Sean McLaughlin

A proof-producing decision procedure for real arithmetic

We present a fully proof-producing implementation of a quantifier elimination procedure for real closed fields. To our knowledge, this is the first generally useful proof-producing implementation of such an algorithm. While many problems within the domain are intractable, we demonstrate convincing examples of its value in interactive theorem proving.

Cooperating Theorem Provers: A Case Study Combining HOL-Light and CVC Lite

This paper is a case study in combining theorem provers. We define a derived rule in HOL-Light, CVC_PROVE, which calls CVC Lite and translates the resulting proof object back to HOL-Light. As a result, we obtain a highly trusted proof-checker for CVC Lite, while also fundamentally expanding the capabilities of HOL-Light.

Efficient Intuitionistic Theorem Proving with the Polarized Inverse Method

The inverse method is a generic proof search procedure applicable to non-classical logics satisfying cut elimination and the subformula property. In this paper we describe a general architecture and several high-level optimizations that enable its efficient implementation. Some of these rely on logic-specific properties, such as polarization and focusing, which have been shown to hold in a wide range of non-classical logics. Others, such as rule subsumption and recursive backward subsumption apply in general. We empirically evaluate our techniques on first-order intuitionistic logic with our implementation Imogen and demonstrate a substantial improvement over all other existing intuitionistic theorem provers on problems from the ILTP problem library.

The dodecahedral conjecture

This article gives a summary of a proof of Fejes Toth’s Dodecahedral conjecture: the volume of a Voronoi polyhedron in a three-dimensional packing of balls of unit radius is at least the volume of a regular dodecahedron of unit inradius.

An interpretation of Isabelle/HOL in HOL light

We define an interpretation of the Isabelle/HOL logic in HOL Light and its metalanguage, OCaml. Some aspects of the Isabelle logic are not representable directly in the HOL Light object logic. The interpretation thus takes the form of a set of elaboration rules, where features of the Isabelle logic that cannot be represented directly are elaborated to functors in OCaml. We demonstrate the effectiveness of the interpretation via an implementation, translating a significant part of the Isabelle standard library into HOL Light.

Tool Building Requirements for an API to First-Order Solvers

Effective formal verification tools require that robust implementations of automatic procedures for first-order logic and satisfiability modulo theories be integrated into expressive interactive frameworks for logical deduction, such as higher-order logic theorem provers. This paper states some pragmatic requirements for implementations of decision procedures that make them well-suited to integration into such frameworks. The aim is to open a dialogue with the designers of decision procedure software that will lead to greater and easier uptake of their implementations by verification users.

Object Oriented XML Query by Example

This paper describes an XML query language called XML-QBE, which can be used to both query and update XML documents and databases. The language itself has a simple XML form, and uses a query by example paradigm. This language was designed as a middleware layer between UML data models and backend database schemas, as part of a solution to the distributed, heterogeneous data-base problem and legacy database problem. Because the XML layer is derived from UML, XML-QBE is object-oriented. Queries and updates have a very similar form, and the form itself is XML. Therefore this language is also easy to process and analyze. We describe the language, the rationale, and our solution architecture.