The codensity monad on a type constructor f is defined by: It is well known that C f is a monad for any type constructor f (not necessarily covaria ...
The codensity monad on a type constructor f is defined by: It is well known that C f is a monad for any type constructor f (not necessarily covaria ...
The (covariant) functor definition in cats-laws looks like this: But if I translate the functor composition rule to Scala, it should be: Why a ...
In https://www.cs.ox.ac.uk/ralf.hinze/LN.pdf On page 10, equations (13) and (14) it seems to me that outl on the left of the equations is not the sam ...
Sorry if I'm a bit lost. I've recently started learning about different programming language paradigms and I found that all texts presuppose that all ...
I've been wondering what a complete, all-encompassing context for instance Functor (f :.: g) would be. The immediate thought that pops into my head is ...
I am busy reading Bartosz Milewski's Category Theory book for programmers and I'm struggling with the depiction of non-identity morphisms when moving ...
While learning about the Yoneda lemma, I came across the following encoding of the underlying natural isomorphism in Haskell: I tried to simplify t ...
I've been experimenting with monoids and Distributives lately, and I think I've found something of interest (described in my answer) - are these alrea ...
I started to learn Prolog and I just read that the atom at the beginning of an structure is usually called functor. I'm also familiar with the term f ...
I was struggling to prove a more basic version of lawvere's fixed point theorem in agda. Precisely I am trying to figure out the proof for the bottom ...
At one time, I thought I understood Monad. However, when I try to connect my understanding of code to the piece of theory, I found myself still not cl ...
I've been on a bit of a "distilling everything to its fundamentals" kick lately, and I've been unable to find clear theoretical reasons for how the Tr ...
The functor of the identity monad can be defined as: Because this monad is free, an alternative definition is the following: Since this is the s ...
In the past 2 years, I was interested in using free monad to helping me to solve practical software engineering problem. And came up my own constructi ...
I was recently reading Category Theory for Programmers and in one of the challenges, Bartosz proposed to write a function called memoize which takes a ...
In his paper Generics for the Masses Hinze reviews encoding of data type. Starting from Nat data Nat :: ⋆ where Zero :: Nat Succ :: Nat → Nat ...
On page 12 of One Monad to Prove Them All, it is written that "a prominent example [of container] is the list data type. A list can be represented by ...
Question I'm looking to describe processes in chemical engineering that that transmute some substances into others. Is there a category that describe ...
Is there anything in Haskell resembling the following type class? class Mergeable (f :: Type -> Type -> Type) where merge :: f a b -> f c ...
Various recursion scheme boil down to specific instantiation of refold refold :: Functor s => (s b -> b) -> (a -> s a) -> a -> b re ...