Inductive types in the Calculus of Algebraic Constructions

Authors:
Frédéric Blanqui
Affiliations:
LORIA & INRIA 615 rue du Jardin Botanique, BP 101, 54602 Villers-lèès-Nancy, France. blanqui@loria.fr (Corresp.)
Venue:
Fundamenta Informaticae - Typed Lambda Calculi and Applications 2003, Selected Papers
Year:
2004

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Abstract

In a previous work, we proved that an important part of the Calculus of Inductive Constructions (CIC), the basis of the Coq proof assistant, 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 almost all CIC can be seen as a CAC, and that it can be further extended with non-strictly positive types and inductive-recursive types together with non-free constructors and pattern-matching on defined symbols.