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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 => true
| _ => 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 => true
| _ => false
<B><FONT COLOR="#A020F0">fun</FONT></B> pb (b: bool): unit =
print (concat [Bool.toString b, <B><FONT COLOR="#BC8F8F">"\n"</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 -> 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 => true | _ => 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">"\n"</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 -> exn) * (exn -> '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 => x | _ => <B><FONT COLOR="#A020F0">raise</FONT></B> Fail <B><FONT COLOR="#BC8F8F">"f"</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 -> exn, _) = f ()
<B><FONT COLOR="#A020F0">val</FONT></B> (_, get: exn -> '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 -> int) <B><FONT COLOR="#5F9EA0">14</FONT></B>
</PRE>
</p>
<p>
If exceptions weren't generative, then each call <tt>f ()</tt> would yield the same exception constructor <tt>E</tt>. Then, our <tt>cast</tt> function could use <tt>make: 'a -> exn</tt> to convert any value into an exception and then <tt>get: exn -> '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 "f"</tt>.
</p>
<h2 id="head-76c74bd071dd73f01696fddbbffc77712a479faf">Applications</h2>
<p>
The <tt>exn</tt> type is effectively a <a href="UniversalType">universal type</a>.
</p>
<h2 id="head-a4bc8bf5caf54b18cea9f58e83dd4acb488deb17">Also see</h2>
<ul>
<li>
<p>
<a href="GenerativeDatatype">GenerativeDatatype</a>
</p>
</li>
</ul>
</div>
<p>
<hr>
Last edited on 2010-03-02 15:11:39 by <span title="fenrir.cs.rit.edu"><a href="MatthewFluet">MatthewFluet</a></span>.
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