Introduction to higher order categorical logic
Introduction to higher order categorical logic
An introduction to mathematical logic and type theory: to truth through proof
An introduction to mathematical logic and type theory: to truth through proof
Introduction to HOL: a theorem proving environment for higher order logic
Introduction to HOL: a theorem proving environment for higher order logic
A type-theoretical alternative to ISWIM, CUCH, OWHY
Theoretical Computer Science - A collection of contributions in honour of Corrado Bo¨hm on the occasion of his 70th birthday
Ivy: a preprocessor and proof checker for first-order logic
Computer-Aided reasoning
HOL Light: A Tutorial Introduction
FMCAD '96 Proceedings of the First International Conference on Formal Methods in Computer-Aided Design
The HOL Logic Extended with Quantification over Type Variables
HOL'92 Proceedings of the IFIP TC10/WG10.2 Workshop on Higher Order Logic Theorem Proving and its Applications
Representing Higher-Order Logic Proofs in HOL
Proceedings of the 7th International Workshop on Higher Order Logic Theorem Proving and Its Applications
Trust and Automation in Verification Tools
ATVA '08 Proceedings of the 6th International Symposium on Automated Technology for Verification and Analysis
Directly reflective meta-programming
Higher-Order and Symbolic Computation
Combined satisfiability modulo parametric theories
TACAS'07 Proceedings of the 13th international conference on Tools and algorithms for the construction and analysis of systems
HOL2P - a system of classical higher order logic with second order polymorphism
TPHOLs'07 Proceedings of the 20th international conference on Theorem proving in higher order logics
Proving valid quantified Boolean formulas in HOL light
ITP'11 Proceedings of the Second international conference on Interactive theorem proving
A verified runtime for a verified theorem prover
ITP'11 Proceedings of the Second international conference on Interactive theorem proving
ITP'10 Proceedings of the First international conference on Interactive Theorem Proving
Electronic Notes in Theoretical Computer Science (ENTCS)
Steps towards verified implementations of HOL light
ITP'13 Proceedings of the 4th international conference on Interactive Theorem Proving
Communications of the ACM
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The HOL Light prover is based on a logical kernel consisting of about 400 lines of mostly functional OCaml, whose complete formal verification seems to be quite feasible. We would like to formally verify (i) that the abstract HOL logic is indeed correct, and (ii) that the OCaml code does correctly implement this logic. We have performed a full verification of an imperfect but quite detailed model of the basic HOL Light core, without definitional mechanisms, and this verification is entirely conducted with respect to a set-theoretic semantics within HOL Light itself. We will duly explain why the obvious logical and pragmatic difficulties do not vitiate this approach, even though it looks impossible or useless at first sight. Extension to include definitional mechanisms seems straightforward enough, and the results so far allay most of our practical worries.