MIU in Haskell

In the Theory Lunch of the last week, James Chapman talked about the MU puzzle from Douglas Hofstadter’s book Gödel, Escher, Bach. This puzzle is about a string rewriting system. James presented a Haskell program that computes derivations of strings. Inspired by this, I wrote my own implementation, with the goal of improving efficiency. This blog post presents this implementation. As usual, it is available as a literate Haskell file, which you can load into GHCi. Continue reading

The Constraint kind

A recent language extension of the Glasgow Haskell Compiler (GHC) is the Constraint kind. In this blog post, I will show some examples of how this new feature can be used. This is a write-up of my Theory Lunch talk from 7 February 2013. The source of this article is a literate Haskell file, which you can download and load into GHCi. Continue reading

Some interesting features of Haskell’s type system

One of the most important ingredients of Haskell is its type system. Standard Haskell already provides a lot of useful mechanisms for having things checked at compile time, and the language extensions provided by the Glasgow Haskell Compiler (GHC) improve heavily on this.

In this article, I will present several of Haskell’s type system features. Some of them belong to the standard, others are only available as extensions. This is a write-up of a talk I gave on 31 January 2013 during the Theory Lunch of the Institute of Cybernetics. This talk provided the basics for another Theory Lunch talk, which was about the Constraint kind. Continue reading

Three talks about ideal monads

Two months ago, we started the theory lunch meetings at the Institute of Cybernetics. In these meetings, we have lunch together and discuss all kinds of interesting things related to theoretical computer science. We also started the Theory Lunch blog, where an article is posted for every lunch session. I used three of the lunch meetings to talk about ideal monads, and published summaries of my talks in the following articles: Continue reading

Dependently typed programming and theorem proving in Haskell

Programming languages with dependent types allow us to specify powerful properties of values using the type system. By employing the Curry–Howard correspondence, we can also use these languages as proof languages for higher-order logics. In this blog post, I want to demonstrate that Haskell as supported by the Glasgow Haskell Compiler (GHC) can give us almost the same features. Continue reading

Natural numbers in Haskell

It is a bit surprising that Haskell has no type for natural numbers. The Haskell Report defines only Integer for, well, integers and Int for integers that are reasonably small. The base package then adds Word as the unsigned variant of Int as well as types for signed and unsigned integers with a fixed number of bits. An unsigned variant of Integer is missing. Continue reading