An Abstract Machine for Strong Call by Value

TL;DR

This paper introduces an abstract machine that implements a strong call-by-value strategy for pure lambda calculus, derived through a series of transformations from existing normalization techniques, and proves its correctness.

Contribution

It presents a novel abstract machine for strong call-by-value, derived via a functional correspondence and correctness proof, expanding the understanding of evaluation strategies in lambda calculus.

Findings

The machine implements a strong call-by-value reduction strategy.

It subsumes the fireball-calculus variant of call by value.

It can be used for checking term convertibility based on partial normalization.

Abstract

We present an abstract machine that implements a full-reducing (a.k.a. strong) call-by-value strategy for pure $\lambda$-calculus. It is derived using Danvy et al.'s functional correspondence from Cr\'egut's KN by: (1) deconstructing KN to a call-by-name normalization-by-evaluation function akin to Filinski and Rohde's, (2) modifying the resulting normalizer so that it implements the right-to-left call-by-value function application, and (3) constructing the functionally corresponding abstract machine. This new machine implements a reduction strategy that subsumes the fireball-calculus variant of call by value studied by Accattoli et al. We describe the strong strategy of the machine in terms of a reduction semantics and prove the correctness of the machine using a method based on Biernacka et al.'s generalized refocusing. As a byproduct, we present an example application of the machine to checking term convertibility by discriminating on the basis of their partially normalized forms.