HOL Light: An Overview
HOL Light is an interactive proof assistant for classical higher-order logic, intended as a clean and simplified version of Mike Gordon’s original HOL system. Theorem provers in this family use a version of ML as both the implementation and interaction language; in HOL Light’s case this is Objective CAML (OCaml). Thanks to its adherence to the so-called ‘LCF approach’, the system can be extended with new inference rules without compromising soundness. While retaining this reliability and programmability from earlier HOL systems, HOL Light is distinguished by its clean and simple design and extremely small logical kernel. Despite this, it provides powerful proof tools and has been applied to some non-trivial tasks in the formalization of mathematics and industrial formal verification.
KeywordsInference Rule High Order Logic Prime Number Theorem Polymorphic Type Jordan Curve Theorem
Unable to display preview. Download preview PDF.
- 4.Gordon, M.J.C.: Representing a logic in the LCF metalanguage. In: Néel, D. (ed.) Tools and notions for program construction: an advanced course, pp. 163–185. Cambridge University Press, Cambridge (1982)Google Scholar
- 7.Hales, T.C.: Introduction to the Flyspeck project. In: Coquand, T., Lombardi, H., Roy, M.-F. (eds.) Mathematics, Algorithms, Proofs. Dagstuhl Seminar Proceedings, vol. 05021. Internationales Begegnungs- und Forschungszentrum fuer Informatik (IBFI), Schloss Dagstuhl, Germany (2006)Google Scholar
- 13.Harrison, J.: Formalizing an analytic proof of the Prime Number Theorem (dedicated to Mike Gordon on the occasion of his 60th birthday). Journal of Automated Reasoning (to appear, 2009)Google Scholar
- 17.Solovay, R.M., Arthan, R., Harrison, J.: Some new results on decidability for elementary algebra and geometry. ArXiV preprint 0904.3482 (2009); submitted to Annals of Pure and Applied Logic, http://arxiv.org/PS_cache/arxiv/pdf/0904/0904.3482v1.pdf