Today, I was working on coding a solver for the game "doublets". It's a word game where you transform the start word into the end word one letter at a time (and the intermediate states must also be valid words). For example, one solution to ("warm", "cold") is ["warm", "ward", "card", "cord", "cold"] So, one of my first goals was to write a function that would generate the possible words a given word could transition to. Here's a simple recursive implementation: transition :: [Char] -> [[Char]] transition [] = [] transition (c:cs) = map (c:) (transition cs) ++ map (:cs) ['a'..'z'] For some reason, I find this formulation to be strangely unsatisfying. It seems to me that this sort of computation -- i.e. modifying each element of a container (but only one at a time) -- should be expressible with some higher order function. In a nutshell, what I'm looking for would be a function, say "each" with this type. each :: (Container c) => (a -> a) -> c a -> c (c a) I'm not particularly sure what Class to substitute for "Container". Comonad seemed like a promising solution initially, and provides the basis for my current implementation of the "doublets" solver. The problem being that cobind (extend) takes a function of type (w a -
a) instead of (a -> a). I suspect that there may be a clever way to write "each" by using liftW in combination with .>> or something like that, but presently, I'm at a loss.
Has anyone else encountered this sort of abstraction before. I'd love to hear your ideas about what Classes "each" should support, and how to implement it. Matt