Peter Sewell, Francesco Zappa Nardelli, Scott Owens, Gilles Peskine, Tom Ridge, Susmit Sarkar, Rok Strnisa. Ott: effective tool support for the working semanticist. In Ralf Hinze, Norman Ramsey, editors, Proceedings of the 12th ACM SIGPLAN International Conference on Functional Programming, ICFP 2007, Freiburg, Germany, October 1-3, 2007. pages 1-12, ACM, 2007. [doi]
Semantic definitions of full-scale programming languages are rarely given, despite the many potential benefits. Partly this is because the available metalanguages for expressing semantics – usually either LATEX for informal mathematics or the formal mathematics of a proof assistant – make 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 LATEX 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 (OCamllight, 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.