>> Mathematica doesn't work this way. The core implements a transformation
>> engine, and arbitrary precision math. Beyond that, the parser, the
>> printer, the simplification rules, *everything* is Mathematica source
>> code, which can be altered at will (if you're so-inclined).
>
> Yep :) pretty much how Maxima works. You can define your own operators,
> their associativity (if any), precedence, and a number of other things.
> Rules are defined in much the way you described. They're all written in
> Maxima's language. There are a few intrinsic things: assignment,
> function calls, and some other syntax glue.... But just about anything
> can be defined as just about anything else.

I haven't tried this, but I understand that the actual input parser for 
Mathematica is user-defined. You can make it parse, e.g., chemical 
formulas rather than algebra. You can change what function-call syntax 
looks like. And so on.

Then again, you don't buy a £7,000 CAS system in order to modify it into 
something that doesn't do math. ;-)

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