A syntactic correspondence between context-sensitive calculi and abstract machines

Abstract

We present a systematic construction of environment-based abstract machines from context-sensitive calculi of explicit substitutions, and we illustrate it with ten calculi and machines for applicative order with an abort operation, normal order with generalized reduction and call/cc, the lambda-mu-calculus, delimited continuations, stack inspection, proper tail-recursion, and lazy evaluation. Most of the machines already exist but have been obtained independently and are only indirectly related to the corresponding calculi. All of the calculi are new and they make it possible to directly reason about the execution of the corresponding machines. In connection with the functional correspondence between evaluation functions and abstract machines initiated by Reynolds, the present syntactic correspondence makes it possible to construct reduction-free normalization functions out of reductionbased ones, which was an open problem in the area of normalization by evaluation.

A Rational Deconstruction of Landin's J Operator

“…Programmatically, the J operator has been superseded by control operators that capture the current continuation (i.e., both C and D) instead of the continuation of the caller (i.e., D), even though it is simple to simulate escape and call/cc in terms of J. Yet as we have shown here, both the SECD machine and the J operator fit in the functional correspondence [3,4,6,7,13,16,30,31] as well as in the syntactic correspondence [12,14,15,29,31,40], which made it possible for us to mechanically characterize them in new and precise ways. 7 In turn it was Landin who, through the J operator, invented what we know today as first-class continuations [49].…”

“…Symmetrically to the functional correspondence between evaluation functions and abstract machines that was sparked by the first rational deconstruction of the SECD machine [3,4,6,7,13,16,30,31], a syntactic correspondence exists between calculi and abstract machines, as investigated by Biernacka, Danvy, and Nielsen [12,14,15,29,31,40]. This syntactic correspondence is also derivational, and hinges not on defunctionalization but on a 'refocusing' transformation that mechanically connects an evaluation function defined as the iteration of one-step reduction, and an abstract machine.…”

“…As abundantly illustrated elsewhere [14,15], deforesting the intermediate terms yields a refocused evaluation function in the form of an abstract machine. Simplifying this machine (again as abundantly illustrated elsewhere [14,15]) precisely yields the caller-save, stackless SECD abstract machine of Section 6.1.…”

“…Simplifying this machine (again as abundantly illustrated elsewhere [14,15]) precisely yields the caller-save, stackless SECD abstract machine of Section 6.1. The following proposition, whose proof is routine [14,15], captures the raison d'être of this reduction semantics: Proposition 9 (syntactic correspondence) For any program t in the λ ρJ-calculus,…”

Towards Compatible and Interderivable Semantic Specifications for the Scheme Programming Language, Part I: Denotational Semantics, Natural Semantics, and Abstract Machines

“…Like Clinger, we focus on Core Scheme and do not consider primitive procedures and first-class continuations here. (These are unproblematic to add [4,7].) Figure 4], we fixed one typo in the declaration of the evaluation-context constructor for calls, which holds a list of semantic values, not a list of syntactic terms.…”