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  <h2><a name="programming-with-concepts" id=
  "programming-with-concepts">Programming with Concepts</a></h2>

  <p>The process of deciding how to group requirements into concepts and
  deciding which concepts to use in each algorithm is perhaps the most
  difficult (yet most important) part of building a generic library. A
  guiding principle to use during this process is one we call the
  <i>requirement minimization principle</i>.</p>

  <p><b>Requirement Minimization Principle:</b> Minimize the requirements on
  the input parameters of a component to increase its reusability.</p>

  <p>There is natural tension in this statement. By definition, the input
  parameters must be used by the component in order for the component to
  accomplish its task (by ``component'' we mean a function or class
  template). The challenge then is to implement the component in such a way
  that makes the fewest assumptions (the minimum requirements) about the
  inputs while still accomplishing the task.</p>

  <p>The traditional notions of <i>abstraction</i> tie in directly to the
  idea of minimal requirements. The more abstract the input, the fewer the
  requirements. Thus, concepts are simply the embodiment of generic abstract
  data types in C++ template programming.</p>

  <p>When designing the concepts for some problem domain it is important to
  keep in mind their purpose, namely to express the requirements for the
  input to the components. With respect to the requirement minimization
  principle, this means we want to minimize concepts. 
  <!-- the following discussion does not match the Standard definition
 of LessThanComparable and needs to be changed -Jeremy

<p>
It is important to note, however, that
minimizing concepts does not mean simply 
reducing the number of valid expressions
in the concept.
For example, the
<tt>std::stable_sort()</tt> function requires that the value type of
the iterator be <a
href="http://www.boost.org/sgi/stl/LessThanComparable.html">
LessThanComparable</a>, which not only
includes <tt>operator&lt;()</tt>, but also <tt>operator&gt;()</tt>,
<tt>operator&lt;=()</tt>, and <tt>operator&gt;=()</tt>.  
It turns out that <tt>std::stable_sort()</tt> only uses
<tt>operator&lt;()</tt>.  The question then arises: should 
<tt>std::stable_sort()</tt> be specified in terms of the concept
<a
href="http://www.boost.org/sgi/stl/LessThanComparable.html">
LessThanComparable</a> or in terms of a concept that only
requires <tt>operator&lt;()</tt>?

<p>
We remark first that the use of <a
href="http://www.boost.org/sgi/stl/LessThanComparable.html">
LessThanComparable</a> does not really violate the requirement
minimization principle because all of the other operators can be
trivially implemented in terms of <tt>operator&lt;()</tt>. By
``trivial'' we mean one line of code and a constant run-time cost.  
More fundamentally, however, the use of <a
href="http://www.boost.org/sgi/stl/LessThanComparable.html">
LessThanComparable</a> does not violate the requirement minimization
principle because all of the comparison operators (<tt>&lt;</tt>,
<tt>></tt>, <tt><=</tt>, <tt>>=</tt>) are conceptually equivalent (in
a mathematical sense).  Adding conceptually equivalent valid
expressions is not a violation of the requirement minimization
principle because no new semantics are being added === only new
syntax. The added syntax increases re-usability.

<p>
For example,
the
maintainer of the <tt>std::stable_sort()</tt> may some day change the
implementation in places to use <tt>operator>()</tt> instead of
<tt>operator<()</tt>, since, after all, they are equivalent.  Since the
requirements are part of the public interface, such a change could
potentially break client code.  If instead
<a
href="http://www.boost.org/sgi/stl/LessThanComparable.html">
LessThanComparable</a> is given as the requirement for
<tt>std::stable_sort()</tt>, then the maintainer is given a reasonable
amount of flexibility within which to work.

--></p>

  <p>Minimality in concepts is a property associated with the underlying
  semantics of the problem domain being represented. In the problem domain of
  basic containers, requiring traversal in a single direction is a smaller
  requirement than requiring traversal in both directions (hence the
  distinction between <a href=
  "http://www.boost.org/sgi/stl/ForwardIterator.html">ForwardIterator</a> and
  <a href=
  "http://www.boost.org/sgi/stl/BidirectionalIterator.html">BidirectionalIterator</a>).
  The semantic difference can be easily seen in the difference between the
  set of concrete data structures that have forward iterators versus the set
  that has bidirectional iterators. For example, singly-linked lists would
  fall in the set of data structures having forward iterators, but not
  bidirectional iterators. In addition, the set of algorithms that one can
  implement using only forward iterators is quite different than the set that
  can be implemented with bidirectional iterators. Because of this, it is
  important to factor families of requirements into rather fine-grained
  concepts. For example, the requirements for iterators are factored into the
  six STL iterator concepts (trivial, output, input, forward, bidirectional,
  and random access).</p>

  <p><a href="./implementation.htm">Next: Implementation</a><br />
  <a href="./concept_covering.htm">Prev: Concept Covering and
  Archetypes</a><br /></p>
  <hr />

  <table>
    <tr valign="top">
      <td nowrap="nowrap">Copyright &copy; 2000</td>

      <td><a href="http://www.boost.org/people/jeremy_siek.htm">Jeremy Siek</a>(<a href=
      "mailto:jsiek@osl.iu.edu">jsiek@osl.iu.edu</a>) Andrew
      Lumsdaine(<a href="mailto:lums@osl.iu.edu">lums@osl.iu.edu</a>),
        2007 <a href="mailto:dave@boost-consulting.com">David Abrahams</a>.
    </tr>
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