Encoding monomorphic and polymorphic types
Journal article, 2016

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 po lymorphism 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.


Jasmin Christian Blanchette

Max Planck Society

Laboratoire Lorrain de Recherche en Informatique et ses Applications

Sascha Böhme

Technical University of Munich

Andrei Popescu

Middlesex University

Nicholas Smallbone

Functional Programming

Logical Methods in Computer Science

18605974 (eISSN)

Vol. 12 4 13

Subject Categories

Algebra and Logic

Language Technology (Computational Linguistics)

Computer Science



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