Mathematics and Computation

I have added two new languages to the PL Zoo. The minor addition is miniml+error, which is just MiniML with an error exception (raised by division by 0) that cannot be caught. The purpose is to demonstrate handling of fatal errors during runtime. The more interesting new animal is levy (written by Matija Pretnar and myself), an implementation of Paul Levy’s call-by-push-value language. If you only know about Haskell’s call-by-name and ML’s call-by-value, I invite you to learn about call-by-push-value. Start by reading Paul’s FAQ.

I show how monads in Haskell can be used to structure infinite search algorithms, and indeed get them for free. This is a follow-up to my blog post Seemingly impossible functional programs. In the two papers Infinite sets that admit fast exhaustive search (LICS’07) and Exhaustible sets in higher-type computation (LMCS’08), I discussed what kinds of infinite sets admit exhaustive search in finite time, and how to systematically build such sets. Here I build them using monads, which makes the algorithms more transparent (and economic). (more…)

Lately I’ve been thinking about computational effects in general, i.e., what is the structure of the “space of all computational effects”. We know very little about this topic. I am not even sure we know what “the space of all computational effects” is. Because Haskell is very popular and in Haskell computational effects are expressed as monads, many people might think that I am talking about the space of all monads. But I am not, and in this post I show two computational effects which are not of the usual Haskell monad kind. They should present a nice programming challenge to Haskell fans. (more…)