Implementing the Meta-Theory of Deductive Systems

We exhibit a methodology for formulating and verifying metatheorems about deductive systems in the Elf language, an implementation of the LF Logical Framework with an operational semantics in the spirit of logic programming. It is based on the mechanical verification of properties of transformations between deductions, which relies on type reconstruction and schema-checking. The latter is justified by induction principles for closed LF objects, which can be constructed over a given signature. We illustrate our technique through several examples, the most extensive of which is an interpretation of classical logic in minimal logic through a continuation-passing-style transformation on proofs.