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

2006-10-12

arxiv.org/abs/cs/0610073v1

Fundamenta Informaticae 65, 1-2 (2005) 61-86

Computer Science

Logic in Computer Science

Journal version of TLCA'03

Scientific paper

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.

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