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] (B
Comonads are the category-theoretic dual of monads. While monads have been found to be a very useful design pattern for structuring programs in functional languages, such as Haskell, comonads have so far failed to gain much traction. In this talk we will look at what comonads are and how they are defined in Haskell, comparing them with the Haskell definition of monads. We will then look at some sp
This is part 23 of Categories for Programmers. Previously: Monads Categorically. See the Table of Contents. Now that we have covered monads, we can reap the benefits of duality and get comonads for free simply by reversing the arrows and working in the opposite category. Recall that, at the most basic level, monads are about composing Kleisli arrows: a -> m b where m is a functor that is a monad.
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