External Rewriting for Skeptical Proof Assistants
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Termination of rewriting in the Calculus of Constructions
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Definitions by rewriting in the Calculus of Constructions
Mathematical Structures in Computer Science
Expressing combinatory reduction systems derivations in the rewriting calculus
Higher-Order and Symbolic Computation
Inductive types in the Calculus of Algebraic Constructions
Fundamenta Informaticae - Typed Lambda Calculi and Applications 2003, Selected Papers
Strong normalisation in two pure pattern type systems
Mathematical Structures in Computer Science
The Computability Path Ordering: The End of a Quest
CSL '08 Proceedings of the 22nd international workshop on Computer Science Logic
Rewriting modulo in deduction modulo
RTA'03 Proceedings of the 14th international conference on Rewriting techniques and applications
Inductive types in the calculus of algebraic constructions
TLCA'03 Proceedings of the 6th international conference on Typed lambda calculi and applications
Inductive types in the Calculus of Algebraic Constructions
Fundamenta Informaticae - Typed Lambda Calculi and Applications 2003, Selected Papers
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Abstract: The main novelty of this paper is to consider an extension of the Calculus of Constructions where predicates can be defined with a general form of rewrite rules. We prove the strong normalization of the reduction relation generated by the β-rule and the user-defined rules under some general syntactic conditions including confluence. As examples, we show that two important systems satisfy these conditions: a sub-system of the Calculus of Inductive Constructions which is the basis of the proof assistant Coq, and the Natural Deduction Modulo a large class of equational theories.