5,564 research outputs found
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 AndalucÃa Tech
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
Superposition as a logical glue
The typical mathematical language systematically exploits notational and
logical abuses whose resolution requires not just the knowledge of domain
specific notation and conventions, but not trivial skills in the given
mathematical discipline. A large part of this background knowledge is expressed
in form of equalities and isomorphisms, allowing mathematicians to freely move
between different incarnations of the same entity without even mentioning the
transformation. Providing ITP-systems with similar capabilities seems to be a
major way to improve their intelligence, and to ease the communication between
the user and the machine. The present paper discusses our experience of
integration of a superposition calculus within the Matita interactive prover,
providing in particular a very flexible, "smart" application tactic, and a
simple, innovative approach to automation.Comment: In Proceedings TYPES 2009, arXiv:1103.311
Guided Unfoldings for Finding Loops in Standard Term Rewriting
In this paper, we reconsider the unfolding-based technique that we have
introduced previously for detecting loops in standard term rewriting. We
improve it by guiding the unfolding process, using distinguished positions in
the rewrite rules. This results in a depth-first computation of the unfoldings,
whereas the original technique was breadth-first. We have implemented this new
approach in our tool NTI and compared it to the previous one on a bunch of
rewrite systems. The results we get are promising (better times, more
successful proofs).Comment: Pre-proceedings paper presented at the 28th International Symposium
on Logic-Based Program Synthesis and Transformation (LOPSTR 2018), Frankfurt
am Main, Germany, 4-6 September 2018 (arXiv:1808.03326
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