Encoding monomorphic and polymorphic types

Authors:
Jasmin Christian Blanchette;Sascha Böhme;Andrei Popescu;Nicholas Smallbone
Affiliations:
Fakultät für Informatik, Technische Universität München, Germany;Fakultät für Informatik, Technische Universität München, Germany;Fakultät für Informatik, Technische Universität München, Germany;Dept. of CSE, Chalmers University of Technology, Gothenburg, Sweden
Venue:
TACAS'13 Proceedings of the 19th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Year:
2013

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Abstract

Most 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. 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, and partly proved correct, in Isabelle/HOL. Our evaluation finds them vastly superior to previous schemes.