Jean-Jacques L'evy. Optimal reductions in the lambda-calculus. In J. P. Seldin and J. R. Hindley, editors, To H. B. Curry: Essays in Combinatory Logic, Lambda Calculus and Formalism, pages 159--191. Academic Press, 1980.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... shared but how do we unshare its two uses, namely the respective applications to M and N A more complex example where both sharing and unsharing is needed can be seen in the evaluation of the Scheme code ( lambda (x) x z) x t) lambda (y) lambda (z) z) y) using the substitution model [L ev80, AS85] 3 to be surmounted to make this technology work is to get these two kinds of sharing to work in tandem. Think for a minute about how much effort has gone into static program analysis to get effects like the functionality of call by name, with the efficiency of call by value. For ....

....can push this novel technology. 3 Previous work 3.1 Some brief history A brief history of this research area tells a lot about how theory and practice can meet to build good software artifacts. In the late 1970s, Jean Jacques L evy was working on the idea of shared computation in the calculus [L ev80] he knew what a solution would have to do, but lacked all the algorithmic pieces to put together a solution. The problem was really solved by John Lamping about 1990 [Lam90] using a graph reduction technology that was very similar to one invented by Yves Lafont, who was using it for other ....

Jean-Jacques L'evy. Optimal reductions in the lambda-calculus. In J. P. Seldin and J. R. Hindley, editors, To H. B. Curry: Essays in Combinatory Logic, Lambda Calculus and Formalism, pages 159--191. Academic Press, 1980.

....graphs defined by the algebraic semantics are the ones that normalize to a graph without muxes for which the box nesting property holds. 1. 4 Optimality and other related works Sharing graphs have been introduced by Lamping [Lam90] for the implementation of L evy s optimal reductions of terms [L ev80]. Several refinements of sharing graphs have been successively proposed by Gonthier et al. GAL92a,GAL92b] and by Asperti and Laneve [AL94,Asp95] The work of Gonthier et al. addressed how Lamping s formalism can be interpreted inside the so called Geometry of Interaction (GOI) of Girard [Gir89] ....

....But, this is possible iff the oe reduction ae corresponding to ae s is infinite. iv) Trivial. v) Remind that the normal form of a proper s structure G is equal to R(G) see Proposition 49) 11.3 Optimality The sharing implementations are tightly related to calculus optimal reductions [L ev80] and to their generalization to Interaction Systems [AL94] Anyhow, because of the generality of the rewriting system oe, such a correspondence is restricted to the implementation of the fi rule only (i.e. we cannot say anything on how to optimize the number of fl rules) Let us assume the ....

[Article contains additional citation context not shown here]

Jean-Jacques L'evy. Optimal reductions in the lambda-calculus. In Jonathan P. Seldin and J. Roger Hindley, editors, To H.B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism, pages 159--191. Academic Press, 1980.

.... then r 2 R i implies r 0 2 R i ) Finally, a call by need reduction of N is a sequence of rewritings in which at least a needed cut is reduced at any step (a cut is needed when it, or more precisely a residual of it, appears in any reduction sequence starting from N) Main argument of L evy [L ev80] is that the optimal cost of the reduction of a term is the number of fi reductions of a call by need complete family reduction (in the calculus case, the left most outer most strategy is call by need) We assume the same measure (fi contractions) for proof nets. Remark 10 Any redex of a ....

Jean-Jacques L'evy. Optimal reductions in the lambda-calculus. In Jonathan P. Seldin and J. Roger Hindley, editors, To H.B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism, pages 159--191. Academic Press, 1980.

....family, then r 2 R i implies r 0 2 R i ) Finally, a call by need reduction of N is a sequence of rewritings where at any step we reduce at least a needed cut a cut which appears (more precisely, a residual of which appears) in any rewriting sequence starting from N . Main argument of L evy [L ev80] is that, in the case of calculus, the optimal cost of the reduction of a term may be taken as the number of fi reductions of a call by need complete family reduction (in the calculus case, a call by need strategy is left most outer most) We assume the same measure (fi contractions) for ....

Jean-Jacques L'evy. Optimal reductions in the lambda-calculus. In Jonathan P. Seldin and J. Roger Hindley, editors, To H.B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism, pages 159--191. Academic Press, 1980.

....we will see that the proper sharing graphs defined by it are the ones which normalize to a graph without muxes for which the box nesting property holds. 1. 4 Optimality and other related works Sharing graphs were introduced by Lamping [Lam90] to implement L evy s optimal reductions of terms [L ev80]. Several refinements of them where successively proposed by Gonthier et al. GAL92a,GAL92b] and by Asperti and Laneve [AL94,Asp95] The work of Gonthier et al. addressed how Lamping s formalism could be interpreted inside the so called Geometry of Interaction (GOI) of Girard [Gir89] Asperti ....

....s or fl. But this is possible iff the oe reduction ae corresponding to ae s is infinite. iv) Trivial. v) Remind that the normal form of a proper s structure G is equal to R(G) see Proposition 49) 11.3 Optimality Sharing implementations are tightly related to calculus optimal reductions [L ev80] and to their generalization to Interaction Systems [AL94] Anyhow, because of the generality of the rewriting system oe, such a correspondence is restricted to the implementation of the fi rule only. Let us assume the hypotheses and notations of Theorem 62. A oe s reduction ae s : G oe s G 0 ....

[Article contains additional citation context not shown here]

Jean-Jacques L'evy. Optimal reductions in the lambda-calculus. In Jonathan P. Seldin and J. Roger Hindley, editors, To H.B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism, pages 159--191. Academic Press, 1980.

....using any relativity theory, any quantum theory, or for that matter, any mathematics. Lamping described a graph reduction implementation of the calculus. The implementation provides a new, fine analysis of computation in the calculus, to the point of being optimal in the sense defined in [L ev80]. After trying 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 ....

....associated with various graph representations and graph reduction mechanisms. In a graph, sharing is represented by a fan in. Some time ago, an optimality criterion for calculus reductions was defined. It was soon recognized that sharing of common subexpressions is not sufficient for optimality [Wad71, L ev80, Fie90]. Recently, a generalization of sharing was introduced that does support optimal reductions. The idea is to allow not only fan in but also fan out. Fan in nodes and fan out nodes are drawn Fan in nodes and fan out nodes have symmetrical syntactic and semantic descriptions. As the graphs of ....

[Article contains additional citation context not shown here]

Jean-Jacques L'evy. Optimal reductions in the lambda-calculus. In J.P. Seldin and J.R. Hindley, editors, To H.B. Curry: Essays in Combinatory Logic, Lambda Calculus and Formalism, pages 159--191. Academic Press, 1980.

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Jean-Jacques Levy. Optimal reductions in the lambda-calculus. To H. B. Curry: Essays in Combinatory Logic, Lambda Calculus and Formalism, (Jonathan P. Seldin and J. Roger Hindley, editors), pp. 159{ 191. Academic Press, 1980.

No context found.

Jean-Jacques L'evy. Optimal reductions in the lambda-calculus. To H. B. Curry: Essays in Combinatory Logic, Lambda Calculus and Formalism, (Jonathan P. Seldin and J. Roger Hindley, editors), pp. 159-- 191. Academic Press, 1980.

No context found.

Jean-Jacques L'evy. Optimal reductions in the lambda-calculus. To H. B. Curry: Essays in Combinatory Logic, Lambda Calculus and Formalism, (Jonathan P. Seldin and J. Roger Hindley, editors), pp. 159--191. Academic Press, 1980.

No context found.

Jean-Jacques L'evy. Optimal reductions in the lambda-calculus. To H. B. Curry: Essays in Combinatory Logic, Lambda Calculus and Formalism, (Jonathan P. Seldin and J. Roger Hindley, editors), pp. 159--191. Academic Press, 1980.

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