Abstract
Leo-II is an automated theorem prover for classical higher-order logic. The prover has pioneered cooperative higher-order–first-order proof automation, it has influenced the development of the TPTP THF infrastructure for higher-order logic, and it has been applied in a wide array of problems. Leo-II may also be called in proof assistants as an external aid tool to save user effort. For this it is crucial that Leo-II returns proof information in a standardised syntax, so that these proofs can eventually be transformed and verified within proof assistants. Recent progress in this direction is reported for the Isabelle/HOL system.
Highlights
Leo-II is a standalone, resolution-based higher-order (HO) automated theorem prover (ATP) that is designed for cooperation with specialist provers for fragments of HO logic
Leo-II implements a method devised by Claessen et al [32], who describe an analysis on the cardinalities of types in order to safely erase some information
To illustrate THF0 syntax we present in Fig. 2 a small example theory
Summary
Leo-II is a standalone, resolution-based higher-order (HO) automated theorem prover (ATP) that is designed for cooperation with specialist provers for fragments of HO logic. The prover already supported native (versus Huet’s axiomatic) treatment of the extensionality principles [8] and it cooperated with first-order (FO) ATPs via the flexible ΩAnts agent architecture within Ωmega [26] Both native extensionality treatment and cooperation with specialist reasoners for fragments of HO logic have been adopted in Leo-II, and in other systems, most notably in the recent Satallax prover by Brown [30]. In that section it is explained why Leo-II (and other THF0 compliant provers) can readily be used for automating a wide spectrum of quantified non-classical logics via semantic embeddings. The source code is freely available from http://www.leoprover.org under a BSD-style license
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