This paper describes the rules for inductive definitions in the system Coq and proves strong normalization for a subsystem of Coq corresponding to the pure Calculus of Constructions plus Inductive Definitions with only weak eliminations.Expand

Coq is a proof assistant based on a higher-order logic allowing powerful definitions of functions. Coq V6.1 is available by anonymous ftp at ftp.inria.fr:/INRIA/Projects/coq/V6.1 and… Expand

The basic structure of an environment for proving Java programs annotated with JML specifications is described, which is generic with respect to the API, and thus well suited for JavaCard applets certification.Expand

It is shown that all primitive recursive functionals over these inductively defined types are also representable, and it is sketched some results that show that the extension of the Calculus of Construction by induction principles does not alter the set of functions in its computational fragment, F ω.Expand

This paper presents a new method for proving properties of randomized algorithms in a proof assistant based on higher-order logic based on the monadic interpretation of randomized programs as probabilistic distributions (Giry, Ramsey and Pfeffer).Expand

This paper defines a notion of realizability for the Calculus of Constructions and introduces a distinction between informative and non-informative propositions that allows the removal of the “logical” part in the development of a program.Expand

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… Expand