Georges Gonthier, Martin Abadi, and Jean-Jacques Levy. The geometry of optimal lambda reduction. 1992 ACM Symposium on Principles of Programming Languages, pp. 15-26.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....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 they are optimal, are they ....

....their common characteristics, as well as their shared failures. We give a lower bound on the efficiency of sharing graphs by identifying a class of terms that are normalizable in Theta(n) time, and require Theta(n) fan interactions, but require Omega Gammaq n ) bookkeeping steps. For [GAL92], we analyze this anomaly in terms of the dynamic maintenance of deBruijn indices for intermediate terms. We give another lower bound showing that sharing graphs can do Omega Gammao n ) work (via fan interactions) on graphs that have no fi redexes. Finally, we criticize a proposed cost model ....

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Georges Gonthier, Martin Abadi, and JeanJacques L'evy. The geometry of optimal lambda reduction. 1992 ACM Symposium on Principles of Programming Languages, pp. 15--26.

....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, GAL92a]. Lamping s sharing nodes allow a single, shared representation of a redex family, and thus provide a means to implement L evy s notion of parallel reduction. The varied implementations of this graph reduction framework di er in the underlying bookkeeping technology used to control interactions ....

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

....Lamping introduced a beautiful graph reduc tion 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 [GAL92a]. Lamping s sharing nodes allow a single, shared representation of a redex family, and thus provide a means to implement L evy s notion of parallel reduction. The varied implementations of this graph reduction framework differ in the underlying bookkeeping technology used to control interactions ....

Georges Gonthier, Martin Abadi, and Jean-Jacques L'evy. The geometry of optimal lambda reduction. 1992 ACM Symposium on Principles of Programming Languages, pp. 15--26.

....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, GAL92a]. Lamping s sharing nodes allow a single, shared representation of a redex family, and thus provide a means to implement L evy s notion of parallel reduction. The varied implementations of this graph reduction framework differ in the underlying bookkeeping technology used to control interactions ....

Georges Gonthier, Martin Abadi, and Jean-Jacques L'evy. The geometry of optimal lambda reduction. 1992 ACM Symposium on Principles of Programming Languages, pp. 15--26.

.... 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 augment it with sharing nodes that lazily duplicate pieces of the graph. Traditional sharing nodes, found in implementations of lazy evaluation, allow the ....

....of a term, however, quickly yields intermediate graphs (i.e. representing intermediate terms in the reduction) whose structure is utterly obscure. Formidable problems then exist with respect to readback of a term represented by a graph. In fact, the problem becomes so tortuous that [GAL92] largely dispenses with readback, substituting instead the use of context semantics to read back the (invariant ) Bohm tree of the term. Equally intractible seems the problem of simply finding a fi redex in the graph, which is by contrast absurdly trivial when reducing terms. The difficulty is ....

[Article contains additional citation context not shown here]

Georges Gonthier, Martin Abadi, and Jean-Jacques L'evy. The geometry of optimal lambda reduction. 1992 ACM Symposium on Principles of Programming Languages, pp. 15--26.

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