File: GenerativeException

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In <a href="StandardML">Standard ML</a>, exception declarations are said to be <em>generative</em>, because each time an exception declaration is evaluated, it yields a new exception. <p>
The following program demonstrates the generativity of exceptions. 
<pre class=code>
<B><FONT COLOR="#A020F0">exception</FONT></B> E
<B><FONT COLOR="#A020F0">val</FONT></B> e1 <B><FONT COLOR="#5F9EA0">=</FONT></B> E
<B><FONT COLOR="#A020F0">fun </FONT></B><B><FONT COLOR="#0000FF"><B><I><FONT COLOR="#000000">isE1</FONT></I></B></FONT></B> (e: exn): <B><FONT COLOR="#228B22">bool</FONT></B> <B><FONT COLOR="#5F9EA0">=</FONT></B>
   <B><FONT COLOR="#A020F0">case</FONT></B> e <B><FONT COLOR="#A020F0">of</FONT></B>
      E <B><FONT COLOR="#5F9EA0">=</FONT></B><B><FONT COLOR="#5F9EA0">&gt;</FONT></B> true
    <B><FONT COLOR="#5F9EA0">|</FONT></B> _ <B><FONT COLOR="#5F9EA0">=</FONT></B><B><FONT COLOR="#5F9EA0">&gt;</FONT></B> false
<B><FONT COLOR="#A020F0">exception</FONT></B> E
<B><FONT COLOR="#A020F0">val</FONT></B> e2 <B><FONT COLOR="#5F9EA0">=</FONT></B> E
<B><FONT COLOR="#A020F0">fun </FONT></B><B><FONT COLOR="#0000FF"><B><I><FONT COLOR="#000000">isE2</FONT></I></B></FONT></B> (e: exn): <B><FONT COLOR="#228B22">bool</FONT></B> <B><FONT COLOR="#5F9EA0">=</FONT></B>
   <B><FONT COLOR="#A020F0">case</FONT></B> e <B><FONT COLOR="#A020F0">of</FONT></B>
      E <B><FONT COLOR="#5F9EA0">=</FONT></B><B><FONT COLOR="#5F9EA0">&gt;</FONT></B> true
    <B><FONT COLOR="#5F9EA0">|</FONT></B> _ <B><FONT COLOR="#5F9EA0">=</FONT></B><B><FONT COLOR="#5F9EA0">&gt;</FONT></B> false
<B><FONT COLOR="#A020F0">fun </FONT></B><B><FONT COLOR="#0000FF"><B><I><FONT COLOR="#000000">pb</FONT></I></B></FONT></B> (b: <B><FONT COLOR="#228B22">bool</FONT></B>): <B><FONT COLOR="#228B22">unit</FONT></B> <B><FONT COLOR="#5F9EA0">=</FONT></B>
   <B><FONT COLOR="#A020F0">print</FONT></B> (<B><FONT COLOR="#A020F0">concat</FONT></B> [Bool.toString b, <B><FONT COLOR="#BC8F8F">&quot;\n&quot;</FONT></B>])
<B><FONT COLOR="#A020F0">val</FONT></B> () <B><FONT COLOR="#5F9EA0">=</FONT></B> (pb (isE1 e1)
          ;pb (isE1 e2)
          ; pb (isE2 e1)
          ; pb (isE2 e2))
</PRE>
 In the above program, two different exception declarations declare an exception <tt>E</tt> and a corresponding function that returns <tt>true</tt> only on that exception.  Although declared by syntactically identical exception declarations, <tt>e1</tt> and <tt>e2</tt> are different exceptions.  The program, when run, prints <tt>true</tt>, <tt>false</tt>, <tt>false</tt>, <tt>true</tt>. 
</p>
<p>
A slight modification of the above program shows that even a single exception declaration yields a new exception each time it is evaluated. 
<pre class=code>
<B><FONT COLOR="#A020F0">fun </FONT></B><B><FONT COLOR="#0000FF"><B><I><FONT COLOR="#000000">f</FONT></I></B></FONT></B> (): exn <B><FONT COLOR="#5F9EA0">*</FONT></B> (exn <B><FONT COLOR="#5F9EA0">-</FONT></B><B><FONT COLOR="#5F9EA0">&gt;</FONT></B> <B><FONT COLOR="#228B22">bool</FONT></B>) <B><FONT COLOR="#5F9EA0">=</FONT></B>
   <B><FONT COLOR="#A020F0">let</FONT></B>
      <B><FONT COLOR="#A020F0">exception</FONT></B> E
   <B><FONT COLOR="#A020F0">in</FONT></B>
      (E, <B><FONT COLOR="#A020F0">fn</FONT></B> E <B><FONT COLOR="#5F9EA0">=</FONT></B><B><FONT COLOR="#5F9EA0">&gt;</FONT></B> true <B><FONT COLOR="#5F9EA0">|</FONT></B> _ <B><FONT COLOR="#5F9EA0">=</FONT></B><B><FONT COLOR="#5F9EA0">&gt;</FONT></B> false)
   <B><FONT COLOR="#A020F0">end</FONT></B>
<B><FONT COLOR="#A020F0">val</FONT></B> (e1, isE1) <B><FONT COLOR="#5F9EA0">=</FONT></B> f ()
<B><FONT COLOR="#A020F0">val</FONT></B> (e2, isE2) <B><FONT COLOR="#5F9EA0">=</FONT></B> f ()
<B><FONT COLOR="#A020F0">fun </FONT></B><B><FONT COLOR="#0000FF"><B><I><FONT COLOR="#000000">pb</FONT></I></B></FONT></B> (b: <B><FONT COLOR="#228B22">bool</FONT></B>): <B><FONT COLOR="#228B22">unit</FONT></B> <B><FONT COLOR="#5F9EA0">=</FONT></B>
   <B><FONT COLOR="#A020F0">print</FONT></B> (<B><FONT COLOR="#A020F0">concat</FONT></B> [Bool.toString b, <B><FONT COLOR="#BC8F8F">&quot;\n&quot;</FONT></B>])
<B><FONT COLOR="#A020F0">val</FONT></B> () <B><FONT COLOR="#5F9EA0">=</FONT></B> (pb (isE1 e1)
          ; pb (isE1 e2)
          ; pb (isE2 e1)
          ; pb (isE2 e2))
</PRE>
 Each call to <tt>f</tt> yields a new exception and a function that returns <tt>true</tt> only on that exception.  The program, when run, prints <tt>true</tt>, <tt>false</tt>, <tt>false</tt>, <tt>true</tt>. 
</p>
<h2 id="head-86469abfaa44f69bd741f559ff1bb935309ad35e">Type Safety</h2>
<p>
Exception generativity is required for type safety.  Consider the following valid SML program. 
<pre class=code>
<B><FONT COLOR="#A020F0">fun </FONT></B><B><FONT COLOR="#0000FF"><B><I><FONT COLOR="#000000">f</FONT></I></B></FONT></B> (): ('a <B><FONT COLOR="#5F9EA0">-</FONT></B><B><FONT COLOR="#5F9EA0">&gt;</FONT></B> exn) <B><FONT COLOR="#5F9EA0">*</FONT></B> (exn <B><FONT COLOR="#5F9EA0">-</FONT></B><B><FONT COLOR="#5F9EA0">&gt;</FONT></B> 'a) <B><FONT COLOR="#5F9EA0">=</FONT></B>
   <B><FONT COLOR="#A020F0">let</FONT></B>
      <B><FONT COLOR="#A020F0">exception</FONT></B> E <B><FONT COLOR="#A020F0">of</FONT></B> 'a
   <B><FONT COLOR="#A020F0">in</FONT></B>
      (E, <B><FONT COLOR="#A020F0">fn</FONT></B> E x <B><FONT COLOR="#5F9EA0">=</FONT></B><B><FONT COLOR="#5F9EA0">&gt;</FONT></B> x <B><FONT COLOR="#5F9EA0">|</FONT></B> _ <B><FONT COLOR="#5F9EA0">=</FONT></B><B><FONT COLOR="#5F9EA0">&gt;</FONT></B> <B><FONT COLOR="#A020F0">raise</FONT></B> Fail <B><FONT COLOR="#BC8F8F">&quot;f&quot;</FONT></B>)
   <B><FONT COLOR="#A020F0">end</FONT></B>
<B><FONT COLOR="#A020F0">fun </FONT></B><B><FONT COLOR="#0000FF"><B><I><FONT COLOR="#000000">cast</FONT></I></B></FONT></B> (a: 'a): 'b <B><FONT COLOR="#5F9EA0">=</FONT></B>
   <B><FONT COLOR="#A020F0">let</FONT></B>
      <B><FONT COLOR="#A020F0">val</FONT></B> (make: 'a <B><FONT COLOR="#5F9EA0">-</FONT></B><B><FONT COLOR="#5F9EA0">&gt;</FONT></B> exn, _) <B><FONT COLOR="#5F9EA0">=</FONT></B> f ()
      <B><FONT COLOR="#A020F0">val</FONT></B> (_, get: exn <B><FONT COLOR="#5F9EA0">-</FONT></B><B><FONT COLOR="#5F9EA0">&gt;</FONT></B> 'b) <B><FONT COLOR="#5F9EA0">=</FONT></B> f ()
   <B><FONT COLOR="#A020F0">in</FONT></B>
      get (make a)
   <B><FONT COLOR="#A020F0">end</FONT></B>
<B><FONT COLOR="#A020F0">val</FONT></B> _ <B><FONT COLOR="#5F9EA0">=</FONT></B> ((cast 13): <B><FONT COLOR="#228B22">int</FONT></B> <B><FONT COLOR="#5F9EA0">-</FONT></B><B><FONT COLOR="#5F9EA0">&gt;</FONT></B> <B><FONT COLOR="#228B22">int</FONT></B>) 14
</PRE>
 
</p>
<p>
If exceptions weren't generative, then each call <tt>f&nbsp;()</tt> would yield the same exception constructor <tt>E</tt>.  Then, our <tt>cast</tt> function could use <tt>make:&nbsp;'a&nbsp;-&gt;&nbsp;exn</tt> to convert any value into an exception and then <tt>get:&nbsp;exn&nbsp;-&gt;&nbsp;'b</tt> to convert that exception to a value of arbitrary type.  If <tt>cast</tt> worked, then we could cast an integer as a function and apply.  Of course, because of generative exceptions, this program raises <tt>Fail&nbsp;"f"</tt>. 
</p>
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Last edited on 2005-01-26 20:34:34 by <span title="cfs36.cs.cornell.edu"><a href="MatthewFluet">MatthewFluet</a></span>.
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