I didn't make it past the fizzbuzz example. But I wouldn't call the solution with cycle all that clever. Here's a better one: https://themonadreader.files.wordpress.com/2014/04/fizzbuzz.... the punchline reproduced below:

  fizzbuzz' :: Int -> String
  fizzbuzz' n = (test 3 "fizz" . test 5 "buzz") id (show n)
    where
     test d s x | n `mod` d == 0 = const (s ++ x "")
                | otherwise = x

  fizzbuzz :: [String]
  fizzbuzz = map fizzbuzz' [1..]

The article is very interesting and worth a read. In particular, this implementation doesn't come out of "thin air": it's been golfed from an implementation that defines a simple domain specific language to solve FizzBuzz. And if you understand your problem well enough, DSLs are an extreme force multiplier.