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A 2Categorical Presentation of Term Graph Rewriting
 CATEGORY THEORY AND COMPUTER SCIENCE, VOLUME 1290 OF LNCS
, 1997
"... It is wellknown that a term rewriting system can be faithfully described by a cartesian 2category, where horizontal arrows represent terms, and cells represent rewriting sequences. In this paper we propose a similar, original 2categorical presentation for term graph rewriting. Building on a re ..."
Abstract

Cited by 34 (17 self)
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It is wellknown that a term rewriting system can be faithfully described by a cartesian 2category, where horizontal arrows represent terms, and cells represent rewriting sequences. In this paper we propose a similar, original 2categorical presentation for term graph rewriting. Building on a result presented in [8], which shows that term graphs over a given signature are in onetoone correspondence with arrows of a gsmonoidal category freely generated from the signature, we associate with a term graph rewriting system a gsmonoidal 2category, and show that cells faithfully represent its rewriting sequences. We exploit the categorical framework to relate term graph rewriting and term rewriting, since gsmonoidal (2)categories can be regarded as "weak" cartesian (2)categories, where certain (2)naturality axioms have been dropped.
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 ..."
Abstract

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 ...