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\coverpage{The standard library}%
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\section*{The \Coq\ standard library}

This document is a short description of the \Coq\ standard library.
This library comes with the system as a complement of the core library
(the {\bf Init} library ; see the Reference Manual for a description
of this library). It provides a set of modules directly available
through the \verb!Require! command.

The standard library is composed of the following subdirectories:

\medskip
\begin{tabular}{lp{12cm}}
  {\bf Logic}   & Classical logic and dependent equality \\
  {\bf Arith}   & Basic Peano arithmetic \\
  {\bf Zarith}  & Basic integer arithmetic \\
  {\bf Bool}    &  Booleans (basic functions and results) \\
  {\bf Lists}   & Monomorphic and polymorphic lists (basic functions and
            results), Streams (infinite sequences defined with co-inductive
            types) \\
  {\bf Sets}    & Sets (classical, constructive, finite, infinite, power set,
            etc.) \\
  {\bf IntMap}    & Representation of finite sets by an efficient
  structure of map (trees indexed by binary integers).\\
 {\bf Reals}   & Axiomatization of Real Numbers (classical, basic functions 
                 and results, integer part and fractional part,
                 requires the \textbf{Zarith} library).\\
 {\bf Relations} & Relations (definitions and basic results). \\
 {\bf Wellfounded} & Well-founded relations (basic results). \\

\end{tabular}
\medskip

Each of these subdirectories contains a set of modules, whose
specifications ({\sf Gallina} files) have
been roughly, and automatically, pasted in the following pages. There
is also a version of this document in HTML format on the WWW, which
you can access from the \Coq\ home page at
\texttt{http://pauillac.inria.fr/coq/coq-eng.html}.

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