Encoding monomorphic and polymorphic types

Blanchette, Jasmin Christian, Böhme, Sascha, Popescu, Andrei and Smallbone, Nicholas (2013) Encoding monomorphic and polymorphic types. Tools and Algorithms for the Construction and Analysis of Systems: 19th International Conference, TACAS 2013, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2013, Rome, Italy, March 16-24, 2013. Proceedings. In: 19th International Conference on Tools and Algorithms for the Construction and Analysis of Systems (TACAS), 16-24 Mar 2013, Rome. ISBN 9783642367410. ISSN 0302-9743 [Conference or Workshop Item]

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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.

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