Abstract. We give a coinductive characterisation of the set of continuous functions defined on a compact real interval, and extract certified programs that construct and combine exact real number algorithms with respect to the binary signed digit representation of real numbers. The data type corresponding to the coinductive definition of continuous functions consists of finitely branching non-wellfounded trees describing when the algorithm writes and reads digits. This is a pilot study in using proof-theoretic methods for obtaining certified algorithms in exact real arithmetic. 1

Abstract. We prove the correctness of a formalised realisability interpretation of extensions of first-order theories by inductive and coinductive definitions in an untyped λ-calculus with fixed-points. We illustrate the use of this interpretation for program extraction by some simple examples in the area of exact real number computation, and hint at further non-trivial applications in computable analysis. 1

AVOCS, the workshop on Automated Verification of Critical Systems, is an annual meeting that brings together researchers and practitioners to exchange new results on tools and techniques for the verification of critical systems. Topics of interest cover all aspects of automated verification, including model checking, theorem proving, abstract interpretation, and refinement pertaining to various types of critical systems (safety-critical, security-critical, business-critical, performance-critical, etc.). Contributions that describe different techniques, or industrial case studies are encouraged.

Abstract. We study a realisability interpretation for inductive and coinductive definitions and discuss its application to program extraction from proofs. A speciality of this interpretation is that realisers are given by terms that correspond directly to programs in a lazy functional programming language such as Haskell. Programs extracted from proofs using coinduction can be understood as perpetual processes producing infinite streams of data. Typical applications of such processes are computations in exact real arithmetic. As an example we show how to extract a program computing the average of two real numbers w.r.t. to the binary signed digit representation. 1