From Interpreter to Compiler and Virtual Machine: A Functional Derivation

Abstract

We show how to derive a compiler and a virtual machine from a compositional interpreter. We first illustrate the derivation with two evaluation functions and two normalization functions. We obtain Krivine's machine, Felleisen et al.'s CEK machine, and a generalization of these machines performing strong normalization, which is new. We observe that several existing compilers and virtual machines--e.g., the Categorical Abstract Machine (CAM), Schmidt's VEC machine, and Leroy's Zinc abstract machine--are already in derived form and we present the corresponding interpreter for the CAM and the VEC machine. We also consider Hannan and Miller's CLS machine and Landin's SECD machine.<br /> <br />We derived Krivine's machine via a call-by-name CPS transformation and the CEK machine via a call-by-value CPS transformation. These two derivations hold both for an evaluation function and for a normalization function. They provide a non-trivial illustration of Reynolds's warning about the evaluation order of a meta-language.