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The Tile Model
 PROOF, LANGUAGE AND INTERACTION: ESSAYS IN HONOUR OF ROBIN MILNER
, 1996
"... In this paper we introduce a model for a wide class of computational systems, whose behaviour can be described by certain rewriting rules. We gathered our inspiration both from the world of term rewriting, in particular from the rewriting logic framework [Mes92], and of concurrency theory: among the ..."
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Cited by 66 (24 self)
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In this paper we introduce a model for a wide class of computational systems, whose behaviour can be described by certain rewriting rules. We gathered our inspiration both from the world of term rewriting, in particular from the rewriting logic framework [Mes92], and of concurrency theory: among the others, the structured operational semantics [Plo81], the context systems [LX90] and the structured transition systems [CM92] approaches. Our model recollects many properties of these sources: first, it provides a compositional way to describe both the states and the sequences of transitions performed by a given system, stressing their distributed nature. Second, a suitable notion of typed proof allows to take into account also those formalisms relying on the notions of synchronization and sideeffects to determine the actual behaviour of a system. Finally, an equivalence relation over sequences of transitions is defined, equipping the system under analysis with a concurrent semantics, ...
Dactl: An Experimental Graph Rewriting Language
 Proc. 4th International Workshop on Graph Grammars
, 1991
"... This paper gives some examples of how computation in a number of languages may be described as graph rewriting, giving the Dactl notation for the examples shown. It goes on to present the Dactl model more formally before giving a formal definition of the syntax and semantics of the language. 2 Examp ..."
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Cited by 36 (7 self)
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This paper gives some examples of how computation in a number of languages may be described as graph rewriting, giving the Dactl notation for the examples shown. It goes on to present the Dactl model more formally before giving a formal definition of the syntax and semantics of the language. 2 Examples of Computation by Graph Rewriting
Process and Term Tile Logic
, 1998
"... In a similar way as 2categories can be regarded as a special case of double categories, rewriting logic (in the unconditional case) can be embedded into the more general tile logic, where also sideeffects and rewriting synchronization are considered. Since rewriting logic is the semantic basis o ..."
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Cited by 34 (25 self)
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In a similar way as 2categories can be regarded as a special case of double categories, rewriting logic (in the unconditional case) can be embedded into the more general tile logic, where also sideeffects and rewriting synchronization are considered. Since rewriting logic is the semantic basis of several language implementation efforts, it is useful to map tile logic back into rewriting logic in a conservative way, to obtain executable specifications of tile systems. We extend the results of earlier work by two of the authors, focusing on some interesting cases where the mathematical structures representing configurations (i.e., states) and effects (i.e., observable actions) are very similar, in the sense that they have in common some auxiliary structure (e.g., for tupling, projecting, etc.). In particular, we give in full detail the descriptions of two such cases where (net) processlike and usual term structures are employed. Corresponding to these two cases, we introduce two ca...
Explicit Cyclic Substitutions
, 1993
"... In this paper we consider rewrite systems that describe the lambdacalculus enriched with recursive and nonrecursive local definitions by generalizing the `explicit substitutions' used by Abadi, Cardelli, Curien, and Lévy [1] to describe sharing in lambdaterms. This leads to `explicit cyclic ..."
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Cited by 25 (2 self)
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In this paper we consider rewrite systems that describe the lambdacalculus enriched with recursive and nonrecursive local definitions by generalizing the `explicit substitutions' used by Abadi, Cardelli, Curien, and Lévy [1] to describe sharing in lambdaterms. This leads to `explicit cyclic substitutions' that can describe the mutual sharing of local recursive definitions. We demonstrate how this may be used to describe standard binding constructions (let and letrec)  directly using substitution and fixed point induction as well as using `smallstep' rewriting semantics where substitution is interleaved with the mechanics of the following betareductions. With this we hope to contribute to the synthesis of denotational and operational specifications of sharing and recursion.
A rewriting calculus for cyclic higherorder term graphs
 in &quot;2nd International Workshop on Term Graph Rewriting  TERMGRAPH’2004
, 2004
"... graphs ..."
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 14 (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.
Tiles, Rewriting Rules and CCS
"... In [12] we introduced the tile model, a framework encompassing a wide class of computational systems, whose behaviour can be described by certain rewriting rules. We gathered our inspiration both from the world of term rewriting and of concurrency theory, and our formalism recollects many properties ..."
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Cited by 14 (8 self)
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In [12] we introduced the tile model, a framework encompassing a wide class of computational systems, whose behaviour can be described by certain rewriting rules. We gathered our inspiration both from the world of term rewriting and of concurrency theory, and our formalism recollects many properties of these sources. For example, it provides a compositional way to describe both the states and the sequences of transitions performed by a given system, stressing their distributed nature. Moreover, a suitable notion of typed proof allows to take into account also those formalisms relying on the notions of synchronization and sideeffects to determine the actual behaviour of a system. In this work we narrow our scope, presenting a restricted version of our tile model and focussing our attention on its expressive power. To this aim, we recall the basic definitions of the process algebras paradigm [3,24], centering the paper on the recasting of this framework in our formalism.
Graph Rewrite Systems for Program Optimization
, 2000
"... Graph rewrite systems can be used to specify and generate program optimizations. For termination of the systems... ..."
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Cited by 13 (1 self)
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Graph rewrite systems can be used to specify and generate program optimizations. For termination of the systems...
A Learning Mechanism for Logic Programs Using Dynamically Shared Substructures
 In Machine Intelligence 15
, 1995
"... : A reasoning method that proves a predicate logic formula by reducing its graph representation is proposed. Since the method directly reduces a logic formula represented by a graph, it can be understood to selfoptimize a graph representation, meaning that it automatically transforms a logic formu ..."
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Cited by 3 (3 self)
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: A reasoning method that proves a predicate logic formula by reducing its graph representation is proposed. Since the method directly reduces a logic formula represented by a graph, it can be understood to selfoptimize a graph representation, meaning that it automatically transforms a logic formula into an efficient form equivalent to that acquired by ExplanationBased Learning. By sharing the original subgraphs between the learned formulae, reasoning efficiency does not deteriorate even after learning several examples. Therefore, the utility problem is overcome in the sense that no extra search is necessary for macros. The present paper demonstrates these facts in simple list manipulation problems and by proving geometric theories. 1 Introduction Neural networks are superior to knowledge representation due to their natural learning ability. However, in contrast to pattern recognition or voice synthesis, AI applications require structured descriptions with variables, which are not ...