Definitions by Rewriting in the Calculus of Constructions

Details Definitions by Rewriting in the Calculus of Constructions Definitions by Rewriting in the Calculus of Constructions

2006-10-11

arxiv.org/abs/cs/0610065v1

Dans 16th Annual IEEE Symposium on Logic in Computer Science (2001)

Computer Science

Logic in Computer Science

Best student paper (Kleene Award)

Scientific paper

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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