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diff --git a/src/boost/libs/utility/LessThanComparable.html b/src/boost/libs/utility/LessThanComparable.html new file mode 100644 index 00000000..15b938fc --- /dev/null +++ b/src/boost/libs/utility/LessThanComparable.html @@ -0,0 +1,210 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"> + +<html> +<!-- + == Copyright (c) 1996-1999 + == Silicon Graphics Computer Systems, Inc. + == + == Permission to use, copy, modify, distribute and sell this software + == and its documentation for any purpose is hereby granted without fee, + == provided that the above copyright notice appears in all copies and + == that both that copyright notice and this permission notice appear + == in supporting documentation. Silicon Graphics makes no + == representations about the suitability of this software for any + == purpose. It is provided "as is" without express or implied warranty. + == + == Copyright (c) 1994 + == Hewlett-Packard Company + == + == Permission to use, copy, modify, distribute and sell this software + == and its documentation for any purpose is hereby granted without fee, + == provided that the above copyright notice appears in all copies and + == that both that copyright notice and this permission notice appear + == in supporting documentation. Hewlett-Packard Company makes no + == representations about the suitability of this software for any + == purpose. It is provided "as is" without express or implied warranty. + == + --> + +<head> + <meta http-equiv="Content-Language" content="en-us"> + <meta http-equiv="Content-Type" content="text/html; charset=us-ascii"> + + <title>LessThanComparable</title> +</head> + +<body bgcolor="#FFFFFF" link="#0000EE" text="#000000" vlink="#551A8B" alink= +"#FF0000"> + <img src="../../boost.png" alt="C++ Boost" width="277" height= + "86"><br clear="none"> + + <h1>LessThanComparable</h1> + + <h3>Description</h3> + + <p>A type is LessThanComparable if it is ordered: it must be possible to + compare two objects of that type using <tt>operator<</tt>, and + <tt>operator<</tt> must be a strict weak ordering relation.</p> + + <h3>Refinement of</h3> + + <h3>Associated types</h3> + + <h3>Notation</h3> + + <table summary=""> + <tr> + <td valign="top"><tt>X</tt></td> + + <td valign="top">A type that is a model of LessThanComparable</td> + </tr> + + <tr> + <td valign="top"><tt>x</tt>, <tt>y</tt>, <tt>z</tt></td> + + <td valign="top">Object of type <tt>X</tt></td> + </tr> + </table> + + <h3>Definitions</h3> + + <p>Consider the relation <tt>!(x < y) && !(y < x)</tt>. If + this relation is transitive (that is, if <tt>!(x < y) && !(y + < x) && !(y < z) && !(z < y)</tt> implies <tt>!(x + < z) && !(z < x)</tt>), then it satisfies the mathematical + definition of an equivalence relation. In this case, <tt>operator<</tt> + is a <i>strict weak ordering</i>.</p> + + <p>If <tt>operator<</tt> is a strict weak ordering, and if each + equivalence class has only a single element, then <tt>operator<</tt> is + a <i>total ordering</i>.</p> + + <h3>Valid expressions</h3> + + <table border summary=""> + <tr> + <th>Name</th> + + <th>Expression</th> + + <th>Type requirements</th> + + <th>Return type</th> + </tr> + + <tr> + <td valign="top">Less</td> + + <td valign="top"><tt>x < y</tt></td> + + <td valign="top"> </td> + + <td valign="top">Convertible to <tt>bool</tt></td> + </tr> + </table> + + <h3>Expression semantics</h3> + + <table border summary=""> + <tr> + <th>Name</th> + + <th>Expression</th> + + <th>Precondition</th> + + <th>Semantics</th> + + <th>Postcondition</th> + </tr> + + <tr> + <td valign="top">Less</td> + + <td valign="top"><tt>x < y</tt></td> + + <td valign="top"><tt>x</tt> and <tt>y</tt> are in the domain of + <tt><</tt></td> + + <td valign="top"> </td> + </tr> + </table> + + <h3>Complexity guarantees</h3> + + <h3>Invariants</h3> + + <table border summary=""> + <tr> + <td valign="top">Irreflexivity</td> + + <td valign="top"><tt>x < x</tt> must be false.</td> + </tr> + + <tr> + <td valign="top">Antisymmetry</td> + + <td valign="top"><tt>x < y</tt> implies !(y < x) <a href= + "#n2">[2]</a></td> + </tr> + + <tr> + <td valign="top">Transitivity</td> + + <td valign="top"><tt>x < y</tt> and <tt>y < z</tt> implies <tt>x + < z</tt> <a href="#n3">[3]</a></td> + </tr> + </table> + + <h3>Models</h3> + + <ul> + <li>int</li> + </ul> + + <h3>Notes</h3> + + <p><a name="n1" id="n1">[1]</a> Only <tt>operator<</tt> is fundamental; + the other inequality operators are essentially syntactic sugar.</p> + + <p><a name="n2" id="n2">[2]</a> Antisymmetry is a theorem, not an axiom: it + follows from irreflexivity and transitivity.</p> + + <p><a name="n3" id="n3">[3]</a> Because of irreflexivity and transitivity, + <tt>operator<</tt> always satisfies the definition of a <i>partial + ordering</i>. The definition of a <i>strict weak ordering</i> is stricter, + and the definition of a <i>total ordering</i> is stricter still.</p> + + <h3>See also</h3> + + <p><a href= + "http://www.sgi.com/tech/stl/EqualityComparable.html">EqualityComparable</a>, + <a href= + "http://www.sgi.com/tech/stl/StrictWeakOrdering.html">StrictWeakOrdering</a><br> + </p> + <hr> + + <p><a href="http://validator.w3.org/check?uri=referer"><img border="0" src= + "../../doc/images/valid-html401.png" alt="Valid HTML 4.01 Transitional" + height="31" width="88"></a></p> + + <p>Revised + <!--webbot bot="Timestamp" s-type="EDITED" s-format="%d %B, %Y" startspan -->05 + December, 2006<!--webbot bot="Timestamp" endspan i-checksum="38516" --></p> + + <table summary=""> + <tr valign="top"> + <td nowrap><i>Copyright © 2000</i></td> + + <td><i><a href="http://www.lsc.nd.edu/~jsiek">Jeremy Siek</a>, Univ.of + Notre Dame (<a href= + "mailto:jsiek@lsc.nd.edu">jsiek@lsc.nd.edu</a>)</i></td> + </tr> + </table> + + <p><i>Distributed under the Boost Software License, Version 1.0. (See + accompanying file <a href="../../LICENSE_1_0.txt">LICENSE_1_0.txt</a> or + copy at <a href= + "http://www.boost.org/LICENSE_1_0.txt">http://www.boost.org/LICENSE_1_0.txt</a>)</i></p> +</body> +</html> |