N. Mart-Oliet and J. Meseguer. Rewriting logic as a logical and semantic framework. Technical report,  Home/Search   Document Details and Download   Summary   Related Articles   Check

....the associativity equation. Finally we sketch a new method of combining matching algorithms for regular collapse theories and give examples that involve the identity and idempotence equations. 1 Introduction Rewriting logic provides a general way of specifying computational and logical systems [10,11]. An important part of this generality is making equational theories into an explicit parameter of the formalism. Since any computable data type can be equationally axiomatized [3] this allows specification of the data part of a system in a fully general way. We view a rewrite as acting on data ....

Narciso Mart'i-Oliet and Jos'e Meseguer. Rewriting logic as a logical and semantic framework. Technical Report SRI-CSL-93-05, SRI International, Computer Science Laboratory, August 1993.

....are de ned directly, not through categories, while paths, which are not rst class citizens in graphs, are important in the comparison (see, e.g. 5] In categories, paths are composite arrows, so, as arrows, they are rst class citizens. 4. 2 RWL and the Semantics of Programming Languages [10] describes how rewriting logic can be used to give the semantics of programming languages, with a mini ML as an example. Use of rewriting modulo equations for the same purpose is exposed in [15] for describing the operational semantics of the calculus. Our speci cation of the machine looks ....

Narciso Mart-Oliet and Jose Meseguer. Rewriting logic as a logical and semantic framework. Technical Report SRI-CSL-93-05, SRI International, 1993. To appear in Handbook of Philosophical Logic, Kluwer Academic Publishers.

....to write algebraic compilers and hopefully this work is a contribution toward moving algebraic compilers in a more pragmatic direction. Thus the two methodologies could be said to be heading toward the same goal, but from di erent starting points. Rewriting Logic. The rewriting logic system [MOM93] of the Maude [Mes00] language provides very general and powerful mechanisms for implementing logics as well as a semantic framework for specifying languages and systems. Many di erent models of computation can be uni ed using rewriting logic. The semantics of functional (speci cation ) ....

Narciso Mart-Oliet and Jose Meseguer. Rewriting logic as a logical and semantic framework. Technical Report SRI-CSL-93-05, SRI International, Computer Science Laboratory, August 1993. To appear in D. Gabbay, editor, Handbook of Philosophical Logic, Second Edition, Volume 6, Kluwer Academic Publishers, 2001.

.... Symbolic Semantics in Maude Alberto Verdejo Technical Report 122 02 Dpto. Sistemas Inform aticos y Programaci on Universidad Complutense de Madrid. Spain January 2002 Research supported by CICYT project Desarrollo Formal de Sistemas Basados en Agentes M oviles (TIC2000 0701 C02 01) Abstract We present a formal tool where LOTOS speci cations without ....

....logic and Maude Rewriting logic was introduced by Meseguer [13] as a uni ed model of concurrency in which several well known models of concurrent systems can be represented in a common framework. Since then much work has been done on the use of rewriting logic as a logical and semantic framework [12] in which many di erent logics, models of computation, and a wide range of languages, including The union of the behaviour and data type description parts is known as Full LOTOS. We use in this paper the term LOTOS to refer to the whole language. formal speci cation languages like LOTOS, can ....

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N. Mart-Oliet and J. Meseguer. Rewriting logic as a logical and semantic framework. Technical Report SRI-CSL-93-05, SRI International, Computer Science Laboratory, Aug. 1993.

.... at all one simply adds the following new rules: var I (I 7 l ) I : E l : E l : s l contents(l) C 1 C 1 ; C 2 1 ; C 2 ( C 2 C 2 3 Prototyping Semantics using Rewriting Logic Since SOS can be represented straightforwardly in rewriting logic [7], one may in principle use systems such as Maude and ELAN (see the other papers in this volume for current references) for interpreting programs according to their speci ed semantics. Perhaps also Maude s object oriented modules could be exploited to express the intended operational semantics ....

N. Mart-Oliet and J. Meseguer. Rewriting logic as a logical and semantic framework. In D. Gabbay, editor, Handbook of Philosophical Logic, volume 6. Kluwer Academic Publishers,

....framework has been defined in [7] as the search within the space of logics for a logic F such that many other logics L can be represented in F by means of mappings L Gamma F that have particularly nice properties such as being conservative translations. In this line, Mart i Oliet and Meseguer [8] have recently proposed rewriting logic as a very flexible logical framework. The fact that rewriting logic is reflective has very important practical consequences for its use as a logical framework. Note that a representation map Psi : L RWLogic between a logic L and rewriting logic is by its ....

....data types Module L and Module, representing the finitely presentable theories of L and RWLogic respectively; 7 Clavel then, the map Psi can itself be reified as an equationally defined function Psi : Module L Gamma Module. Following this method, Mart i Oliet and Meseguer defined in [8] the reification of a map of logics OE : LinLogic Gamma RWLogic mapping theories in full quantifier free first order linear logic to rewrite theories. In [2, Section 4.1.1] we give the complete specification of this map as has been implemented in the Maude system. 4.2 Maude as a Semantic ....

N. Mart'i-Oliet and J. Meseguer. Rewriting logic as a logical and semantic framework. In Meseguer [12], pages 189--224.

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Narciso Mart'i-Oliet and Jos'e Meseguer. Rewriting logic as a logical and semantic framework. This volume.

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Narciso Mart'i-Oliet and Jos'e Meseguer. Rewriting logic as a logical and semantic framework. Technical Report SRI-CSL-93-05, SRI International, Computer Science Laboratory, August 1993.

....can be used to analyze CCS processes. 1. INTRODUCTION Rewriting logic was introduced by Meseguer [8] as a uni ed model of concurrency in which several well known models of concurrent systems can be represented in a common framework. This goal was further extended by Mart Oliet and Meseguer [7] to the idea of rewriting logic as a logical and semantic framework. It was shown that many other logics, widely di erent in nature, can be represented inside rewriting logic in a natural and direct way. The general way in which such representations are achieved is by: Representing formulas or ....

....axioms. Similar techniques can be used to naturally specify and prototype many languages and systems in rewriting logic. In particular, the similarities between rewriting logic and structural operational semantics were noted by Meseguer [8] and further explored by Mart Oliet and Meseguer [7]. As an illustrative example, Mart Oliet and Meseguer [7] completely developed a representation of Milner s CCS [9] in rewriting logic. However, this representation cannot be directly executed in the default interpreter of Maude [3] a high performance language and system supporting both ....

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N. Mart-Oliet and J. Meseguer. Rewriting logic as a logical and semantic framework. Technical Report SRI-CSL-93-05, SRI International, 1993. To appear in Handbook of Philosophical Logic, Kluwer Academic Publishers.

....and semantic framework in which specification, rapid prototyping, and efficient parallel and distributed execution, as well as formal transformations from specifications to programs can be naturally supported [14] Multiparadigm. Since rewriting logic conservatively extends equational logic [15], a equational style of functional programming is naturally supported in a sublanguage. A declarative style of concurrent object oriented programming is also supported with a simple logical semantics. Since rewriting logic also extends Horn logic with equality in a conservative way [15] Horn ....

....logic [15] a equational style of functional programming is naturally supported in a sublanguage. A declarative style of concurrent object oriented programming is also supported with a simple logical semantics. Since rewriting logic also extends Horn logic with equality in a conservative way [15], Horn logic programming can also be supported and extended in an implementation with basic facilities for unification. Reflective. Rewriting logic is reflective [8,7] The design of Maude capitalizes on this fact to support a novel style of metaprogramming with very powerful module combining ....

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Narciso Mart'i-Oliet and Jos'e Meseguer. Rewriting logic as a logical and semantic framework. Technical Report SRI-CSL-93-05, SRI International, Computer Science Laboratory, August 1993. To appear in D. Gabbay, ed., Handbook of Philosophical Logic, Kluwer Academic Publishers.

.... namely Maude [3] with an explicit state on the y linear temporal logic (LTL) model checker with time and space performance comparable to that of current high performance model checkers of that kind such as SPIN [1] The great generality and exibility of rewriting logic as a semantic framework [15,18] is of course the reason for Maude s expressiveness. The high expressive power at the system speci cation level has been achieved without sacri cing performance by taking into account the latest research developments in optimized B uchi automata constructions and in explicit state model checking ....

Mart-Oliet, N. and J. Meseguer, Rewriting logic as a logical and semantic framework, Technical Report SRI-CSL-93-05, SRI International, Computer Science Laboratory (1993), to appear in D. Gabbay, ed., Handbook of Philosophical Logic, Kluwer Academic Publishers.

....processes. We compare this implementation with a previous one where transitions become judgements and inference rules become rewrites, and also comment on extensions to the LOTOS language. 1 Introduction In the context of proposing rewriting logic as a logical and semantic framework, the paper [10] illustrated several di erent ways of mapping inference systems into rewriting logic. A very general possibility is to map an inference rule of the form S 1 : S n S 0 into a rewrite rule of the form S 1 : S n S 0 that rewrites multisets of judgements S i . This mapping is correct from an ....

....is correct, and in both cases the intuitive idea is that the rewriting relation corresponds to the horizontal bar separating conclusion from premises in the typical textbook presentation of inference rules. These mappings can be applied to a wide variety of inference systems, as detailed in [10], including sequent systems for logics and also structural Research supported by CICYT project Desarrollo Formal de Sistemas Basados en Agentes M oviles (TIC2000 0701 C02 01) c 2002 Published by Elsevier Science B. V. operational semantics de nitions for languages. However, in the ....

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N. Mart-Oliet and J. Meseguer. Rewriting logic as a logical and semantic framework. Technical Report SRI-CSL-93-05, SRI International, Computer Science Laboratory, Aug. 1993.

....t. They are entirely user definable as an algebraic data type satisfying certain equational axioms, so that rewriting deduction takes place modulo such axioms. Because of this ecumenical neutrality, rewriting logic has, from a logical viewpoint, good properties as a logical framework [107], in which many other logics can be naturally represented. And, computationally, it has also good properties as a semantic framework [118] in which many different system styles and models of concurrent computation and many different languages can be naturally expressed without any distorting ....

N. Mart'i-Oliet and J. Meseguer. Rewriting logic as a logical and semantic framework. In J. Meseguer, editor, Proc. First Intl. Workshop on Rewriting Logic and its Applications, volume 4 of Electronic Notes in Theoretical Computer Science. Elsevier, 1996. http://www1.elsevier.nl/mcs/tcs/pc/volume4.htm.

....rules are Church Rosser. In this way, a seamless integration of parallel functional programming within the more general framework of rewriting logic is naturally achieved. More abstractly, such an integration can be viewed as a conservative embedding of equational logic within rewriting logic [105]. For higher order functions, the key observation is that rewriting logic allows rewriting modulo equational axioms. We can then take advantage of the different reductions of lambda calculi to first order equational logic using an equational theory of explicit substitution to view lambda calculus ....

....The rules in R are subject to certain syntactic restrictions that guarantee an efficient form of matching modulo ACI . See [115] for some more discussion. 3. 6 CCS, LOTOS and the Calculus Kokichi Futatsugi, Timothy Winkler and I [121] and in a different later version Narciso Mart i Oliet and I [105], have shown two different ways in which Milner s CCS can be naturally represented in rewriting logic. One representation essentially treats the transitions as rewrite rules, with some syntactic care to record in the term the actions that have been performed. The other representation considers the ....

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N. Mart'i-Oliet and J. Meseguer. Rewriting logic as a logical and semantic framework. Technical Report SRI-CSL-93-05, SRI International, Computer Science Laboratory, August 1993. To appear in D. Gabbay, ed., Handbook of Philosophical Logic, Kluwer Academic Publishers.

....concurrent and distributed ones and languages can be naturally represented. Because of the intrinsic duality between logic and computation that rewriting logic supports, the very same reasons making rewriting logic a suitable semantic framework, make it also an attractive logical framework [20] to represent many di erent logics. Thanks to the sustained e orts of many researchers, particularly in the ELAN, Pisa, Stanford, and Maude teams, there is by now very extensive evidence supporting the claim that rewriting logic is indeed a 5 Clavel et al. very exible and simple semantic ....

.... to the sustained e orts of many researchers, particularly in the ELAN, Pisa, Stanford, and Maude teams, there is by now very extensive evidence supporting the claim that rewriting logic is indeed a 5 Clavel et al. very exible and simple semantic framework [21,23,24,4] and logical framework [20,18,34,19,3,32,6,14,7,10]. Moreover, object oriented design languages, architectural description languages, and languages for distributed components also have a natural semantics in rewriting logic [35,25,33,27,28] What is common to all these applications is that the models of computation, logics, or languages are ....

N. Mart-Oliet and J. Meseguer. Rewriting logic as a logical and semantic framework. Technical Report SRI-CSL-93-05, SRI International, Computer Science Laboratory, August 1993. To appear in D. Gabbay, ed., Handbook of Philosophical Logic, Kluwer Academic Publishers.

....t. They are entirely user de nable as an algebraic data type satisfying certain equational axioms, so that rewriting deduction takes place modulo such axioms. Because of this ecumenical neutrality, rewriting logic has, from a logical viewpoint, good properties as a logical framework [31], in which many other logics can be naturally represented. And, computationally, it has also good properties as a semantic framework [35] in which many di erent system styles and models of concurrent computation can be naturally expressed without any distorting encodings. 4 The design of the ....

N. Mart-Oliet and J. Meseguer. Rewriting logic as a logical and semantic framework. In Meseguer [34].

....Maude as a formal metatool to generate formal tools from their declarative speci cations. The paper [11] discusses several other such formal tool generator applications developed by di erent authors, including: 1) formal translation tools from HOL to Nuprl, from linear logic to rewriting logic [30, 7], from the Wright architectural description language to CSP and from CSP to rewriting logic, and from pure (higher order) type systems to rewriting logic [38] 2) a proof assistant for the open calculus of constructions (an equational extension of the calculus of constructions) 38] and (3) ....

N. Mart-Oliet and J. Meseguer. Rewriting logic as a logical and semantic framework. Technical Report SRI-CSL-93-05, SRI International, August 1993. To appear in D.M. Gabbay, ed., Handbook of Philosophical Logic, Kluwer Academic Publishers.

....have been shown to have a very natural conservative representation in rewriting logic [25] The point is that all such representation maps can be rei ed using the re ective method described above. For the case of the representation map from linear logic into rewriting logic this was de ned in [26] and has been implemented in Maude by Clavel and Mart Oliet [8] Finally, rewriting logic may also be used to reason about the models of computation expressed in di erent languages [8,6,27] providing a semantic foundation for building connections between diverse models of computation. 4.4 ....

N. Mart-Oliet and J. Meseguer. Rewriting logic as a logical and semantic framework. In J. Meseguer, editor, Proc. First Intl. Workshop on Rewriting Logic and its Applications, volume 4 of Electronic Notes in Theoretical Computer Science. Elsevier, 1996. http://www1.elsevier.nl/mcs/tcs/pc/ volume4.htm.

....L to terms in Module. In a similar 14 Clavel et al. way, one can reify translations between two di erent languages or logics L and L 0 as functions from Module L to Module L 0 . Rewriting logic de nitions of several languages have been given by di erent authors: lambda calculus and mini ML [24,25], Prolog and narrowing languages like BABEL [36] CCS (see [33,25] the work of Bruni and Clavel [8,6] and the tile rewrite rules in [20] the calculus [35] and sketches of UNITY [29] and Gamma [30] Similarly, many di erent logics have been shown to have a very natural conservative ....

....reify translations between two di erent languages or logics L and L 0 as functions from Module L to Module L 0 . Rewriting logic de nitions of several languages have been given by di erent authors: lambda calculus and mini ML [24,25] Prolog and narrowing languages like BABEL [36] CCS (see [33,25], the work of Bruni and Clavel [8,6] and the tile rewrite rules in [20] the calculus [35] and sketches of UNITY [29] and Gamma [30] Similarly, many di erent logics have been shown to have a very natural conservative representation in rewriting logic [25] The point is that all such ....

[Article contains additional citation context not shown here]

N. Mart-Oliet and J. Meseguer. Rewriting logic as a logical and semantic framework. Technical Report SRI-CSL-93-05, SRI International, Computer Science Laboratory, August 1993. To appear in D. Gabbay, ed., Handbook of Philosophical Logic, Kluwer Academic Publishers. 20 Clavel et al.

....both membership equational logic [39] and rewriting logic [37] speci cation and programming for a wide range of applications. Rewriting logic is re ective [14] and has very good properties as a logical framework, in which many other logics and many semantic formalisms can be naturally represented [36]. Maude has been in uenced in important ways by the OBJ3 language [34] which can be regarded as an equational logic sublanguage. Maude s language design and implementation make systematic use of the fact that rewriting logic is re ective, making the metatheory of rewriting logic accessible to ....

.... functions for rewriting and evaluating terms at the metalevel, namely, meta apply, meta reduce, and meta rewrite, and also generic parsing and pretty printing functions meta parse and meta pretty print [7,8] Re ection, together with the good properties of rewriting logic as a logical framework [36,40], make it quite easy to develop formal tools in Maude for any logic L of interest, including as in the case of Full Maude s module algebra rewriting logic itself. Suppose, for example, that we want to build a theorem prover for a logic, or to implement an executable formal speci cation language. ....

[Article contains additional citation context not shown here]

N. Mart-Oliet and J. Meseguer. Rewriting logic as a logical and semantic framework. Technical Report SRI-CSL-93-05, Computer Science Laboratory, SRI International, August 1993. To appear in D.M. Gabbay, editor, Handbook of Philosophical Logic, Kluwer Academic Publishers.

....concurrent system. Logically, they are interpreted as inference rules in a logical system. As already mentioned, this makes rewriting logic both a general semantic framework to specify concurrent systems and languages [47] and a general logical framework to represent and execute di erent logics [41]. Rewriting in (T ; R) happens modulo the equational axioms in T . Maude supports rewriting modulo most of the di erent combinations of associativity, commutativity, identity, and idempotency axioms. The rules in R need not be Church Rosser and need not be terminating. Many di erent rewriting ....

Narciso Mart-Oliet and Jose Meseguer. Rewriting logic as a logical and semantic framework. In J. Meseguer, editor, Proc. First Intl. Workshop on Rewriting Logic and its Applications, volume 4 of Electronic Notes in Theoretical Computer Science. Elsevier, 1996. http://www.elsevier.nl/cas/tree/store/ tcs/free/noncas/pc/volume4.htm.

.... of rewriting logic are like two sides of the same coin, the same reasons making it a good semantic framework at the computational level make it also a good logical framework at the logical level, that is, a metalogic in which many other logics can be naturally represented and implemented [40, 39, 36, 37, 3, 57, 10, 22, 11, 17]. Moreover, object oriented design languages, architectural description languages, and languages for distributed components also have a natural semantics in rewriting logic [61, 51, 58, 53, 54] Consequently, some of the most interesting applications of Maude are metalanguage applications, in ....

....concurrent and distributed ones and languages can be naturally represented. Because of the intrinsic duality between logic and computation that rewriting logic supports, the very same reasons making rewriting logic a suitable semantic framework, make it also an attractive logical framework [39] to represent many di erent logics. What is common to all these logical and semantic framework applications is that the models of computation, logics, or languages are represented in rewriting logic by mappings of the form (y) L RWLogic: The representations are typically very simple and ....

Narciso Mart-Oliet and Jose Meseguer. Rewriting logic as a logical and semantic framework. Technical Report SRI-CSL-93-05, Computer Science Laboratory, SRI International, August 1993. To appear in D.M. Gabbay, editor, Handbook of Philosophical Logic, Kluwer Academic Publishers.

.... states t. They are entirely user definable as an algebraic data type satisfying certain equational axioms, so that rewriting deduction takes place modulo such axioms. Because of this ecumenical neutrality, rewriting logic has, from a logical viewpoint, good properties as a logical framework [20], in which many other logics can be naturally represented. And, computationally, it has also good properties as a semantic framework [23] in which many different system styles and models of concurrent computation can be naturally expressed without any distorting encodings. The design of the ....

N. Mart'i-Oliet and J. Meseguer. Rewriting logic as a logical and semantic framework. In J. Meseguer, editor, Proceedings of the First International Workshop on Rewriting Logic and its Applications, RWLW'96, Asilomar, California, volume 4 of Electronic Notes in Theoretical Computer Science. Elsevier, September 1996.

.... The computational and logical interpretations of rewriting logic lead to applications that use it: as a semantic framework, in which different languages and models of computation are expressed; or as a logical framework, in which different logics and inference systems are likewise expressed [208]. We first discuss semantic framework applications. 4.1 Models of Computation This section presents concrete evidence (in highly condensed form; see [223,227] for much more detailed discussions) for the thesis that a wide variety of models of computation, including concurrent ones, can be ....

.... labeled transition systems [218] 4) grammars and string rewriting systems [218] 5) Petri nets, including place transition nets, contextual nets, algebraic nets, colored nets, and timed Petri nets [218,223,293,297,268,289] 6) Gamma and the Chemical Abstract Machine [218] 7) CCS and LOTOS [230,208,314,45,89,311,309,201]; 8) the calculus [316,292] 9) concurrent objects and actors [218,220,300,302,304] 10) the UNITY language [218] 11) concurrent graph rewriting [223] 12) dataflow [223] 13) neural networks [223] 14) real time systems, including timed automata, timed transition systems, hybrid ....

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Narciso Mart'i-Oliet and Jos'e Meseguer. Rewriting logic as a logical and semantic framework. Technical Report SRI-CSL-93-05, SRI International, Computer Science Laboratory, August

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N. Mart-Oliet and J. Meseguer. Rewriting logic as a logical and semantic framework. Technical report,

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