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Inductive Consequences in the Calculus of Constructions

  • Daria Walukiewicz-Chrząszcz
  • Jacek Chrząszcz
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6172)

Abstract

Extending the calculus of constructions with rewriting would greatly improve the efficiency of proof assistants such as Coq. In this paper we address the issue of the logical power of such an extension.

In our previous work we proposed a procedure to check completeness of user-defined rewrite systems. In many cases this procedure demonstrates that only a basic subset of the rules is sufficient for completeness. Now we investigate the question whether the remaining rules are inductive consequences of the basic subset.

We show that the answer is positive for most practical rewrite systems. It is negative for some systems whose critical pair diagrams require rewriting under a lambda. However the positive answer can be recovered when the notion of inductive consequences is modified by allowing a certain form of functional extensionality.

Keywords

Inductive Consequence Type Theory Additional Rule Critical Pair Proof Assistant 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Daria Walukiewicz-Chrząszcz
    • 1
  • Jacek Chrząszcz
    • 1
  1. 1.Institute of InformaticsWarsaw UniversityWarsawPoland

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