A Functional Correspondence between Evaluators and Abstract Machines

Abstract

We bridge the gap between functional evaluators and abstract machines for the λ-calculus, using closure conversion, transformation into continuation-passing style, and defunctionalization of continuations.We illustrate this bridge by deriving Krivine's abstract machine from an ordinary call-by-name evaluator and by deriving an ordinary call-byvalue evaluator from Felleisen et al.'s CEK machine. The first derivation is strikingly simpler than what can be found in the literature. The second one is new. Together, they show that Krivine's abstract machine and the CEK machine correspond to the call-by-name and call-by-value facets of an ordinary evaluator for the λ-calculus.We then reveal the denotational content of Hannan and Miller's CLS machine and of Landin's SECD machine. We formally compare the corresponding evaluators and we illustrate some relative degrees of freedom in the design spaces of evaluators and of abstract machines for the λ-calculus with computational effects.For the purpose of this work, we distinguish between virtual machines, which have an instruction set, and abstract machines, which do not. The Categorical Abstract Machine, for example, has an instruction set, but Krivine's machine, the CEK machine, the CLS machine, and the SECD machine do not; they directly operate on λ-terms instead. We present the abstract machine that corresponds to the Categorical Abstract Machine.

A Resource-Aware Semantics and Abstract Machine for a Functional Language with Explicit Deallocation

“…For instance, in [4] and [1] a number of such derivations are done. Well known abstract machines for the λ-calculus such as SECD, Krivine's, CLS and CAM are derived and proved correct.…”

“…Definition 8. 1 We say that the environment E and the pair (ρ, S) are equivalent, Given c 0 = (is, h, k 0 , k, S, cs) and S a suffix of S, we denote by c 0 → * S c n a derivation in which all the stacks in configurations c i are never smaller than S . Should the top instruction of a configuration create a smaller stack, then the machine would stop at that configuration.…”

A functional correspondence between call-by-need evaluators and lazy abstract machines

“…Sestoft concentrates on deriving one particular abstract machine out of one natural semantics, whereas the present article is part of a general investigation of a correspondence between evaluators and abstract machines [1,2,7].…”

“…The derivation originates in our previous work [1,7]. It consists of three successive program transformations: closure conversion, CPS transformation, and defunctionalization.…”

“…In previous work [1], we reported a simple derivation that makes it possible to derive Krivine's machine from an ordinary call-by-name evaluator and the CEK machine from an ordinary call-by-value evaluator, and to construct evaluators that correspond to the SECD machine, the CLS machine, the VEC machine, and the CAM. This derivation consists of three successive off-the-shelf program transformations: closure conversion, transformation into continuation-passing style (CPS), and Reynolds's defunctionalization.…”