---
title: Definitions by Rewriting in the Calculus of Constructions
url: https://www.emergentmind.com/papers/0610065
type: paper
arxiv_id: '0610065'
arxiv_url: https://arxiv.org/abs/0610065
published: '2006-10-11'
categories:
- cs.LO
---

# 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 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.