John Lamping. An algorithm for optimal lambda calculus reduction. 1990 ACM Symposium on Principles of Programming Languages, pp. 16-30.  Home/Search   Document Not in Database   Summary   Related Articles   Check

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

....nodes or alternatively, if we speak only of the abstract algorithm, the oracle. We remark only that the naive oracle of labelling each sharing node in the initial graph with a unique identi er, to be copied when the sharing node is copied, fails to distinguish the appropriate pairs of nodes (see [Lam90]) Again, since the body of the function x:M does not play any role in this reduction, it can be formally expressed as a local interaction between a fan and a , as described in Figure 7. Note that the type of fan nodes l b a b a b a b a b a a b l l a b b b a a Figure 7: Fan ....

John Lamping. An algorithm for optimal lambda calculus reduction. 1990 ACM Symposium on Principles of Programming Languages, pp. 16-30.

....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, ....

....alternatively, if we speak only of the abstract algorithm, the oracle. We remark only that the naive oracle of labelling each sharing node in the initial graph with a unique identifier, to be copied when the sharing node is copied, fails to distinguish the appropriate pairs of nodes (see [Lam90]) Again, since the body of the function x:M does not play any role in this reduction, it can be formally expressed as a local interaction between a fan and a , as described in Figure 7. Note that the type of fan nodes l b a b a b a b a b a a b l l a b b b a a Figure 7: Fan interaction ....

John Lamping. An algorithm for optimal lambda calculus reduction. 1990 ACM Symposium on Principles of Programming Languages, pp. 16--30.

....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 ....

....a positive node, and reverse concatenated by a negative node. These rules, shown in Figure 6, preserve the fidelity of representation and of readback. d e f ) de df d e f ) ed fd Figure 6: Commuting labels and sharing nodes 3 An invariant on intermediate graphs As observed by Lamping [Lam90], it is not the case that every link in the graph is associated with a unique L evy label. We can state an invariant, however, relating L evy labels to intermediate graphs. This invariant will be essential in accounting for the cost of reductions. Path label Invariant: If there are two distinct ....

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John Lamping. An algorithm for optimal lambda calculus reduction. 1990 ACM Symposium on Principles of Programming Languages, pp. 16--30.

....of the lambda calculus Julia L. Lawall IRISA Campus Universitaire de Beaulieu 35042 Rennes Cedex France Harry G. Mairson y Computer Science Department Brandeis University Waltham, Massachusetts 02254 Abstract We investigate the computational efficiency of the sharing graphs of Lamping [Lam90], Gonthier, Abadi, and L evy [GAL92] and Asperti [Asp94] designed to effect so called optimal evaluation, with the goal of reconciling optimality, efficiency, and the clarification of reasonable cost models for the calculus. Do these graphs suggest reasonable cost models for the calculus If ....

....cultures of algorithmics 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 ....

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John Lamping. An algorithm for optimal lambda calculus reduction. 1990 ACM Symposium on Principles of Programming Languages, pp. 16--30.

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