J. Meseguer. Rewriting as a unified model of concurrency. In Baeten and Klop  Home/Search   Document Not in Database   Summary   Related Articles   Check

....= B 1 [out i] B 1 [in i] i ( tt) in tt out tt) Figure 1: Structure of model checking tools semantics, one has to find a suitable way to specify its semantics. We propose Meseguer s rewriting logic. 3 Rewriting Logic Rewriting logic was developed by Meseguer and was first presented in [Mes90]. It was shown in a number of examples that it is suitable as a common framework for concurrency. This introduction is given along the lines of [Mes96] Rewriting logic is based on the observation that several models for concurrency have the notion of a state and a transition in common. However, ....

Jose Meseguer. Rewriting as a unified model of concurrency. In Proceedings, Concur'90 Conference, Lecture Notes in Computer Science, Volume 458, pages 384--400, Amsterdam, August 1990. Springer. Also, Report SRI-CSL-90-02R, Computer Science Lab, SRI International.

....the integration and interoperation of different models and languages whose combination offers attractive advantages. Section 4 explains how different models of concurrent computation can be naturally represented in rewriting logic. Some of these model representations were known from earlier work [74, 75]; they are briefly reviewed here in an updated form. Others, such as the treatment of simultaneous access to objects, graph rewriting, dataflow, neural networks, and real time systems are new and are therefore discussed in greater detail. To place the subject in perspective, the paper begins with ....

....functors and denoting by Mod(L T ; Set) the category with objects those functors and morphims natural transformations between them the assignment, A 7 A becomes an isomorphism of categories Alg Sigma ;E = Mod(L T ; Set) where Alg Sigma ;E is the category of T algebras. As pointed out in [74], this situation generalizes very naturally to the case of rewriting logic, where models are algebraic structures on categories instead than on sets. That is, the ground on which they exist is the 2 category [67, 45] Cat, instead of the category Set. Intuitively, C is a 2 category when the ....

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Jos'e Meseguer. Rewriting as a unified model of concurrency. Technical Report SRI-CSL-90-02, SRI International, Computer Science Laboratory, February 1990. Revised June 1990.

..... 35 6.7 Nondeterminism . 35 7 Concluding Remarks : 35 1 Introduction Since the first conference paper on rewriting logic in CONCUR 90 [73], dozens of authors in Europe, the US, Japan, and Northern Africa have vigorously advanced the rewriting logic research program in over sixty papers. By a serendipitous coincidence, the first international workshop on rewriting logic will take place in Asilomar, California, the week after ....

Jos'e Meseguer. Rewriting as a unified model of concurrency. In Proceedings of the Concur'90 Conference, Amsterdam, August 1990, pages 384--400. Springer LNCS 458, 1990.

....specification of a spreadsheet is presented and related issues of the transformation from synchrony to asynchrony, of deadlock and fairness are discussed. In general, Meseguer refers to a categorical semantics of Maude and relates the rewriting logic to other logical frameworks [17] In [14], a rewrite relation similar to the configuration transition relation used by us is defined and a mechanism for an implementation relation between Lawvere categories is presented. c: A different approach to integrating the specification of static data types and of dynamic process behavior, ....

J. Meseguer. Rewriting as a unified model of concurrency. Technical Report SRI-CSL90 -02R, SRI International, February 1990.

....of the system: problems related to concurrency and communication, peculiarities due to the kind of communication, whether it is synchronous or asynchronous, sequential execution of tasks and also the particular goals of individual agents. In the classical approaches to concurrent programming [34, 28, 53, 48, 42, 33, 44], all these issues are addressed simultaneously and treated at the same level, without making any explicit distinction between problems related to communication and computation problems. At present, in fact, many concurrent applications use a set of ad hoc patterns for the coordination of the ....

....of the ideal which can be used to reduce polynomials so that every polynomial in the ideal reduce to 0 and every polynomial in the polynomial ring reduces to a unique normal form. The approach adopted here is based on the Rewrite Theory [36, 21, 23] More exhaustive definitions can be found in [23, 30, 42, 43]. A polynomial ideal can be considered as an equational theory; its Grobner basis is a complete rewriting system, when polynomials are viewed as rewrite rules, which in turn can be used to generate canonical forms for residue classes defined by the ideal on a polynomial ring. In this approach ....

J. Meseguer. Rewriting as a unified model of concurrency. Technical report, SRI CSL-93-02R, 1990.

....several formal techniques are being defined for reasoning about the behavioural properties of rewriting theories that will enable us to analyse the evolution of the architectures themselves. In the next section, we detail this semantics. 5 Transient connectors as rewrite rules Rewriting logic [9, 10] expresses an essential equivalence between logic and computation in a particularly simple way. Namely, system states are in bijective correspondence with formulas (modulo whatever structural axioms are satisfied by such formulas: for example, modulo the associativity and commutativity of a ....

J. Meseguer. Rewriting as a unified model of concurrency. In Proceedings of the Concur'90 Conference, Amsterdam, August 1990, pages 384--400. Springer LNCS 458, 1990.

....could be considered as particular entity specifications in the small. Recently it has been considered also the problem of using algebraic techniques for the formal modelling and specifications of classical object oriented systems, see for example [BZ] and [FB] a very recent paper of Meseguer [M] tries to offer a unifying and integrated framework for the specifications of dynamic system based on rewriting. Since the technical framework of all these approaches is quite different from the present one, it is not easy to make a comparison; some special effort should be made for investigating ....

Meseguer J. Rewriting as a Unified Model of Concurrency, draft, 1990.

....of tiles into ordinary rewrite rules can be found in the Technical Report [5] and in the forthcoming PhD Thesis of one of the authors [4] In particular, we have investigated the similarities between rewriting logic and tile logic from the categorical model point of view. It has been shown in [33], that a rewriting theory R yields a cartesian 2 category 3 LR , which does for R what a Lawvere theory does for a signature. Gadducci and Montanari pointed out in [21] that if also side effects 3 A 2 category [25, 30] is a category C such that, for any two objects a, and b, the class C[a; ....

J. Meseguer. Rewriting as a Unified Model of Concurrency, SRI Technical Report, CSL-90-02R, February 1990. Revised June 1990. See the appendix on Functorial Semantics of Rewrite Systems.

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Jose Meseguer. Rewriting as a unified model of concurrency. Technical Report SRI-CSL-90-02, SRI International, Computer Science Laboratory, February 1990.

....From that perspective a term t denotes a state of the system, and a rewrite t Gamma t denotes a possibly concurrent computation. A system module can contain one or more parameter theories. The inclusion from the parameter(s) into the module then gives rise to a free extension functor [18], which provides the semantics for the module. This of course means that we can compose systems by putting together the rewrite theories 15 Clavel et al. in which they are specified. A rewrite theory has both rules and equations, so that rewriting is performed modulo such equations. However, ....

Jos'e Meseguer. Rewriting as a unified model of concurrency. Technical Report SRI-CSL-90-02, SRI International, Computer Science Laboratory, February 1990.

.... respect to its model theory, and that our results generalize the original results for unsorted rewrite theories in [10] Future work will make more explicit the 2 categorical nature of our model theory, and will develop the semantics of generalized rewrite theory morphisms, extending the ideas in [9]. When evaluating the trade offs between the complexity of the presentation and the expressiveness of the proposed rewrite theories, we have preferred to give the precise foundational semantics for the most general form of rewrite theories used in practice. Although the result suggests that MEL ....

J. Meseguer. Rewriting as a unified model of concurrency. Technical Report SRI-CSL-9002R, SRI International, Computer Science Laboratory, 1990.

....and denoting by Mod(L T ; Set) the category with objects those functors, and with morphisms natural transformations between them, the assignment A 7 A becomes an isomorphism of categories Alg Sigma ;E = Mod(L T ; Set) where Alg Sigma ;E is the category of T algebras. As pointed out in [114], this situation generalizes very naturally to the case of rewriting logic, where models are algebraic structures on categories instead than on sets. That is, the ground on which they exist is the 2 category [102, 78] Cat, instead of the category Set. Intuitively, C is a 2 category when the ....

.... given by [ff] fi] ff; fi] The horizontal composition of proofs m n 1 ( u1 ] u n ] t] v 1 ] v n ] t 0 ] fi] ff 1 ] ff n ] w w 7 7 is then given by the proof term [t(ff=x) fi(v=x) t(u=x) Gamma [t 0 (v=x) The point is that, as mentioned in [114], LR does for R systems what in the Set case L T does for T algebras. That is, given an R system S the assignment to each rule r : t] Gamma [t 0 ] in R of a natural transformation r S : t S ) t 0 S between the functors t S ; t 0 S : S n Gamma S extends naturally to a 2 product ....

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J. Meseguer. Rewriting as a unified model of concurrency. Technical Report SRI-CSL-90-02, SRI International, Computer Science Laboratory, February

....and Building Formal Methods Tools 6.3 Metaprogramming 6.4 Avoiding the Frame Problem 6.5 Towards Formal Interoperability 7 Formal Reasoning, Refinement, and Transformation 7.1 Refinement and Transformation 7. 2 Modal and Temporal Logics 8 Concluding Remarks 1 Introduction Rewriting logic [113, 115] is like a two faced Janus, in that it expresses an essential equivalence between logic and computation in a particularly simple way. Namely, system states are in bijective correspondence with formulas (modulo whatever structural axioms are satisfied by such formulas: for example, modulo the ....

J. Meseguer. Rewriting as a unified model of concurrency. In Proceedings of the Concur'90 Conference, Amsterdam, August

....R Sys; j= the satisfaction relation conveniently extended to conditional rewrite rules as discussed above. Since Sign is discrete, this trivially defines an institution. Admittedly, this restriction seems to be not justified. In fact, two types of morphisms of RL theories are proposed in [11]. Basically, they are equational theory morphisms preserving the rules in the RL theories; a complete study of the institution IRL extended with these morphisms will be undertaken in a future occasion. For our purposes, the present definition is general enough as it stands, and its extension ....

J. Meseguer. Rewriting as a unified model of concurrency. Technical Report SRICSL -90-02, SRI International, Computer Science Laboratory, Feb.

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Jos'e Meseguer. Rewriting as a unified model of concurrency. In J. C. M. Baeten and J. W. Klop, editors, CONCUR'90, Theories of Concurrency: Unification and Extension, Amsterdam, The Netherlands, August

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Jos'e Meseguer. Rewriting as a unified model of concurrency. Technical Report SRI-CSL-90-02R, SRI International, Computer Science Laboratory, February

....transitions (or proofs) as morphisms, and sequential composition as morphism composition, and in them dynamic behavior exactly corresponds to deduction. In the parameterized case (see Section 4) the inclusion from the parameter(s) into the module then gives rise to a free extension 13 functor [42], which provides the semantics for the module. As a first example of system module, we consider an extension of the module defining integer arrays in Section 2.3. mod INT SORTING is protecting INT ARRAY . vars I J X Y : MachineInt . var L : IntPairList . crl [sort] I, X) L (J, Y) I, ....

J. Meseguer. Rewriting as a unified model of concurrency. Technical Report SRI-CSL-90-02, SRI International, Computer Science Laboratory, Feb.

....and calculating with Fork Algebras offers the advantage of the equational reasoning, which for a wide class of problems and approaches (as the rewriting one) is very convenient. 2. 3 Rewriting Logic Rewriting logic was first proposed by Meseguer as a unifying framework for concurrency in 1990 [69, 62]. Since then a large body of work, including more than 100 research papers and three language implementations, by researchers around the world has contributed to the development of several aspects of the logic and its applications in different areas of computer science. The recent proceedings of ....

Jose Meseguer. Rewriting as a unified model of concurrency. In Proceedings of the Concur'90 Conference, Amsterdam, August 1990, pages 384--400. Springer LNCS 458, 1990.

....that perspective, a term t denotes a state of the system, and a proof term ff : t Gamma t 0 denotes a possibly concurrent computation. A system module can contain one or more parameter theories. The inclusion from the parameter(s) into the module then gives rise to a free extension functor [36], which provides the semantics for the module. This of course means that we can compose systems by putting together the rewrite theories in which they are specified, as done in Full Maude. A rewrite theory has both rules and equations, so that rewriting is performed modulo such equations. ....

Jos'e Meseguer. Rewriting as a unified model of concurrency. Technical Report SRI-CSL-90-02, SRI International, Computer Science Laboratory, February 1990. Revised June 1990. BIBLIOGRAPHY 137

....as a (complex) diagram whose colimit returns the behaviour of the system, with transient connectors we avoid the explosion of connectors that clutters the configuration diagram, but we need to provide a mathematical semantics for them. 4 4 Transient connectors as rewrite rules Rewriting logic [8, 9] expresses an essential equivalence between logic and computation in a particularly simple way. Namely, system states are in bijective correspondence with formulas (modulo whatever structural axioms are satisfied by such formulas: for example, modulo the associativity and commutativity of a ....

J. Meseguer. Rewriting as a unified model of concurrency. In Proceedings of the Concur'90 Conference, Amsterdam, August 1990, pages 384--400. Springer LNCS 458, 1990.

No context found.

J. Meseguer. Rewriting as a Unified Model of Concurrency. SRI Technical Report, CSL-90-02R, February 1990. Revised June 1990.

....and in parallel (concurrent steps) to generate larger steps. These three operations are denoted by , Delta and Omega respectively, and satisfy particular copmposition properties. Although the tile model can be equipped with a purely logical presentation (by analogy with rewriting logic (Meseguer 1990; Meseguer 1992) where the tiles are considered as special sequents subject to certain inference rules, tile systems can be more generally seen as monoidal double categories where the tiles are just cells, the configurations are arrows of the 1 horizontal category, and the side effects are ....

....systems, where the structural rules, called tiles, have a very general format. Tiles can be composed horizontally (through side effects) vertically (computational evolutions of a certain component) and in parallel (concurrent steps) to generate larger steps. By analogy with rewriting logic (Meseguer 1990; Meseguer 1992) where a logical theory is associated to a rewriting system in such a way that each computation is represented by a sequent entailed by the theory, the tile model also comes equipped with a purely logical presentation (Gadducci and Montanari 1997) where tiles become special ....

Meseguer, J. (1990) Rewriting as a Unified Model of Concurrency. Tech. Report CSL-90-02R, Computer Science Laboratory, SRI International, Menlo Park, California, USA.

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J. Meseguer. Rewriting as a unified model of concurrency. In Baeten and Klop

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J. Meseguer. Rewriting as a unified model of concurrency. In Proceedings of the Concur'90 Conference, Amsterdam, volume 458 of Lecture Notes in Computer Science, pages 384--400. Springer-Verlag, 1990.

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J. Meseguer, Rewriting as a Unified Model of Concurrency , SRI Technical Report, CSL-93-02R, 1990. See in particular the appendix on Functorial Semantics of Rewrite Systems.

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