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Symmetric Monoidal and Cartesian Double Categories as a Semantic Framework for Tile Logic
 MATHEMATICAL STRUCTURES IN COMPUTER SCIENCE
, 2002
"... Tile systems offer a general paradigm for modular descriptions of concurrent systems, based on a set of rewriting rules with sideeffects. Monoidal double categories are a natural semantic framework for tile systems, because the mathematical structures describing system states and synchronizing acti ..."
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Cited by 13 (9 self)
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Tile systems offer a general paradigm for modular descriptions of concurrent systems, based on a set of rewriting rules with sideeffects. Monoidal double categories are a natural semantic framework for tile systems, because the mathematical structures describing system states and synchronizing actions (called configurations and observations, respectively, in our terminology) are monoidal categories having the same objects (the interfaces of the system). In particular, configurations and observations based on netprocesslike and term structures are usually described in terms of symmetric monoidal and cartesian categories, where the auxiliary structures for the rearrangement of interfaces correspond to suitable natural transformations. In this paper we discuss the lifting of these auxiliary structures to double categories. We notice that the internal construction of double categories produces a pathological asymmetric notion of natural transformation, which is fully exploited in one dimension only (for example, for configurations or for observations, but not for both). Following Ehresmann (1963), we overcome this biased definition, introducing the notion of generalized natural transformation between four double functors (rather than two). As a consequence, the concepts of symmetric monoidal and cartesian (with consistently chosen products) double categories arise in a natural way from the corresponding ordinary versions, giving a very good relationship between the auxiliary structures of configurations and observations. Moreover, the Kelly–Mac Lane coherence axioms can be lifted to our setting without effort, thanks to the characterization of two suitable diagonal categories that are always present in a double category. Then, symmetric monoidal and cartesian double categories are shown to offer an adequate semantic setting for process and term tile systems.
Tile Bisimilarity Congruences for Open Terms and Term Graphs
 in: Proc. CONCUR 2000, LNCS 1877 (2000
, 2000
"... The definition of sos formats ensuring that bisimilarity on closed terms is a congruence has received much attention in the last two decades. For dealing with open system specifications, the congruence is usually lifted from closed terms to open terms by instantiating the free variables in all possi ..."
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Cited by 12 (7 self)
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The definition of sos formats ensuring that bisimilarity on closed terms is a congruence has received much attention in the last two decades. For dealing with open system specifications, the congruence is usually lifted from closed terms to open terms by instantiating the free variables in all possible ways; the only alternatives considered in the literature relying on Larsen and Xinxin's context systems and Rensink's conditional transition systems. We propose a different approach based on tile logic, where both closed and open terms are managed analogously. In particular, we analyze the `bisimilarity as congruence' property for several tile formats that accomplish di erent concepts of subterm sharing.
Metalevel Computation in Maude
, 1998
"... Maude's language design and implementation make systematic use of the fact that rewriting logic is reflective. This makes the metatheory of rewriting logic accessible to the user in a clear and principled way, and makes possible many advanced metaprogramming applications, including userdefinable st ..."
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Cited by 11 (7 self)
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Maude's language design and implementation make systematic use of the fact that rewriting logic is reflective. This makes the metatheory of rewriting logic accessible to the user in a clear and principled way, and makes possible many advanced metaprogramming applications, including userdefinable strategy languages, language extensions by new module composition operations, development of theorem proving tools, and reifications of other languages and logics within rewriting logic. A naive implementation of reflection can be computationally very expensive. We explain the semantic principles and implementation techniques through which efficient ways of performing reflective computations are achieved in Maude through its predefined METALEVEL module.
An Interactive Semantics of Logic Programming
 THEORY AND PRACTICE OF LOGIC PROGRAMMING
, 2001
"... We apply to logic programming some recently emerging ideas from the field of reductionbased communicating systems, with the aim of giving evidence of the hidden interactions and the coordination mechanisms that rule the operational machinery of such a programming paradigm. The semantic framework we ..."
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Cited by 8 (6 self)
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We apply to logic programming some recently emerging ideas from the field of reductionbased communicating systems, with the aim of giving evidence of the hidden interactions and the coordination mechanisms that rule the operational machinery of such a programming paradigm. The semantic framework we have chosen for presenting our results is tile logic, which has the advantage of allowing a uniform treatment of goals and observations and of applying abstract categorical tools for proving the results. As main contributions, we mention the finitary presentation of abstract unification, and a concurrent and coordinated abstract semantics consistent with the most common semantics of logic programming. Moreover, the compositionality of the tile semantics is guaranteed by standard results, as it reduces to check that the tile systems associated to logic programs enjoy the tile decomposition property. An extension of the approach for handling constraint systems is also discussed.
Open Ended Systems, Dynamic Bisimulation and Tile Logic
, 2000
"... The sos formats ensuring that bisimilarity is a congruence often fail in the presence of structural axioms on the algebra of states. Dynamic bisimulation, introduced to characterize the coarsest congruence for ccs which is also a (weak) bisimulation, reconciles the bisimilarity as congruence pro ..."
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Cited by 8 (4 self)
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The sos formats ensuring that bisimilarity is a congruence often fail in the presence of structural axioms on the algebra of states. Dynamic bisimulation, introduced to characterize the coarsest congruence for ccs which is also a (weak) bisimulation, reconciles the bisimilarity as congruence property with such axioms and with the specication of open ended systems, where states can be recongured at runtime, at the cost of an innitary operation at the metalevel. We show that the compositional framework oered by tile logic is suitable to deal with structural axioms and open ended systems specications, allowing for a nitary presentation of context closure. Keywords: Bisimulation, sos formats, dynamic bisimulation, tile logic. Introduction The semantics of dynamic systems can be conveniently expressed via labelled transition systems (lts) whose states are terms over a certain algebra and whose labels describe some abstract behavioral information. Provided such informatio...
The Maude Specification of Full Maude
, 1999
"... This document describes the executable formal specification of Full Maude  a version of Maude supporting a rich module algebra with module hierarchies, parameterization, views, theories, module expressions, and objectoriented modules  which is in fact its implementation in the Maude 1.00 system ..."
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Cited by 7 (2 self)
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This document describes the executable formal specification of Full Maude  a version of Maude supporting a rich module algebra with module hierarchies, parameterization, views, theories, module expressions, and objectoriented modules  which is in fact its implementation in the Maude 1.00 system
Symmetric and Cartesian Double Categories as a Semantic Framework for Tile Logic
, 1995
"... this paper we discuss the lifting of these auxiliary structures to double categories. We notice that the internal construction of double categories produces a pathological asymmetric notion of natural transformation, which is fully exploited in one dimension only (e.g., for configurations or for eff ..."
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Cited by 6 (5 self)
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this paper we discuss the lifting of these auxiliary structures to double categories. We notice that the internal construction of double categories produces a pathological asymmetric notion of natural transformation, which is fully exploited in one dimension only (e.g., for configurations or for effects, but not for both). Following Ehresmann (1963), we overcome this biased definition, introducing the notion of generalized natural transformation between four
Normal Forms for Algebras of Connections
 Theoretical Computer Science
, 2000
"... Recent years have seen a growing interest towards algebraic structures that are able to express formalisms different from the standard, treelike presentation of terms. Many of these approaches reveal a specific interest towards the application to the `distributed and concurrent systems' field, but ..."
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Cited by 5 (4 self)
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Recent years have seen a growing interest towards algebraic structures that are able to express formalisms different from the standard, treelike presentation of terms. Many of these approaches reveal a specific interest towards the application to the `distributed and concurrent systems' field, but an exhaustive comparison between them is sometimes difficult, because their presentations can be quite dissimilar. This work is a first step towards a unified view: Focusing on the primitive ingredients of distributed spaces (namely interfaces, links and basic modules), we introduce a general schema for describing a normal form presentation of many algebraic formalisms, and show that those normal forms can be thought of as arrows of suitable monoidal categories.
Logical Specification of Operational Semantics
 IN CSL'99, PROC. CONF. ON COMPUTER SCIENCE LOGIC, VOLUME 1683 OF LNCS
, 1999
"... Various logicbased frameworks have been proposed for specifying the operational semantics of programming languages and concurrent systems, including inference systems in the styles advocated by Plotkin and by Kahn, Horn logic, equational specifications, reduction systems for evaluation contexts ..."
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Cited by 4 (3 self)
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Various logicbased frameworks have been proposed for specifying the operational semantics of programming languages and concurrent systems, including inference systems in the styles advocated by Plotkin and by Kahn, Horn logic, equational specifications, reduction systems for evaluation contexts, rewriting logic, and tile logic. We consider
Strategic Reflection
 Proceedings of the CADE15 Workshop on Strategies in Automated Deduction
, 1998
"... . The Maude system incorporates reflective capabilities that enable quite sophisticated strategies to be expressed very conveniently. Maude's strategy languages have been used to control the execution of large and small rewriting systems, in several areas of application. Strategies have been used to ..."
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Cited by 1 (1 self)
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. The Maude system incorporates reflective capabilities that enable quite sophisticated strategies to be expressed very conveniently. Maude's strategy languages have been used to control the execution of large and small rewriting systems, in several areas of application. Strategies have been used to encode winning strategies for games, and can also be used for more serious purposes, such as theoremproving strategies, and strategies taking the place of model checkers or finitestate exploration tools in the analysis of finitestate systems. In particular, finiteor infinitestate systems, such as secure communication protocols, can be specified in rewriting logic and can be subjected to formal analysis through strategies at the metalevel. Communication protocols can be specified as concurrent objectoriented systems communicating through message passing, and can be executed as Maude programs. Nondeterministic behavior such as the order of messages arrival in such protocols can be contro...