Completion of a set of rules modulo a set of equations
SIAM Journal on Computing
Counterexamples to termination for the direct sum of term rewriting systems
Information Processing Letters
On termination of the direct sum of term-rewriting systems
Information Processing Letters
Information and Computation - Semantics of Data Types
Proofs and types
ISSAC '89 Proceedings of the ACM-SIGSAM 1989 international symposium on Symbolic and algebraic computation
Polymorphic rewriting conserves algebraic strong normalization
Selected papers of the 16th international colloquium on Automata, languages, and programming
Handbook of theoretical computer science (vol. B)
An algorithm for testing conversion in type theory
Logical frameworks
Adding algebraic rewriting to the untyped lambda calculus
Information and Computation
Handbook of logic in computer science (vol. 2)
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
Theoretical Computer Science - Special issue on theories of types and proofs
Weak Orthogonality Implies Confluence: The Higher Order Case
LFCS '94 Proceedings of the Third International Symposium on Logical Foundations of Computer Science
The Higher-Order Recursive Path Ordering
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
Definitions by Rewriting in the Calculus of Constructions
LICS '01 Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science
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
Higher-order termination: from kruskal to computability
LPAR'06 Proceedings of the 13th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
LPAR'06 Proceedings of the 13th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
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
Computability closure: ten years later
Rewriting Computation and Proof
Rewriting Computation and Proof
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We study the termination of rewriting modulo a set of equations in the Calculus of Algebraic Constructions, an extension of the Calculus of Constructions with functions and predicates defined by higher-order rewrite rules. In a previous work, we defined general syntactic conditions based on the notion of computability closure for ensuring the termination of the combination of rewriting and β-reduction. Here, we show that this result is preserved when considering rewriting modulo a set of equations if the equivalence classes generated by these equations are finite, the equations are linear and satisfy general syntactic conditions also based on the notion of computability closure. This includes equations like associativity and commutativity and provides an original treatment of termination modulo equations.