Twenty Years of Theorem Proving for HOLs Past, Present and Future

Authors:
Mike Gordon
Affiliations:
The University of Cambridge Computer Laboratory, Cambridge, United Kingdom CB3 0FD
Venue:
TPHOLs '08 Proceedings of the 21st International Conference on Theorem Proving in Higher Order Logics
Year:
2008

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Abstract

There are two kinds of theorem provers for higher order logics: fully automatic (e.g. TPS and Leo) and user guided (e.g. HOL4, HOL Light, ProofPower, Isabelle/HOL, Coq, Nuprl and PVS). All the user guided systems, except PVS, are based on the LCF "fully expansive" approach invented by Robin Milner. PVS evolved from a different tradition that doesn't expand everything down to primitive inferences.The emphasis here is on user guided proof assistants, but future developments in automatic higher order proof methods are likely to be incorporated into these as the automatic methods available today are mainly propositional or first order.