Inductive types in the Calculus of Algebraic Constructions

Details Inductive types in the Calculus of Algebraic Constructions Inductive types in the Calculus of Algebraic Constructions

2006-10-11

arxiv.org/abs/cs/0610070v1

Dans Typed Lambda Calculi and Applications, 6th International Conference, TLCA 2003 2701 (2003)

Computer Science

Logic in Computer Science

Scientific paper

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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