Separation logic + superposition calculus = heap theorem prover

Program analysis and verification tools crucially depend on the ability to symbolically describe and reason about sets of program behaviors. Separation logic provides a promising foundation for dealing with heap manipulating programs, while the development of practical automated deduction/satisfiability checking tools for separation logic is a challenging problem. In this paper, we present an efficient, sound and complete automated theorem prover for checking validity of entailments between separation logic formulas with list segment predicates. Our theorem prover integrates separation logic inference rules that deal with list segments and a superposition calculus to deal with equality/aliasing between memory locations. The integration follows a modular combination approach that allows one to directly incorporate existing advanced techniques for first-order reasoning with equality, as well as account for additional theories, e.g., linear arithmetic, using extensions of superposition. An experimental evaluation of our entailment prover indicates speedups of several orders of magnitude with respect to the available state-of-the-art tools. © 2011 ACM

Spatial Interpolants

We propose Splinter, a new technique for proving properties of heap-manipulating programs that marries (1) a new separation logic-based analysis for heap reasoning with (2) an interpolation-based technique for refining heap-shape invariants with data invariants. Splinter is property directed, precise, and produces counterexample traces when a property does not hold. Using the novel notion of spatial interpolants modulo theories, Splinter can infer complex invariants over general recursive predicates, e.g., of the form all elements in a linked list are even or a binary tree is sorted. Furthermore, we treat interpolation as a black box, which gives us the freedom to encode data manipulation in any suitable theory for a given program (e.g., bit vectors, arrays, or linear arithmetic), so that our technique immediately benefits from any future advances in SMT solving and interpolation.Comment: Short version published in ESOP 201

Automated Deduction – CADE 28

This open access book constitutes the proceeding of the 28th International Conference on Automated Deduction, CADE 28, held virtually in July 2021. The 29 full papers and 7 system descriptions presented together with 2 invited papers were carefully reviewed and selected from 76 submissions. CADE is the major forum for the presentation of research in all aspects of automated deduction, including foundations, applications, implementations, and practical experience. The papers are organized in the following topics: Logical foundations; theory and principles; implementation and application; ATP and AI; and system descriptions

12th International Workshop on Termination (WST 2012) : WST 2012, February 19–23, 2012, Obergurgl, Austria / ed. by Georg Moser

This volume contains the proceedings of the 12th International Workshop on Termination (WST 2012), to be held February 19–23, 2012 in Obergurgl, Austria. The goal of the Workshop on Termination is to be a venue for presentation and discussion of all topics in and around termination. In this way, the workshop tries to bridge the gaps between different communities interested and active in research in and around termination. The 12th International Workshop on Termination in Obergurgl continues the successful workshops held in St. Andrews (1993), La Bresse (1995), Ede (1997), Dagstuhl (1999), Utrecht (2001), Valencia (2003), Aachen (2004), Seattle (2006), Paris (2007), Leipzig (2009), and Edinburgh (2010). The 12th International Workshop on Termination did welcome contributions on all aspects of termination and complexity analysis. Contributions from the imperative, constraint, functional, and logic programming communities, and papers investigating applications of complexity or termination (for example in program transformation or theorem proving) were particularly welcome. We did receive 18 submissions which all were accepted. Each paper was assigned two reviewers. In addition to these 18 contributed talks, WST 2012, hosts three invited talks by Alexander Krauss, Martin Hofmann, and Fausto Spoto

Separation Logic Modulo Theories

Logical reasoning about program data often requires dealing with heap structures as well as scalar data types. Recent advances in Satisfiability Modular Theory (SMT) already offer efficient procedures for dealing with scalars, yet they lack any support for dealing with heap structures. In this paper, we present an approach that integrates Separation Logic---a prominent logic for reasoning about list segments on the heap---and SMT. We follow a model-based approach that communicates aliasing among heap cells between the SMT solver and the Separation Logic reasoning part. An experimental evaluation using the Z3 solver indicates that our approach can effectively put to work the advances in SMT for dealing with heap structures. This is the first decision procedure for the combination of separation logic with SMT theories.Comment: 16 page