Section: New Results

Implementations of Strong Call-by-Name, Revisited

Participant : Beniamino Accattoli.

The literature about abstract machines for the strong evaluation (i.e., possibly under abstraction) of the ordinary (i.e., call-by-name) $\lambda$-calculus is scarce. Essentially, there is a single, old work: Crégut's abstract machine [60] (1990), that is an extension of Krivine abstract machine to compute full normal forms. Crégut studies the correctness of the machine by means of an explicit substitutions calculus. In this joint work with Barenbaum and Mazza [17] , Crégut's work is revisited and simplified in the extreme. An alternative, simpler machine is introduced, the Strong Milner abastract machine. Its correctness is studied via linear substitution calculus, a new approach to explicit substitutions developed by Accattoli and Kesner that is much simpler than Crégut's approach. Moreover, a complexity analysis of the machine is provided: its overhead is shown to be linear in the number of steps in the linear substitution calculus and in the size of the inital term.