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\coverpage{The standard library}%
{\ }
{This material is distributed under the terms of the GNU Lesser
General Public License Version 2.1.}

\tableofcontents

\newpage
% \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:
\begin{description}
  \item[Logic]  Classical logic and dependent equality
  \item[Bool]   Booleans (basic functions and results)
  \item[Arith]  Basic Peano arithmetic
  \item[ZArith] Basic integer arithmetic
  \item[Reals]  Classical Real Numbers and Analysis
  \item[Lists]  Monomorphic and polymorphic lists (basic functions and
                  results), Streams (infinite sequences defined
                  with co-inductive types)
  \item[Sets]   Sets (classical, constructive, finite, infinite, power set,
                  etc.)
  \item[Relations] Relations (definitions and basic results).
  \item[Sorting] Sorted list (basic definitions and heapsort
                 correctness).
  \item[Wellfounded] Well-founded relations (basic results).
  \item[Program] Tactics to deal with dependently-typed programs and
    their proofs.
  \item[Classes] Standard type class instances on relations and
    Coq part of the setoid rewriting tactic.
\end{description}


Each of these subdirectories contains a set of modules, whose
specifications (\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://coq.inria.fr/library}.

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