On the Relative Usefulness of Fireballs

Beniamino Accattoli (1, 2) , Claudio Sacerdoti Coen (3)

1 PARSIFAL - Proof search and reasoning with logic specifications
2 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
3 DISI - Department of Computer Science and Engineering [Bologna]

In CSL-LICS 2014, Accattoli and Dal Lago [1] showed that there is an implementation of the ordinary (i.e. strong, pure, call-by-name) λ-calculus into models like RAM machines which is polynomial in the number of β-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, that is an intermediary step towards the strong case, and we present three results. First, we adapt useful sharing, refining the meta-theory. Then, we introduce 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 optimisation that leads to an implementation having only a linear overhead with respect to the number of β-steps.

Mots clés: Lambda Calculus; Cost Models; Abstract Machines

Domaines: Logique en informatique [cs.LO]

Beniamino Accattoli, Claudio Sacerdoti Coen. On the Relative Usefulness of Fireballs. 30th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2015, Jul 2015, Kyoto, Japan. ⟨10.1109/LICS.2015.23⟩. ⟨hal-01244833⟩