A logic programming language with Lambda-abstraction, function variables, and simple unification
Proceedings of the international workshop on Extensions of logic programming
Combinatory reduction systems: introduction and survey
Theoretical Computer Science - A collection of contributions in honour of Corrado Bo¨hm on the occasion of his 70th birthday
Proving the correctness of reactive systems using sized types
POPL '96 Proceedings of the 23rd ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Termination and Confluence of Higher-Order Rewrite Systems
RTA '00 Proceedings of the 11th International Conference on Rewriting Techniques and Applications
Transforming Termination by Self-Labelling
CADE-13 Proceedings of the 13th International Conference on Automated Deduction: Automated Deduction
Abstract Syntax and Variable Binding
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
Dependent Types for Program Termination Verification
LICS '01 Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science
Inductive definition in type theory
Inductive definition in type theory
Type-based termination of recursive definitions
Mathematical Structures in Computer Science
Definitions by rewriting in the Calculus of Constructions
Mathematical Structures in Computer Science
Higher-order semantic labelling for inductive datatype systems
Proceedings of the 9th ACM SIGPLAN international conference on Principles and practice of declarative programming
LPAR'06 Proceedings of the 13th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
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
RTA'06 Proceedings of the 17th international conference on Term Rewriting and Applications
Termination Of Term Rewriting By Semantic Labelling
Fundamenta Informaticae
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We investigate the relationship between two independently developed termination techniques. On the one hand, sized-types based termination (SBT) uses types annotated with size expressions and Girard's reducibility candidates, and applies on systems using constructor matching only. On the other hand, semantic labelling transforms a rewrite system by annotating each function symbol with the semantics of its arguments, and applies to any rewrite system. First, we introduce a simplified version of SBT for the simply-typed lambda-calculus. Then, we give new proofs of the correctness of SBT using semantic labelling, both in the first and in the higher-order case. As a consequence, we show that SBT can be extended to systems using matching on defined symbols (e.g. associative functions).