Inductive Types in the Calculus of Algebraic Constructions
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- Blanqui F. (2003) Inductive Types in the Calculus of Algebraic Constructions. In: Hofmann M. (eds) Typed Lambda Calculi and Applications. TLCA 2003. Lecture Notes in Computer Science, vol 2701. Springer, Berlin, Heidelberg
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.
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