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22
Soft Linear Logic and Polynomial Time
 THEORETICAL COMPUTER SCIENCE
, 2002
"... We present a subsystem of second order Linear Logic with restricted rules for exponentials so that proofs correspond to polynomial time algorithms, and viceversa. ..."
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Cited by 48 (0 self)
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We present a subsystem of second order Linear Logic with restricted rules for exponentials so that proofs correspond to polynomial time algorithms, and viceversa.
Coinductive Techniques for Operational Equivalence of Interaction Nets
, 1998
"... In this paper we study a notion of operational equivalence for interaction nets, following the recent success of applying methods based on bisimulation to functional and object oriented programming languages. We set up notions of contextual equivalence and bisimilarity and show that they coincide. A ..."
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Cited by 9 (5 self)
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In this paper we study a notion of operational equivalence for interaction nets, following the recent success of applying methods based on bisimulation to functional and object oriented programming languages. We set up notions of contextual equivalence and bisimilarity and show that they coincide. A coinduction principle then gives a simple and robust way of showing when two interaction nets are contextually equivalent. We include several examples to demonstrate the usefulness of the approach, in particular for optimizing interaction nets. 1 Introduction One of the most fundamental notions in programming languages is that of program equivalence: when can one program fragment be replaced by another. A notion of equivalence should be substitutive so that programs remain equivalent in all contexts. Amongst other applications, this facilitates proving properties of programs, and gives a sound basis for program optimization. Interaction nets provide an interesting new perspective as both a...
Type Assignment and Termination of Interaction Nets
"... Interaction nets have proved to be a useful tool for the study of computational aspects of different formalisms (e.g. calculus, term rewriting systems), but they are also a programming paradigm in themselves, and this is actually how they were introduced by Lafont. In this paper we consider semisi ..."
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Cited by 7 (4 self)
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Interaction nets have proved to be a useful tool for the study of computational aspects of different formalisms (e.g. calculus, term rewriting systems), but they are also a programming paradigm in themselves, and this is actually how they were introduced by Lafont. In this paper we consider semisimple interaction nets as a programming language, and present a type assignment system using intersection types. First we show that interactions preserve types (i.e. the system enjoys subject reduction), and we compare this type assignment system with the intersection systems for calculus and term rewriting systems. Then we define a recursion scheme that ensures termination of all interaction sequences. By relaxing the scheme and using the type assignment system, we derive another sufficient condition for termination of interaction nets. Finally, we show that although the type system based on general intersection types is not decidable, its restriction to rank 2 types is, and we give an algo...
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.
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 ...
A Graph Rewriting Semantics for the Polyadic πCalculus (Extended Version)
, 2000
"... We give a hypergraph rewriting semantics for the polyadic πcalculus, based on rewriting rules equivalent to those in the doublepushout approach. The structural congruence of the πcalculus is replaced by hypergraph isomorphism. The correctness of the encoding from the graphbased notation into πc ..."
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Cited by 5 (2 self)
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We give a hypergraph rewriting semantics for the polyadic πcalculus, based on rewriting rules equivalent to those in the doublepushout approach. The structural congruence of the πcalculus is replaced by hypergraph isomorphism. The correctness of the encoding from the graphbased notation into πcalculus can be shown by using an intermediate notation, socalled namebased graph terms, which form a bridge from graphs with explicit connections (by fusing nodes) to process calculi with implicit connections (by common channel names).
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
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
Observational equivalence for the interaction combinators and internal separation
 Proceedings of TERMGRAPH 2006. ENTCS
, 2006
"... We define an observational equivalence for Lafont’s interaction combinators, which we prove to be the least discriminating nontrivial congruence on total nets (nets admitting a deadlockfree normal form) respecting reduction. More interestingly, this equivalence enjoys an internal separation proper ..."
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Cited by 4 (3 self)
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We define an observational equivalence for Lafont’s interaction combinators, which we prove to be the least discriminating nontrivial congruence on total nets (nets admitting a deadlockfree normal form) respecting reduction. More interestingly, this equivalence enjoys an internal separation property similar to that of Böhm’s Theorem for the λcalculus.