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Abstract Interpretation for Liveness using Metric Spaces

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Abstract: We will give a brief overview of a abstract interpretation based framework for defining static analyses for liveness properties. Currently abstract interpretation provides an elegant framework for defining and proving the soundness of abstract interpreters for safety properties. Unfortunately we do not have an equivelant understanding for liveness properties. In this work we make a novel use of metric spaces in order to prove the soundness of an abstract interpreter to prove termination for a simple language with arbitary recursion. We make use of existing ideas from semantics of programming languages using metric spaces to define a general framework for proving liveness properties using abstract interpretation.

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