Isabelle's Metalogic: Formalization and Proof Checker

04/25/2021

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by   Tobias Nipkow, et al.

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Isabelle is a generic theorem prover with a fragment of higher-order logic as a metalogic for defining object logics. Isabelle also provides proof terms. We formalize this metalogic and the language of proof terms in Isabelle/HOL, define an executable (but inefficient) proof term checker and prove its correctness w.r.t. the metalogic. We integrate the proof checker with Isabelle and run it on a range of logics and theories to check the correctness of all the proofs in those theories.