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.
14 Citations
Formalization of the Embedding Path Order for Lambda-Free Higher-Order Terms
- Computer ScienceArch. Formal Proofs
- 2018
The embedding path order is a variant of the recursive path order for untyped λ-free higher-order terms that is a groundtotal and well-founded simplification order, making it more suitable for the superposition calculus.
A Transfinite Knuth-Bendix Order for Lambda-Free Higher-Order Terms
- MathematicsCADE
- 2017
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
- Computer ScienceIJCAR
- 2018
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 for Lambda-Free Higher-Order Logic ( Technical Report )
- Computer Science
- 2018
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
- Computer ScienceCADE
- 2019
A superposition calculus for a clausal fragment of extensional polymorphic higher-order logic that includes anonymous functions but excludes Booleans is designed and the results suggest that superposition is a suitable basis for higher- order reasoning.
Implementation of Lambda-Free Higher-Order Superposition
- Computer Science
- 2018
This thesis extends E, a state-of-the-art first-order ATP, to a fragment of HOL that is devoid of lambda abstractions (LFHOL), and devise generalizations of E’s indexing data structures to LFHOL, as well as algorithms like matching and unification to support HOL features in an efficient manner.
Extending a brainiac prover to lambda-free higher-order logic
- Computer ScienceInt. J. Softw. Tools Technol. Transf.
- 2022
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.
Extending a Brainiac Prover to Lambda-Free Higher-Order Logic
- Computer ScienceTACAS
- 2019
This work proposes to start with the state-of-the-art superposition-based prover E and gradually enrich it with higher-order features, explaining how to extend the prover’s data structures, algorithms, and heuristics to \(\lambda \)-free higher- order logic, a formalism that supports partial application and applied variables.
A Knuth-Bendix-Like Ordering for Orienting Combinator Equations
- MathematicsIJCAR
- 2020
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
- Mathematics, Computer ScienceFSCD
- 2017
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).
References
SHOWING 1-10 OF 48 REFERENCES
Formalization of Recursive Path Orders for Lambda-Free Higher-Order Terms
- Computer ScienceArch. Formal Proofs
- 2016
This Isabelle/HOL formalization of recursive path orders (RPOs) for higher-order terms without λ-abstraction and proves many useful properties about them and appears promising as the basis of a higher- order superposition calculus.
A Higher-Order Iterative Path Ordering
- Computer ScienceLPAR
- 2008
An iterative version of HORPO is presented by means of an auxiliary term rewriting system, following an approach originally due to Bergstra and Klop, and well-foundedness of the iterative definition is studied.
A Recursive Path Ordering for Higher-Order Terms in eta-Long beta-Normal Form
- Computer ScienceRTA
- 1996
A recursive path ordering for simply typed higher-order terms in η-long β-normal form is defined, which is powerful enough to show termination of several complex examples.
A Recursive Path Ordering for Higher-order Terms in -long -normal Form ?
- Mathematics
- 1996
This paper extends the termination proof techniques based on rewrite orderings to a higher-order setting, by deening a recursive path ordering for simply typed higher-order terms in-long-normal form.…
An LPO-based Termination Ordering for Higher-Order Terms without lambda-abstraction
- Computer ScienceTPHOLs
- 1998
A new precedence-based termination ordering for (polymorphic) higher-order terms without λ-abstraction is presented, which can be used to prove termination of many higher- order rewrite systems, especially those corresponding to typical functional programs.
Higher-order critical pairs
- Computer Science[1991] Proceedings Sixth Annual IEEE Symposium on Logic in Computer Science
- 1991
The notion of critical pair is generalized to higher-order rewrite systems, and the analog of the critical pair lemma is proved.
Extensional Higher-Order Resolution
- MathematicsCADE
- 1998
An extensional higher-order resolution calculus that is complete relative to Henkin model semantics is presented and the long-standing conjecture, that it is sufficient to restrict the order of primitive substitutions to the orders of input formulae is proved.
A Termination Ordering for Higher Order Rewrite System
- Computer ScienceRTA
- 1995
We present an extension of the recursive path ordering for the purpose of showing termination of higher order rewrite systems. Keeping close to the general path ordering of Dershowitz and Hoot, we…
The recursive path and polynomial ordering for first-order and higher-order terms
- MathematicsJ. Log. Comput.
- 2013
A simple ordering is presented that combines both RPO and POLO and defines a family of orderings that includes both and is extended to higher-order terms, providing a new fully automatable use of polynomial interpretations in combination with beta-reduction.
Polymorphic higher-order recursive path orderings
- MathematicsJACM
- 2007
A family of recursive path orderings for terms of a typed lambda-calculus generated by a signature of polymorphic higher-order function symbols is defined, which can be generated from two given well-founded orderings, on the function symbols and on the type constructors.