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Rewriting On Cyclic Structures: Equivalence Between The Operational And The Categorical Description
, 1999
"... . We present a categorical formulation of the rewriting of possibly cyclic term graphs, based on a variation of algebraic 2theories. We show that this presentation is equivalent to the wellaccepted operational definition proposed by Barendregt et aliibut for the case of circular redexes, fo ..."
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Cited by 12 (6 self)
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. We present a categorical formulation of the rewriting of possibly cyclic term graphs, based on a variation of algebraic 2theories. We show that this presentation is equivalent to the wellaccepted operational definition proposed by Barendregt et aliibut for the case of circular redexes, for which we propose (and justify formally) a different treatment. The categorical framework allows us to model in a concise way also automatic garbage collection and rules for sharing/unsharing and folding/unfolding of structures, and to relate term graph rewriting to other rewriting formalisms. R'esum'e. Nous pr'esentons une formulation cat'egorique de la r'e'ecriture des graphes cycliques des termes, bas'ee sur une variante de 2theorie alg'ebrique. Nous prouvons que cette pr'esentation est 'equivalente `a la d'efinition op'erationnelle propos'ee par Barendregt et d'autres auteurs, mais pas dons le cas des radicaux circulaires, pour lesquels nous proposons (et justifions formellem...
Traced Premonoidal Categories
, 1999
"... Motivated by some examples from functional programming, we propose a generalization of the notion of trace to symmetric premonoidal categories and of Conway operators to Freyd categories. We show that in a Freyd category, these notions are equivalent, generalizing a wellknown theorem relating trace ..."
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Cited by 7 (0 self)
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Motivated by some examples from functional programming, we propose a generalization of the notion of trace to symmetric premonoidal categories and of Conway operators to Freyd categories. We show that in a Freyd category, these notions are equivalent, generalizing a wellknown theorem relating traces and Conway operators in cartesian categories.
Process Algebra with Feedback
"... We consider process graphs over a set of pins, i.e. with multiple entries and exits. On process graphs modulo bisimulation, we can define all standard process algebra operators plus the feedback operator from flowchart theory. We provide a complete axiomatisation for finite processes. Considering th ..."
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We consider process graphs over a set of pins, i.e. with multiple entries and exits. On process graphs modulo bisimulation, we can define all standard process algebra operators plus the feedback operator from flowchart theory. We provide a complete axiomatisation for finite processes. Considering the onepoint pin structure, we get back standard process algebra. 1980 Mathematics Subject Classification (1985 revision): 68Q55, 68Q10, 68Q45. 1987 CR Categories: F.1.2, D.3.1, F.3.1, D.1.3. Key words & Phrases: process algebra, feedback, pin. Note: The research of the first two authors was supported in part by ESPRIT basic research action 7166, CONCUR2. 1 Introduction Semantics of process theory is often given in terms of graphs. The process graphs considered usually have exactly one entry and exactly one exit. In [BeS94], this was adapted to allow for multiple entries and multiple exits. The resulting model was used to model key constructs of ACP and of the algebra of flownomials [St...