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+// -*- C++ -*-
+// Copyright (C) 2013, Gabriel Dos Reis.
+// All rights reserved.
+// Written by Gabriel Dos Reis.
+//
+// Redistribution and use in source and binary forms, with or without
+// modification, are permitted provided that the following conditions are
+// met:
+//
+//     - Redistributions of source code must retain the above copyright
+//       notice, this list of conditions and the following disclaimer.
+//
+//     - Redistributions in binary form must reproduce the above copyright
+//       notice, this list of conditions and the following disclaimer in
+//       the documentation and/or other materials provided with the
+//       distribution.
+//
+//     - Neither the name of OpenAxiom, nor the names of its contributors may
+//       be used to endorse or promote products derived from this software
+//       without specific prior written permission.
+//
+// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS
+// IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
+// TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
+// PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER
+// OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+// LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+#ifndef OPENAXIOM_DEFAULTS_included
+#define OPENAXIOM_DEFAULTS_included
+
+namespace OpenAxiom {
+   // -- The sole purpose of classes defines in this header is to
+   // -- provoke the automatic generation of definitions for functions
+   // -- defined within.  These functions are not really friend.  The
+   // -- friendship is such a mechanism to convince the C++ compiler
+   // -- to do something else.  This is standard technique, also
+   // -- known as `based class parameterized by derived classes', or
+   // -- `curiously recurring pattern'.
+   namespace defaults {
+      // generate definition for != assuming existence of ==.
+      template<typename t>
+      struct neq {
+         friend bool operator!=(t x, t y) { return not(x == y); }
+      };
+
+      // generate definitions for ordering functions assuming <.
+      template<typename t>
+      struct ordering {
+         friend bool operator<=(t x, t y) { return not(y < x); }
+         friend bool operator>(t x, t y) { return y < x; }
+         friend bool operator>=(t x, t y) { return not(x < y); }
+      };
+   }
+}
+
+#endif  // OPENAXIOM_DEFAULTS_included
+
+