Information and Computation - Semantics of Data Types
Proofs and types
Handbook of theoretical computer science (vol. B)
Handbook of logic in computer science (vol. 2)
Combinatory reduction systems: introduction and survey
Theoretical Computer Science - A collection of contributions in honour of Corrado Bo¨hm on the occasion of his 70th birthday
Parametricity and variants of Girard's J operator
Information Processing Letters
COLOG '88 Proceedings of the International Conference on Computer Logic
Definitions by Rewriting in the Calculus of Constructions
LICS '01 Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science
Inductive definition in type theory
Inductive definition in type theory
Polymorphic higher-order recursive path orderings
Journal of the ACM (JACM)
Recursive functions with higher order domains
TLCA'05 Proceedings of the 7th international conference on Typed Lambda Calculi and Applications
Rewriting Computation and Proof
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In a previous work, we proved that almost all of the Calculus of Inductive Constructions (CIC), the basis of the proof assistant Coq, can be seen as a Calculus of Algebraic Constructions (CAC), an extension of the Calculus of Constructions with functions and predicates defined by higher-order rewrite rules. In this paper, we prove that CIC as a whole can be seen as a CAC, and that it can be extended with nonstrictly positive types and inductive-recursive types together with nonfree constructors and pattern-matching on defined symbols.