J. Lamping. An algorithm for optimal lambda-calculus reductions. In Conf. Rec. 17th Ann. ACM Symp. Princ. of Prog. Langs., pages 16--30, 1990. Referenced on pp. 4  Home/Search   Document Not in Database   Summary   Related Articles   Check

....unless there is no other choice, so that it produces a normal form (answer) 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 ....

J. Lamping. An algorithm for optimal lambda calculus reduction. In POPL '90. Proceedings of the Seventeenth Annual ACM Symposium on Principles of Programming Languages, January 17--19, 1990, San Francisco, CA, pages 16--30, New York, NY, USA, 1990. ACM Press.

....language has been designed, # , starting from the implicational fragment of Elementary A#ne Logic. The interest of such a language deals not only in its computational bound, but in the fact that EAL typeable terms can be reduced with the abstract subset of Lamping s optimal reduction algorithm [11] obtaining excellent performances. # is untyped and it can be assigned types which are formulas of EAL through a type assignment system in natural deduction style (NEAL) proving statements (typings) of the shape # NEAL M : A, where the context # assigns types to variables. However the ....

Lamping, J.: An algorithm for optimal lambda calculus reduction. In ACM, ed.: POPL '90. Proceedings of the seventeenth annual ACM symposium on Principles of programming languages, January 17--19, 1990, San Francisco, CA, New York, NY, USA, ACM Press (1990) 16--30

....of the MELL fragment. They reduced Hilbert spaces to simple data structures, known as context semantics, and developed a proofnet technology which implemented the context semantics locally. Reduction on proofnets preserves the semantics, and Lamping s algorithm for optimal reduction of A terms [14] is a method of graph reduction. They further indicated how to read back any part of the BShm tree (normal form) of a A term from its context semantics. Can this program be carried out for full Linear Logic In this paper we extend these result to the MALL fragment (multiplicatives and ....

J. Lamping. An algorithm for optimal lambda-calculus reductions. In POPL'90, pages 16-30. ACM Press, Jan. 1990.

....practical implications and to re ne them as needed. One category of choices concerns the representation of lambda terms. Explicit substitution notations provide only a framework for this and an actual realization has to address many additional issues such as sharing and optimality in reduction [11, 12], the extent of laziness and destructive versus non destructive realization. Another possibility not discussed at all here is that of lifting higher order uni cation directly to such a notation [5] Doing this simpli es the construction and application of substitutions but also necessitates ....

J. Lamping. An algorithm for optimal lambda calculus reduction. In Seventeenth Annual ACM Symposium on Principles of Programming Languages, pages 16-30. ACM Press, 1990.

.... essentially the set of hyperedge replacement rules used in [CR93] The only difference concerns the sharing and discarding of terms, which has to be made explicitly in our approach by special duplicator edges and garbage collection edges, which appear in several graph reduction formalisms, e.g. [Lam90], Laf90] Laf95] The second part of H(R) does not depend on R and is equivalent to an interaction net, see [Laf90] Interaction nets are a generalization of proof nets in linear logic. They are a local and deterministic model of computation, where confluence is guaranteed. The encoding of a ....

.... Delta Delta Delta Delta Delta Delta Delta Delta Delta Delta Delta Delta Delta Delta Fig. 4. H(f; 4) The rule H(f; f) defines f labeled edges as destructors, which select the arguments s 1 ; s n of a term f(s 1 ; s n ) 5 labeled edges act as duplicators (see also[Lam90], Laf90] Laf95] A 4 labeled edge has a contrary effect as the rules H(5;4) and H(f; 4) show. It merges the trees, rooted at its two source nodes, provided that they are equal trees (otherwise it blocks) Thus, the effect of these rules is similar to the folding rules in [HP91] But in ....

J. Lamping. An algorithm for optimal lambda-calculus reductions. In Proceedings of the Seventeenth ACM Symposium on Principles of Programming Languages, pages 16--30. ACM, ACM Press, January 1990.

....also formally proved the correctness of his graph reduction technique. As an aside, Wadsworth also showed that his graph reduction did not capture enough sharing to lead to an optimal interpreter. More recently a new graph structure, which allows sharing of contexts , has been proposed in [14, 17]. This latter technique leads to provably optimal interpreters for the calculus [18] In this paper, however, we are not concerned with optimality questions, and we restrict our attention to argument sharing in a language which is simpler than the calculus. Much of the past work on graph ....

J. Lamping. An algorithm for optimal lambda calculus reduction. In Proc. ACM Conference on Principles of Programming Languages, San Francisco, CA, January 1990.

....di Porta S. Donato 5, Bologna, Italy asperti cs.unibo.it 2 Ecole Normale Sup erieure 45 r. d Ulm, 75005 Paris, France jch clipper.ens.fr Abstract. Considerations from category theory described in [As94] have permitted to add new rewriting rules for optimal reductions of the calculus [Lam90, GAL92a]. These rules produce an impressive improvement in the performance of the reduction system, and provide a first step towards the solution of the well known and crucial problem of accumulation of control operators. In this paper, after an introduction to optimal reductions, we exhibit the ....

....6454 CONFER. the computational overhead introduced for handling sharing; the complexity of beta reduction, which, in the calculus (and all the more so in family reduction) is not an atomic operation (due to the meta operation of substitution) The first problem was solved by Lamping [Lam90] using a complex graph reduction technique. However, he did not provide any measure of the complexity of his normalization algorithm (which actually fails to solve the second problem above) Lamping s graph rewriting rules can be classified in two main groups: 1. the rules involving application, ....

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J. Lamping. An algorithm for optimal lambda calculus reductions. Proc. of the 17th Symposium on Principles of Programming Languages (POPL 90), 16--30. San Francisco. 1990.

....obvious labelling scheme that the reader probably has in mind does not work for the following reason: a single fan out node can itself be shared, thus representing two sharings; an unshared fan in could be paired with one of those, but not with the other. An example of this situation is given in [Lam89]. Let us also remark that all graph rewriting rules in Fig. 15 can be seen as local interactions between pairs of nodes in the graph. Such graph rewriting systems have studied by Lafont, under the name of Interaction Nets. Note in particular that each node has a unique, distinguished port where ....

....a situation that the two brackets match, this notion being analogous to that of pairing in the case of fans. The questions of interest are therefore as follows. First, we must formally define the notion of matching; we do so in section 7. 1 after recalling the basic notions of context semantics [Lam89]. Then, we need a simply and efficiently computable class of brackets that can never match those are the safe operators (section 7.2) which do not match by Theorem 25. Having done that, we can exhibit the new rules proposed, which we call the safe rules, and prove their correctness whenever ....

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J. Lamping. An algorithm for optimal lambda calculus reductions. Internal Report, Xerox Palo-Alto Research Center (PARC). Palo-Alto. 1989.

....graphs, presented by Lee, Jones BenAmram [7] Size change graphs approximate the data ow from one function to another, by capturing size changes of parameters. The dag rewrite mechanism we have presented turns out to have a lot in common with the fan in fan out rewrites presented by Lamping [6], in the quest for optimal reduction in the calculus. The fan in fan outs represent a complex way of synchronising di erent parts of a graph, whereas our dag rewrites only perform a simple use once synchronisation. The rewriting mechanism is also akin to graph substitution in hyper graph ....

Lamping, J. An algorithm for optimal lambda calculus reduction. In POPL '90. Proceedings of the seventeenth annual ACM symposium on Principles of programming languages, January 17-19,

....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. ....

J. Lamping. An algorithm for optimal lambda calculus reduction. In Seventeenth Annual Symposium on Principles of Programming Languages (POPL '90), pages 16--46, San Francisco, California, 1990. ACM Press.

....to bound nets. This formalism was introduced because several proofs in sequent calculus which are not essentially different (see for example the exchange rule or commutable rules) correspond to the same proof net. Nets go beyond logic because they may be used to perform fi reduction in calculus [Lam90, Mac95] or used as a model of calculus as interaction nets [Laf90] However, not every net corresponds to linear logic proofs and a criterion serves to distinguish between bad proof structures and proof nets. Using linear logic with mix rule (saying that two proofs side by side form a proof) this ....

J. Lamping. An algorithm for optimal lambda calculus reduction. In Seventeenth Annual ACM Symposium on Principles of Programming Languages, pages 16--30. ACM, January 1990.

....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. ....

J. Lamping. An algorithm for optimal lambda calculus reduction. In Seventeenth Annual ACM Symposium on Principles of Programming Languages, pages 1630. ACM, January 1990.

....logical theory closer to implementation technology, we hope to make researchers think about the pragmatics of continuations in simple, novel and useful ways. Our methodology is founded on proofnets 1 for multiplicative exponential linear logic, following the beautiful insights of John Lamping [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, ....

J. Lamping. An algorithm for optimal lambda calculus reduction. In Conference Record of the Seventeenth Annual ACM Symposium on Principles of Programming Languages, pages 16-30, San Francisco, California, January 1990.

....from logical theory closer to implementation technology, we hope to make researchers think about the pragmatics of continuations in simple, novel, and useful ways. Our methodology is founded on proofnets for multiplicative exponential linear logic, following the beautiful insights of John Lamping [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, ....

J. Lamping. An algorithm for optimal lambda calculus reduction. In Conference Record of the Seventeenth Annual ACM Symposium on Principles of Programming Languages, pages 16-30, San Francisco, California, January 1990.

....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 ....

J. Lamping. An algorithm for optimal lambda calculus reduction. In 19thAnn. ACM Symp. on Principles of Programming Languages (POPL), pages 16--30, San Francisco, California, 1990. ACM Press.

....every multi step would be represented by contraction of a single redex [L ev78, L ev80] There was no other way Barendregt et al. [BBKV76] showed that there does not exist a onestep optimal 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 ....

Lamping J. An algorithm for optimal lambda calculus reduction. In POPL'90, p.16-30.

.... the same origin , and according to L evy s approach to optimal evaluation, these are the redexes that must be shared in a graph implementation of the calculus. Such implementations UEA Norwich, UK Technical Report SYS C98 04 Z. Khasidashvili and J. Glauert 3 have indeed been achieved by Lamping [Lam90] and Kathail [Kat90] Although in general there may be reductions that are not complete family reductions and that can be decomposed w.r.t. an independent basis, there seems to be no simple characterization of such a class of decomposable reductions independent from the particular rewrite system ....

Lamping, J. An algorithm for optimal lambda calculus reduction. In: Proc. 17th ACM Symp. on Principles of Programming Languages, POPL'90, 1990, pp. 6-30.

.... in contrast, studies optimal (i.e. shortest) computations of terms using their sharing graph representation, which implements the optimal family reduction of lambda terms developed by L evy (L evy 1980) xxviii Introduction xxix and is based on the graph representation of terms originated by Lamping (Lamping 1990). Guerrini introduces a general concept of sharing graph rewriting, and develops a semantic approach for comparing deferent degrees of sharing of nodes in sharing graphs, and the optimal implementation of fi reduction becomes a restricted form of sharing graph rewriting. The technical contribution ....

Lamping, John. 1990. An Algorithm for Optimal Lambda Calculus Reduction. In Proc. Seventeenth POPL, 16--30. San Francisco.

....time cut elimination. This system might serve as a basis for a modular calculus of efficient algorithms. Recent topics include the use of geometry of interaction by Gonthier et al. 55, 56] in a correctness proof for Lamping s graph reduction. A com5 panion reference is Asperti [13] Lamping [68] discovered an optimal graphreduction implementation of the lambda calculus, independently of Girard s work on geometry of interaction (see above) Gonthier et al. show how the geometry of interaction provides a suitable semantic basis for explaining and improving Lamping s system. On the other ....

J. Lamping. An algorithm for optimal lambda calculus reduction. In Proc. 17-th Annual ACM Symposium on Principles of Programming Languages, San Francisco, pages 16--30. ACM Press, New York, NY, January 1990.

....sense . Destructors and constructors respectively corresponds to left and right logical introduction rules, interaction is cut and reduction is cut elimination. Interaction Systems have been primarily motivated by the necessity of extending the practice of optimal evaluators for calculus [Lamping 1990, Gonthier et al. 1992a] to other computational constructs as conditionals and recursion. In this paper we focus on the theoretical aspects of optimal reductions. In particular, we generalize the family relation in [L evy 1978, L evy 1980] thus defining the amount of sharing an optimal ....

....it should be possible to share their reduction, therefore avoiding any duplication of work. For a long time, no implementation was able to achieve the theoretical performance fixed by L evy (see [Field 1990] for a survey) and it is only in recent years that this problem has been finally solved [Lamping 1990, Kathail 1990] In particular, the graph reduction technique proposed by Lamping, and remarkably simplified in [Gonthier et al. 1992a] has put in evidence a restricted set of operators (fan, croissant and bracket) which provide an optimal sharing of common subexpressions. The amount of work ....

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J. Lamping (1990) An algorithm for optimal lambda calculus reductions. In Proceedings 17 th ACM Symposium on Principles of Programmining Languages, pages 16 -- 30.

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J. Lamping. An algorithm for optimal lambda-calculus reductions. In Conf. Rec. 17th Ann. ACM Symp. Princ. of Prog. Langs., pages 16--30, 1990. Referenced on pp. 4

No context found.

J. Lamping. An algorithm for optimal lambda-calculus reductions. In POPL '90 [38], pages 16--30.

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J. Lamping. An algorithm for optimal lambda calculus reduction. In Conference Record of the Seventeenth Annual ACM Symposium on Principles of Programming Languages, pages 16--30, San Francisco, California, January 1990.

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J. Lamping. An algorithm for optimal lambda-calculus reduction. In proceedings of the 17th Annnual ACM Symposium on Principles of Programming Languages, Orlando (Fla., USA), 1990.

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Lamping J. An algorithm for optimal lambda calculus reduction. In Proc. of the 17 th ACM Symposium on Principles of Programming Languages, POPL'90, pp. 16-30, 1990.

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