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  • Cited by 3
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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Jouannaud, Jean-Pierre and Rubio, Albert 2015. Normal Higher-Order Termination. ACM Transactions on Computational Logic, Vol. 16, Issue. 2, p. 1.

    Bunder, M.W. and Seldin, Jonathan P. 2004. Variants of the basic calculus of constructions. Journal of Applied Logic, Vol. 2, Issue. 2, p. 191.

    Blanqui, F. 2001. Proceedings 16th Annual IEEE Symposium on Logic in Computer Science. p. 9.


Termination of rewriting in the Calculus of Constructions

  • DOI:
  • Published online: 01 March 2003

We show how to incorporate rewriting into the Calculus of Constructions and we prove that the resulting system is strongly normalizing with respect to beta and rewrite reductions. An important novelty of this paper is the possibility to define rewriting rules over dependently typed function symbols. We prove strong normalization for any term rewriting system, such that all function symbols satisfy the, so called, star dependency condition, and every rule is accepted by the Higher Order Recursive Path Ordering (which is an extension of the method created by Jouannaud and Rubio for the setting of the simply typed lambda calculus). The proof of strong normalization is done by using a typed version of reducibility candidates due to Coquand and Gallier. Our criterion is general enough to accept definitions by rewriting of many well-known higher order functions, for example dependent recursors for inductive types or proof carrying functions. This makes it a very good candidate for inclusion in a proof assistant based on the Curry-Howard isomorphism.

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Journal of Functional Programming
  • ISSN: 0956-7968
  • EISSN: 1469-7653
  • URL: /core/journals/journal-of-functional-programming
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