Julia L. Lawall and Harry G. Mairson. Optimality and ineciency: what isn't a cost model of the lambda calculus? 1996 ACM International Conference on Functional Programming, pp. 92-101. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Relating the lambda sigma- and lambda s-Styles of.. - Kamareddine, Ríos (2000) (1 citation) (Correct)
....e.g. environments. Because explicit substitution is closer to real implementations, it has the potential to provide a more accurate cost model. This possibility is particularly interesting in light of the diculty encountered in formulating a useful cost model in terms of graph reduction [LM96, Pey87]. Proof assistants may bene t from explicit substitution, due to the desire to perform substitutions locally and in a formal manner. Local substitutions are needed as follows. Given xx[x: y] one may not be interested in having yy as the result of xx[x: y] but rather only yx[x: y] In other ....
J. L. Lawall and H. Mairson. Optimality and ineciency: What isn't a cost model of the lambda calculus? Proc. 1996 ACM SIGPLAN Int'l Conf. Functional Programming, pages 92-101, 1996.
(Optimal) duplication is not elementary recursive - Asperti, Coppola, Martini (2000) (Correct)
....greater, since the algorithms also perform both duplication (in the abstract algorithm) and bookkeeping. Is it possible to bound the total work as a ( xed) function of the number of shared reductions It is this question that has been behind several contributions by Asperti, Lawall, and Mairson [Asp96, LM96, LM97], culminated in [AM98] De ne the Kalm ar elementary functions K (n) as K0 (n) n and K 1 (n) 2 K (n) Then [AM98] shows that there are terms that can be normalized with n shared reductions, and for which the total work needed to reach the normal form with any algorithm (and ....
Julia L. Lawall and Harry G. Mairson. Optimality and ineciency: What isn't a cost model of the lambda calculus? ACM SIGPLAN Notices, 31(6):92-101, June 1996.
Parallel Beta Reduction is Not Elementary Recursive - Asperti, Mairson (1998) (5 citations) Self-citation (Mairson) (Correct)
....between sharing nodes. A fundamental and unresolved question about this sharing technology, proposed by Lamping and o ered in modi ed form by others, is to understand the computational complexity of sharing as a function of the real work of reduction. In recent years, various papers [Asp96, LM96, LM97] have begun to address this issue. This question concerning algorithm analysis only begs more global questions that one can pose about the inherent complexity of optimal evaluation and parallel reduction by any implementation technology. In this paper, we take major steps towards resolving such ....
....number of graph reduction steps counts not only interactions between , apply, and sharing nodes, but also interactions involving the croissant and bracket nodes used to manage the indices that control the behavior of the sharing nodes. For more information on how this index management works, see [LM96, AG98]. Finally, in renditions of optimal graph reduction rules, there is some ambiguity de ning where reduction ends, and where readback begins. For example, if a graph has no more redexes, and thus represents a normalized term, one way to read back the term is to continue graph reduction ....
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Julia L. Lawall and Harry G. Mairson. Optimality and ineciency: what isn't a cost model of the lambda calculus? 1996 ACM International Conference on Functional Programming, pp. 92-101.
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