Nested cartesian product of Haskell lists

Question

I would like to make a method where I could give it a list of lengths and it would return all combinations of cartesian coordinates up to those lengths. Easier to explain with a

Answer 1

I bet your procedural solution would involve recursion. Our Haskell solution will involve recursion too.

So, recursion. First the recursive case.

cart (c : cs) = [i : r | i <- [0 .. c-1], r <- rcart]
  where rcart = cart cs

Here we're just saying that for each possible initial co-ordinate, and each possible combination of cartesian co-ordinates from the remaining lengths, we do the obvious thing of combining the co-ordinate with the remaining co-ordinates.

Then the base case.

cart [] = [[]]

You might think cart [] = []. I did at first. But think about what the recursive case requires from the base case.