Hi Edgar I'm not sure what a 'lawful' monad would be for your zipper, so I can sympathize with the author of the package on Hackage who omitted one. Monads have three laws which instances of the Monad class are obliged to obey, but the language cannot check that they do (i.e the type system can't check you obey them): http://www.haskell.org/haskellwiki/Monad_Laws A text book on Haskell would cover the monad laws if it covers monads, for instance in Paul Hudak's book they are on page 254. For a more general zipper, Chung-chieh Shan has a monad: http://conway.rutgers.edu/~ccshan/wiki/blog/posts/WalkZip3/ However that monad looks very similar to a resumption monad (resumption monads are commonly used to model concurrency as they can pause computations and so yield to other threads). This seems appropriate to a zipper - I think that Gerard Huet, the inventor of the zipper, originally used it to move a cursor around a tree structure within an interactive editor. A quick web search reveals another one here, I've never looked at this one before but it looks close to a state monad: http://www.haskell.org/haskellwiki/Zipper_monad

From your definition, I suspect if you use GHCs deriving mechanism it will make a quadruple list monad which will obviously compile and run but doesn't seem appropriate.

Best wishes Stephen