comonad

What is the Comonad typeclass in Haskell? As in Comonad from Control.Comonad in the comonad package (explanations of any other packages that provide a Comonad typeclass are also welcome). I've vaguely heard about Comonad, but all I really know about it is that is provides extract :: w a -> a , sort of a parallel to Monad's return :: a -> m a . Bonus points for noting "real life" uses of Comonad in "real" code. These links may be helpful: Evaluating cellular automata is comonadic . In particular, "whenever you see large datastructures pieced together from lots of small but similar computations

Given any container type we can form the (element-focused) Zipper and know that this structure is a Comonad. This was recently explored in wonderful detail in another Stack Overflow question for the following type: data Bin a = Branch (Bin a) a (Bin a) | Leaf a deriving Functor with the following zipper data Dir = L | R data Step a = Step a Dir (Bin a) deriving Functor data Zip a = Zip [Step a] (Bin a) deriving Functor instance Comonad Zip where ... It is the case that Zip is a Comonad though the construction of its instance is a little hairy. That said, Zip can be completely mechanically

Is there a built-in function with signature :: (Monad m) => m a -> a ? Hoogle tells that there is no such function. Can you explain why? A monad only supplies two functions: return :: Monad m => a -> m a (>>=) :: Monad m => m a -> (a -> m b) -> m b Both of these return something of type m a , so there is no way to combine these in any way to get a function of type Monad m => m a -> a . To do that, you'll need more than these two functions, so you need to know more about m than that it's a monad. For example, the Identity monad has runIdentity :: Identity a -> a , and several monads have