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In <a href="StandardML">Standard ML</a>, datatype declarations are said to be <em>generative</em>, because each time a datatype declaration is evaluated, it yields a new type.  Thus, any attempt to mix the types will lead to a type error at compile-time.  The following program, which does not type check, demonstrates this. 
<pre class=code>
<B><FONT COLOR="#0000FF">functor</FONT></B> F () =
   <B><FONT COLOR="#0000FF">struct</FONT></B>
      <B><FONT COLOR="#A020F0">datatype</FONT></B><B><FONT COLOR="#228B22"> t </FONT></B>=<B><FONT COLOR="#228B22"> <FONT COLOR="#B8860B">T</FONT>
   </FONT></B><B><FONT COLOR="#0000FF">end</FONT></B>
<B><FONT COLOR="#0000FF">structure</FONT></B> S1 = F ()
<B><FONT COLOR="#0000FF">structure</FONT></B> S2 = F ()
<B><FONT COLOR="#A020F0">val</FONT></B> _: S1.t -&gt; S2.t = <B><FONT COLOR="#A020F0">fn</FONT></B> x =&gt; x
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Generativity also means that two different datatype declarations define different types, even if they define identical constructors. The following program does not type check due to this. 
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<pre class=code>
<B><FONT COLOR="#A020F0">datatype</FONT></B><B><FONT COLOR="#228B22"> t </FONT></B>=<B><FONT COLOR="#228B22"> <FONT COLOR="#B8860B">A</FONT> </FONT></B>|<B><FONT COLOR="#228B22"> <FONT COLOR="#B8860B">B</FONT>
</FONT></B><B><FONT COLOR="#A020F0">val</FONT></B> a1 = A
<B><FONT COLOR="#A020F0">datatype</FONT></B><B><FONT COLOR="#228B22"> t </FONT></B>=<B><FONT COLOR="#228B22"> <FONT COLOR="#B8860B">A</FONT> </FONT></B>|<B><FONT COLOR="#228B22"> <FONT COLOR="#B8860B">B</FONT>
</FONT></B><B><FONT COLOR="#A020F0">val</FONT></B> a2 = A
<B><FONT COLOR="#A020F0">val</FONT></B> _ = <B><FONT COLOR="#A020F0">if</FONT></B> true <B><FONT COLOR="#A020F0">then</FONT></B> a1 <B><FONT COLOR="#A020F0">else</FONT></B> a2
</PRE>
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Last edited on 2005-01-26 20:34:48 by <span title="cfs36.cs.cornell.edu"><a href="MatthewFluet">MatthewFluet</a></span>.
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