The development of mechanised language specification based on structured operational semantics, with applications to verified compilers and sound program analysis, requires huge effort. General theory and frameworks have been proposed to help with this effort. However, none of this work provides a systematic way of developing concrete and abstract semantics, connected together by a general consistency result. We introduce a skeletal semantics of a language, where each skeleton describes the complete semantic behaviour of a language construct. We define a general notion of interpretation , which provides a systematic and language-independent way of deriving semantic judgements from the skeletal semantics. We explore four generic interpretations: a simple well-formedness interpretation; a concrete interpretation; an abstract interpretation; and a constraint generator for flow-sensitive analysis. We prove general consistency results between interpretations, depending only on simple language-dependent lemmas. We illustrate our ideas using a simple While language.

The R programming language is very popular for developing statistical software and data analysis, thanks to rich libraries, concise and expressive syntax, and support for interactive programming. Yet, the semantics of R is fairly complex, contains many subtle corner cases, and is not formally specified. This makes it difficult to reason about R programs. In this work, we develop a big-step operational semantics for R in the form of an interpreter written in the Coq proof assistant. We ensure the trustworthiness of the formalization by introducing a monadic encoding that allows the Coq interpreter, CoqR, to be in direct visual correspondence with the reference R interpreter, GNU R. Additionally, we provide a testing framework that supports systematic comparison of CoqR and GNU R. In its current state, CoqR covers the nucleus of the R language as well as numerous additional features, making it pass a significant number of realistic test cases from the GNU R and FastR projects. To exercise the formal specification, we prove in Coq the preservation of memory invariants in selected parts of the interpreter. This work is an important first step towards a robust environment for formal verification of R programs.

This paper describes an investigation into developing certified abstract interpreters from big-step semantics using the Coq proof assistant. We base our approach on Schmidt's abstract interpretation principles for natural semantics, and use a pretty-big-step (PBS) semantics, a semantic format proposed by Charguéraud. We propose a systematic representation of the PBS format and implement it in Coq. We then show how the semantic rules can be abstracted in a methodical fashion, independently of the chosen abstract domain, to produce a set of abstract inference rules that specify an abstract interpreter. We prove the correctness of the abstract interpreter in Coq once and for all, under the assumption that abstract operations faithfully respect the concrete ones. We finally show how to define correct-by-construction analyses: their correction amounts to proving they belong to the abstract semantics.

JavaScript is the most widely used web language for client-side applications. Whilst the development of JavaScript was initially just led by implementation, there is now increasing momentum behind the ECMA standardisation process. The time is ripe for a formal, mechanised specification of JavaScript, to clarify ambiguities in the ECMA standards, to serve as a trusted reference for high-level language compilation and JavaScript implementations, and to provide a platform for high-assurance proofs of language properties.