Michi’s blog » archive for 'Category theory'

[Stanford] MATH 198: Category Theory and Functional Programming

  • August 29th, 2009

Category theory, with an origin in algebra and topology, has found use in recent decades for computer science and logic applications. Possibly most clearly, this is seen in the design of the programming language Haskell – where the categorical paradigm suffuses the language design, and gives rise to several of the language constructs, most prominently the Monad.

In this course, we will teach category theory from first principles with an eye towards its applications to and correspondences with Haskell and the theory of functional programming. We expect students to previously or currently be taking CS242 and to have some level of mathematical maturity. We also expect students to have had contact with linear algebra and discrete mathematics in order to follow the motivating examples behind the theory expounded.

Wednesdays at 4.15.

Online notes will appear successively on the Haskell wiki on http://haskell.org/haskellwiki/User:Michiexile/MATH198

(143 words)

Soliciting advice

  • July 22nd, 2009

Dear blogosphere,

come this fall, I shall be teaching. My first lecture course, ever.

The subject shall be on introducing Category Theory from the bottom up, in a manner digestible for Computer Science Undergraduates who have seen Haskell and been left wanting more from that contact.

And thus comes my question to you all: what would you like to see in such a course? Is there any advice you want to give me on how to make the course awesome?

The obvious bits are obvious. I shall have to discuss categories, functors, (co)products, (co)limits, monads, monoids, adjoints, natural transformations, the Curry-Howard isomorphism, the Hom-Tensor adjunction, categorical interpretation of data types. And all of it with explicit reference to how all these things influence Haskell, as well as plenty of mathematical examples.

But what ideas can you give me to make this greater than I’d make it on my own?

(150 words)

PROPs and patches

  • February 15th, 2008

Brent Yorgey wrote a post on using category theory to formalize patch theory. In the middle of it, he talks about the need to commute a patch to the end of a patch series, in order to apply a patch undoing it. He suggests a necessary condition to do this is that, given patches P and Q, we need to be able to find patches Q’ and P’ such that PQ=Q’P', and preferably such that Q’ and P’ capture some of the info in P and Q.

However, as such, this is not enough to solve the issue. For one thing, we can set Q’=P and P’=Q, and things are the way he asks for.

Now, I wonder whether we can solve this by using PROPs (or possibly di-operads or something like that). Let’s represent a document as a list of some sort of tokens. We’ll set D_n the set of all lists of length n, and we’ll set P_n^m to denote operations that take a list of length n and returns a list of length m.

This is a preview of PROPs and patches. Read the full post (412 words, 4 images)

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Michi is a recent PhD working in homological algebra and applied algebraic topology. This blog is his outlet for texts with some manner of thought put into them. Over at his LiveJournal intimate details and streams of consciousness might be found.
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