Many-Sorted Logic in a Learning Theorem Prover

In a learning theorem prover, formulas can be veriied by reusing proofs of previously veriied conjectures. Reuse proceeds by transforming a successful proof into a valid schematic formula which can be instantiated subsequently. In this paper, we show how this reuse approach is extended to many-sorted logic: We rst present the logical foundations for reasoning w.r.t. diierent sortings. Then their operational realization is given by developing a many-sorted proof analysis calculus for extracting the sort constraints imposed by a proof. For guaranteeing the validity of subsequent instantiations, we extend the second-order matching calculi for retrieving and adapting schematic formulas such that the computed sort constraints are satissed. Finally we demonstrate the relevance of our extensions with several examples of many-sorted reuse.