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The coq proof assistant reference manual
Inductive Definitions in the system Coq - Rules and Properties
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
The Coq proof assistant : reference manual, version 6.1
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 andExpand
The KRAKATOA tool for certificationof JAVA/JAVACARD programs annotated in JML
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
Inductively Defined Types in the Calculus of Constructions
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
Proofs of randomized algorithms in Coq
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
The Coq Proof Assistant A Tutorial
Extracting ω's programs from proofs in the calculus of constructions
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
Introduction to the Calculus of Inductive Constructions
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 pureExpand