# Program extraction using real arithmetic in Coq.

## Sylvain Dailler

(Lyon, currently Internship Swansea)

At first, I will present the Coq proof assistant (http://coq.inria.fr) and give a small interactive tutorial about how to prove theorems and extract programs using Coq. Then, I will show how to create certified programs only relying on the axioms of real arithmetic. This can be done with easy specifications and without having to construct a huge set of functions and theorems. As an example, we used our framework to define: unary natural numbers, binary natural numbers, a redundant version of rational numbers and a coinductive characterisation of real numbers that have a signed digit representation.

**Thursday 5th August 2010, 14:00**

Robert Recorde Room

Department of Computer Science