A Lambda-Free Higher-Order Recursive Path Order

@inproceedings{Blanchette2017ALH,
  title={A Lambda-Free Higher-Order Recursive Path Order},
  author={Jasmin Christian Blanchette and Uwe Waldmann and Daniel Wand},
  booktitle={FoSSaCS},
  year={2017}
}
We generalize the recursive path order RPO to higher-order terms without $$\lambda $$-abstraction. This new order fully coincides with the standard RPO on first-order terms also in the presence of currying, distinguishing it from previous work. It has many useful properties, including well-foundedness, transitivity, stability under substitution, and the subterm property. It appears promising as the basis of a higher-order superposition calculus. 
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13 Citations
Background Citations
6
Methods Citations
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13 Citations

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Citation Type

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The Knuth–Bendix order is generalized to higher-order terms without \(\lambda \)-abstraction and appears promising as the basis of a higher- order superposition calculus.
Superposition for Lambda-Free Higher-Order Logic
TLDR
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Superposition for Lambda-Free Higher-Order Logic ( Technical Report )
TLDR
Refutationally complete superposition calculi for intentional and extensional λ-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.
Implementation of Lambda-Free Higher-Order Superposition
TLDR
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Extending a brainiac prover to lambda-free higher-order logic
TLDR
This work proposes to start with the state-of-the-art superposition prover E and gradually enrich it with higher-order features, explaining how to extend the prover’s data structures, algorithms, and heuristics to higher- order logic, a formalism that supports partial application and applied variables.
A Knuth-Bendix-Like Ordering for Orienting Combinator Equations
TLDR
A number of desirable properties about the KBO are proved including it having the subterm property for ground terms, being transitive and being well-founded, and the ordering fails to be a reduction ordering as it lacks compatibility with certain contexts.
Nested Multisets, Hereditary Multisets, and Syntactic Ordinals in Isabelle/HOL
TLDR
Formal proofs of the main properties of the nested multiset order that are useful in applications are presented: preservation of well-foundedness and preservation of totality (linearity).
Higher-Order in SMT Higher-Order in SMT
TLDR
Satisfiability Modulo Theories solvers rely on state-of-the-art techniques based on the advances in SAT technology to make them usable tools to solve specific first-order problems.
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References

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