On the Relative Usefulness of Fireballs

Beniamino Accattoli; Claudio Sacerdoti Coen

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arXiv · 1505.03791

On the Relative Usefulness of Fireballs

Beniamino Accattoli·Claudio Sacerdoti Coen

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Abstract

In CSL-LICS 2014, Accattoli and Dal Lago showed that there is an implementation of the ordinary (i.e. strong, pure, call-by-name) $\lambda$-calculus into models like RAM machines which is polynomial in the number of $\beta$-steps, answering a long-standing question. The key ingredient was the use of a calculus with useful sharing, a new notion whose complexity was shown to be polynomial, but whose implementation was not explored. This paper, meant to be complementary, studies useful sharing in a call-by-value scenario and from a practical point of view. We introduce the Fireball Calculus, a natural extension of call-by-value to open terms for which the problem is as hard as for the ordinary lambda-calculus. We present three results. First, we adapt the solution of Accattoli and Dal Lago, improving the meta-theory of useful sharing. Then, we refine the picture by introducing the GLAMoUr, a simple abstract machine implementing the Fireball Calculus extended with useful sharing. Its key feature is that usefulness of a step is tested---surprisingly---in constant time. Third, we provide a further optimization that leads to an implementation having only a linear overhead with respect to the number of $\beta$-steps.

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Beniamino Accattoli, Claudio Sacerdoti Coen. 2015-05-14. On the Relative Usefulness of Fireballs. https://arxiv.org/abs/1505.03791

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