Typed Lambda Calculi and Applications

Volume 2701 of the series Lecture Notes in Computer Science pp 46-59


Inductive Types in the Calculus of Algebraic Constructions

  • Frédéric BlanquiAffiliated withLaboratoire d’Informatique de l’École Polytechnique

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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 non-strictly positive types and inductive-recursive types together with non-free constructors and pattern-matching on defined symbols.