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Many automatic theorem provers are restricted to untyped logics, and existing translations from typed logics are bulky or unsound. Recent research proposes monotonicity as a means to remove some clutter when translating monomorphic to untyped first-order logic. Here we pursue this approach systematically, analysing formally a variety of encodings that further improve on efficiency while retaining soundness and completeness. We extend the approach to rank-1 polymorphism and present alternative schemes that lighten the translation of polymorphic symbols based on the novel notion of "cover". The new encodings are implemented in Isabelle/HOL as part of the Sledgehammer tool. We include informal proofs of soundness and correctness, and have formalised the monomorphic part of this work in Isabelle/HOL. Our evaluation finds the new encodings vastly superior to previous schemes.
Source : ScholeXplorer
IsCitedBy ARXIV 2205.01981 Source : ScholeXplorer IsCitedBy DOI 10.4230/lipics.itp.2022.16 Source : ScholeXplorer IsCitedBy DOI 10.48550/arxiv.2205.01981
Goertzel, Zarathustra A. ; Jakubův, Jan ; Kaliszyk, Cezary ; Olšák, Miroslav ; Piepenbrock, Jelle ; Urban, Josef ; |