Many-sorted logic in a learning theorem prover

Abstract

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