Definitions by Rewriting in the Calculus of Constructions
<|reference_start|>Definitions by Rewriting in the Calculus of Constructions: 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 beta-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.<|reference_end|>
@article{blanqui2006definitions,
    title={Definitions by Rewriting in the Calculus of Constructions},
    author={Fr'ed'eric Blanqui (LRI)},
    journal={Dans 16th Annual IEEE Symposium on Logic in Computer Science
  (2001)},
    year={2006},
    archivePrefix={arXiv},
    eprint={cs/0610065},
    primaryClass={cs.LO}
}