A Human-Oriented Term Rewriting System

© Springer Nature Switzerland AG 2019. We introduce a fully automatic system, implemented in the Lean theorem prover, that solves equality problems of everyday mathematics. Our overriding priority in devising the system is that it should construct proofs of equality in a way that is similar to that of humans. A second goal is that the methods it uses should be domain independent. The basic strategy of the system is to operate with a subtask stack: whenever there is no clear way of making progress towards the task at the top of the stack, the program finds a promising subtask, such as rewriting a subterm, and places that at the top of the stack instead. Heuristics guide the choice of promising subtasks and the rewriting process. This makes proofs more human-like by breaking the problem into tasks in the way that a human would. We show that our system can prove equality theorems simply, without having to preselect or orient rewrite rules as in standard theorem provers, and without having to invoke heavy duty tools for performing simple reasoning

Two Decades of Maude

This paper is a tribute to José Meseguer, from the rest of us in the Maude team, reviewing the past, the present, and the future of the language and system with which we have been working for around two decades under his leadership. After reviewing the origins and the language's main features, we present the latest additions to the language and some features currently under development. This paper is not an introduction to Maude, and some familiarity with it and with rewriting logic are indeed assumed.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

A Rewriting-Logic-Based Technique for Modeling Thermal Systems

This paper presents a rewriting-logic-based modeling and analysis technique for physical systems, with focus on thermal systems. The contributions of this paper can be summarized as follows: (i) providing a framework for modeling and executing physical systems, where both the physical components and their physical interactions are treated as first-class citizens; (ii) showing how heat transfer problems in thermal systems can be modeled in Real-Time Maude; (iii) giving the implementation in Real-Time Maude of a basic numerical technique for executing continuous behaviors in object-oriented hybrid systems; and (iv) illustrating these techniques with a set of incremental case studies using realistic physical parameters, with examples of simulation and model checking analyses.Comment: In Proceedings RTRTS 2010, arXiv:1009.398

Smart matching

One of the most annoying aspects in the formalization of mathematics is the need of transforming notions to match a given, existing result. This kind of transformations, often based on a conspicuous background knowledge in the given scientific domain (mostly expressed in the form of equalities or isomorphisms), are usually implicit in the mathematical discourse, and it would be highly desirable to obtain a similar behavior in interactive provers. The paper describes the superposition-based implementation of this feature inside the Matita interactive theorem prover, focusing in particular on the so called smart application tactic, supporting smart matching between a goal and a given result.Comment: To appear in The 9th International Conference on Mathematical Knowledge Management: MKM 201

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