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Mapping tile logic into rewriting logic

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Recent Trends in Algebraic Development Techniques (WADT 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1376))

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Abstract

Rewriting logic extends to concurrent systems with state changes the body of theory developed within the algebraic semantics approach. It is both a foundational tool and the kernel language of several implementation efforts (Cafe, ELAN, Maude). Tile logic extends (unconditional) rewriting logic since it takes into account state changes with side effects and synchronization. It is especially useful for defining compositional models of computation of reactive systems, coordination languages, mobile calculi, and causal and located concurrent systems. In this paper, the two logics are defined and compared using a recently developed algebraic specification methodology, membership equational logic. Given a theory T, the rewriting logic of T is the free monoidal 2-category, and the tile logic of T is the free monoidal double category, both generated by T. An extended version of monoidal 2-categories, called 2VH-categories, is also defined, able to include in an appropriate sense the structure of monoidal double categories. We show that 2VH-categories correspond to an extended version of rewriting logic, which is able to embed tile logic, and which can be implemented in the basic version of rewriting logic using suitable internal strategies. These strategies can be significantly simpler when the theory is uniform. A uniform theory is provided in the paper for CCS, and it is conjectured that uniform theories exist for most process algebras.

Research supported by Office of Naval Research Contracts N00014-95-C-0225 and N00014-96-C-0114, by National Science Foundation Grant CCR-9633363, and by the Information Technology Promotion Agency, Japan, as part of the Industrial Science and Technology Frontier Program “New Models for Software Architechture” sponsored by NEDO (New Energy and Industrial Technology Development Organization). Also research supported in part by U.S. Army contract DABT63-96-C-0096 (DARPA); CNR Integrated Project Metodi e Strumenti per la Progettazione e la Verifica di Sistemi Eterogenei Connessi mediante Reti di Comunicazione; and Esprit Working Groups CONFER2 and COORDINA. Research carried out while. the second author was on leave at Computer Science Laboratory, SRI International, and visiting scholar at Stanford University.

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Authors and Affiliations

  1. Computer Science Laboratory, SRI International, Menlo Park

    José Meseguer

  2. Dipartimento di Informatica, Università di Pisa, Italy

    Ugo Montanari

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  1. José Meseguer
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  2. Ugo Montanari
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Francesco Parisi Presicce

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Meseguer, J., Montanari, U. (1998). Mapping tile logic into rewriting logic. In: Presicce, F.P. (eds) Recent Trends in Algebraic Development Techniques. WADT 1997. Lecture Notes in Computer Science, vol 1376. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-64299-4_27

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  • DOI: https://doi.org/10.1007/3-540-64299-4_27

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