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avram


			
				
					
						
						
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<h5 class="subsubsection">2.7.4.2 Semantics</h5>

<p>Declarations in <code>silly</code> should be understood in the obvious way as
preprocessor directives to perform parenthetic textual substitutions (similar to
<code>#define id (exp)</code> in C). All identifiers in expressions are thereby
eliminated during the preprocessing phase.

   <p><a name="index-semantic-function-257"></a>The overall meaning of the program is the meaning of the expression in
the last declaration.  A denotational semantics for expressions is given
by the following equations, where [[<var>x</var>]] should be read as
&ldquo;the meaning of <var>x</var>&rdquo;, and <var>x</var>, <var>y</var> and <var>z</var>
are metavariables. (That is, they stand for any source code fragment
that could fit there subject to the constraint, informally speaking,
that it has to correspond to a connected subtree of the parse tree as enforced
by the unambiguous grammar in the context of the rest of the program.)

<pre class="display">     
     [[<code>()</code>]] = <code>nil</code>
     
     [[<code>(</code><var>x</var><code>)</code>]] = [[<var>x</var>]]
     
     [[<code>(</code><var>x</var><code>,</code><var>y</var><code>)</code>]] = <code>cons(</code>[[<var>x</var>]]<code>,</code>[[<var>y</var>]]<code>)</code>
     
     [[<var>x</var> <var>y</var>]] = [[<var>x</var><code>(</code><var>y</var><code>)</code>]] = [[<var>x</var>]] [[<var>y</var>]]
     
     [[<var>x</var><code> (</code><var>y</var><code>,</code><var>z</var><code>)</code>]] = [[<var>x</var><code>(</code><var>y</var><code>,</code><var>z</var><code>)</code>]] = [[<var>x</var>]] [[<code>(</code><var>y</var><code>,</code><var>z</var><code>)</code>]]
     
</pre>
   <p class="noindent">Toy languages like this are among the few situations a
<a name="index-denotational-semantics-258"></a>denotational semantics stands a chance of clarifying more than it
obfuscates, so the reader is invited to take a moment to savor it.

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