Abstract
Since its introduction, more than a decade ago, rewriting logic has attracted the interest of both theorists and practitioners, who have contributed in showing its generality as a semantic and logical framework and also as a programming paradigm. The experimentation conducted in these years has suggested that some significant extensions to the original definition of the logic would be very useful in practice. In particular, the Maude system now supports subsorting and conditions in the equational logic for data, and also frozen arguments to block undesired nested rewritings; moreover, it allows equality and membership assertions in rule conditions. In this paper, we give a detailed presentation of the inference rules, model theory, and completeness of such generalized rewrite theories.
Research supported by the MIUR Project COFIN 2001013518 CoMeta, by the FET-GC Project IST-2001-32747 Agile, and by ONR Grant N00014-02-1-0715. The first author is also supported by a CNR fellowship for research on Information Sciences and Technologies.
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References
H. Cirstea, C. Kirchner, and L. Liquori. The Rho Cube. Proc. FoSSaCS’01, LNCS 2030, pp. 168–183. Springer, 2001.
M. Clavel, F. Durán, S. Eker, P. Lincoln, N. Martí-Oliet, J. Meseguer, and J. Quesada. Maude: Specification and programming in rewriting logic. TCS 285:187–243, 2002.
R. Diaconescu and K. Futatsugi. CafeOBJ Report: The language, proof techniques, and methodologies for object-oriented algebraic specification, AMAST Series in Computing volume 6. World Scientific, 1998.
S. Lucas. Termination of rewriting with strategy annotations. Proc. LPAR’01, Lect. Notes in Artificial Intelligence 2250, pp. 669–684. Springer, 2001.
N. Martí-Oliet and J. Meseguer. Rewriting logic as a logical and semantic framework. Handbook of Philosophical Logic volume 9, pp. 1–87. Kluwer, second edition, 2002.
N. Martí-Oliet and J. Meseguer. Rewriting logic: roadmap and bibliography. Theoret. Comput. Sci. 285(2):121–154, 2002.
N. Martí-Oliet, K. Sen, and P. Thati. An executable specification of asynchronous pi-calculus semantics and may testing in Maude 2.0. Proc. WRLA’02, ENTCS 71. Elsevier, 2002.
N. Martí-Oliet and A. Verdejo. Implementing CCS in Maude 2. Proc. WRLA’02, ENTCS 71. Elsevier, 2002.
J. Meseguer. Rewriting as a unified model of concurrency. Technical Report SRICSL-90-02R, SRI International, Computer Science Laboratory, 1990.
J. Meseguer. Conditional rewriting logic as a unified model of concurrency. Theoret. Comput. Sci., 96:73–155, 1992.
J. Meseguer. Membership algebra as a logical framework for equational specification. Proc. WADT’97, LNCS 1376, pp. 18–61. Springer, 1998.
Protheo Team. The ELAN home page, 2001. www page http://elan.loria.fr.
M.-O. Stehr, J. Meseguer, and P. Ölveczky. Rewriting logic as a unifying framework for Petri nets. Unifying Petri Nets, LNCS 2128, pp. 250–303. Springer, 2001.
M.-O. Stehr and J. Meseguer. Pure Type Systems in Rewriting Logic. Proc. LFM’99. 1999.
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Bruni, R., Meseguer, J. (2003). Generalized Rewrite Theories. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds) Automata, Languages and Programming. ICALP 2003. Lecture Notes in Computer Science, vol 2719. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45061-0_22
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DOI: https://doi.org/10.1007/3-540-45061-0_22
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