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Conference Papers Year : 2003

Inductive types in the Calculus of Algebraic Constructions

Abstract

In a previous work, we proved that almost all of the Calculus of Inductive Constructions (CIC), which is 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 not only prove that CIC as a whole can be seen as a CAC, but also that it can be extended with non-free constructors, pattern-matching on defined symbols, non-strictly positive types and inductive-recursive types.
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inria-00105617 , version 1 (11-10-2006)

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Frédéric Blanqui. Inductive types in the Calculus of Algebraic Constructions. Typed Lambda Calculi and Applications, 6th International Conference, TLCA 2003, Jun 2003, Valencia, Spain. ⟨inria-00105617⟩
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