Collatz sequences in Haskell using a Writer monad. Not that you need one. For science!

Collatz.hs

module Collatz where
  
import Control.Monad.Writer

collatzSeq :: Integer ->  Writer [Integer] Integer
collatzSeq n = do
  n <- collatz n
  if n==1 then return 1 else collatzSeq n

collatz :: Integer -> Writer [Integer] Integer
collatz n
  | n == 1 = do
      tell [n]
      return 1
  | even n = do 
      tell [n]
      return (n `div` 2)
  | otherwise = do 
      tell [n] 
      return (3 * n + 1)
      
-- ghci> runWriter $ return 13 >>= collatzSeq
-- (1,[13,40,20,10,5,16,8,4,2])