A Semantics for Context-Sensitive Reduction Semantics

Abstract

Abstract. This paper explores the semantics of the meta-notation used in the style of operational semantics introduced by Felleisen and Hieb. Specifically, it defines a formal system that gives precise meanings to the notions of contexts, decomposition, and plugging (recomposition) left implicit in most expositions. This semantics is not naturally algorithmic, so the paper also provides an algorithm and proves a correspondence with the declarative definition. The motivation for this investigation is PLT Redex, a domain-specific programming language designed to support Felleisen-Hieb-style semantics. This style of semantics is the de-facto standard in operational semantics and, as such, is widely used. Accordingly, our goal is that Redex programs should, as much as possible, look and behave like those semantics. Since Redex's first public release more than seven years ago, its precise interpretation of contexts has changed several times, as we repeatedly encountered reduction systems that did not behave according to their authors' intent. This paper describes the culimation of that experience. To the best of our knowledge, the semantics given here accommodates even the most complex uses of contexts available.

From Specification to Testing: Semantics Engineering for Lua 5.2

“…As a running example, we show how to mechanize a fragment of λ-calculus with normal order reduction, in Redex. For a better introduction to these topics, the reader can consult Felleisen et al (2009); Klein et al (2012) and the original paper on which our mechanization is based (Casey Klein and Findler, 2011). Also, its reference manual presents the most up-to-date information about Redex's features.…”

“…These patterns constitute a highly expressive language, whose semantics is explained specifying which terms match against a given pattern. This formalization of the notion of matching against Redex's patterns is the main focus of Casey Klein and Findler (2011), together with the development of an algorithmic interpretation of this specification. Mechanize this work in Coq, solving problems like finding a primitive recursive implementation of the matching process, constitutes the main work presented in this paper.…”

“…This is so, since the tool implements a particular meaning of reduction semantics with evaluation contexts, offering an expressive language to the user that includes several features, useful to express concepts like context-dependent syntactic rules. The actual semantics of this language may not coincide with what the researcher understands (see Casey Klein and Findler (2011) for a development of this issue).…”

“…In this work we present a first step into the development of a tool to automate the translation of a Redex model into a semantically equivalent model in Coq, and to provide automation to the proof of essential properties of such models. The present work is heavily based on the model of Redex's semantics developed by Klein et al (Casey Klein and Findler, 2011) (from now on, RedexK). In summary:…”

Coalgebraic Operational Semantics for an Imperative Language

“…Reduction semantics with evaluation contexts does precisely that it allows to formally define evaluation contexts; rules become mostly unconditional and reductions can only happen "in context". Reduction semantics is considered as yet another way to define single-step semantic relation [14], a small-step semantics where the atomic execution step is a rewrite of the program. For modeling programming languages, Felleisen-Hieb-style reduction semantics, and their type systems, a powerful software tool PLT Redex has been designed [6].…”