Making Higher-Order Superposition Work
Petar Vukmirović, Alexander Bentkamp, Jasmin Christian Blanchette, Simon Cruanes, Visa Nummelin, Sophie Tourret
Abstract
Abstract Superposition is among the most successful calculi for first-order logic. Its extension to higher-order logic introduces new challenges such as infinitely branching inference rules, new possibilities such as reasoning about formulas, and the need to curb the explosion of specific higher-order rules. We describe techniques that address these issues and extensively evaluate their implementation in the Zipperposition theorem prover. Largely thanks to their use, Zipperposition won the higher-order division of the CASC-J10 competition.
Topics & Concepts
Automated theorem provingComputer scienceGas meter proverSuperposition principleFirst-order logicOrder (exchange)Rule of inferenceBranching (polymer chemistry)Calculus (dental)Theoretical computer scienceAutomated reasoningProgramming languageMathematicsMathematical proofDentistryComposite materialEconomicsMathematical analysisMedicineGeometryFinanceMaterials scienceLogic, programming, and type systemsLogic, Reasoning, and KnowledgeAdvanced Database Systems and Queries