A Rational Deconstruction of Landin's SECD Machine

Abstract

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.

A Dynamic Continuation-Passing Style for Dynamic Delimited Continuations

“…Inlining the abstraction layer provided by the monad yields the evaluator of Figure 3. Dynamic continuation-passing style therefore fits the functional correspondence between evaluators and abstract machines advocated by the first two authors [1,2,13]. Furthermore, and as has been observed before for other CPS transformations and for the continuation monad [27,43], the dynamic CPS transformation itself can be factored through Moggi's monadic metalanguage and the monad above.…”

A functional correspondence between monadic evaluators and abstract machines for languages with computational effects

“…As we have already observed in previous work [2,6,9,11,12], the evaluation contexts, together with the cont transition function, are the defunctionalized counterpart of a continuation. We can therefore "refunctionalize" this continuation and then write the evaluator in direct style.…”

“…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). The correspondence builds on the observation that defunctionalized continuation-passing evaluators are abstract machines.…”

“…These two machines have been independently developed and-to the best of our knowledge-have never been associated with defunctionalization, CPS transformation, and closure conversion. The correspondence has also let us reveal the evaluators underlying Landin's SECD machine, Schmidt's VEC machine, Hannan and Miller's CLS machine, and Curien et al's Categorical Abstract Machine [2,9].…”

A Concrete Framework for Environment Machines

“…Obtaining staged abstract machines was one of the goals of Hardin, Maranget, and Pagano's study of functional runtime systems using explicit substitutions [26]; these machines arise mechanically here. As investigated by Danvy and his students in their study of the functional correspondence between compositional evaluation functions and abstract machines [4][5][6]16], the eval/apply machines are in defunctionalized form [17,35] and they can be 'refunctionalized' into a continuation-passing evaluation function which itself can be written in direct style [14] and implements a big-step operational semantics. (Because of the closures, the result is again in defunctionalized form and can be refunctionalized into a compositional evaluation function implementing the valuation function of a denotational semantics.…”