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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><B><FONT COLOR="#228B22"> <FONT COLOR="#B8860B">E</FONT>
</FONT></B><B><FONT COLOR="#A020F0">val</FONT></B> e1 = E
<B><FONT COLOR="#A020F0">fun</FONT></B> isE1 (e: exn): bool =
   <B><FONT COLOR="#A020F0">case</FONT></B> e <B><FONT COLOR="#A020F0">of</FONT></B>
      E =&gt; true
    | _ =&gt; false
<B><FONT COLOR="#A020F0">exception</FONT></B><B><FONT COLOR="#228B22"> <FONT COLOR="#B8860B">E</FONT>
</FONT></B><B><FONT COLOR="#A020F0">val</FONT></B> e2 = E
<B><FONT COLOR="#A020F0">fun</FONT></B> isE2 (e: exn): bool =
   <B><FONT COLOR="#A020F0">case</FONT></B> e <B><FONT COLOR="#A020F0">of</FONT></B>
      E =&gt; true
    | _ =&gt; false
<B><FONT COLOR="#A020F0">fun</FONT></B> pb (b: bool): unit =
   print (concat [Bool.toString b, <B><FONT COLOR="#BC8F8F">&quot;\n&quot;</FONT></B>])
<B><FONT COLOR="#A020F0">val</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> f (): exn * (exn -&gt; bool) =
   <B><FONT COLOR="#A020F0">let</FONT></B>
      <B><FONT COLOR="#A020F0">exception</FONT></B><B><FONT COLOR="#228B22"> <FONT COLOR="#B8860B">E</FONT>
   </FONT></B><B><FONT COLOR="#A020F0">in</FONT></B>
      (E, <B><FONT COLOR="#A020F0">fn</FONT></B> E =&gt; true | _ =&gt; false)
   <B><FONT COLOR="#A020F0">end</FONT></B>
<B><FONT COLOR="#A020F0">val</FONT></B> (e1, isE1) = f ()
<B><FONT COLOR="#A020F0">val</FONT></B> (e2, isE2) = f ()
<B><FONT COLOR="#A020F0">fun</FONT></B> pb (b: bool): unit =
   print (concat [Bool.toString b, <B><FONT COLOR="#BC8F8F">&quot;\n&quot;</FONT></B>])
<B><FONT COLOR="#A020F0">val</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> f (): ('a -&gt; exn) * (exn -&gt; 'a) =
   <B><FONT COLOR="#A020F0">let</FONT></B>
      <B><FONT COLOR="#A020F0">exception</FONT></B><B><FONT COLOR="#228B22"> <FONT COLOR="#B8860B">E</FONT> <B><FONT COLOR="#A020F0">of</FONT></B> 'a
   </FONT></B><B><FONT COLOR="#A020F0">in</FONT></B>
      (E, <B><FONT COLOR="#A020F0">fn</FONT></B> E x =&gt; x | _ =&gt; <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> cast (a: 'a): 'b =
   <B><FONT COLOR="#A020F0">let</FONT></B>
      <B><FONT COLOR="#A020F0">val</FONT></B> (make: 'a -&gt; exn, _) = f ()
      <B><FONT COLOR="#A020F0">val</FONT></B> (_, get: exn -&gt; '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> _ = ((cast <B><FONT COLOR="#5F9EA0">13</FONT></B>): int -&gt; int) <B><FONT COLOR="#5F9EA0">14</FONT></B>
</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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<hr>
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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