Extending a Brainiac Prover to Lambda-Free Higher-Order Logic

Abstract : Decades of work have gone into developing efficient proof calculi, data structures, algorithms, and heuristics for first-order automatic theorem proving. Higher-order provers lag behind in terms of efficiency. Instead of developing a new higher-order prover from the ground up, we propose to start with the state-of-the-art superposition-based prover E and gradually enrich it with higher-order features. We explain how to extend the prover's data structures, algorithms, and heuristics to λ-free higher-order logic, a formalism that supports partial application and applied variables. Our extension outperforms the traditional encoding and appears promising as a stepping stone towards full higher-order logic.
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Submitted on : Tuesday, July 9, 2019 - 4:31:06 PM
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Petar Vukmirovic, Jasmin Christian Blanchette, Simon Cruanes, Stephan Schulz. Extending a Brainiac Prover to Lambda-Free Higher-Order Logic. TACAS 2019 - 25th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, Apr 2019, Prague, Czech Republic. pp.192-210. ⟨hal-02178274⟩

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