary number of element ? For instance via a monad.

Something like

import Control.Monad

allCombination eltcnt n =  do
  newlst <- traverse undefined [0..eltcnt]
  guard $  (sum newlst) == n
  where lst = [0..n]


main = putStrLn $ show $ length (allCombination 4 18)

Issue is, I'm not sure traverse will work as I expect it to do

if I replace undefined by \_-> lst it doesn't work unfortunatly

hmm actually it does weird

nvm I got my interval wrong

If you use this guy, you could do it like this:

allCombination eltcnt n = do
  candidate <- variateRep eltcnt [0..n]
  guard (sum candidate == n)

Or more simply:

allCombination eltcnt n = filter (\ candidate -> sum candidate == n) (variateRep eltcnt [0..n])

More generally, replicateM does the same thing and lives in the base library. (Not sure what the advantage of variateRep would be. Better handling if eltcnt is negative, maybe? Performance?)

Yes, I’d do:

allCombination n = fmap tuplize $ filter ((==18) . sum) $ replicateM 4 [0..n]
  where tuplize [a,b,c,d] = (a,b,c,d)

nice functions !

Bernd Losert said:

If you use this guy, you could do it like this:

allCombination eltcnt n = do
  candidate <- variateRep eltcnt [0..n]
  guard (sum candidate == n)

I imagine you could even use it with MonadComprehensions, then it looks even more like the original.