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Definitions by Rewriting in the Calculus of Constructions

Frédéric Blanqui
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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 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.

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Frédéric Blanqui. 2006-10-11. Definitions by Rewriting in the Calculus of Constructions. https://arxiv.org/abs/cs/0610065

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