Abstract machines for programming language implementation

Landin's SECD machine was the first abstract machine for the λ-calculus viewed as a programming language. Both theoretically as a model of computation and practically as an idealized implementation, it has set the tone for the subsequent development of abstract machines for functional programming languages. However, and even though variants of the SECD machine have been presented, derived, and invented, the precise rationale for its architecture and modus operandi has remained elusive. In this article, we deconstruct the SECD machine into a λ-interpreter, i.e., an evaluation function, and we reconstruct λ-interpreters into a variety of SECD-like machines. The deconstruction and reconstructions are transformational: they are based on equational reasoning and on a combination of simple program transformations-mainly closure conversion, transformation into continuation-passing style, and defunctionalization.The evaluation function underlying the SECD machine provides a precise rationale for its architecture: it is an environment-based eval-apply evaluator with a callee-save strategy for the environment, a data stack of intermediate results, and a control delimiter. Each of the components of the SECD machine (stack, environment, control, and dump) is therefore rationalized and so are its transitions.The deconstruction and reconstruction method also applies to other abstract machines and other evaluation functions. It makes it possible to systematically extract the denotational content of an abstract machine in the form of a compositional evaluation function, and the (small-step) operational content of an evaluation function in the form of an abstract machine.

Section: Introductionmentioning

confidence: 99%

A Rational Deconstruction of Landin's SECD Machine

Danvy

2003

“…Designing abstract machines is a favorite among functional programmers [14]. On the one hand, few abstract machines are actually derived with meaningpreserving steps, and on the other hand, few abstract machines are invented from scratch.…”

Section: Related Workmentioning

confidence: 99%

A Functional Correspondence between Call-by-Need Evaluators and Lazy Abstract Machines

Ager¹,

Danvy²,

Midtgaard³

2004

We bridge the gap between compositional evaluators and abstract machines for the lambda-calculus, using closure conversion, transformation into continuation-passing style, and defunctionalization of continuations. This article is a followup of our article at PPDP 2003, where we consider call by name and call by value. Here, however, we consider call by need.We derive a lazy abstract machine from an ordinary call-by-need evaluator that threads a heap of updatable cells. In this resulting abstract machine, the continuation fragment for updating a heap cell naturally appears as an 'update marker', an implementation technique that was invented for the Three Instruction Machine and subsequently used to construct lazy variants of Krivine's abstract machine. Tuning the evaluator leads to other implementation techniques such as unboxed values. The correctness of the resulting abstract machines is a corollary of the correctness of the original evaluators and of the program transformations used in the derivation.

“…As observed by Diehl, Hartel, and Sestoft [14], research on abstract machines has chiefly focused on developing new machines and proving them correct. The thrust of our work is to explore a correspondence between interpreters and abstract machines [2,4,6,9] that takes its roots in Reynolds seminal work on definitional interpreters [30].…”

Section: Related Workmentioning

confidence: 99%

“…Diehl, Hartel, and Sestoft's overview of abstract machines for programming-language implementation [14] concluded on the need to develop a theory of abstract machines. In previous work [2,9], we have attempted to contribute to this theory by identifying a correspondence between interpreters (i.e., evaluation functions in the sense of denotational semantics) and abstract machines (i.e., transition functions in the sense of operational semantics).…”

Section: Introductionmentioning

confidence: 99%

A Functional Correspondence between Monadic Evaluators and Abstract Machines for Languages with Computational Effects

Ager¹,

Danvy²,

Midtgaard³

2004

Abstract. We extend our correspondence between evaluators and abstract machines from the pure setting of the λ-calculus to the impure setting of the computational λ-calculus. We show how to derive new abstract machines from monadic evaluators for the computational λ-calculus. Starting from (1) a generic evaluator parameterized by a monad and (2) a monad specifying a computational effect, we inline the components of the monad in the generic evaluator to obtain an evaluator written in a style that is specific to this computational effect. We then derive the corresponding abstract machine by closure-converting, CPS-transforming, and defunctionalizing this specific evaluator. We illustrate the construction with the identity monad, obtaining yet again the CEK machine, and with a lifted state monad, obtaining a variant of the CEK machine with error and state.In addition, we characterize the tail-recursive stack inspection presented by Clements and Felleisen at ESOP 2003 as a lifted state monad. This enables us to combine the stackinspection monad with other monads and to construct abstract machines for languages with properly tail-recursive stack inspection and other computational effects. The construction scales to other monads-including one more properly dedicated to stack inspection than the lifted state monad-and other monadic evaluators.