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**11 - 13**of**13**### A Generic Proof Checker

, 2001

"... The use of formal methods in software development seeks to increase our confidence in the resultant system. Their use often requires tool support, so the integrity of a development using formal methods is dependent on the integrity of the tool-set used. Specifically its integrity depends on the theo ..."

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The use of formal methods in software development seeks to increase our confidence in the resultant system. Their use often requires tool support, so the integrity of a development using formal methods is dependent on the integrity of the tool-set used. Specifically its integrity depends on the theorem prover, since in a typical formal development system the theorem prover is used to establish the validity of the proof obligations incurred by all the steps in the design and refinement process. In this

### Author manuscript, published in "Interactive Theorem Proving 6172 (2010) 307-322" Importing HOL Light into Coq

, 2010

"... Abstract. We present a new scheme to translate mathematical developments from HOL Light to Coq, where they can be re-used and rechecked. By relying on a carefully chosen embedding of Higher-Order Logic into Type Theory, we try to avoid some pitfalls of inter-operation between proof systems. In parti ..."

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Abstract. We present a new scheme to translate mathematical developments from HOL Light to Coq, where they can be re-used and rechecked. By relying on a carefully chosen embedding of Higher-Order Logic into Type Theory, we try to avoid some pitfalls of inter-operation between proof systems. In particular, our translation keeps the mathematical statements intelligible. This translation has been implemented and allows the importation of the HOL Light basic library into Coq.

### Checking Proofs from Linked Tools

"... We describe a Cambridge project (now completed) which demonstrated the feasibility of producing independent, veri ed proof checkers for the HOL theorem proving system 1. We then brie y overview a joint Cambridge University/Hong Kong Baptist University proof checking project which is about to commenc ..."

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We describe a Cambridge project (now completed) which demonstrated the feasibility of producing independent, veri ed proof checkers for the HOL theorem proving system 1. We then brie y overview a joint Cambridge University/Hong Kong Baptist University proof checking project which is about to commence. It aims to extend the HOL work to other logics and proof tools. We discuss how this relates to the formal linking of tools and theories. 1 Independent Proof Checking There is a growing interest in the use of formal methods in the validation of computer systems. Correctness proofs tend to be very long and shallow in the sense that they are not mathematically interesting. As such they can only realistically be carried out with any degree of con dence using machine assistance. A wide variety of di erent theorem proving systems incorporating various degrees of automation have been developed to this end, embodying various underlying logics. However, theorem provers are themselves just computer systems which can themselves contain errors. In many correctness-critical applications (eg safety