Fabio Gadducci and Ugo Montanari. The tile model. In Gordon Plotkin, Colin Stirling, and Mads Tofte, editors, Proof, Language and Interaction: Essays in Honour of Robin Milner. MIT Press, 1999. To appear.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....implementing a speci c proof assistant or integrated environment for each of them. Three research groups of the tosca project, in Milano, Pisa and Udine, have been actively involved in the area of metalanguages and metamodels developing and experimenting cospan span categories, tile logic (tl) [14, 4] and logical frameworks (e.g. lf) 15, 27] respectively. We refer the reader to [13] for a comparison between the two rst metamodels. In this paper, we discuss tile logic and logical frameworks. The foundations of both metamodels are by now well established, various tools based on them are ....

....vertically ( extending computations of a component; and in parallel ( modeling concurrent steps. We say that a tile is entailed by R, written R , if can be obtained by composing basic and auxiliary tiles via , These compositions satisfy the laws of monoidal double categories [14, 24]. For : s id x and : t id y with x the i.i.i. of , we write as a shorthand for ( 1 ) Similarly, for : id x and : id y t with y the f.o.i. of , we write . for (1 ) These compositions are called diagonal and yield two monoidal categories. ....

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Gadducci, F. and U. Montanari, The tile model, in: Proof, Language and Interaction: Essays in Honour of Robin Milner, MIT Press (2000).

.... Work Strongly connected with the idea of a graph transformation based speci cation of changes in environments and of agent systems in particular, investigations in the context of logistics management have been furthered in the direction of Mass Customisation [TKH 01, TWK 01] Tile Logic [GM00] is a rule based framework that exploits a three dimensional view of concurrent systems: the horizontal dimension (space) is devoted to the modeling of states and components; the vertical dimension (time) models computation steps; and the third dimension (concurrency) accounts for the ....

F. Gadducci and U. Montanari. The tile model. In G. Plotkin, C. Stirling, and M. Tofte, editors, Proof, Language and Interaction: Essays in Honour of Robin Milner. MIT Press, 2000. Also Technical Report TR-27/96, Dipartimento di Informatica, Universita di Pisa, 1996.

....and process logics, thus avoiding the daunting task of implementing a specific proof assistant or integrated environment for each of them. Our research groups in Pisa and Udine have been actively involved in the area of metalanguages and metamodels developing and experimenting tile logic (tl) [13, 4] and logical frameworks (e.g. lf) 14, 26] respectively. The foundations of both metamodels are by now well established, various tools based on them are available (e.g. 18, 7] and several case studies concerning widely used calculi and programming paradigms have been carried out. The two ....

....( extending computations of a component; and in parallel ( modeling concurrent steps. We say that a tile # is entailed by R, written R # #, if # can be obtained by composing basic and auxiliary tiles via #, #. These compositions satisfy the laws of monoidal double categories [13, 23]. For # : s # idx id x and # : t # idy id y with x the i.i.i. of #, we write # # # as a shorthand for (# ) #. Similarly, for # : id x idx # a and # : id y idy t with y the f.o.i. of #, we write # # # for # (1 #) These compositions are called diagonal and yield ....

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Gadducci, F. and U. Montanari, The tile model, in: Proof, Language and Interaction: Essays in Honour of Robin Milner, MIT Press (2000).

....called correctness and completeness, and thus strict ) implies the equivalence induced by the universal closure. Reduction semantics can be obviously recasted in LTS s as the special case with a unique label. For PC whose rules are in a quite general format, called algebraic format [16], we provide a constructive way of defining a spatio temporal logic and we give an algorithm for building a correct and complete STS over such a logic. The algorithm, expressed as a Prolog program, builds labels by computing recursively the most general unifiers between coordinators and left hand ....

....large and strict symbolic bisimilarities and showing that both relations imply bisimilarity via universal closure. In 3, first we illustrate the algorithmic construction of correct and complete STS s for process calculi with no structural axioms and operational rules in the algebraic format of [16], and then we show how to deal with the common AC1 axioms for the parallel composition operator. In 4, we test our approach against a simple case study consisting of a fragment of the ambient calculus with CCS like communication within ambients. Related work. The aforementioned papers by Sewell, ....

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F. Gadducci and U. Montanari. The tile model. In Proof, Language and Interaction: Essays in Honour of Robin Milner. MIT Press, 2000.

....sequentially (plugging the terms of one context into the holes of another) and in parallel (concatenating tuples of terms over the same variables) together with units and projections. In TL, steps may a#ect the interfaces of contexts, and the steps themselves have a rich algebraic structure; see [13, 14] for the details. Here we shall merely introduce the notation of TL, and illustrate its use to express the operational semantics of a familiar fragment of CCS. The conventional algebraic notation for a tile is s a # b t (ignoring the label of the tile, for simplicity) where s t is a ....

F. Gadducci and U. Montanari. The tile model. In Proof, Language, and Interaction. The MIT Press, 1999. To appear. 16

....transition system (LTS) where the labels are the arrows of a category. In contrast Full version of [24] reporting research carried out while visiting SRI International and Stanford University, USA to other frameworks where labels are equipped with categorical structure (e.g. Tile Logic [11] and Rewriting Logic [15] composition here is generally a partial operation, and computations are restricted to those where all adjacent labels are composable. Note that the labels are no longer the simple atomic actions often used in studies of process algebra, but here usually have entities ....

....in the framework of Enhanced Operational Semantics. However, they did not abstract from the structure of labels (which is a crucial step for obtaining full modularity and extensibility) nor did they consider partial composition of labels. The Tile Model framework of Gadducci and Montanari [11] provides categorical structure on labels, but is otherwise not closely related to the present approach. There has been extensive work on various formats of small step SOS (see a recent paper by Fokkink and Verhoef [10] for references) but the conservativity results obtained there concern ....

F. Gadducci and U. Montanari. The tile model. In Proof, Language, and Interaction. The MIT Press, 1999. To appear.

....systems. They use well known constraint propagation techniques to 15 cope with the problem of efficiently combining productions together. This helps reducing the possible choices for each process and thus simplify the combination problem. This same approach is also be modelled via the Tile Model [GM98b], which has been used to model a graph rewriting formalism aimed at describing the concurrent, synchronized evolution of local processes. Tiles are much like SOS inference rules, but they can be composed horizontally and vertically to build larger proof steps. Tile systems can be seen as double ....

F. Gadducci and U. Montanari. The Tile Model. In G. Plotkin, C. Stirling, and M. Tofte, editors, Proof, Language and Interaction: Essays in Honour of Robin Milner. MIT Press, 1998.

.... 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 automata, and timed Petri nets [268,262] and (15) the tile logic [146,147,135] model of synchronized concurrent computation [232,39,34,148] Since the above specifications of models of computation as rewrite theories are typically executable, this suggests that rewriting logic is a very flexible operational semantic framework to specify the semantics of such models. What ....

Fabio Gadducci and Ugo Montanari. The tile model. In G. Plotkin, C. Stirling, and M. Tofte, editors, Proof, Language and Interaction: Essays in Honour of Robin Milner. The MIT Press, 2000. http://www.di.unipi.it/~ugo/ festschrift.ps.

....of these transformations allows the specification of properties that are not in a natural way input output properties. 4.3. 3 Computer supported Cooperative Work Several contributions to the semantic foundation of Computer supported Cooperative Work have appeared whose formal basis is Tile Logic [GM99] Tiles are rewrite rules with side effects, and they are well suited for modeling coordination languages, since they can be composed both statically and dynamically via possibly complex synchronization and work flow mechanisms. By analogy with rewriting logic, the tile model has purely logical ....

....both statically and dynamically via possibly complex synchronization and work flow mechanisms. By analogy with rewriting logic, the tile model has purely logical presentation, where tiles are considered as suitable sequents subject to simple inference rules. The basic tile model presented in [GM99] is extended in [BMM98c, Bru99] where it is shown how to deal with configurations and observations relying on common auxiliary structures (e.g. for tupling and projecting components) In [FM97] a tile based semantics for located CCS is proposed where the 21 operational and abstract concurrent ....

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F. Gadducci and U. Montanari. The tile model. In G. Plotkin, C. Stirling, and M. Tofte, editors, Proof, Language and Interaction: Essays in Honour of Robin Milner. MIT Press, 1999. To appear.

....to pass from concurrent to concurrent, object oriented agents. x C D t A2 A1 s u1 u2 v1 v2 2 2 2 b b b 1 1 1 a a a B1 B2 Fig. 5. An interactive system for spiral words Our model has some similarities with the tile model studied by Montanari and his Pisa group (see, e.g. Bru99] BrM97] or [GaM99]) but the precise relationship still has to be investigated. We also expect that a logic similar to the spatial logic of [CaG00] may be associated to interaction systems and use for the veri cation of concurrent, object oriented systems. ....

F. Gadducci and U. Montanari. The tile model. In Papers dedicated to R. Milner festschrift. The MIT Press, Cambridge, to appear,

....separation between internal operations or actions on an individual node or agent and their struc27 tural coordination. 4.3. 3 Computer Supported Cooperative Work Several contributions to the semantic foundation of Computer Supported Cooperative Work have appeared whose formal basis is Tile Logic [GM00] Tiles are rewrite rules with side e ects, and they are well suited for modeling coordination languages, since they can be composed both statically and dynamically via possibly complex synchronization and work ow mechanisms. By analogy with rewriting logic, the tile model has purely logical ....

F. Gadducci and U. Montanari. The tile model. In G. Plotkin, C. Stirling, and M. Tofte, editors, Proof, Language and Interaction: Essays in Honour of Robin Milner. MIT Press, 2000. To appear.

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F. Gadducci and U. Montanari. The tile model. In Proof, Language and Interaction: Essays in Honour of Robin Milner, MIT Press, 2000. To appear.

No context found.

F. Gadducci, U. Montanari, The tile model, in: G. Plotkin, C. Stirling, M. Tofte (Eds.), Proof, Language and Interaction: Essays in Honour of Robin Milner, MIT Press, 2000.

No context found.

F. Gadducci, U. Montanari, The tile model, in: G. Plotkin, C. Stirling, M. Tofte (Eds.), Proof, Language and Interaction: Essays in Honour of Robin Milner, MIT Press, 2000.

....notion of a tile. De nition 8. Let H and V be two categories which coincide in their set of objects, which is fn j n 2 lNg. We call H the horizontal category and V the vertical category. The arrows of H are also called con gurations and the arrows of V are called observations. A tile (compare [11]) is of the form s a b ## t where s : n m; t : n 0 m 0 are elements of H, and a : n n 0 ; b : m m 0 are elements of V. Tiles can be depicted as squares (see the leftmost square in Figure 4) Tile Parallel composition Horizontal composition Vertical composition n s ## a ## ....

....c 2 V ; t 1 ; t 2 2 H such that s 1 a c ## t 1 , t 1 c b ## t 2 and t = t 1 ; t 2 (2) if s = s 1 s 2 then there exist a 1 ; a 2 ; b 1 ; b 2 2 V ; t 1 ; t 2 2 H such that s 1 a1 b1 ## t 1 , s 2 a2 b2 ## t 2 , a = a 1 a 2 , b = b 1 b 2 and t = t 1 t 2 . Proposition 4 (cf. [11]) If a tile system satis es the decomposition property, then bisimilarity de ned on its transition system is a congruence. Similar to the case of de Simone [5] or tyft tyxt formats [12] there is a sucient syntactical property ensuring that bisimilarity is indeed a congruence, which is stated in ....

F. Gadducci and U. Montanari. The tile model. In Gordon Plotkin, Colin Stirling, and Mads Tofte, editors, Proof, Language and Interaction: Essays in Honour of Robin Milner. MIT Press, 1999.

....at the expense of a ner notion of observational congruence, which anyway is the coarsest possible, if it must be a bisimulation. In a preliminary version of this paper which appeared as [7] similar concepts and results have been developed for the restricted class of rules in algebraic format [13], and the basic construction of the lifted functor considered only derived rules in DeSimone format [9] Besides adding complete proofs, the present paper generalises these results to quite a wider class of SOS speci cations, using in the de nition of the lifted functor rules in tyft format. 5 2 ....

F. Gadducci and U. Montanari. The tile model. In G. Plotkin, C. Stirling, and M. Tofte, editors, Proof, Language and Interaction: Essays in Honour of Robin 34 Milner. MIT Press, 2000. To appear. Paper available from http://www.di. unipi.it/~ugo/festschrift.ps.

.... systems to enforce security property, e.g. 17, 8] and the approach based on proof carrying code [12] This variety of models has motivated the introduction of more general approaches, like Action Calculi and Control Structures [10] Interaction Categories [1] Rewriting Logic [9] and Tile Logic [38]. All of them abstract at some extent from the concrete syntactical representations of process calculi to develop algebraic, universal models of distributed computing. Among programming languages, there are languages designed to support distributed scope and access such as Obliq [4] and ....

....Esprit working group Appligraph. We also contributed with a total of three chapters to the Handbooks on the subject, edited by Grzegorz Rozenberg. The rst chapter is in the Handbook [14] The others are [19, 44] The work on structured transition systems evolved in a new model, called tile logic [38]. The basic algebraic structure involved is that of a double category. Tiles (i.e. double cells) are rules de ning the behaviour of open con gurations, i.e. system components, which may interact through their interfaces. Rewriting logic (a rather general formalism developed by Jose Meseguer [9] ....

F. Gadducci, U. Montanari. The Tile Model. In: G. Plotkin, C. Stirling and M. Tofte, Eds., Proofs, Languages and Interaction: Essays in Honour of Robin Milner, MIT Press, to appear.

....corresponding to prefixing is proved adequate to model asynchronous calculus [38] We close the section presenting an original contribution of the paper, namely, an encoding of (the closed variant of) the generic action calculus into rewriting logic, and proving its soundness. Tile logic [30] has been proposed by the authors as a general framework for the specification of rule based systems, whose actual behaviour relies on the notions of synchronization and side effects. The main idea is to enrich each rewrite rule with a notion of observation, carrying information on the possible ....

....generic open configurations of reactive systems with coordination. Section 5 has a three part structure. We start reviewing the basic definitions of tile logic, then presenting two case studies that involve languages for process description. The first example is the encoding of ccs proposed in [30]. The second is the encoding of the asynchronous calculus; it is original to this paper, even if it is loosely based on [28] We close the section sketching the encoding of tile logic into (unconditional) rewriting logic [11,58] and briefly surveying term tile logic [10] an extension of the ....

[Article contains additional citation context not shown here]

F. Gadducci and U. Montanari. The tile model. In G. Plotkin, C. Stirling, and M. Tofte, editors, Proof, Language and Interaction: Essays in Honour of Robin Milner. MIT Press, 2000. To appear.

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Fabio Gadducci and Ugo Montanari. The tile model. In Gordon Plotkin, Colin Stirling, and Mads Tofte, editors, Proof, Language and Interaction: Essays in Honour of Robin Milner. MIT Press, 1999. To appear.

No context found.

Fabio Gadducci and Ugo Montanari. The tile model. In Gordon Plotkin, Colin Stirling, and Mads Tofte, editors, Proof, Language and Interaction: Essays in Honour of Robin Milner. MIT Press, 1998. To appear.

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Fabio Gadducci and Ugo Montanari. The tile model. In Gordon Plotkin, Colin Stirling, and Mads Tofte, editors, Proof, Language and Interaction: Essays in Honour of Robin Milner. MIT Press, 1998. To appear. 72 REFERENCES

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F. Gadducci and U. Montanari. The tile model. In G. Plotkin, C. Stirling, and M. Tofte, editors, Proof, Language and Interaction: Essays in Honour of Robin Milner, pages 133--

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F. Gadducci and U. Montanari. The tile model. In G. Plotkin, C. Stirling and M. Tofte, eds., Proof, Language and Interaction: Essays in Honour of Robin Milner, MIT Press, 133--166, 2000.

No context found.

F. Gadducci and U. Montanari. The tile model. In Proof, Language and Interaction: Essays in Honour of Robin Milner. MIT Press, 2000.

No context found.

F. Gadducci and U. Montanari. The tile model. In G. Plotkin, C. Stirling, and M. Tofte, editors, Proof, Language and Interaction: Essays in Honour of Robin Milner. MIT Press, 2000. Also Technical Report TR-27/96, Dipartimento di Informatica, Universita di Pisa, 1996.

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