All combinations of elements of two lists in Haskell

Question

Given two lists, [a, b] and [c, d], I\'d like to get the following result:

[(a,c), (a,d), (b         


        

Answer 1

How can you do this in an imperative pseudocode?

for each element x in [a,b]:
    for each element y in [c,d]:
        produce (x,y)

In Haskell, this is written as

outerProduct xs ys =
   do
       x <- xs          -- for each x drawn from xs:
       y <- ys          --   for each y drawn from ys:
       return (x,y)     --      produce the (x,y) pair

---

(following comments by leftaroundabout) this is of course extremely close to how liftM2 monadic combinator is defined, so in fact

outerProduct = liftM2 (,)

which is the same as liftA2 (,), and its various re-writes in terms of list comprehensions, concatMap function, >>=, <$> and <*> operators.

Conceptually though this is the stuff of the Applicative – which would be better named as Pairing, – because this pairing up of the elements of two "containers" ⁄ "carriers" ⁄ whatever is exactly what Applicative Functor is about. It just so happens that Haskell's do notation works for monads, and not (yet) for applicatives.

In some sense compile-time nested loops are Applicative ⁄ Pairing functors; Monads add the ability to create nested loops on the fly, depending on the values produced by an "outer" enumeration.