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arXiv · 1609.08916

Encoding Monomorphic and Polymorphic Types

Jasmin Christian Blanchette·Sascha Böhme·Andrei Popescu·Nicholas Smallbone
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Abstract

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.

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Jasmin Christian Blanchette, Sascha Böhme, Andrei Popescu, Nicholas Smallbone. 2016-09-28. Encoding Monomorphic and Polymorphic Types. https://doi.org/10.2168/lmcs-12(4:13)2016

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