Adding two pointers

[R. Vuurboom]

In article <924 at garcon.cso.uiuc.edu> mcdaniel at uicsrd.csrd.uiuc.edu (Tim McDaniel) writes:
>I've thought of one more argument against pointer addition in C.  It
>is of a more philosophical nature (and thus I grant that it's not as
>strong as my previous ones).
>
Perhaps more of a mathematical nature.

> [Gives argument showing that if addition is added an equation can 
   result that has different types...]

The properties stated result in fact from some basic properties present
in arithmetic models: fields. (These models model our
arithmetic or arithmetic is based on these models - take your pick).

These properties include (math books everyone!) associativity, closure,
inverseness (having an inverse),distribution and a null element and other
pleasant niceties . 

Lets assume pointer addition (new style). There seems to be a consensus that 
this should result in a pointer type. In other words:

		P + Q = R	(where P,Q,R are pointer types)
also
		M + n = P   	( where M,P are pointer types, n is an integer)
		  ^
Now a little operator overloading is going on here. The first + and the
second + are conceptually different operators. So lets use '+' for the 2nd 
operator.

Thus
		M '+' n = P

This is something akin to scalar multiplication of vectors.

Now in "standard" arithmetic models the operation '+' would have to 
support distribution i.e.

		n '+' (P+Q) = (n'+'P) +  (n'+'Q)

Just as 3(a+b) = 3a + 3b.

However the semantics we seem to be aiming for is:

		n '+' (P+Q) = (n'+'P) + Q = P + (n'+'Q)

Now this is going to result in a "nonstandard" model with any number of
(for us) strange arithmetic properties. (Left as exercise to the reader :-).

Now theres nothing intrinsically wrong with nonstandard arithmetic models.
However the makers of C in their infinite wisdom (naive innocence?) were
probably just trying to model standard arithmetic. Which I think is as
it should be. Introducing pointer addition with the above semantics would
have introduced nonstandard arithmetic into the language.


Disclaimer: Opinions are my own, for my employers you pay extra.