Generalized Monads --> Gonads :-)

Here is the usual (basic) definition of monads:

class Monad m where
  return :: a -> m a
  (>>=) :: m a -> (a -> m b) -> m b

This is very much restricted to ordinary function types!
Let's see how this restriction can be lifted...

class Category (~>) => Geonad (g (~>)) where
  return :: a ~> g (~>) a
  (>>=) :: g (~>) a ~> (a ~> g (~>) b) ~> g (~>) b

Since the semantics of gonads are already eminently taken, I settled for the name Geonad.

No idea whether this can produce something relevant for our lives :-)

Cheers,
      Gabor