Theoretical Computer Science - Special issue on theories of types and proofs
Dependent Types for Program Termination Verification
Higher-Order and Symbolic Computation
A Monotonic Higher-Order Semantic Path Ordering
LPAR '01 Proceedings of the Artificial Intelligence on Logic for Programming
RtA '99 Proceedings of the 10th International Conference on Rewriting Techniques and Applications
On Termination of Higher-Order Rewriting
RTA '01 Proceedings of the 12th International Conference on Rewriting Techniques and Applications
From Higher-Order to First-Order Rewriting
RTA '01 Proceedings of the 12th International Conference on Rewriting Techniques and Applications
Well-Founded Recursive Relations
CSL '01 Proceedings of the 15th International Workshop on Computer Science Logic
Termination and Reduction Checking for Higher-Order Logic Programs
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
Term rewriting with variable binding: an initial algebra approach
Proceedings of the 5th ACM SIGPLAN international conference on Principles and practice of declaritive programming
Termination of rewriting in the Calculus of Constructions
Journal of Functional Programming
Definitions by rewriting in the Calculus of Constructions
Mathematical Structures in Computer Science
Verifying Termination and Reduction Properties about Higher-Order Logic Programs
Journal of Automated Reasoning
An initial algebra approach to term rewriting systems with variable binders
Higher-Order and Symbolic Computation
Abstract canonical presentations
Theoretical Computer Science - Clifford lectures and the mathematical foundations of programming semantics
Polymorphic higher-order recursive path orderings
Journal of the ACM (JACM)
Higher-order semantic labelling for inductive datatype systems
Proceedings of the 9th ACM SIGPLAN international conference on Principles and practice of declarative programming
The Computability Path Ordering: The End of a Quest
CSL '08 Proceedings of the 22nd international workshop on Computer Science Logic
A Higher-Order Iterative Path Ordering
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
Languages: From Formal to Natural
Expression reduction systems with patterns
RTA'03 Proceedings of the 14th international conference on Rewriting techniques and applications
RTA'03 Proceedings of the 14th international conference on Rewriting techniques and applications
Rewriting modulo in deduction modulo
RTA'03 Proceedings of the 14th international conference on Rewriting techniques and applications
HORPO with computability closure: a reconstruction
LPAR'07 Proceedings of the 14th international conference on Logic for programming, artificial intelligence and reasoning
Simplifying algebraic functional systems
CAI'11 Proceedings of the 4th international conference on Algebraic informatics
Harnessing first order termination provers using higher order dependency pairs
FroCoS'11 Proceedings of the 8th international conference on Frontiers of combining systems
Higher-order termination: from kruskal to computability
LPAR'06 Proceedings of the 13th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Recursive path orderings can also be incremental
LPAR'05 Proceedings of the 12th 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
Universal algebra for termination of higher-order rewriting
RTA'05 Proceedings of the 16th international conference on Term Rewriting and Applications
Decidability of type-checking in the calculus of algebraic constructions with size annotations
CSL'05 Proceedings of the 19th international conference on Computer Science Logic
Certified higher-order recursive path ordering
RTA'06 Proceedings of the 17th international conference on Term Rewriting and Applications
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
Computability closure: ten years later
Rewriting Computation and Proof
Rewriting Computation and Proof
Jumping and escaping: Modular termination and the abstract path ordering
Theoretical Computer Science
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This paper extends the termination proof techniques based on reduction orderings to a higher-order setting, by adapting the recursive path ordering definition to terms of a typed lambda-calculus generated by a signature of polymorphic higher-order function symbols. The obtained ordering is well-founded, compatible with _-reductions and with polymorphic typing, monotonic with respect to the function symbols, and stable under substitution. It can therefore be used to prove the strong normalization property of higher-order calculi in which constants can be defined by higher-order rewrite rules. 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. Several other non-trivial examples are given which examplify the expressive power of the ordering.