Metric spaces and termination analyses

Authors:
Aziem Chawdhary;Hongseok Yang
Affiliations:
Durham University and Queen Mary University of London;Queen Mary University of London
Venue:
APLAS'10 Proceedings of the 8th Asian conference on Programming languages and systems
Year:
2010

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Abstract

We present a framework for defining abstract interpreters for liveness properties, in particular program termination. The framework makes use of the theory of metric spaces to define a concrete semantics, relates this semantics with the usual order-theoretic semantics of abstract interpretation, and identifies a set of conditions for determining when an abstract interpreter is sound for analysing liveness properties. Our soundness proof of the framework is based on a novel relationship between unique fixpoints in metric semantics and post-fixpoints computed by abstract interpreters. We illustrate the power of the framework by providing an instance that can automatically prove the termination of programs with general (not necessarily tail) recursion.