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Cartesian Closed Double Categories, their LambdaNotation, and the PiCalculus
, 1999
"... We introduce the notion of cartesian closed double category to provide mobile calculi for communicating systems with specific semantic models: One dimension is dedicated to compose systems and the other to compose their computations and their observations. Also, inspired by the connection between s ..."
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Cited by 22 (12 self)
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We introduce the notion of cartesian closed double category to provide mobile calculi for communicating systems with specific semantic models: One dimension is dedicated to compose systems and the other to compose their computations and their observations. Also, inspired by the connection between simply typed calculus and cartesian closed categories, we define a new typed framework, called double notation, which is able to express the abstraction /application and pairing/projection operations in all dimensions. In this development, we take the categorical presentation as a guidance in the interpretation of the formalism. A case study of the ßcalculus, where the double  notation straightforwardly handles name passing and creation, concludes the presentation.
Comparing Logics for Rewriting: Rewriting logic, action calculi and tile logic
 Theoretical Computer Science
, 2002
"... The large diffusion of concurrent and distributed systems has spawned in recent years a variety of new formalisms, equipped with features for supporting an easy specification of such systems. The aim of our paper is to analyze three proposals, namely rewriting logic, action calculi and tile logic, c ..."
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Cited by 13 (3 self)
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The large diffusion of concurrent and distributed systems has spawned in recent years a variety of new formalisms, equipped with features for supporting an easy specification of such systems. The aim of our paper is to analyze three proposals, namely rewriting logic, action calculi and tile logic, chosen among those formalisms designed for the description of rulebased systems. For each of these logics we first try to understand their foundations, then we briefly sketch some applications. The overall goal of our work is to find out a common layout where these logics can be recast, thus allowing for a comparison and an evaluation of their specific features.
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 13 (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.
Tile Transition Systems as Structured Coalgebras
 FUNDAMENTALS OF COMPUTATION THEORY, VOLUME 1684 OF LNCS
, 1999
"... The aim of this paper is to investigate the relation between two models of concurrent systems: tile rewrite systems and coalgebras. Tiles are rewrite rules with side effects which are endowed with operations of parallel and sequential composition and synchronization. Their models can be described as ..."
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Cited by 5 (3 self)
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The aim of this paper is to investigate the relation between two models of concurrent systems: tile rewrite systems and coalgebras. Tiles are rewrite rules with side effects which are endowed with operations of parallel and sequential composition and synchronization. Their models can be described as monoidal double categories. Coalgebras can be considered, in a suitable mathematical setting, as dual to algebras. They can be used as models of dynamical systems with hidden states in order to study concepts of observational equivalence and bisimilarity in a more general setting. In order to capture in the coalgebraic presentation the algebraic structure given by the composition operations on tiles, coalgebras have to be endowed with an algebraic structure as well. This leads to the concept of structured coalgebras, i.e., coalgebras for an endofunctor on a category of algebras. However, structured coalgebras are more restrictive than tile models. Those models which can be presented as st...
Appligraph: Applications of Graph Transformation  Fourth Annual Progress Report
, 2001
"... This report summarizes the activities in the fourth year of the ESPRIT Working Group APPLIGRAPH, covering the period from April 1, 2000, to March 31, 2001. The principal objective of this Working Group is to promote applied graph transformation as a rulebased framework for the specication and devel ..."
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Cited by 1 (0 self)
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This report summarizes the activities in the fourth year of the ESPRIT Working Group APPLIGRAPH, covering the period from April 1, 2000, to March 31, 2001. The principal objective of this Working Group is to promote applied graph transformation as a rulebased framework for the specication and development of systems, languages, and tools and to improve the awareness of its industrial relevance
Comparing HigherOrder Encodings in Logical Frameworks and Tile Logic
, 2001
"... In recent years, logical frameworks and tile logic have been separately proposed by our research groups, respectively in Udine and in Pisa, as suitable metalanguages with higherorder features for encoding and studying nominal calculi. This paper discusses the main features of the two approaches, tr ..."
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In recent years, logical frameworks and tile logic have been separately proposed by our research groups, respectively in Udine and in Pisa, as suitable metalanguages with higherorder features for encoding and studying nominal calculi. This paper discusses the main features of the two approaches, tracing di#erences and analogies on the basis of two case studies: late #calculus and lazy simply typed #calculus.
Dynamic Bisimilarity for Reconfigurable and Mobile Systems Via Tile Logic
"... this paper we consider bisimulation equivalences [33, 37] (with bisimilarity meaning the maximal bisimulation), where the entire branching structure of the transition system is accounted for: informally, two states are equivalent if whatever transition one can perform, the other can simulate it via ..."
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this paper we consider bisimulation equivalences [33, 37] (with bisimilarity meaning the maximal bisimulation), where the entire branching structure of the transition system is accounted for: informally, two states are equivalent if whatever transition one can perform, the other can simulate it via a transition with the same observation, still ending in equivalent states.
The Tile Model  Errata to draft available on the net
"... xtend Definition 13, in order to include also the new concept of algebraicity. In the first version it is was stated as follows. Definition 13 (tile functoriality). Let R = h\Sigma oe ; \Sigma ; N;Ri be an ars. A symmetric equivalence relation =f` A(\Sigma oe ) \Theta A(\Sigma oe ) is functorial ..."
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xtend Definition 13, in order to include also the new concept of algebraicity. In the first version it is was stated as follows. Definition 13 (tile functoriality). Let R = h\Sigma oe ; \Sigma ; N;Ri be an ars. A symmetric equivalence relation =f` A(\Sigma oe ) \Theta A(\Sigma oe ) is functorial for R if, whenever s =f t; s 0 =f t 0 for generic s; s 0 ; t; t 0 elements of A(\Sigma oe ), then s; s 0 =f t; t 0 (whenever defined) and s
A 2category View for Double Categories with Shared Structure
, 1999
"... 2categories and double categories are respectively the natural semantic ground for rewriting logic (rl) and tile logic (tl). Since 2categories can be regarded as a special case of double categories, then rl can be easily embedded into tl, where also rewriting synchronization is considered. Since ..."
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2categories and double categories are respectively the natural semantic ground for rewriting logic (rl) and tile logic (tl). Since 2categories can be regarded as a special case of double categories, then rl can be easily embedded into tl, where also rewriting synchronization is considered. Since rl is the semantic basis of several existing languages, it is useful to map tl back into rl to have an executable framework for tile specifications. We extend the results of a previous work of two of the authors, focusing on tile systems where the algebraic structures for configurations and observations rely on some common auxiliary structure (e.g., for pairing, projecting, etc.). The new model theory required to relate the categorical models of the two logics is an extended version of the theory of 2categories, and is defined using partial membership equational logic. More concretely, this semantic mapping yields a rewriting logic implementation of tile logic, where a metalayer is requir...
Cartesian Closed Double Categories,
"... their LambdaNotation, and the PiCalculus We introduce the notion of cartesian closed double category to provide mobile calculi for communicating systems with specific semantic models: One dimension is dedicated to compose systems and the other to compose their computations and their observations. ..."
Abstract
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their LambdaNotation, and the PiCalculus We introduce the notion of cartesian closed double category to provide mobile calculi for communicating systems with specific semantic models: One dimension is dedicated to compose systems and the other to compose their computations and their observations. Also, inspired by the connection between simply typed ¢calculus and cartesian closed categories, we define a new typed framework, called double ¢notation, which is able to express the abstraction/application and pairing/projection operations in all dimensions. In this development, we take the categorical presentation as a guidance in the interpretation of the formalism. A case study of the £calculus, where the double ¢notation straightforwardly handles name passing and creation, concludes the presentation.