Optimality and Inefficiency : What Isn't a Cost Model of the Lambda Calculus? (1996)
| Venue: | In Proceedings of the 1996 ACM SIGPLAN International Conference on Functional Programming |
| Citations: | 15 - 2 self |
BibTeX
@INPROCEEDINGS{Lawall96optimalityand,
author = {Julia Lawall and Harry G. Mairson},
title = {Optimality and Inefficiency : What Isn't a Cost Model of the Lambda Calculus?},
booktitle = {In Proceedings of the 1996 ACM SIGPLAN International Conference on Functional Programming},
year = {1996},
pages = {92--101},
publisher = {ACM}
}
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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 efficient? We present a brief survey of these optimal evaluators, identifying 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 interactio...
