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seL4: formal verification of an OS kernel
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Isabelle/HOL: a proof assistant for higher-order logic
Isabelle/HOL: a proof assistant for higher-order logic
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MKM'05 Proceedings of the 4th international conference on Mathematical Knowledge Management
Towards self-verification of HOL light
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
TRX: a formally verified parser interpreter
ESOP'10 Proceedings of the 19th European conference on Programming Languages and Systems
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For interactive theorem provers a very desirable property is consistency: it should not be possible to prove false theorems. However, this is not enough: it also should not be possible to think that a theorem that actually is false has been proved. More precisely: the user should be able to know what it is that the interactive theorem prover is proving. To make these issues concrete we introduce the notion of Pollack-consistency. This property is related to a system being able to correctly parse formulas that it printed itself. In current systems it happens regularly that this fails. We argue that a good interactive theorem prover should be Pollack-consistent. We show with examples that many interactive theorem provers currently are not Pollack-consistent. Finally we describe a simple approach for making a system Pollack-consistent, which only consists of a small modification to the printing code of the system.