The Useful MAM, a Reasonable Implementation of the Strong λ-Calculus

It has been a long-standing open problem whether the strong lambda-calculus is a reasonable computational model, i.e. whether it can be implemented within a polynomial overhead with respect to the number of beta-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 lambda-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 lambda-calculus is reasonable and an improvement on the technology for implementing strong evaluation.