Fundamentals of Algebraic Specification I
Fundamentals of Algebraic Specification I
Inductive Definitions in the system Coq - Rules and Properties
TLCA '93 Proceedings of the International Conference on Typed Lambda Calculi and Applications
The Calculus of algebraic Constructions
RtA '99 Proceedings of the 10th International Conference on Rewriting Techniques and Applications
Termination of rewriting in the Calculus of Constructions
Journal of Functional Programming
Modularity of strong normalization in the algebraic-λ-cube
Journal of Functional Programming
Definitions by rewriting in the Calculus of Constructions
Mathematical Structures in Computer Science
PLPV '07 Proceedings of the 2007 workshop on Programming languages meets program verification
A Modular Type-Checking Algorithm for Type Theory with Singleton Types and Proof Irrelevance
TLCA '09 Proceedings of the 9th International Conference on Typed Lambda Calculi and Applications
TYPES'02 Proceedings of the 2002 international conference on Types for proofs and programs
Extensionality in the calculus of constructions
TPHOLs'05 Proceedings of the 18th international conference on Theorem Proving in Higher Order Logics
Inductive consequences in the calculus of constructions
ITP'10 Proceedings of the First international conference on Interactive Theorem Proving
Building decision procedures in the calculus of inductive constructions
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
Inductive consequences in the calculus of constructions
ITP'10 Proceedings of the First international conference on Interactive Theorem Proving
Rewriting Computation and Proof
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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.