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Expressive Completeness of Separation Logic with Two Variables and No Separating Conjunction

Expressive Completeness of Separation Logic with Two Variables and No Separating Conjunction Expressive Completeness of Separation Logic with Two Variables and No Separating Conjunction STEPHANE DEMRI, LSV, ENS Cachan, CNRS, Universit´ Paris-Saclay e MORGAN DETERS, New York University Separation logic is used as an assertion language for Hoare-style proof systems about programs with pointers, and there is an ongoing quest for understanding its complexity and expressive power. Herein, we show that first-order separation logic with one record field restricted to two variables and the separating implication (no separating conjunction) is as expressive as weak second-order logic, substantially sharpening a previous result. Capturing weak second-order logic with such a restricted form of separation logic requires substantial updates to known proof techniques. We develop these and, as a by-product, identify the smallest fragment of separation logic known to be undecidable: first-order separation logic with one record field, two variables, and no separating conjunction. Because we forbid ourselves the use of many syntactic resources, this underscores even further the power of separating implication on concrete heaps. Categories and Subject Descriptors: F.3.1 [Specifying and Verifying and Reasoning about Programs]: Logics of Programs General Terms: Theory, Verification Additional Key Words and Phrases: Separation logic, expressive completeness, two-variable logics, undecidability ACM Reference Format: Stephane Demri and http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM Transactions on Computational Logic (TOCL) Association for Computing Machinery

Expressive Completeness of Separation Logic with Two Variables and No Separating Conjunction

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References (68)

Publisher
Association for Computing Machinery
Copyright
Copyright © 2016 by ACM Inc.
ISSN
1529-3785
DOI
10.1145/2835490
Publisher site
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Abstract

Expressive Completeness of Separation Logic with Two Variables and No Separating Conjunction STEPHANE DEMRI, LSV, ENS Cachan, CNRS, Universit´ Paris-Saclay e MORGAN DETERS, New York University Separation logic is used as an assertion language for Hoare-style proof systems about programs with pointers, and there is an ongoing quest for understanding its complexity and expressive power. Herein, we show that first-order separation logic with one record field restricted to two variables and the separating implication (no separating conjunction) is as expressive as weak second-order logic, substantially sharpening a previous result. Capturing weak second-order logic with such a restricted form of separation logic requires substantial updates to known proof techniques. We develop these and, as a by-product, identify the smallest fragment of separation logic known to be undecidable: first-order separation logic with one record field, two variables, and no separating conjunction. Because we forbid ourselves the use of many syntactic resources, this underscores even further the power of separating implication on concrete heaps. Categories and Subject Descriptors: F.3.1 [Specifying and Verifying and Reasoning about Programs]: Logics of Programs General Terms: Theory, Verification Additional Key Words and Phrases: Separation logic, expressive completeness, two-variable logics, undecidability ACM Reference Format: Stephane Demri and

Journal

ACM Transactions on Computational Logic (TOCL) – Association for Computing Machinery

Published: Jan 7, 2016

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