G. Gonthier, M. Abadi, and J.-J. Levy. The geometry of optimal lambda reduction. In Conf. Rec. 19th Ann. ACM Symp. Princ. of Prog. Langs., pages 15--26, 1992. Referenced on pp. 3, 4  Home/Search   Document Details and Download   Summary   Related Articles   Check

....if there is one. An optimal evaluator shares redexes (procedure calls) in a technically maximal sense: the problem here is that evaluation can easily duplicate redexes, for example in (#x.xx) #w.w)y) John Lamping [12] found the algorithm that Levy specified. Then Gonthier, Abadi, and Levy [9, 10] made a lovely discovery: they gave a denotational semantics to Lamping s algorithm, called context semantics, and showed that it was equivalent to Jean Yves Girard s geometry of interaction (GoI) 8] Girard s GoI is an abstract mathematical notion, employing a lot of higher mathematics that ....

....form of S. Consider a term (#x.E)F ; focus on the contexts that travel on the wire down from the node to the function #x.E, and on the same wire up from the function to the node. First, a call is made down to the function; if The generation of Op moves from Pl answers is called shunting in [9], evoking a train at a head variable shunting o# a track of applications to one of its arguments. its head variable h 0 is the parameter, a context travels up that is the address . of the variable. Then the call is made to the argument F ; if its head variable h 1 , is bound, its address is ....

G. Gonthier, M. Abadi, and J.-J. Levy. The geometry of optimal lambda reduction. In Conference record of the Nineteenth Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages: papers presented at the symposium, Albuquerque, New Mexico, January 19--22, 1992, pages 15--26, New York, NY, USA, 1992. ACM Press.

....property that has proved surprisingly difficult to capture in a rewrite system. Another joint paper by Gonthier, Abadi and Levy has exposed links between this algorithm and linear logic, a relationship that reveals deep connections between Levy labelling and Girard s Geometry of Interaction [GAL92a]. Andrea Asperti and Stefano Guerrini have implemented a simple compiler, the B ohm machine, for a pure functional language whose implemented reduction strategy is Levy optimal; the implementation is described in their book [AG98] We call this family of graphs inspired by Lamping s formalism ....

.... a pure functional language whose implemented reduction strategy is Levy optimal; the implementation is described in their book [AG98] We call this family of graphs inspired by Lamping s formalism partial sharing graphs, following the terminology of Gonthier, Abadi and Levy in their joint paper [GAL92a]. The concurrent pattern matching problem arises in the design of a compiler with similar aims to that described in Alan Bawden s PhD thesis: namely to compile a typical high level programming language into an executable capable of being run on a cluster of machines in a manner that permits very ....

G. Gonthier, M. Abadi, and J.-J. Levy. The geometry of optimal lambda reduction. In Proc. 19th Annual Symposium on Principles of Programming Languages, pages 15--26. ACM Press, 1992.

....spine redex; and when doing this reduction some other tricks are employed in order to keep subexpressions shared as long as possible. The properties of this strategy would surely be worth a closer study; Grue (personal communication) has not investigated the issue further. in [Lam90] which [GAL92] attempts to elaborate on) an algorithm for graph reduction of # expressions is given which attempts to 36 avoid duplication of computation by keeping track of how redices propagate on the other hand, accidental sharing (that is redices which are identical but not copies of the same ....

Georges Gonthier, Mart in Abadi, and Jean-Jacques Levy. The geometry of optimal lambda reduction. In ACM Symposium on Principles of Programming Languages, pages 15--26, 1992.

....property that has proved surprisingly difficult to capture in a rewrite system. Another joint paper by Gonthier, Abadi and Levy has exposed links between this algorithm and linear logic, a relationship that reveals deep connections between Levy labelling and Girard s Geometry of Interaction [GAL92a]. Andrea Asperti and Stefano Guerrini have implemented a simple compiler, the B ohm machine, for a pure functional language whose implemented reduction strategy is Levy optimal; the implementation is described in their book [AG98] This paper proposes a graph grammar framework, the static port ....

G. Gonthier, M. Abadi, and J.-J. Levy. The geometry of optimal lambda reduction. In Proc. 19th Annual Symposium on Principles of Programming Languages, pages 15--26. ACM Press, 1992.

....by types can be used to obtain a more refined equivalence relation between nets, recovering the results of [2] We remark that interaction nets are also used as an object language for the coding of other rewriting systems. The calculus is perhaps the most studied example of this (see e.g. [4, 9]) Our results are also applicable here, so we have a proof technique for optimizations of such systems. The paper is organized as follows. In the next section we set up the definition of interaction nets and define our evaluation strategy. Section 3 sets up to notion of bisimilarity. In Section ....

Georges Gonthier, Martn Abadi, and Jean-Jacques Levy. The geometry of optimal lambda reduction. In Proceedings of the 19th ACM Symposium on Principles of Programming Languages (POPL'92), pages 15--26. ACM Press, January 1992.

....This imposes a synchronization among edges and hinders a completely local view of the computation. It is therefore interesting that we can restrict such code duplications to a small constant number of edges. In this respect, we are mainly inspired by local implementations of linear logic boxes [7] and Parrow s trios [18] In our solos calculus, boxes may be decomposed to boxes of three edges, without a ecting the expressiveness: Theorem 12 (Decomposition) eu) n Y i=1 i ) z i 1 i n ) n Y i=1 (eu) z i e u j i j z i 1 e u) 9 z y x z y x Fig. 6. The edge box ....

G. Gonthier, M. Abadi, and J.-J. Levy. The geometry of optimal lambda reduction. In Proc. of POPL '92, pages 15-26. ACM Press, 1992.

....by types can be used to obtain a more re ned equivalence relation between nets, recovering the results of [3] We remark that interaction nets are also used as an object language for the coding of other rewriting systems. The calculus is perhaps the most studied example of this (see e.g. [7,14]) Our results are also applicable here, so we have a proof technique for optimizations of such systems. Related Work. Surprisingly, there is very little in the literature about equivalence of interaction nets. Only ad hoc techniques, or very restrictive no2 tions like having the same normal ....

G. Gonthier, M. Abadi, and J.-J. Levy. The geometry of optimal lambda reduction. In Proceedings of the 19th ACM Symposium on Principles of Programming Languages (POPL'92), pages 15-26. ACM Press, January 1992.

....restriction, the formalism enjoys strong local con uence. Although the system has been introduced as a visual, simple, and inherently parallel programming language, translations have been given of other formalisms into Interaction Nets, speci cally term rewriting systems [1] and the calculus [2, 4]. When used as an intermediate implementation language for these systems, Interaction Nets allow to keep a close control on the sharing of reductions. Interaction Nets have always seemed to be particularly adequate for being implemented in parallel, since there can never be interference between ....

Georges Gonthier, Martn Abadi, and Jean-Jacques Levy. The geometry of optimal lambda reduction. In Proceedings of the 19th ACM Symposium on Principles of Programming Languages (POPL'92), pages 15-26. ACM Press, January 1992.

....seen a number of developments in the use of interaction nets, both as a programming and implementation language. There are now many techniques for reasoning about interaction nets [1, 7] implementations [10] and also encodings of other rewriting systems such as linear logic [9, 5] calculus [8, 4], term rewriting systems [2] One of the main aspects of interaction nets is that they are very simple, and moreover they capture all of the low level computational details. For instance, the encoding of the calculus requires that the substitution propagation, including duplication and erasing, ....

G. Gonthier, M. Abadi, and J.-J. L'evy. The geometry of optimal lambda reduction. In Proceedings of the 19th ACM Symposium on Principles of Programming Languages (POPL'92), pages 15--26. ACM Press, January 1992.

....no more than 3 auxiliary ports. Keywords: proof net, interaction net, combinator, universal system. 1 Introduction In [6] Yves Lafont introduces interaction nets, a programming paradigm inspired by Girard s proof nets for linear logic [3] Some translations from calculus into interaction nets [9, 4, 5] or from proof nets [7, 10, 2, 1, 11] show that universal interaction systems are interesting for computation. We can explain this interest for these translations by the fact that computation with interaction nets is purely local and naturally confluent. Reductions can be made in parallel. ....

....fact that computation with interaction nets is purely local and naturally confluent. Reductions can be made in parallel. Moreover, the number of steps that are necessary to reduce completely a net is independent of the way one may choose. From the point of view of calculus, translations used in [4, 5] captures optimal reduction. In [8] Lafont introduces a universal interaction system with only three different symbols fl, ffi and ffl. ffi and ffl are respectively a duplicator and an eraser and fl is a constructor. This system preserves the complexity of computation for a particular system. ....

G. Gonthier, M. Abadi, and J.-J. Levy. The geometry of optimal lambda reduction. In Proceedings of the Nineteenth Annual Symposium on Principles of Programming Languages (POPL '90), pages 15--26, Albuquerque, New Mexico, January 1992. ACM Press.

....system, syntax analyser, grammar, symbolic evaluation, data specialization. 1 Introduction This paper describes an attempt to mix parallelism and partial evaluation. This is motivated by the increasing interest for parallelism based on linear logic [Gir87] The geometry of interaction [Lam90, GAL92, Abr90], interaction nets [Laf90] games semantics [Bla, LS91] are promising theories for understanding concurrency and relation between processes. We have already worked on partial evaluation of interaction nets [Bec92] However, here, we are interesting to know if classical partial evaluation (i.e. ....

G. Gonthier, M. Abadi, and J.J. L#vy. The geometry of optimal lambda reduction. In Proceedings of the Nineteenth ACM Symposium om Principles of Programming Languages, pages 1526. ACM, 1992.

.... what may be broadly called functional programming (often involving certain aspects of parallelism) computation is seen as term reduction corresponding to proof reduction (i.e. to the process of cut elimination) Recent work in this area includes Abramsky [1] Benton et al. 6] Gonthier et al. [17, 18], Chirimar et al. 9, 10] and Danos and Regnier [12] On the other hand, in what may be broadly called logic programming (again, often involving concurrency) computation is seen as cut free proof search in certain linear logic theories. From this latter perspective, the cut elimination property ....

G. Gonthier, M. Abadi, and J.-J. Levy. The geometry of optimal lambda reduction. In Proc. 19-th Annual ACM Symposium on Principles of Programming Languages, Albuquerque, New Mexico. ACM Press, New York, NY, January 1992.

.... [20] who realized Jean Jacques L evy s speci cation of correct, optimal reduction for the calculus [21] and of Gonthier, Abadi, and L evy, who reinterpreted Lamping s insights in the guise of Girard s geometry of interaction, and the related embedding of intuitionistic logic in linear logic [14, 15]. Linear logic [12, 13] provides an ideal substrate for the implementation of control operators, as it makes no asymmetric distinctions between inputs and outputs, or analogous expressions and continuations. We extend the optimal reduction technology to implement explicit control and sharing of ....

.... a unit cost operation [3] In summary, all of the translations we outline possess a simple graph reduction on translated terms (cut elimination for linear logic) a consistent semantics that is preserved by reduction (geometry of interaction, via the so called context semantics of Gonthier [14]) and a mechanism whereby continuations can be incrementally evaluated (optimal reduction) The situation of this technology within multiplicative exponential linear logic ensures that the semantic characterization given is equivalent to the operational semantics of graph reduction. Viewing data ....

[Article contains additional citation context not shown here]

G. Gonthier, M. Abadi, and J.-J. Levy. The geometry of optimal lambda reduction. In Conference record of the Nineteenth Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, pages 15-26, Albuquerque, New Mexico, January 1992.

.... [17] who realized Jean Jacques L evy s speci cation of correct, optimal reduction for the calculus [18] and of Gonthier, Abadi, and L evy, who reinterpreted Lamping s insights in the guise of Girard s geometry of interaction, and the related embedding of intuitionistic logic in linear logic [12, 13]. Linear logic [11] provides an ideal substrate for the implementation of control operators, as it makes no asymmetric distinctions between inputs and outputs, or analogous expressions and continuations. We extend the optimal reduction technology to implement explicit control and sharing of ....

....the sharing of continuations. In summary, all of the translations we outline possess a simple graph reduction on translated terms (cut elimination for linear logic) a consistent semantics that is preserved by reduction (geometry of interaction, via the so called context semantics of Gonthier [12]) and a mechanism whereby continuations can be incrementally evaluated (optimal reduction) The situation of this technology within multiplicative exponential linear logic ensures that the semantic characterization given is equivalent to the operational semantics of graph reduction. Viewing data ....

[Article contains additional citation context not shown here]

G. Gonthier, M. Abadi, and J.-J. Levy. The geometry of optimal lambda reduction. In Conference record of the Nineteenth Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, pages 15-26, Albuquerque, New Mexico, January 1992.

....This imposes a synchronization among edges and hinders a completely local view of the computation. It is therefore interesting that we can restrict such code duplications to a small constant number of edges. In this respect, we are mainly inspired by local implementations of linear logic boxes [7] and Parrow s trios [15] In our calculus of solos, boxes may be decomposed to boxes of three edges, without a ecting the expressiveness: Theorem 22 (Decomposition) eu) n Y i=1 i ) z i 1 i n ) n Y i=1 (eu) z i e u j i j z i 1 e u) where i are solos, z i , 1 i n ....

G. Gonthier, M. Abadi, and J.-J. Levy. The geometry of optimal lambda reduction. In POPL '92. Proceedings of the nineteenth annual ACM Symposium on Principles of Programming Languages, pages 15-26. ACM Press, 1992. 18

.... by cut elimination (see [3] More abstractly, the presentation of the GoI may be generalized in the framework of traced monoidal categories [10] Because of its local feature, the GoI has proved to be a useful tool for studying the theory and implementation of optimal reduction of the calculus [9, 2]. It is also strongly connected to some work on games semantics for Linear Logic and PCF (starting with [1] Maybe the most exciting use of the locality of GoI is the current work, aiming at using it for implementing some parallel execution scheme [12] Although the GoI has been very present in ....

Georges Gonthier, Martin Abadi, and Jean-Jacques Levy. The geometry of optimal lambda reduction. In Proceedings of the 19 th Annual ACM Symposium on Principles of Programming Languages, pages 15-26. Association for Computing Machinery, ACM Press, 1992.

....which is the natural deduction of Intuitionistic Logic. Using different translations of the # calculus into Proof Nets, new abstract machines have been proposed, exploiting the Geometry of Interaction and the Dynamic Algebras [17, 2, 9] culminating in the recent workson optimal reduction [18, 26]. In this paper, we study the relationship between a calculus with explicit substitutions suggested in [29, 30] to study leftmost derivations in the # calculus and deeply studied, independently, in [34, 5] as the #x calculus. We define a typed version of #x and we show how to translate it into ....

G. Gonthier, M. Abadi, and J.-J. Levy. The geometry of optimal lambda reduction. In 19thAnn. ACM Symp. on Principles of Programming Languages(POPL), pages 15--26, Albuquerque, New Mexico, 1992. ACM Press.

....recursive fi reduction strategy on terms. Such an implementation has indeed been achieved by Lamping [Lam90] and Kathail [Kat90] reviving interest in optimal graph reduction. Maranget [Mar91] generalized L evy s optimality theory to Orthogonal Term Rewriting Systems (OTRSs) Gonthier et al. [GAL92] simplified Lamping s technique, and Asperti and Laneve generalized both L evy s optimality theory, and Gonthier s implementation of it, to Interaction Systems, which cover most of the languages with a constructor destructor discipline [AsLa93, AsLa96] Recently, van Oostrom has generalized the ....

Gonthier G., Abadi M., L'evy J.-J. The geometry of optimal lambda reduction. In: POPL'92, p.15-26.

No context found.

G. Gonthier, M. Abadi, and J.-J. Levy. The geometry of optimal lambda reduction. In Conf. Rec. 19th Ann. ACM Symp. Princ. of Prog. Langs., pages 15--26, 1992. Referenced on pp. 3, 4

No context found.

G. Gonthier, M. Abadi, and J.-J. L evy. The geometry of optimal lambda reduction. In Conf. Rec. 19th Ann. ACM Symp. Princ. of Prog. Langs., pages 15--26, 1992.

No context found.

G. Gonthier, M. Abadi, and J.-J. Levy. The geometry of optimal lambda reduction. In Proc. 19-th Annual ACM Symposium on Principles of Programming Languages, Albuquerque, New Mexico. ACM Press, New York, NY, January 1992.

No context found.

G. Gonthier, M. Abadi, and J.-J. Levy, The geometry of optimal lambda reduction. In Principles of Programming Languages (POPL), ACM Press, Albuquerque, New Mexico, January 1992.

No context found.

G. Gonthier, M. Abadi, and J.-J. Levy. The geometry of optimal lambda reduction. In Conference record of the Nineteenth Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, pages 15--26, Albuquerque, New Mexico, January 1992.

No context found.

M. Abadi G. Gonthier and J.-J. L evy. The geometry of optimal lambda reduction. In proceedings of the 19th Annnual ACM Symposium on Principles of Programming Languages (POPL'92), ACM Press., pages 15-26, 1992.

No context found.

Georges Gonthier, Martin Abadi, and Jean-Jacques Levy. The geometry of optimal lambda reduction. 1992 POPL Conference.

First 50 documents  Next 50

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC