Generating a list of lists in Haskell

Question

I'm trying to create a function that generates a set of sets of tuples, but I'm new to Haskell and don't know how to implement it. Here's pseudocode of what I'd like my code to do (I'll use {} to denote set):

mySet :: Int -> {{(Int,Int,Int,Int,Int)}}
mySet n = { {a_1,a_2,...,a_n} | P(a_1,a_2,...,a_n) }

The part I've written so far is the list that I'm taking each a_i from. The code is

firstList :: Int -> [(Int,Int,Int,Int,Int)]
firstList n = [(a,b,c,d,e) | a <- [0,1,(-1)], b <- [1..n], c <- [1..(2*n)], d <- [1..n], e <- [1..(2*n)]]

Basically, I want to have mySet take from the list of the form

[(a1,a2,a3,a4,a5),(b1,b2,b3,b4,b5),...]

and create a list (or set, actually) that, for example when n=3, looks like

[[(a1,a2,a3,a4,a5),(b1,b2,b3,b4,b5),(c1,c2,c3,c4,c5)],[(d1,d2,d3,d4,d5),(e1,e2,e3,e4,e5),(f1,f2,f3,f4,f5)],...]

As far as implementations go, I'd prefer readability over speed, but ideally I'd like both.

so you have a list that contains 5-uples? like [(1,2,3,4,5), (6,7,8,9,10), ...] and you want mySet n to return a subset of this list depending on a predicate P? Then why aren't you writing [x | x <- originalList, predicate x] to check one tuple at a time? Or is the 5 in 5-uple parametric? In this case note that you actually cannot do anything really generic because 3-uples are a different type from 5-uples. — Bakuriu
– Bakuriu, Commented Jun 24, 2016 at 19:36
Please show us the type signatures of that list you've already written code to generate and the one you're trying to build. — leftaroundabout
– leftaroundabout, Commented Jun 24, 2016 at 19:42
Hmmm, wording sounds a lot like stackoverflow.com/questions/37949703/… before the edit... — Alec
– Alec, Commented Jun 24, 2016 at 19:42
@user348307 Put relevant information in the question itself, not in a comment below. — melpomene
– melpomene, Commented Jun 24, 2016 at 19:59

CR Drost · Accepted Answer · 2016-06-24 20:48:19Z

You haven't told us precisely how you want to do this, so we're left speculating, but a function that I have defined many times to do a very similar task takes a list of elements and breaks it into sublists of a certain size:

chunkify :: Int -> [x] -> [[x]]
chunkify n [] = []
chunkify n list = chunk : chunkify n rest 
    where (chunk, rest) = splitAt n list

You could then take your 12 n⁴ tuples coming from firstList n and split them into 12 n³ lists of length n via:

myLists n = chunkify n (firstList n)

Or if you really want to be pointfree, that's just myLists = chunkify <*> firstList because (Int ->) is an instance of a Reader-like applicative functor and the above <*> is defined for applicative functors in Prelude and/or Control.Applicative, depending on what version of GHC you're running.

If you want something more sophisticated you'll have to let us know; we're not mind-readers.

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