Semantics of type theory: correctness, completeness, and independence results
Semantics of type theory: correctness, completeness, and independence results
Handbook of logic in computer science (vol. 2)
Theoretical Computer Science
A compiled implementation of strong reduction
Proceedings of the seventh ACM SIGPLAN international conference on Functional programming
Some Lambda Calculus and Type Theory Formalized
Journal of Automated Reasoning
Subtyping Calculus of Construction (Extended Abstract)
MFCS '97 Proceedings of the 22nd International Symposium on Mathematical Foundations of Computer Science
Using Reflection to Build Efficient and Certified Decision Procedures
TACS '97 Proceedings of the Third International Symposium on Theoretical Aspects of Computer Software
Journal of Functional Programming
Remarks on the equational theory of non-normalizing pure type systems
Journal of Functional Programming
Consistency and completeness of rewriting in the calculus of constructions
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
Extending coq with imperative features and its application to SAT verification
ITP'10 Proceedings of the First international conference on Interactive Theorem Proving
Full reduction at full throttle
CPP'11 Proceedings of the First international conference on Certified Programs and Proofs
Rewriting Computation and Proof
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In proof systems like Coq [16], proof-checking involves comparing types modulo β-conversion, which is potentially a time-consuming task. Significant speed-ups are achieved by compiling proof terms, see [9]. Since compilation erases some type information, we have to show that convertibility is preserved by type erasure. This article shows the equivalence of the Calculus of Inductive Constructions (formalism of Coq) and its domain-free version where parameters of inductive types are also erased. It generalizes and strengthens significantly a similar result by Barthe and Sørensen [5] on the class of functional Domain-free Pure Type Systems.