Tag : category theory

This is the third part of my serie about Haskell and category theory. In the previous post, I described a bit the Hask category and some categorical constructs. The goal of this text is to understand the meaning of a recursive type like List. For that, we will have to understand what is a free algebra and have a quick look at the relationship with monads (for applications look at the blog of sigfpe). But first, I would like to highlight a problem with the category Hask.

In my previous post, I explained that with category theory you can define some concepts in such a way that they can be used in several different contexts. As a side effect, the definitions are rather abstract since they are forbidden from talking about the implementation of the objects and must rely only on the provided interfaces. So, a first thing to do when studying category theory is learning some of these definitions. Some of them are just generalizations of ideas commonly used in set theory.

"Category theory" is an expression that is generally frightening people. But, if you have attempted to read some research papers in Computer Science, Mathematics, Physics or even Philosophy, you've surely remarked that Category theory is used a lot and you probably asked yourself : what is Category theory ? Why is it so useful ? Is it so difficult ? What the link(s) with computer science ? Answering to those questions in an easy way that can be understood by most people is really challenging but I am going to try and I'll use the category of Haskell programs to illustrate some points. I hope the expert will forgive me some slight inaccuracies and/or an unconventional presentation.

From time to time, I continue my experiments with Haskell and web development and try to build my own framework. I will never release anything because I am just exploring a few ideas. Recently, I experimented with a common problem : when a client is getting an URL, it is communicating the formats it wants with some preference values. The server should return the best format according to what is requested by the client and what is supported by the server.