LEO II: An Effective Higher-Order Theorem Prover

Lawrence C. Paulson is Professor of Computational Logic at the University of Cambridge, where he has held established posts since 1983. One of his main activities is developing proof tools. His early work made fundamental contributions to Prof. M. J. C. Gordon’s proof assistant, HOL. In 1986, Paulson introduced Isabelle, a generic proof assistant. Isabelle supports higher-order logic (HOL), ZermeloFraenkel set theory (ZF) and other formalisms. Many developments are due to Prof. Tobias Nipkow’s group at the Technical University of Munich. Automatic proof search, one of Isabelle’s particular strengths, is however due to Paulson [17]. The designated Visiting Researcher, Dr. Christoph Benzmüller, is indispensable for this project. He is the principal architect of LEO, the only higher-order theorem prover to incorporate modern techniques. Benzmüller’s previous work [11] is the starting point for the current proposal, which is to develop a new automatic theorem prover for higher-order logic. More generally, Benzmüller has an outstanding reputation in the field of automated reasoning. He heads the research group at Saarland University that is developing OMEGA, an integrated mathematics assistance environment. The work will be done within the Cambridge Automated Reasoning Group. Hardware verification was pioneered here by Prof. Gordon and his students. They introduced what have become standard techniques, such as the use of higher-order logic to model hardware and software systems. The group’s work continues to attract worldwide attention. Former members such as Dr. John Harrison have taken formal verification to Intel and other companies. The group has built two of the world’s leading proof environments, namely HOL and Isabelle. Institutes using Isabelle as a basis for their research include the University of Edinburgh, CarnegieMellon University and Australia’s Defence Science and Technology Organisation (DSTO). The Verisoft project, which uses Isabelle extensively, comprises 11 partners, including Infineon Technologies and BMW.1 The EPSRC has funded several projects at Cambridge involving Isabelle. They include the following: