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Models of Sharing Graphs: A Categorical Semantics of let and letrec
, 1997
"... To my parents A general abstract theory for computation involving shared resources is presented. We develop the models of sharing graphs, also known as term graphs, in terms of both syntax and semantics. According to the complexity of the permitted form of sharing, we consider four situations of sha ..."
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Cited by 62 (10 self)
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To my parents A general abstract theory for computation involving shared resources is presented. We develop the models of sharing graphs, also known as term graphs, in terms of both syntax and semantics. According to the complexity of the permitted form of sharing, we consider four situations of sharing graphs. The simplest is firstorder acyclic sharing graphs represented by letsyntax, and others are extensions with higherorder constructs (lambda calculi) and/or cyclic sharing (recursive letrec binding). For each of four settings, we provide the equational theory for representing the sharing graphs, and identify the class of categorical models which are shown to be sound and complete for the theory. The emphasis is put on the algebraic nature of sharing graphs, which leads us to the semantic account of them. We describe the models in terms of the notions of symmetric monoidal categories and functors, additionally with symmetric monoidal adjunctions and traced
Recursion from Cyclic Sharing: Traced Monoidal Categories and Models of Cyclic Lambda Calculi
, 1997
"... . Cyclic sharing (cyclic graph rewriting) has been used as a practical technique for implementing recursive computation efficiently. To capture its semantic nature, we introduce categorical models for lambda calculi with cyclic sharing (cyclic lambda graphs), using notions of computation by Moggi / ..."
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Cited by 45 (5 self)
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. Cyclic sharing (cyclic graph rewriting) has been used as a practical technique for implementing recursive computation efficiently. To capture its semantic nature, we introduce categorical models for lambda calculi with cyclic sharing (cyclic lambda graphs), using notions of computation by Moggi / Power and Robinson and traced monoidal categories by Joyal, Street and Verity. The former is used for representing the notion of sharing, whereas the latter for cyclic data structures. Our new models provide a semantic framework for understanding recursion created from cyclic sharing, which includes traditional models for recursion created from fixed points as special cases. Our cyclic lambda calculus serves as a uniform language for this wider range of models of recursive computation. 1 Introduction One of the traditional methods of interpreting a recursive program in a semantic domain is to use the least fixedpoint of continuous functions. However, in the real implementations of program...
From Action Calculi to Linear Logic
, 1998
"... . Milner introduced action calculi as a framework for investigating models of interactive behaviour. We present a typetheoretic account of action calculi using the propositionsastypes paradigm; the type theory has a sound and complete interpretation in Power's categorical models. We go on to give ..."
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Cited by 19 (7 self)
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. Milner introduced action calculi as a framework for investigating models of interactive behaviour. We present a typetheoretic account of action calculi using the propositionsastypes paradigm; the type theory has a sound and complete interpretation in Power's categorical models. We go on to give a sound translation of our type theory in the (type theory of) intuitionistic linear logic, corresponding to the relation between Benton's models of linear logic and models of action calculi. The conservativity of the syntactic translation is proved by a modelembedding construction using the Yoneda lemma. Finally, we briefly discuss how these techniques can also be used to give conservative translations between various extensions of action calculi. 1 Introduction Action calculi arose directly from the ßcalculus [MPW92]. They were introduced by Milner [Mil96], to provide a uniform notation for capturing many calculi of interaction such as the ßcalculus, the calculus, models of distribut...
Symmetric Action Calculi
 Theoretical Computer Science
, 1999
"... Many calculi for describing interactive behaviour involve names, nameabstraction and namerestriction. Milner's reflexive action calculi provide a framework for exploring such calculi. It is based on names and nameabstraction. We introduce an alternative framework, the symmetric action calculi, ba ..."
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Cited by 5 (1 self)
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Many calculi for describing interactive behaviour involve names, nameabstraction and namerestriction. Milner's reflexive action calculi provide a framework for exploring such calculi. It is based on names and nameabstraction. We introduce an alternative framework, the symmetric action calculi, based on names, conames and namerestriction (or hiding). Nameabstraction is intepreted as a derived operator. The symmetric framework conservatively extends the reflexive framework. It allows for a natural intepretation of a variety of calculi: we give interpretations for the calculus, the I calculus and a variant of the fusion calculus. We then give a combinatory version of the symmetric framework, in which namerestriction also is expressed as a derived operator. This combinatory account provides an intermediate step between our nonstandard use of names in graphs, and the more standard graphical structure arising from category theory. To conclude, we briey illustrate the connection ...
Description and Verification of Mobile Processes with Graph Rewriting Techniques
"... The aim of this thesis is to describe the semantics of a process calculus by means of hypergraph rewriting, creating a specification mechanism combining modularity of process calculi and locality of graph transformation. Verification of processes is addressed by presenting two methods: barbed congru ..."
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Cited by 5 (4 self)
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The aim of this thesis is to describe the semantics of a process calculus by means of hypergraph rewriting, creating a specification mechanism combining modularity of process calculi and locality of graph transformation. Verification of processes is addressed by presenting two methods: barbed congruence for relating processes displaying the same behaviour and generic type systems, forming a central part of this work. Based on existing work in graph rewriting...