The Useful MAM, a Reasonable Implementation of the Strong $\lambda$-Calculus

Beniamino Accattoli (1, 2)

1 PARSIFAL - Proof search and reasoning with logic specifications
2 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]

It has been a long-standing open problem whether the strong λ-calculus is a reasonable computational model, i.e. whether it can be implemented within a polynomial overhead with respect to the number of β-steps on models like Turing machines or RAM. Recently, Accattoli and Dal Lago solved the problem by means of a new form of sharing, called useful sharing, and realised via a calculus with explicit substitutions. This paper presents a new abstract machine for the strong λ-calculus based on useful sharing, the Useful Milner Abstract Machine, and proves that it reasonably implements leftmost-outermost evaluation. It provides both an alternative proof that the λ-calculus is reasonable and an improvement on the technology for implementing strong evaluation.

Domaines: Logique en informatique [cs.LO]

Beniamino Accattoli. The Useful MAM, a Reasonable Implementation of the Strong $\lambda$-Calculus. 23rd International Workshop on Logic, Language, Information, and Computation (WoLLIC 2016), Aug 2016, Puebla, Mexico. pp.1 - 21, ⟨10.1007/978-3-662-52921-8_1⟩. ⟨hal-01425534⟩