Cartesian product of 2 lists in Haskell

Question

I wish to produce the Cartesian product of 2 lists in Haskell, but I cannot work out how to do it. The cartesian product gives all combinations of the list elements:

xs = [1,2,3] ys = [4,5,6]  cartProd :: [a] -> [b] -> [(a,b)] cartProd xs ys ==> [(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)] 

This is not an actual homework question and is not related to any such question, but the way in which this problem is solved may help with one I am stuck on.

Answer 1

This is very easy with list comprehensions. To get the cartesian product of the lists xs and ys, we just need to take the tuple (x,y) for each element x in xs and each element y in ys.

This gives us the following list comprehension:

cartProd xs ys = [(x,y) | x <- xs, y <- ys] 

Answer 2

As other answers have noted, using a list comprehension is the most natural way to do this in Haskell.

If you're learning Haskell and want to work on developing intuitions about type classes like Monad, however, it's a fun exercise to figure out why this slightly shorter definition is equivalent:

import Control.Monad (liftM2)  cartProd :: [a] -> [b] -> [(a, b)] cartProd = liftM2 (,) 

You probably wouldn't ever want to write this in real code, but the basic idea is something you'll see in Haskell all the time: we're using liftM2 to lift the non-monadic function (,) into a monad—in this case specifically the list monad.

If this doesn't make any sense or isn't useful, forget it—it's just another way to look at the problem.