What is Expressiveness in a Computer Language

Chris Smith cdsmith at twu.net
Fri Jun 23 19:08:31 CEST 2006

Marshall <marshall.spight at gmail.com> wrote:
> Ouch; I have a really hard time understanding this.
> I can't see how you'd call + on a and b if you think they might
> not be numbers. If they could be something other than numbers,
> and you're treating them as if they are, is that sort of like
> doing a case analysis and only filling in one of the cases?
> If so, wouldn't you want to record that fact somehow?

The obvious answer -- I don't know if it's what Pascal meant -- is that 
they might be 4x4 matrices, or anything else that behaves predictably 
under some operation that could be called addition.  As a mathematical 
analogy, the entire mathematical field of group theory comes from the 
idea of performing operations on values without really knowing what the 
values (or the operations) really are, but only knowing a few axioms by 
which the relationship between the objects and the operation is 

[As an interesting coincidence, group theory papers frequently use the 
addition symbol to represent the (arbitrary) binary relation of an 
Abelian group.  Not that this has anything to do with choosing "+" for 
the example here.]

Programming languages do this all the time, as well.  The most popular 
example is the OO sense of the word polymorphism.  That's all about 
being able to write code that works with a range of values regardless of 
(or, at least, a range that less constraining than equlity in) types.

Chris Smith - Lead Software Developer / Technical Trainer
MindIQ Corporation

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