Ott: Effective tool support for the working semanticist

Abstract

Semantic definitions of full-scale programming languages are rarely given, despite the many potential benefits. Partly this is because the available metalanguages for expressing semanticsusually either L A T E X for informal mathematics or the formal mathematics of a proof assistantmake it much harder than necessary to work with large definitions. We present a metalanguage specifically designed for this problem, and a tool, Ott, that sanity-checks such definitions and compiles them into proof assistant code for Coq, HOL, and Isabelle/HOL, together with L A T E X code for production-quality typesetting, and OCaml boilerplate. The main innovations are (1) metalanguage design to make definitions concise, and easy to read and edit; (2) an expressive but intuitive metalanguage for specifying binding structures; and (3) compilation to proof assistant code. This has been tested in substantial case studies, including modular specifications of calculi from the TAPL text, a Lightweight Java with Java JSR 277/294 module system proposals, and a large fragment of OCaml (OCaml light , 310 rules), with mechanised proofs of various soundness results. Our aim with this work is to enable a phase change: making it feasible to work routinely, without heroic effort, with rigorous semantic definitions of realistic languages.A context grammar is declared as a normal grammar but with a single occurrence of the terminal __ in each production, e.g. as in the grammar for E below:

GMeta: A Generic Formal Metatheory Framework for First-Order Representations

“…Generative Approaches Closest to our work are generative approaches like LNgen, which uses an external tool, based on Ott (Sewell et al 2010) specifications, to generate the infrastructure lemmas and definitions for a particular language automatically. One advantage of generative approaches is that the generated infrastructure is directly defined in terms of the object language.…”

Dialectica Categories for the Lambek Calculus

“…All of the syntax in this paper was checked using Ott [23]. The goal is to show that our work can shed new light on some of the issues that remained open.…”

Generalised Name Abstraction for Nominal Sets

“…Atom-abstraction nominal sets as a semantics for binding one name at a time are now well established; what of applications involving more complex binding? Such applications, such as the functional programming operator letrec that binds lists of names simultaneously, are known to be imperfectly modelled by one-ata-time binding -see [1,21,24] for varied discussions on this point. This paper explores and critiques the fundamental mathematics that could provide a nominal sets semantics for such general binding.…”