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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{10cm}}
  {\bf LOGIC}   & Classical logic and dependent equality \\
  {\bf ARITH}   & Basic Peano arithmetic \\
  {\bf ZARITH}  & Binary integers \\
  {\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, powerset,
            etc.) \\
 {\bf RELATIONS} & Relations (definitions and basic results). There is
             a subdirectory about well-founded relations ({\bf WELLFOUNDED}) \\
 {\bf SORTING}   & Axiomatizations of sorts \\
 {\bf REALS}   & Axiomatization of Real Numbers (classical, basic functions 
                 and results, integer part and fractional part, require ZARITH
                 library)
\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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