Applications of Proof Theory to Isabelle

Isabelle [3, 4] is a generic theorem prover. It suppports interactive proof in several formal systems, including first-order logic (intuitionistic and classical), higher-order logic, Martin-Löf type theory, and Zermelo-Fraenkel set theory. New logics can be introduced by specifying their syntax and rules of inference. Both natural deduction and sequent calculi are allowed. Isabelle’s approach is to represent the various formal systems, or object-logics, within a single meta-logic. The meta-logic is a fragment of higher-order logic, formulated in natural deduction. The proof theory of meta-logic is the main tool for proving that an object-logic is correctly formalized in Isabelle.