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.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.

Explaining the lazy Krivine machine using explicit substitution and addresses

“…More recently, Ager, Biernacki, Danvy, and Midtgaard have addressed the problem of deriving abstract machines, including Krivine's machine, using continuation passing style transformations applied to evaluators and interpreters of the λ-calculus [3,4]. This is a slightly different approach than the one we have chosen here, because it relates programs (interpreters and abstract machines) that implement the same reduction strategy.…”

Calculating correct compilers

“…The fundamental difference to our work is best understood by looking at the derivation of abstract machines in Ager et al (2003a), on which their later work (Ager et al, 2003b) is based. We formulated our original calculational approach in sections 2.1 to 2.4 as the combination of three transformations steps that first introduce a stack, then a continuation, and finally defunctionalise.…”

“…From Interpreter to Compiler and Virtual Machine: A Functional Derivation (Ager et al, 2003b) Another approach to deriving compilers from semantics has been developed by Ager et al (2003b). In this approach, one begins with a definitional interpreter, from which an abstract machine is derived by first rewriting the semantics in continuationpassing style and then defunctionalising.…”

“…The idea of calculating compilers in this manner has been explored by a number of authors; for example, see Wand (1982a); Meijer (1992); Ager et al (2003b). However, it has traditionally been viewed as an advanced topic that requires considerable knowledge and experience with concepts such as continuations and defunctionalisation (Reynolds, 1972).…”

Cutting Out Continuations

“…These two transformations are often applied together in sequence, for example to transform high-level denotational semantics for programming languages into low-level implementations such as abstract machines or compilers [12,13,11,1,2].…”