Using Well-Founded Relations for Proving Operational Termination

[EN] In this paper, we study operational termination, a proof theoretical notion for capturing the termination behavior of computational systems. We prove that operational termination can be characterized at different levels by means of well- founded relations on specific formulas which can be obtained from the considered system. We show how to obtain such well-founded relations from logical models which can be automatically generated using existing tools.Partially supported by the EU (FEDER), Projects TIN2015-69175-C4-1-R, and GV PROMETEOII/2015/013.Lucas Alba, S. (2020). Using Well-Founded Relations for Proving Operational Termination. Journal of Automated Reasoning. 64(2):167-195. https://doi.org/10.1007/s10817-019-09514-2S167195642Alarcón, B., Gutiérrez, R., Lucas, S., Navarro-Marset, R.: Proving termination properties with MU-TERM. 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Applications and extensions of context-sensitive rewriting

[EN] Context-sensitive rewriting is a restriction of term rewriting which is obtained by imposing replacement restrictions on the arguments of function symbols. It has proven useful to analyze computational properties of programs written in sophisticated rewriting-based programming languages such asCafeOBJ, Haskell, Maude, OBJ*, etc. Also, a number of extensions(e.g., to conditional rewritingor constrained equational systems) and generalizations(e.g., controlled rewritingor forbidden patterns) of context-sensitive rewriting have been proposed. In this paper, we provide an overview of these applications and related issues. (C) 2021 Elsevier Inc. All rights reserved.Partially supported by the EU (FEDER), and projects RTI2018-094403-B-C32 and PROMETEO/2019/098.Lucas Alba, S. (2021). Applications and extensions of context-sensitive rewriting. Journal of Logical and Algebraic Methods in Programming. 121:1-33. https://doi.org/10.1016/j.jlamp.2021.10068013312

Rewriting Modulo SMT and Open System Analysis

This paper proposes rewriting modulo SMT, a new technique that combines the power of SMT solving, rewriting modulo theories, and model checking. Rewriting modulo SMT is ideally suited to model and analyze reachability properties of infinite-state open systems, i.e., systems that interact with a nondeterministic environment. Such systems exhibit both internal nondeterminism, which is proper to the system, and external nondeterminism, which is due to the environment. In a reflective formalism, such as rewriting logic, rewriting modulo SMT can be reduced to standard rewriting. Hence, rewriting modulo SMT naturally extends rewriting-based reachability analysis techniques, which are available for closed systems, to open systems. The proposed technique is illustrated with the formal analysis of: (i) a real-time system that is beyond the scope of timed-automata methods and (ii) automatic detection of reachability violations in a synchronous language developed to support autonomous spacecraft operations.NSF Grant CNS 13-19109 and NASA Research Cooperative Agreement No. NNL09AA00AOpe

Executable Structural Operational Semantics in Maude

This paper describes in detail how to bridge the gap between theory and practice when implementing in Maude structural operational semantics described in rewriting logic, where transitions become rewrites and inference rules become conditional rewrite rules with rewrites in the conditions, as made possible by the new features in Maude 2.0. We validate this technique using it in several case studies: a functional language Fpl (evaluation and computation semantics, including an abstract machine), imperative languages WhileL (evaluation and computation semantics) and GuardL with nondeterminism (computation semantics), Kahn’s functional language Mini-ML (evaluation or natural semantics), Milner’s CCS (with strong and weak transitions), and Full LOTOS (including ACT ONE data type specifications). In addition, on top of CCS we develop an implementation of the Hennessy-Milner modal logic for describing local capabilities of processes, and for LOTOS we build an entire tool where Full LOTOS specifications can be entered and executed (without user knowledge of the underlying implementation of the semantics). We also compare this method based on transitions as rewrites with another one based on transitions as judgements

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

Techniques for Modelling Structured Operational and Denotational Semantics Definitions with Term Rewriting Systems

A fundamental requirement for the application of automatic proof support for program verification is that the semantics of programs be appropriately formalized using the object language underlying the proof tool. This means that the semantics definition must not only be stated as syntactically correct input for the proof tool to be used, but also in such a way that the desired proofs can be performed without too many artificial complications. And it must be clear, of course, that the translation from mathematical metalanguage into the object language is correct. The objective of this work is to present methods for the formalization of structured operational and denotational semantics definitions that meet these requirements. It combines techniques known from implementation of the $\lambda$-calculus with a new way to control term rewriting on object level, thus reaching a conceptually simple representation based on unconditional rewriting. This deduction formalism is available within many of the existent proof tools, and therefore application of the representation methods is not restricted to a particular tool. Correctness of the representations is achieved by proving that the non-trivial formalizations yield results that are equivalent to the meta-level definitions in a strong sense. Since the representation algorithms have been implemented in form of executable programs, there is no need to carry out tedious coding schemes by hand. Semantics definitions can be stated in a format very close to the usual meta language format, and they can be transformed automatically into an object-level representation that is accessible to proof tools. The formalizations of the two semantics definition styles are designed in a consistent way, both making use of the same modelling of the underlying mathematical basis. Therefore, they can be used simultaneously in proofs. This is demonstrated in a larger example, where an operational and a denotational semantics definition for a programming language are proved to be equivalent using the Larch Prover. This proof has been carried out by hand before, and so the characteristics of the automated proof can be made quite clear