Re: OO, C++, and something much better!

[piercarl@sabi.demon.co.uk (Piercarlo Grandi)]

>>> "jsa" == Jon S Anthony <jsa@alexandria> writes:

jsa> In article <yf3afp4nepm.fsf@sabi.demon.co.uk>
jsa> piercarl@sabi.demon.co.uk (Piercarlo Grandi) writes:

alovejoy> Whether it's an operator or not should depend either on some
alovejoy> mathematical property of its semantics (e.g., it is required
alovejoy> to be associative, or transitive, or commutative, or some
alovejoy> such). [ ... ] For example, according to Jon Anthony, an
alovejoy> "operator" in math should be a function of the form "f: A^n ->
alovejoy> A".  That is precisely the sort of thing I was reaching for; [
alovejoy> ... ]

piercarl> Ahhh, but is the definition of "operator" as in ``operator
piercarl> theory''; as you write a *function* is called an "operator
piercarl> [function]" if it is of the given form. But operator functions
piercarl> and operators are quite different entities.

jsa> I think what you really want to say is simply that you don't think
jsa> the standard mathematical usage is appropriate in the context of PL
jsa> definitions.

Not at all: I don't think that the use of the word "operator" as a short
form of "operator function" is what people mean by "operator" on its own.

There in maths operator symbols that do not label operator functions;
viceversa there are operator functions that are not labeled by an
operator symbol.

I am discussing what makes a symbol into an operator symbol
(distinguished syntax and usually lexicon); Alan when a procedure should
be called an "operator", even if is name does not at all look like an
operator.

In my view 'sizeof' is an operator; he seems to be arguing that

  (lambda (x y) (+ (^ y 3) (+ 2 (* y (* e y)))))

is an operator because it computes an operator function.

jsa> Alan, OTOH, seems to think that it is a good idea to maintain some
jsa> consistency with the mathematical usage.  It's not obvious to me
jsa> which of these two views is "better".

piercarl> The discussion was really about what looks like operators. Now
piercarl> there are a lot of things that look like operators in maths,
piercarl> which do not indicate an operator function.

jsa> That's only because you've become attached to this idea that
jsa> operators and operations are some how defined by their "looks".

Well, of course, because we are discussing operaror _symbols_, not
functions or procedures. The discussion arose out of discussing "+", if
I remember well.

jsa> Not so.  If anything, it is the other way around.  The semantics
jsa> come first and if it is deemed "special enough" to call out in a
jsa> certain context, a particular distinctive symbol (and much more
jsa> rarely, syntax) is chosen.

But no! As you argue a few lines below, mathematicians use special
syntax and lexicon to label functions that are not operator functions!;
similarly in programming languages there are many operators that do not
compute operator functions, for example 'sizeof' in ``C'', or '^' in
``Smalltalk''.

piercarl> examples and draw general rules. In maths operators are
piercarl> symbols that essentially always have some distinguished
piercarl> syntatic role, and very often are drawn from some
piercarl> distinguished lexicon too.

jsa> Sorry, this is just is not true.  The following are operators on
jsa> the set of Reals and none have any "distinguished syntax".

jsa> f(x) = x^2 + pi*x^(1/3)
jsa> g(y) = y^3 + 2y*e^y

No, these are two _functions_ that belong to the set of _operator
functions_.

jsa> The next two do have special symbols:

jsa> x^(1/2), Square root
jsa> Sin(x)

piercarl> I am not quite sure that syntactic/lexical shorthands actually
piercarl> help in programming, but most programming language designers,
piercarl> in the doubt, provide some sort of maths-like distinguished
piercarl> syntax for operators.

jsa> it isn't obvious that this helps a lot in programming.

Indeed! That is *my* point. In fact I think it is unhelpful. But then
there is an opinion that programs, in particular OO programs, ``model
directly the real world'', where the ``real world'' can be maths; and
thus:

  class complex a,b,c; ....

  a = b + c;

is a very good idea, for it immediately suggests, notationally, that the
program and the ``real world'' are in such a close relationship, as they
should be.

However I don't subscribe to that point of view; to me using notation to
suggest that 'class complex' and 'the Complex plane' are in close
correspondence is not such a good idea, and not very useful in any case.