A Rational Deconstruction of Landin's SECD Machine with the J Operator

TL;DR

This paper revisits Landin's SECD machine and the J operator, providing modernized versions, formal characterizations, and reduction semantics to deepen understanding of control operators in functional programming.

Contribution

It introduces a modernized, bisimilar SECD machine without a data stack, characterizes the J operator via CPS and delimited-control operators, and offers the first syntactic theories for applicative expressions with J.

Findings

Modernized SECD machine operates in lockstep with the original but without a data stack.

The caller-save version of the machine aligns with Thielecke's double-barrelled continuations.

Provides reduction semantics for applicative expressions with J, linking to explicit substitution calculus.

Abstract

Landin's SECD machine was the first abstract machine for applicative expressions, i.e., functional programs. Landin's J operator was the first control operator for functional languages, and was specified by an extension of the SECD machine. We present a family of evaluation functions corresponding to this extension of the SECD machine, using a series of elementary transformations (transformation into continu-ation-passing style (CPS) and defunctionalization, chiefly) and their left inverses (transformation into direct style and refunctionalization). To this end, we modernize the SECD machine into a bisimilar one that operates in lockstep with the original one but that (1) does not use a data stack and (2) uses the caller-save rather than the callee-save convention for environments. We also identify that the dump component of the SECD machine is managed in a callee-save way. The caller-save counterpart of the modernized SECD machine precisely corresponds to Thielecke's double-barrelled continuations and to Felleisen's encoding of J in terms of call/cc. We then variously characterize the J operator in terms of CPS and in terms of delimited-control operators in the CPS hierarchy. As a byproduct, we also present several reduction semantics for applicative expressions with the J operator, based on Curien's original calculus of explicit substitutions. These reduction semantics mechanically correspond to the modernized versions of the SECD machine and to the best of our knowledge, they provide the first syntactic theories of applicative expressions with the J operator.