Results 1 
8 of
8
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 ..."
Abstract

Cited by 20 (12 self)
 Add to MetaCart
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.
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 ..."
Abstract

Cited by 13 (9 self)
 Add to MetaCart
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.
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 ..."
Abstract

Cited by 8 (6 self)
 Add to MetaCart
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 ..."
Abstract

Cited by 8 (4 self)
 Add to MetaCart
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...
On graph(ic) encodings
 Graph Transformations and Process Algebras for Modeling Distributed and Mobile Systems, number 04241 in Dagstuhl Seminar Proceedings. Internationales Begegnungs und Forschungszentrum (IBFI), Schloss Dagstuhl
, 2005
"... Abstract. This paper is an informal summary of different encoding techniques from process calculi and distributed formalisms to graphic frameworks. The survey includes the use of solo diagrams, term graphs, synchronized hyperedge replacement systems, bigraphs, tile models and interactive systems, al ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
Abstract. This paper is an informal summary of different encoding techniques from process calculi and distributed formalisms to graphic frameworks. The survey includes the use of solo diagrams, term graphs, synchronized hyperedge replacement systems, bigraphs, tile models and interactive systems, all presented at the Dagstuhl Seminar 04241. The common theme of all techniques recalled here is having a graphic presentation that, at the same time, gives both an intuitive visual rendering (of processes, states, etc.) and a rigorous mathematical framework. 1
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 ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
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
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 ..."
Abstract
 Add to MetaCart
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...
Connector Algebras, Petri Nets, and BIP ⋆
"... Abstract. In the area of componentbased software architectures, the term connector has been coined to denote an entity (e.g. the communication network, middleware or infrastructure) that regulate the interaction of independent components. Hence, a rigorous mathematical foundation for connectors is ..."
Abstract
 Add to MetaCart
Abstract. In the area of componentbased software architectures, the term connector has been coined to denote an entity (e.g. the communication network, middleware or infrastructure) that regulate the interaction of independent components. Hence, a rigorous mathematical foundation for connectors is crucial for the study of coordinated systems. In recent years, many different mathematical frameworks have been proposed to specify, design, analyse, compare, prototype and implement connectors rigorously. In this paper, we overview the main features of three notable frameworks and discuss their similarities, differences, mutual embedding and possible enhancements. First, we show that Sobocinski’s nets with boundaries are as expressive as Sifakis et al.’s BI(P), the BIP component framework without priorities. Second, we provide a basic algebra of connectors for BI(P) by exploiting Montanari et al.’s tile model and a recent correspondence result with nets with boundaries. Finally, we exploit the tile model as a unifying framework to compare BI(P) with other models of connectors and to propose suitable enhancements of BI(P). 1