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+<div class="section" id="representing-quantities">
+<h1><a class="toc-backref" href="./dimensional-analysis.html#id43" name="representing-quantities">Representing Quantities</a></h1>
+<p>The types listed above are still pure metadata; to typecheck real
+computations we'll need to somehow bind them to our runtime data.
+A simple numeric value wrapper, parameterized on the number type <tt class="literal"><span class="pre">T</span></tt>
+and on its dimensions, fits the bill:</p>
+<pre class="literal-block">
+template &lt;class T, class Dimensions&gt;
+struct quantity
+{
+    explicit quantity(T x)
+       : m_value(x)
+    {}
+
+    T value() const { return m_value; }
+ private:
+    T m_value;
+};
+</pre>
+<!-- @ quantity_declaration = len(stack) - 1 # Remember position for later -->
+<p>Now we have a way to represent numbers associated with dimensions.
+For instance, we can say:</p>
+<pre class="literal-block">
+quantity&lt;float,length&gt; l( 1.0f );
+quantity&lt;float,mass&gt; m( 2.0f );
+</pre>
+<p>Note that <tt class="literal"><span class="pre">Dimensions</span></tt> doesn't appear anywhere in the definition
+of <tt class="literal"><span class="pre">quantity</span></tt> outside the template parameter list; its <em>only</em>
+role is to ensure that <tt class="literal"><span class="pre">l</span></tt> and <tt class="literal"><span class="pre">m</span></tt> have different types.
+Because they do, we cannot make the mistake of assigning a length
+to a mass:</p>
+<pre class="literal-block">
+m = l;    // compile-time type error
+</pre>
+<!-- @ example.wrap('void f() {', '}')
+compile('all', pop = 1, expect_error = True) -->
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