Loops under Strategies ... Continued

While there are many approaches for automatically proving termination of term rewrite systems, up to now there exist only few techniques to disprove their termination automatically. Almost all of these techniques try to find loops, where the existence of a loop implies non-termination of the rewrite system. However, most programming languages use specific evaluation strategies, whereas loop detection techniques usually do not take strategies into account. So even if a rewrite system has a loop, it may still be terminating under certain strategies. Therefore, our goal is to develop decision procedures which can determine whether a given loop is also a loop under the respective evaluation strategy. In earlier work, such procedures were presented for the strategies of innermost, outermost, and context-sensitive evaluation. In the current paper, we build upon this work and develop such decision procedures for important strategies like leftmost-innermost, leftmost-outermost, (max-)parallel-innermost, (max-)parallel-outermost, and forbidden patterns (which generalize innermost, outermost, and context-sensitive strategies). In this way, we obtain the first approach to disprove termination under these strategies automatically.Comment: In Proceedings IWS 2010, arXiv:1012.533

Refinement Types as Higher Order Dependency Pairs

Refinement types are a well-studied manner of performing in-depth analysis on functional programs. The dependency pair method is a very powerful method used to prove termination of rewrite systems; however its extension to higher order rewrite systems is still the object of active research. We observe that a variant of refinement types allow us to express a form of higher-order dependency pair criterion that only uses information at the type level, and we prove the correctness of this criterion

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