CHAT: Algebra? proramming langs, was Re: CHAT: OS pain

Dennis Paul Himes writes:
 > Brook Conner <nellardo@...> wrote:
 > > Sure, most PLs support some form of mathematical expressions, but even
 > > those have little to do with *algebra*

 >     Well, n-bit bit maps in C are isomorphic to a 2^n element Boolean
 > algebra.

True, but....

Somehow I doubt K & R were thinking of that when they designed
C.... :-)

I would say this is a case of alegbra happening to describe a
particular phenomenon, rather than a feature designed to reflect
algebra.

 > In addition, addition on a numeric data type can be treated as an
 > Abelian group, and multiplication as a field, even though they're not really
 > (due to overflow considerations).

You can be more rigorous with integer types by pretending "+" is
really "+ modulo precision", similarly for multiplication.  But again,
they weren't designed that way, and people don't use them that
way. They just happen to be that way.  This is more of a statement of
the power of abstract algebra than of the design of the PL.

Even this is only a very limited application of algebra, either in its
abstract form or in the kind we all remember from high school.

And the point was that we wanted a *linguistic* PL, not an *algebraic*
PL. :-)

Brook

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