Introduction to the Calculus of Inductive Constructions

Christine Paulin-Mohring 1, 2, *
* Corresponding author
2 TOCCATA - Certified Programs, Certified Tools, Certified Floating-Point Computations
LRI - Laboratoire de Recherche en Informatique, UP11 - Université Paris-Sud - Paris 11, Inria Saclay - Ile de France, CNRS - Centre National de la Recherche Scientifique : UMR8623
Abstract : This paper gives an introduction to the Calculus of Inductive Constructions, the formalism behind the Coq proof assistant. We present the language and the typing rules, starting with the pure functional part and then introducing the inductive declarations. We briefly discuss the properties of this language, both from the theoretical and pragmatic points of view and give examples of applications.
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Christine Paulin-Mohring. Introduction to the Calculus of Inductive Constructions. Bruno Woltzenlogel Paleo; David Delahaye. All about Proofs, Proofs for All, 55, College Publications, 2015, Studies in Logic (Mathematical logic and foundations), 978-1-84890-166-7. ⟨http://www.collegepublications.co.uk/logic/mlf/?00023⟩. ⟨hal-01094195⟩

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