Generating sorted list of all possible coprimes

Question

I need to generate infinite sorted list of all coprimes. The first element in each pair must be less than the second. The sorting must be done in ascending order -- by the sum o

Answer 1

As @Bakuriu suggests, merging an infinite list of infinite lists is a solution, but the devil is in the details.

The diagonal function from the universe-base package can do this, so you could write:

import Data.Universe.Helpers

coprimes = diagonal [ go n | n <- [2..] ]
  where go n = [ (n,k) | k <- [n+1..], gcd n k == 1 ]

Note - this doesn't satisfy your sorted criteria, but I mention it because the functions in that package are useful to know about, and implementing a function like diagonal correctly is not easy.

If you want to write your own, consider decomposing the infinite grid N x N (where N is the natural numbers) into diagonals:

[ (1,1) ] ++ [ (1,2), (2,1) ] ++ [ (1,3), (2,2), (3,1) ] ++ ...

and filtering this list.