is sort of extension.
&gt; 
&gt; [ Note:  I think that the most general name for this in mathematics
&gt; | is the "De Rham Extension", and I have begun to look into this,
&gt; | but it is really just what you do when you add differential forms
&gt; | to analytic geometry.  All in all, I am just exploiting the analogy
&gt; | betweeen Propositional Calculus, as a study of functions B^n -&gt; B,
&gt; | and Real Analysis, as a study of functions R^n -&gt; R, and asking:
&gt; | What is the proper form of differ