Re: Language design values (Re: message primitive)

[Lynn Winebarger <owinebar at free-expression dot org>]

On Tue, 11 Jan 2000, Maciej Stachowiak wrote:

> "Reynolds, Gregg" wrote:
> > 
> > 
> > Question:  how can one express the notion that the members of the basis set
> > themselves are maximally simple?  Presumably one could define a basis set
> > that includes semantically complex functions which could be expressed as a
> > combination of a different basis set.  I'm having trouble at the moment
> > coming up with a realistic example, but suppose you had a "frobnicate"
> > function that really means "first bevorpilate, then pibbelize", but the
> > latter two are excluded from the language for some reason, or are always
> > implicit in other primitives.  Is there a term from mathematics that one
> > could use to indicate a basis set has or has not been maximally decomposed?
> > 
> 
> In linear algebra one basis is as good as another. Obviously this is
> not the case with programming languages. But the metaphor is getting
> quite
> a bit overextended here.

   This is not quite the case.  In _finite_ vector spaces, this is pretty
much true.  However, once you start looking at infinite vector spaces, you
want to choose a basis that minimizes the number of terms needed to
express whatever elements you want to express.  
   This corresponds to tailoring your fundamental metaphors when writing a
language (particularly a domain specific language, or even a library for
that matter) to the kinds of problems you want to make it easy to solve.
It also happens to be a fundamental method in designing compression
algorithms for continuous data (like audio or video).

Lynn
whose been in math grad skool too long