Proofs and types
COLOG-88 Proceedings of the international conference on Computer logic
Functional programming and lambda calculus
Handbook of theoretical computer science (vol. B)
Handbook of logic in computer science (vol. 2)
Comparing curried and uncurried rewriting
Journal of Symbolic Computation
Higher-order rewrite systems and their confluence
Theoretical Computer Science - Special issue: rewriting systems and applications
Term rewriting and all that
Rewrite orderings for higher-order terms in n-long &bgr;-normal form and the recursive path ordering
Theoretical Computer Science - Special issue on rewriting techniques and applications
Theoretical Computer Science - Special issue on theories of types and proofs
Term Rewriting Systems
Strict Functionals for Termination Proofs
TLCA '95 Proceedings of the Second International Conference on Typed Lambda Calculi and Applications
Inductive Definitions and Type Theory: an Introduction (Preliminary Version)
Proceedings of the 14th Conference on Foundations of Software Technology and Theoretical Computer Science
Termination of Combined (Rewrite and lambda-Calculus) Systems
CTRS '92 Proceedings of the Third International Workshop on Conditional Term Rewriting Systems
The Higher-Order Recursive Path Ordering
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
Termination of rewriting in the Calculus of Constructions
Journal of Functional Programming
Inductive types in the calculus of algebraic constructions
TLCA'03 Proceedings of the 6th international conference on Typed lambda calculi and applications
Higher-order termination: from kruskal to computability
LPAR'06 Proceedings of the 13th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Proving and disproving termination of higher-order functions
FroCoS'05 Proceedings of the 5th international conference on Frontiers of Combining Systems
Higher-order orderings for normal rewriting
RTA'06 Proceedings of the 17th international conference on Term Rewriting and Applications
Higher-Order rewriting: framework, confluence and termination
Processes, Terms and Cycles
Higher-order semantic labelling for inductive datatype systems
Proceedings of the 9th ACM SIGPLAN international conference on Principles and practice of declarative programming
Termination Proof of S-Expression Rewriting Systems with Recursive Path Relations
RTA '08 Proceedings of the 19th international conference on Rewriting Techniques and Applications
The Computability Path Ordering: The End of a Quest
CSL '08 Proceedings of the 22nd international workshop on Computer Science Logic
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
A Higher-Order Iterative Path Ordering
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
HORPO with computability closure: a reconstruction
LPAR'07 Proceedings of the 14th international conference on Logic for programming, artificial intelligence and reasoning
Higher-order termination: from kruskal to computability
LPAR'06 Proceedings of the 13th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Higher-order orderings for normal rewriting
RTA'06 Proceedings of the 17th international conference on Term Rewriting and Applications
Semantic labelling for proving termination of combinatory reduction systems
WFLP'09 Proceedings of the 18th international conference on Functional and Constraint Logic Programming
Nominal completion for rewrite systems with binders
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
Orderings and constraints: theory and practice of proving termination
Rewriting Computation and Proof
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This article extends the termination proof techniques based on reduction orderings to a higher-order setting, by defining a family of recursive path orderings for terms of a typed lambda-calculus generated by a signature of polymorphic higher-order function symbols. These relations can be generated from two given well-founded orderings, on the function symbols and on the type constructors. The obtained orderings on terms are well founded, monotonic, stable under substitution and include β-reductions. They can be used to prove the strong normalization property of higher-order calculi in which constants can be defined by higher-order rewrite rules using first-order pattern matching. For example, the polymorphic version of Gödel's recursor for the natural numbers is easily oriented. And indeed, our ordering is polymorphic, in the sense that a single comparison allows to prove the termination property of all monomorphic instances of a polymorphic rewrite rule. Many nontrivial examples are given that exemplify the expressive power of these orderings. All have been checked by our implementation. This article is an extended and improved version of Jouannaud and Rubio [1999]. Polymorphic algebras have been made more expressive than in our previous framework. The intuitive notion of a polymorphic higher-order ordering has now been made precise. The higher-order recursive path ordering itself has been made much more powerful by replacing the congruence on types used there by an ordering on types satisfying some abstract properties. Besides, using a restriction of Dershowitz's recursive path ordering for comparing types, we can integrate both orderings into a single one operating uniformly on both terms and types.