Kathail V. Optimal Interpreters for Lambda-calculus based functional languages, PhD thesis, MIT, 1990.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....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 Gonthier s ....

Kathail V. Optimal Interpreters for Lambda-calculus based functional languages, PhD thesis, MIT, 1990.

....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 and the particular ....

Kathail V. Optimal interpreters for lambda-calculus based functional languages, Ph.D. Thesis, MIT, 1990. UEA Norwich, UK Technical Report SYS-C98-04 Z. Khasidashvili and J. Glauert 31

....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 performed by the ....

V. Kathail (1990) Optimal Interpreters for lambda-calculus based functional languages. PhD thesis, MIT.

....little pieces. As Girard points out, boxes are a bridle to parallelism. They are also an obstacle to sharing: the box formalism does not support some sophisticated mechanisms for partial sharing of common subexpressions available in calculus implementations such as Lamping s [4] and Kathail s [5]. These sharing mechanisms are essential for optimality in reductions, and we believe that they can be of practical value. Moreover, boxes complicate the proof theory of linear logic; with boxes, linear logic falls short of giving a fully local account of computation. In this paper we describe a ....

V. Kathail, Optimal interpreters for lambdacalculus based functional languages. PhD thesis, MIT, May 1990.

....of Theoretical Aspects of Computer Science 1994. This work is partially supported by the ESPRIT Basic Research Project 6454 CONFER. A. Asperti and C. Laneve 2 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 performed by the ....

V. Kathail (1990) Optimal Interpreters for lambda-calculus based functional languages. PhD thesis, MIT.

....expressed in initial term, avoiding useless duplications. For a long time, no implementation was able to achieve L evy s performance (see [Fie90] for a quick survey) People started already to doubt of the existence of optimal evaluators, when Lamping and Kathail independently found a solution [Lam90,Ka90]. The graph reduction technique proposed by Lamping, that looks particularly promising for an actual implementation, has been then refined in [GAL92a, GAL92b] These works have put in evidence a nice relation between Lamping s work, Linear Logic [Gi86] and the Geometry of Interaction ....

V. Kathail. Optimal Interpreters for lambda-calculus based functional languages. Interaction Nets. Ph.D Thesis, MIT. 1990.

....to read Girard s papers on the geometry of interaction, Lamping s An Algorithm for Optimal Lambda Calculus Reduction sounds like TV Digest. Nevertheless, it seems fair to say that Lamping s algorithm is rather complicated and obscure. Recently, Kathail proposed another optimal algorithm [Kat90]; we consider it in the full paper. It is our thesis that the geometry of interaction gives the proper understanding of Lamping s system. This view leads to some considerable simplifications, to a semantic basis, and to principled techPage niques for correctness proofs. It also helps us in ....

Vinod Kathail. Optimal interpreters for lambda-calculus based functional languages. PhD thesis, MIT, May 1990.

....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 one step 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 Gonthier s ....

Kathail V. Optimal Interpreters for Lambda-calculus based functional languages, PhD thesis, MIT, 1990.

....in the present paper. Acyclic lambda graphs were already considered in the wellknown thesis of Wadsworth [Wad71] and recently there has been a lot of activity concerning them [GAL92] following a solution of Levy s optimality problem for lambda rewriting [L e80] by Lamping and Kathail [Lam90, Kat90] As yet, no systematic study has been made of lambda graph rewriting with cycles; but work in progress by the authors [AK94] intends to provide a first step, revealing that there is a remarkable contrast with orthogonal term graph rewriting. The latter is confluent, but lambda graph rewriting ....

V. K. Kathail. Optimal Interpreters for Lambda-calculus Based Functional Languages. PhD thesis, Dept. of Electrical Engineering and Computer Science, MIT, 1990.

....position to identify similar redexes whose reduction should somehow be evaluated at once (via a so called parallel fi reduction) by any efficient scheme. Recent research by Lamping, and independently Kathail, has shown that there indeed exist calculus evaluators satisfying L evy s specification [Lam90, Kat90]. Lamping introduced a beautiful graph reduction technology for sharing evaluation contexts dual to the sharing of values. His pioneering insights have been modified and improved in subsequent implementations of optimal reduction, most notably by Asperti, and by Gonthier, Abadi, and L evy [Asp94, ....

Vinod Kathail. Optimal interpreters for lambda-calculus based functional languages. Ph.D. Thesis, MIT, May 1990.

.... should always keep shared those redexes in a expression that have a common origin (e.g. that are copies of a same redex) For a long time, no implementation achieved Levy s performance (see [8] for a quick survey) Only recently, Lamping and Kathail have independently solved the problem [18,13]. Unfortunately, both Levy s theoretical analysis and the reduction techniques proposed by Lamping and Kathail merely focus on the pure calculus. This is a great limitation in view of an actual implementation, since we must eventually face the problem of extending the language with a wider range ....

V. Kathail. Optimal Interpreters for lambda-calculus based functional languages. PhD thesis, MIT, 1990.

....identify similar redexes whose reduction should somehow be evaluated at once (via a so called parallel fi reduction) by any efficient scheme. Recent research by Lamping, and independently Kathail, has shown that there indeed exist calculus evaluators satisfying L evy s specification [Lam90, Kat90]. Lamping s work, in particular, was followed by variants and simplifications proposed by Asperti, and Gonthier, Abadi, and L evy, among others [Asp94, GAL92] The basic framework was to begin with a straightforward graph reduction scheme made up of application ( and abstraction ( nodes, and ....

Vinod Kathail. Optimal interpreters for lambda-calculus based functional languages. Ph.D. Thesis, MIT, May 1990.

....and semantics. But how efficient is optimal reduction To understand its efficiency, we also need to consider reasonable cost models for calculus. It was an open question for some fifteen years whether optimal reduction strategies exist, answered affirmatively by Lamping [Lam90] Kathail [Kat90], and in a simplified way by Gonthier, Abadi, and L evy [GAL92] henceforth, GAL) as well as Asperti [Asp94] The solution of GAL was appealing because it also gave a static semantics to calculus in the spirit of Girard s geometry of interaction [Gir88] this semantics has also been recently ....

Vinod Kathail. Optimal interpreters for lambdacalculus based functional languages. Ph.D. Thesis, MIT, May 1990.

....the correctness of his graph reduction technique. As an aside, Wadsworth also showed that his graph reduction did not capture enough of sharing of expressions to lead to an optimal interpreter. More recently a new graph structure which allows sharing of contexts , has been proposed by Kathail [Kat90] This latter technique leads to provably optimal interpreters for the calculus [L 78] Much of the past work on graph rewriting has been to prove its correctness with respect to either the calculus or Term Rewriting Systems (TRS) We see graph rewriting as a system in its own right, and ....

V.K. Kathail. Optimal Interpreters for Lambda-calculus Based Functional Languages. PhD thesis, Dept. of Electrical Engineering and Computer Science, MIT, 1990.

.... should always keep shared those redexes in a expression that have a common origin (e.g. that are copies of a same redex) For a long time, no implementation achieved L evy s performance (see [9] for a quick survey) Only recently, Lamping and Kathail have independently solved the problem [19, 14]. Unfortunately, both L evy s theoretical analysis and the reduction techniques proposed by Lamping and Kathail merely focus on the pure calculus. This is a great limitation in view of an actual implementation, since we must eventually face the problem of extending the language with a wider range ....

V. Kathail. Optimal Interpreters for lambda-calculus based functional languages. PhD thesis, MIT, 1990.

....evaluator should utilize all the term sharing present in the lambda expression to be reduced, avoiding structure copying and thus avoiding work duplication. The performance criteria proposed fifteen years ago by L evy remained unachieved for a long time, until recently Lamping [105] and Kathail [93] independently developed optimal reduction algorithms. However their solution is rather involved, and later Gonthier, Abadi and L evy [76, 77] greatly simplified it by reengineering it in terms of LL proof nets. What is more important, this gave a better logical foundation to the algorithm, ....

V. Kathail. Optimal Interpreters for Lambda-Calculus Based Functional Languages. PhD thesis, MIT, 1990.

....a result widely known as a folk s theorem . The exact proof is complicated by the necessity of extending the TRS formalism in two new directions. As demonstrated in [5] finding optimal derivations in the full calculus is a much harder problem, and the effective strategies proposed by [11, 13] along the theoretical work of [15] are more complicated than simple lazy strategy. Acknowledgments I thank Jean Jacques L evy for many helpful discussions. I also thank John Bradley Chen and Xavier Leroy for their editorial work. ....

V. K. Kathail, "Optimal Interpreters for Lambdacalculus Based Functional Languages". Communication at the SEMAGRAPH workshop, Paris, April 1990.

....for substitution (the proofs of the logic) i.e. graph rewriting systems. As a first problem we set out to investigate the rewrite property of optimality of rewriting as defined by L evy [L ev78] Although optimal implementations using graph rewriting do exist both for the lambda calculus ([Lam90, Kat90]) and for the more general class of Interaction Systems ( AL92] we think our approach can shed new light on the subject matter. In this light, the work so far can be 38 References characterised as stating conditions on the form of the rewrite rules allowing to reduce optimality from a rewrite ....

V. Kathail. Optimal Interpreters for lambda-calculus based functional languages. PhD thesis, MIT, 1990.

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Kathail V. Optimal Interpreters for Lambda-calculus based functional languages, PhD thesis, MIT, 1990.

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Kathail V. Optimal Interpreters for Lambda-calculus based functional languages, PhD thesis, MIT, 1990.

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