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Interaction Nets and Term Rewriting Systems
, 1998
"... Term rewriting systems provide a framework in which it is possible to specify and program in a traditional syntax (oriented equations). Interaction nets, on the other hand, provide a graphical syntax for the same purpose, but can be regarded as being closer to an implementation since the reductio ..."
Abstract

Cited by 13 (7 self)
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Term rewriting systems provide a framework in which it is possible to specify and program in a traditional syntax (oriented equations). Interaction nets, on the other hand, provide a graphical syntax for the same purpose, but can be regarded as being closer to an implementation since the reduction process is local and asynchronous, and all the operations are made explicit, including discarding and copying of data. Our aim is to bridge the gap between the above formalisms by showing how to understand interaction nets in a term rewriting framework. This allows us to transfer results from one paradigm to the other, deriving syntactical properties of interaction nets from the (wellstudied) properties of term rewriting systems; in particular concerning termination and modularity. Keywords: term rewriting, interaction nets, termination, modularity. 1 Introduction Term rewriting systems provide a general framework for specifying and reasoning about computation. They can be regarde...
From Term Rewriting to Generalised Interaction Nets
, 1996
"... . In this paper we present a system of interaction that generalises Lafont's interaction nets by allowing computation in several nets in parallel and communication through a state. This framework allows us to represent large classes of term rewriting systems, genuine parallel functions, nondetermin ..."
Abstract

Cited by 7 (4 self)
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. In this paper we present a system of interaction that generalises Lafont's interaction nets by allowing computation in several nets in parallel and communication through a state. This framework allows us to represent large classes of term rewriting systems, genuine parallel functions, nondeterminism, communication, sharing, and hence can be used to code features from Standard ML and Concurrent ML. 1 Introduction Term rewriting systems can be regarded as a multiparadigm specification language, or as an abstract model of computation (abstract in the sense that they specify actions but not control; they are free from strategies). Lafont's interaction nets are a graphical framework based on net rewriting which is much closer to a real model of computation in that all the operations are made explicit, including discarding and copying of data. Moreover, interaction nets can be regarded as a distributed model of computation since all reductions are local. In a previous paper [2] we began...
A general theory of sharing graphs
 THEORET. COMPUT. SCI
, 1999
"... Sharing graphs are the structures introduced by Lamping to implement optimal reductions of lambda calculus. Gonthier's reformulation of Lamping's technique inside Geometry of Interaction, and Asperti and Laneve's work on Interaction Systems have shown that sharing graphs can be used to implement a w ..."
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Cited by 4 (3 self)
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Sharing graphs are the structures introduced by Lamping to implement optimal reductions of lambda calculus. Gonthier's reformulation of Lamping's technique inside Geometry of Interaction, and Asperti and Laneve's work on Interaction Systems have shown that sharing graphs can be used to implement a wide class of calculi. Here, we give a general characterization of sharing graphs independent from the calculus to be implemented. Such a characterization rests on an algebraic semantics of sharing graphs exploiting the methods of Geometry of Interaction. By this semantics we can de ne an unfolding partial order between proper sharing graphs, whose minimal elements are unshared graphs. The leastshared instance of a sharing graph is the unique unshared graph that the unfolding partial order associates to it. The algebraic semantics allows to prove that we can associate a semantical readback to each unshared graph and that such a readback can be computed