research-article

Verifying Procedural Programs via Constrained Rewriting Induction

Authors:

Naoki NishidaAuthors Info & Claims

ACM Transactions on Computational Logic (TOCL), Volume 18, Issue 2

Article No.: 14, Pages 1 - 50

https://doi.org/10.1145/3060143

Published: 02 June 2017 Publication History

Abstract

This article aims to develop a verification method for procedural programs via a transformation into logically constrained term rewriting systems (LCTRSs). To this end, we extend transformation methods based on integer term rewriting systems to handle arbitrary data types, global variables, function calls, and arrays, and to encode safety checks. Then we adapt existing rewriting induction methods to LCTRSs and propose a simple yet effective method to generalize equations. We show that we can automatically verify memory safety and prove correctness of realistic functions. Our approach proves equivalence between two implementations; thus, in contrast to other works, we do not require an explicit specification in a separate specification language.

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Cited By

Kojima MNishida N(2024)A Sufficient Condition of Logically Constrained Term Rewrite Systems for Decidability of All-path Reachability Problems with Constant DestinationsJournal of Information Processing10.2197/ipsjjip.32.41732(417-435)Online publication date: 2024
https://doi.org/10.2197/ipsjjip.32.417
Kojima MNishida N(2024)On Solving All-Path Reachability Problems for Starvation Freedom of Concurrent Rewrite Systems Under Process FairnessReachability Problems10.1007/978-3-031-72621-7_5(54-70)Online publication date: 25-Sep-2024
https://dl.acm.org/doi/10.1007/978-3-031-72621-7_5
Hagens KKop C(2024)Rewriting Induction for Higher-Order Constrained Term Rewriting SystemsLogic-Based Program Synthesis and Transformation10.1007/978-3-031-71294-4_12(202-219)Online publication date: 9-Sep-2024
https://dl.acm.org/doi/10.1007/978-3-031-71294-4_12
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Index Terms

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Rewriting Induction for Higher-Order Constrained Term Rewriting Systems
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Abstract
Logically Constrained Term Rewriting Systems (LCTRSs) provide a framework very suitable for modeling both imperative and functional languages. One may convert programs in traditional languages into LCTRSs, and then use methods from term rewriting ...
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Rewriting induction (RI) frameworks consist of inference rules to prove equations to be inductive theorems of a given term rewriting system, i.e., to be inductively valid w.r.t. reduction of the given system. To prove inductive validity of inequalities ...
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Published In

cover image ACM Transactions on Computational Logic

ACM Transactions on Computational Logic Volume 18, Issue 2

April 2017

306 pages

ISSN:1529-3785

EISSN:1557-945X

DOI:10.1145/3091105

Editor:
Orna Kupferman
School of Computer Science and Engineering, Hebrew University, Israel

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Copyright © 2017 Owner/Author.

This work is licensed under a Creative Commons Attribution-NonCommercial International 4.0 License.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 02 June 2017

Accepted: 01 February 2017

Revised: 01 February 2017

Received: 01 December 2015

Published in TOCL Volume 18, Issue 2

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Japan Society for the Promotion of Science (JSPS)
Austrian Science Fund (FWF) international project
Marie Skłodowska-Curie action “HORIP”
Nagoya University's Graduate Program for Real-World Data Circulation Leaders from MEXT, Japan

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Cited By

Kojima MNishida N(2024)A Sufficient Condition of Logically Constrained Term Rewrite Systems for Decidability of All-path Reachability Problems with Constant DestinationsJournal of Information Processing10.2197/ipsjjip.32.41732(417-435)Online publication date: 2024
https://doi.org/10.2197/ipsjjip.32.417
Kojima MNishida N(2024)On Solving All-Path Reachability Problems for Starvation Freedom of Concurrent Rewrite Systems Under Process FairnessReachability Problems10.1007/978-3-031-72621-7_5(54-70)Online publication date: 25-Sep-2024
https://dl.acm.org/doi/10.1007/978-3-031-72621-7_5
Hagens KKop C(2024)Rewriting Induction for Higher-Order Constrained Term Rewriting SystemsLogic-Based Program Synthesis and Transformation10.1007/978-3-031-71294-4_12(202-219)Online publication date: 9-Sep-2024
https://dl.acm.org/doi/10.1007/978-3-031-71294-4_12
Schöpf JMitterwallner FMiddeldorp A(2024)Confluence of Logically Constrained Rewrite Systems RevisitedAutomated Reasoning10.1007/978-3-031-63501-4_16(298-316)Online publication date: 2-Jul-2024
https://doi.org/10.1007/978-3-031-63501-4_16
Guo LKop C(2024)Higher-Order LCTRSs and Their TerminationProgramming Languages and Systems10.1007/978-3-031-57267-8_13(331-357)Online publication date: 6-Apr-2024
https://dl.acm.org/doi/10.1007/978-3-031-57267-8_13
Milovančević DKunčak V(2023)Proving and Disproving Equivalence of Functional Programming AssignmentsProceedings of the ACM on Programming Languages10.1145/35912587:PLDI(928-951)Online publication date: 6-Jun-2023
https://dl.acm.org/doi/10.1145/3591258
Kojima MNishida N(2023)Reducing non-occurrence of specified runtime errors to all-path reachability problems of constrained rewritingJournal of Logical and Algebraic Methods in Programming10.1016/j.jlamp.2023.100903135(100903)Online publication date: Oct-2023
https://doi.org/10.1016/j.jlamp.2023.100903
Ciobâcă ŞLucanu DBuruiană A(2023)Operationally-based program equivalence proofs using LCTRSsJournal of Logical and Algebraic Methods in Programming10.1016/j.jlamp.2023.100894135(100894)Online publication date: Oct-2023
https://doi.org/10.1016/j.jlamp.2023.100894
Schöpf JMiddeldorp A(2023)Confluence Criteria for Logically Constrained Rewrite SystemsAutomated Deduction – CADE 2910.1007/978-3-031-38499-8_27(474-490)Online publication date: 2-Sep-2023
https://doi.org/10.1007/978-3-031-38499-8_27
Kojima MNishida N(2023)From Starvation Freedom to All-Path Reachability Problems in Constrained RewritingPractical Aspects of Declarative Languages10.1007/978-3-031-24841-2_11(161-179)Online publication date: 8-Jan-2023
https://doi.org/10.1007/978-3-031-24841-2_11
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