Information and Computation - Semantics of Data Types
Unification in a combination of arbitrary disjoint equational theories
Journal of Symbolic Computation
Handbook of logic in computer science (vol. 2)
A Practical Decision Procedure for Arithmetic with Function Symbols
Journal of the ACM (JACM)
LICS '02 Proceedings of the 17th Annual IEEE Symposium on Logic in Computer Science
Structural Recursive Definitions in Type Theory
ICALP '98 Proceedings of the 25th International Colloquium on Automata, Languages and Programming
The Relevance of Proof-Irrelevance
ICALP '98 Proceedings of the 25th International Colloquium on Automata, Languages and Programming
Unification in the Union of Disjoint Equational Theories: Combining Decision Procedures
CADE-11 Proceedings of the 11th International Conference on Automated Deduction: Automated Deduction
COLOG '88 Proceedings of the International Conference on Computer Logic
Definitions by rewriting in the Calculus of Constructions
Mathematical Structures in Computer Science
Extensionality in the calculus of constructions
TPHOLs'05 Proceedings of the 18th international conference on Theorem Proving in Higher Order Logics
Inductive types in the Calculus of Algebraic Constructions
Fundamenta Informaticae - Typed Lambda Calculi and Applications 2003, Selected Papers
Proceedings of the 9th AISC international conference, the 15th Calculemas symposium, and the 7th international MKM conference on Intelligent Computer Mathematics
Weak βη -Normalization and Normalization by Evaluation for System F
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
CSL'10/EACSL'10 Proceedings of the 24th international conference/19th annual conference on Computer science logic
Inductive consequences in the calculus of constructions
ITP'10 Proceedings of the First international conference on Interactive Theorem Proving
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It is commonly agreed that the success of future proof assistants will rely on their ability to incorporate computations within deduction in order to mimic the mathematician when replacing the proof of a proposition P by the proof of an equivalent proposition P' obtained from P thanks to possibly complex calculations. In this paper, we investigate a new version of the calculus of inductive constructions which incorporates arbitrary decision procedures into deduction via the conversion rule of the calculus. The novelty of the problem in the context of the calculus of inductive constructions lies in the fact that the computation mechanism varies along proof-checking: goals are sent to the decision procedure together with the set of user hypotheses available from the current context. Our main result shows that this extension of the calculus of constructions does not compromise its main properties: confluence, subject reduction, strong normalization and consistency are all preserved.