When learning about Control.Arrow and Haskell's built-in proc notation, I had the idea that this language might prove very useful as an eDSL for general monoidal categories (using *** for tensor an...

I understand that an Arrow is a Profunctor, where one can transform its input and its output, but can one map an arrow over a Functor? I understand that as-asked the answer is "no", since the fmap...

Lets say I have the following import Control.Category (Category, (.), id) data Invertible a b = Invertible (a -> b) (b -> a) instance Category Invertible where id = Invertible Prelude.id ...

Some instances of Category are also instances of Functor. For example: {-# LANGUAGE ExistentialQuantification, TupleSections #-} import Prelude hiding (id, (.)) import Control.Category import Con...

I am following this blog, to write a simple http server in haskell, Usage of >>> is not clear to me. What does this code snippet do? handleHttpConnection r c = runKleisli (receiveReques...

I had a thought to generalise ($) like Control.Category generalises (.), and I've done so with the code at the end of this post (also ideone). In this code I've created a class called FunctionObje...

I am having fun learning Category Theory by directly translating the definitions and laws to Haskell. Haskell is not Coq of course but it helps me getting an intuition for Category Theory. My quest...

This question deals with constructing a proper Monad instance from something that is a monad, but only under certain constraints - for example Set. The trick is to wrap it into ContT, which defers ...

I was going through some Arrow tutorial, toying with functions returning a new version of themselves in an attempt to maintain some state. The new type is defined like that: newtype Circuit a b =...

If I find out that something is a Monoid or Monad, I get all to use all kinds of fun functions, like foldMap, sequence or even mapM. They make me happy. What do I get if I find out that something ...

Often you have something like an Applicative without pure, or something like a Monad, but without return. The semigroupoid package covers these cases with Apply and Bind. Now I'm in a similar situa...