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
Higher-order rewrite systems and their confluence
Theoretical Computer Science - Special issue: rewriting systems and applications
Intersection types and computational effects
ICFP '00 Proceedings of the fifth ACM SIGPLAN international conference on Functional programming
Higher-Order and Symbolic Computation
Dependent Types for Program Termination Verification
Higher-Order and Symbolic Computation
Termination and Confluence of Higher-Order Rewrite Systems
RTA '00 Proceedings of the 11th International Conference on Rewriting Techniques and Applications
Comparing Combinatory Reduction Systems and Higher-order Rewrite Systems
HOA '93 Selected Papers from the First International Workshop on Higher-Order Algebra, Logic, and Term Rewriting
Dependent types in practical programming
Dependent types in practical programming
Type-based termination of recursive definitions
Mathematical Structures in Computer Science
Definitions by rewriting in the Calculus of Constructions
Mathematical Structures in Computer Science
Rewriting modulo in deduction modulo
RTA'03 Proceedings of the 14th international conference on Rewriting techniques and applications
Termination and productivity checking with continuous types
TLCA'03 Proceedings of the 6th international conference on Typed lambda calculi and applications
On the confluence of λ-calculus with conditional rewriting
FOSSACS'06 Proceedings of the 9th European joint conference on Foundations of Software Science and Computation Structures
Practical inference for type-based termination in a polymorphic setting
TLCA'05 Proceedings of the 7th international conference on Typed Lambda Calculi 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
Union of Reducibility Candidates for Orthogonal Constructor Rewriting
CiE '08 Proceedings of the 4th conference on Computability in Europe: Logic and Theory of Algorithms
Type-Based Termination with Sized Products
CSL '08 Proceedings of the 22nd international workshop on Computer Science Logic
On the Values of Reducibility Candidates
TLCA '09 Proceedings of the 9th International Conference on Typed Lambda Calculi and Applications
On the stability by union of reducibility candidates
FOSSACS'07 Proceedings of the 10th international conference on Foundations of software science and computational structures
Strong normalization and equi-(co)inductive types
TLCA'07 Proceedings of the 8th international conference on Typed lambda calculi and applications
Mixed inductive/coinductive types and strong normalization
APLAS'07 Proceedings of the 5th Asian conference on Programming languages and systems
On the relation between sized-types based termination and semantic labelling
CSL'09/EACSL'09 Proceedings of the 23rd CSL international conference and 18th EACSL Annual conference on Computer science logic
Higher-order termination: from kruskal to computability
LPAR'06 Proceedings of the 13th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Wellfounded recursion with copatterns: a unified approach to termination and productivity
Proceedings of the 18th ACM SIGPLAN international conference on Functional programming
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In a previous work, the first author extended to higher-order rewriting and dependent types the use of size annotations in types, a termination proof technique called type or size based termination and initially developed for ML-like programs. Here, we go one step further by considering conditional rewriting and explicit quantifications and constraints on size annotations. This allows to describe more precisely how the size of the output of a function depends on the size of its inputs. Hence, we can check the termination of more functions. We first give a general type-checking algorithm based on constraint solving. Then, we give a termination criterion with constraints in Presburger arithmetic. To our knowledge, this is the first termination criterion for higher-order conditional rewriting taking into account the conditions in termination.