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Methods for Proving Termination of Rewriting-based programming Languages by Transformation

ELECTRONIC NOTES IN THEORETICAL COMPUTER SCIENCE 2009年 248卷 93-113页

作者： Duran, Francisco Lucas, Salvador Meseguer, Jose Univ Malaga DLCC Malaga Spain Univ Politecn Valencia DSIC Valencia Spain Univ Illinois CS Dept Urbana IL USA

Despite the remarkable development of the theory of termination of rewriting, its application to high-level (rewriting-based) programming languages is far from being optimal. This is due to the need for features such as conditional equations and rules, types and subtypes, (possibly programmable) strategies for controlling the execution, matching modulo axioms, and so on, that are used in many programs and tend to place such programs outside the scope of current termination tools. The operational meaning of such features is often formalized in a proof theoretic manner by means of an inference system rather than just by a rewriting relation. The corresponding termination notions can also differ from the standard ones. During the last years we have introduced and implemented different notions and transformation techniques which have been proved useful for proving and disproving termination of such programs by using existing tools for proving termination of (variants of) rewriting. In this paper we provide an overview of our main contributions.

关键词： program analysis and verification Rewriting Logic Term Rewriting Termination Tools

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A Calculus for Imperative programs: Formalization and Implementation

A Calculus for Imperative Programs: Formalization and Implem...

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11th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)

作者： Erascu, Madalina Jebelean, Tudor Johannes Kepler Univ Linz Symbol Computat Res Inst A-4040 Linz Austria

ISBN: (纸本)9780769539645

As an extension of our previous work on imperative program verification, we present a formalism for handling the total correctness of While loops in imperative programs, consisting in functional based definitions of the verification conditions for both partial correctness and for termination. A specific feature of our approach is the generation of verification conditions as first order formulae, including the termination condition which is expressed as an induction principle.

关键词： program analysis and verification symbolic execution theorem proving

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Soundness of a Logic-Based verification Method for Imperative Loops

Soundness of a Logic-Based Verification Method for Imperativ...

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14th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC)

作者： Erascu, Madalina Jebelean, Tudor Johannes Kepler Univ Linz Symbol Computat Res Inst A-4040 Linz Austria

ISBN: (纸本)9780769549347;9781467350266

We present a logic-based verification method for imperative loops (including ones with abrupt termination) and the automatic proof of its soundness. The verification method consists in generating verification conditions for total correctness of an imperative loop annotated with an invariant. We realized, in the Theorema system (***), the automatic proof of the soundness of verification method: if the verification conditions hold, then the imperative loop is totally correct with respect to its given invariant. The approach is simpler than the others because it is based on functional semantics (no additional theory of program execution is necessary) and produces verification conditions in the object theory of the program. The computer-supported proofs reveal the minimal collection of logical assumptions (some from natural number theory) and logical inferences (including induction) which are necessary for the soundness of the verification technique.

关键词： program analysis and verification symbolic execution semantics induction termination Theorema system

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