What is the Comonad typeclass in Haskell?
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 :: wa -> a , sort of a parallel to Monad's return :: a -> ma .
Bonus points for noting "real life" uses of Comonad in "real" code.
These links may be helpful:
This doesn't fully answer my question, but I wanted to put some relevant information in answer format:
"co" (loosely) means "flip the arrows". Here's a rough visual of that.
Consider the monadic operations:
return :: a ~> m a
flip (>>=) :: (a ~> m b) -> (m a ~> m b)
Reverse the squiggly arrows and you get the comonadic operations:
extract :: a <~ w a
extend :: (a <~ w b) -> (w a <~ w b)
(Written with normal arrows)
extract :: w a -> a
extend :: (w a -> b) -> w a -> w b
Notice how in this format, return is an arrow that just so happens to fit in the argument slot for flip (>>=) , and the same is true of extract and extend . Monad/comonad laws say that when you put return or extract into that slot, the result is the identity arrow. The laws are the same, "just with the arrows flipped". That's a super handwavey answer but hopefully it provides some insight.