Mathematics and Computation

I recently stumbled upon a blog on machine learning by a good friend of mine, John Langford. The blog has gathered together a community of people who discuss various topics (not limited strictly to machine learning). Naturally I wanted to have a blog, too.

I devote a lot of my time to thinking about the relationship between mathematics and computation. There are two sides of this, which can be expressed by a the slogan “Computable mathematics and mathematics of computation”. Computable mathematics is about how to do mathematics with computers, while mathematics of computation is about mathematics that describes properties of computation in a mathematical, abstract way.

If this is a subject that interests you, I invite you to join me.

With Chris Stone.

Abstract:
We present a system, called RZ, for automatic generation of program specifications from mathematical theories. We translate mathematical theories to specifications by computing their realizability interpretations in the ML language augmented with assertions (as comments). While the system is best suited for descriptions of those data structures that can be easily described in mathematical language (e.g., finitely presented groups, real arithmetic, graphs, etc.), it also elucidates the relationship between data structures and constructive mathematics.

Presented at:
Constructive Logic for Automated Software Engineering (CLASE), Satellite event of ETAPS 2005, Edinburgh, 9th April 2005

Download paper:
rz.pdf,
rz.ps.gz

Download slides:
rz-slides.pdf