Realisability for Induction and Coinduction with Applications to Constructive Analysis

Abstract: We prove the correctness of a formalised realisability interpretation of extensions of first-order theories by inductive and coinductive definitions in an untyped -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. Key Words: realisability, program extraction, coinduction, constructive analysis Category: F.3, F.3.1, F.3.2

• Type: Journal
• Year: 2010
• Where: JUCS
• Authors: Ulrich Berger
• Keywords: Constructive Analysis Category, Exact Real Number, JUCS 2010, Program Extraction