• Corpus ID: 4726555

Superposition for Lambda-Free Higher-Order Logic ( Technical Report )

@inproceedings{Bentkamp2018SuperpositionFL,
  title={Superposition for Lambda-Free Higher-Order Logic ( Technical Report )},
  author={Alexander Bentkamp and Jasmin Christian Blanchette and Simon Cruanes and Uwe Waldmann},
  year={2018}
}
We introduce refutationally complete superposition calculi for intentional and extensional λ-free higher-order logic, two formalisms that allow partial application and applied variables. The calculi are parameterized by a term order that need not be fully monotonic, making it possible to employ the λ-free higherorder lexicographic path and Knuth–Bendix orders. We implemented the calculi in the Zipperposition prover and evaluated them on TPTP benchmarks. They appear promising as a stepping stone… 

Figures from this paper

Superposition for Lambda-Free Higher-Order Logic
TLDR
Refutationally complete superposition calculi for intentional and extensional \(\lambda \)-free higher-order logic, two formalisms that allow partial application and applied variables, appear promising as a stepping stone towards complete, efficient automatic theorem provers for full higher- order logic.
Superposition with Lambdas
TLDR
A superposition calculus for a clausal fragment of extensional polymorphic higher-order logic that includes anonymous functions but excludes Booleans is designed and implemented in the Zipperposition prover and evaluated on TPTP and Isabelle benchmarks.

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