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The Name Discipline of Uniform Receptiveness
 Theoretical Computer Science
, 1997
"... In a process calculus, we say that a name x is uniformly receptive for a process P if: (1) at any time P is ready to accept an input at x, at least as long as there are processes that could send messages at x; (2) the input offer at x is functional, that is, all messages received by P at x are appli ..."
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Cited by 58 (4 self)
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In a process calculus, we say that a name x is uniformly receptive for a process P if: (1) at any time P is ready to accept an input at x, at least as long as there are processes that could send messages at x; (2) the input offer at x is functional, that is, all messages received by P at x are applied to the same continuation. In the calculus this discipline is employed, for instance, when modeling functions, objects, higherorder communications, remoteprocedure calls. We formulate the discipline of uniform receptiveness by means of a type system, and then we study its impact on behavioural equivalences and process reasoning. We develop some theory and proof techniques for uniform receptiveness, and illustrate their usefulness on some nontrivial examples.
Geometry of Interaction and Linear Combinatory Algebras
, 2000
"... this paper was quite di#erent, stemming from the axiomatics of categories of tangles (although the authors were aware of possible connections to iteration theories. In fact, similar axiomatics in the symmetric case, motivated by flowcharts and "flownomials" had been developed some years earlier by S ..."
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Cited by 44 (10 self)
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this paper was quite di#erent, stemming from the axiomatics of categories of tangles (although the authors were aware of possible connections to iteration theories. In fact, similar axiomatics in the symmetric case, motivated by flowcharts and "flownomials" had been developed some years earlier by Stefanescu (Stefanescu 2000).) However, the first author realized, following a stimulating discussion with Gordon Plotkin, that traced monoidal categories provided a common denominator for the axiomatics of both the Girardstyle and AbramskyJagadeesanstyle versions of the Geometry of Interaction, at the basic level of the multiplicatives. This insight was presented in (Abramsky 1996), in which Girardstyle GoI was dubbed "particlestyle", since it concerns information particles or tokens flowing around a network, while the AbramskyJagadeesan style GoI was dubbed "wavestyle", since it concerns the evolution of a global information state or "wave". Formally, this distinction is based on whether the tensor product (i.e. the symmetric monoidal structure) in the underlying category is interpreted as a coproduct (particle style) or as a product (wave style). This computational distinction between coproduct and product interpretations of the same underlying network geometry turned out to have been partially anticipated, in a rather di#erent context, in a pioneering paper by E. S. Bainbridge (Bainbridge 1976), as observed by Dusko Pavlovic. These two forms of interpretation, and ways of combining them, have also been studied recently in (Stefanescu 2000). He uses the terminology "additive" for coproductbased (i.e. our "particlestyle") and "multiplicative" for productbased (i.e. our "wavestyle"); this is not suitable for our purposes, because of the clash with Linear Logic term...
Cyclic Lambda Calculi
, 1997
"... . We precisely characterize a class of cyclic lambdagraphs, and then give a sound and complete axiomatization of the terms that represent a given graph. The equational axiom system is an extension of lambda calculus with the letrec construct. In contrast to current theories, which impose restrictio ..."
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Cited by 36 (5 self)
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. We precisely characterize a class of cyclic lambdagraphs, and then give a sound and complete axiomatization of the terms that represent a given graph. The equational axiom system is an extension of lambda calculus with the letrec construct. In contrast to current theories, which impose restrictions on where the rewriting can take place, our theory is very liberal, e.g., it allows rewriting under lambdaabstractions and on cycles. As shown previously, the reduction theory is nonconfluent. We thus introduce an approximate notion of confluence. Using this notion we define the infinite normal form or L'evyLongo tree of a cyclic term. We show that the infinite normal form defines a congruence on the set of terms. We relate our cyclic lambda calculus to the traditional lambda calculus and to the infinitary lambda calculus. Since most implementations of nonstrict functional languages rely on sharing to avoid repeating computations, we develop a variant of our calculus that enforces the ...
Proof Nets for Intuitionistic Linear Logic
 Essential Nets, Research Report
"... Abstract. We present a class of proof nets that are specially designed for Intuitionistic Linear Logic, for which we give a correctness criterion, as well as a cutelimination procedure. The proof of sequentialization uses a special kind of oriented paths. In this paper we present a class of proof o ..."
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Cited by 35 (1 self)
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Abstract. We present a class of proof nets that are specially designed for Intuitionistic Linear Logic, for which we give a correctness criterion, as well as a cutelimination procedure. The proof of sequentialization uses a special kind of oriented paths. In this paper we present a class of proof objects for intuitionistic linear logic with the connectives ⊗, ⊸, � and! 1; in particular we can interpret the simply typed lambda calculus, with or without product types. We call these proof nets essential nets. We will formulate a correctness criterion for them: there is an intrinsic property that characterizes the essential nets that do come from proofs in the sequent calculus; it turns out that every such (correct) essential net represents a large number of sequent proofs that differ by inessential details. Thus essential nets, as should be the case for proof nets in general, have the power of eliminating a lot of the bureaucracy in the sequent calculus. We will give a cutelimination procedure for essential nets which is based on that correctness criterion. That procedure is not one that can be said to be
A Structural Approach to Reversible Computation
 Theoretical Computer Science
, 2001
"... Reversibility is a key issue in the interface between computation and physics, and of growing importance as miniaturization progresses towards its physical limits. Most foundational work on reversible computing to date has focussed on simulations of lowlevel machine models. By contrast, we develop ..."
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Cited by 18 (3 self)
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Reversibility is a key issue in the interface between computation and physics, and of growing importance as miniaturization progresses towards its physical limits. Most foundational work on reversible computing to date has focussed on simulations of lowlevel machine models. By contrast, we develop a more structural approach. We show how highlevel functional programs can be mapped compositionally (i.e. in a syntaxdirected fashion) into a simple kind of automata which are immediately seen to be reversible. The size of the automaton is linear in the size of the functional term. In mathematical terms, we are building a concrete model of functional computation. This construction stems directly from ideas arising in Geometry of Interaction and Linear Logic—but can be understood without any knowledge of these topics. In fact, it serves as an excellent introduction to them. At the same time, an interesting logical delineation between reversible and irreversible forms of computation emerges from our analysis. 1
Geometry of Synthesis  A structured approach . . .
, 2007
"... We propose a new technique for hardware synthesis from higherorder functional languages with imperative features based on Reynolds’s Syntactic Control of Interference. The restriction on contraction in the type system is useful for managing the thorny issue of sharing of physical circuits. We use a ..."
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Cited by 16 (8 self)
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We propose a new technique for hardware synthesis from higherorder functional languages with imperative features based on Reynolds’s Syntactic Control of Interference. The restriction on contraction in the type system is useful for managing the thorny issue of sharing of physical circuits. We use a semantic model inspired by game semantics and the geometry of interaction, and express it directly as a certain class of digital circuits that form a
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 ..."
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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...
Encoding Linear Logic with Interaction Combinators
 Information and Computation
, 2002
"... The purpose of this paper is to demonstrate how Lafont’s interaction combinators, a system of three symbols and six interaction rules, can be used to encode linear logic. Specifically, we give a translation of the multiplicative, exponential and additive fragments of linear logic together with a str ..."
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Cited by 7 (1 self)
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The purpose of this paper is to demonstrate how Lafont’s interaction combinators, a system of three symbols and six interaction rules, can be used to encode linear logic. Specifically, we give a translation of the multiplicative, exponential and additive fragments of linear logic together with a strategy for cutelimination which can be faithfully simulated. Finally, we show briefly how this encoding can be used for evaluating �terms. In addition to offering a very simple, perhaps the simplest, system of rewriting for linear logic and the �calculus, the interaction net implementation that we present has been shown by experimental testing to offer a good level of sharing, in terms of the number of cutelimination steps (resp. ¬reduction steps). In particular it performs better than all extant finite systems of interaction nets.
Encoding Left Reduction in the λCalculus with Interaction Nets
, 2001
"... This paper presents a simple implementation of the calculus in the interaction net paradigm. It is based on a twofold translation. terms are coded (for duplication) or decoded (for execution) and reduction is achieved by switching between these two states: decoding corresponds to head reduction a ..."
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Cited by 4 (0 self)
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This paper presents a simple implementation of the calculus in the interaction net paradigm. It is based on a twofold translation. terms are coded (for duplication) or decoded (for execution) and reduction is achieved by switching between these two states: decoding corresponds to head reduction and encoding to left reduction
CallbyName and CallbyValue as TokenPassing Interaction Nets
 In Proceedings of the 7th International Conference on Typed Lambda Calculi and Applications (TLCA’05
, 2005
"... Abstract. Two common misbeliefs about encodings of the λcalculus in interaction nets (INs) are that they are good only for strategies that are not very well understood (e.g. optimal reduction) and that they always have to deal in a complex way with boxes. In brief, the theory of interaction nets is ..."
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Cited by 4 (2 self)
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Abstract. Two common misbeliefs about encodings of the λcalculus in interaction nets (INs) are that they are good only for strategies that are not very well understood (e.g. optimal reduction) and that they always have to deal in a complex way with boxes. In brief, the theory of interaction nets is more or less disconnected from the standard theory: we can do things in INs that we cannot do with terms, which is true [5, 10]; and we cannot do in INs things that can easily be done with terms. This paper contributes to fighting this misbelief by showing that the standard callbyname and callbyvalue strategies of the λcalculus are encoded in interaction nets in a very simple and extensible way, and in particular that these encodings do not need any notion of box. This work can also be seen as a first step towards a generic approach to derive graphbased abstract machines. 1