Definitions by Rewriting in the Calculus of Constructions

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 -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.

• Type: Journal
• Year: 2006
• Where: CORR
• Authors: Frédéric Blanqui
• Keywords: CORR 2006, Education, General Syntactic Conditions, Natural Deduction Modulo, Proof Assistant Coq