How do I re-express a list comprehension with two generators to two list comprehensions with one generator each and get the same result?

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I'm trying to learn Haskell, and I'm doing some exercises that involves lists. But I'm struggling with an exercise about list comprehension, and I really need someone to help me with this. The exercise reads:

Show how the list comprehension [(x,y) | x <- [1,2], y <- [3,4]] with two generators can be re-expressed using two comprehensions with single generators.

Hint: nest one comprehension within the other and make use of the library function concat :: [[a]] -> [a].

I appreciate all answers and explanations. Thanks.

list-comprehension functional-programming haskell
1 Answers

First, you can generate [1, 2] using [x | x <- [1, 2]].

Now, for each x, you want to have (x, 3) and (x, 4) instead of just x. So let's replace it with a list comprehension. Then you'll get [[(x, y) | y <- [3, 4]] | x <- [1, 2]].

But this gives you [[(1,3),(1,4)],[(2,3),(2,4)]] because you converted each x to [(x, 3), (x, 4)]. As the hint suggests, you can use concat to squash them.

To put it together, you'll get concat [[(x, y) | y <- [3, 4]] | x <- [1, 2]].

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