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

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

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

jsa> In article <yf3ybcsm5ce.fsf@sabi.demon.co.uk> Piercarlo Grandi
jsa> <piercarl@sabi.demon.co.uk> writes:

piercarl> It names a particular implementation of that conceptual
piercarl> function; the lexical item "+" names a particular conceptual
piercarl> function in maths, not programming languages. The character
piercarl> "+" names procedures in programming languages and functions in
piercarl> maths...

jsa> Just to be clear: "+" does not stand for some _particular_ function
jsa> in mathematics.

But it does, and sorry if I used the word "particular" improperly; I
meant by it something "any definite"; ``maths'' is often rather precise,
and which ``particular'' function "+" stands for must be very clear,
but, as you write:

jsa> It varies on context.  Specifically, a) what the formal system is
jsa> and b) what interpretation is being given to that system.

It was also perhaps not clear that by "maths" I meant something like
``ordinary maths'', a not well defined but hopefully intuitively
perceivable notion; for most any given procedure indicated by "+"
computes *some* mathematical function, even if not necessarily the one
indicated by "+" in most ``ordinary maths'' (one favourite example is
that "+" between 'unsigned' operands in ``C'' computes the function
``addition module 2^N'' rather than addition on nonnegative numbers).

piercarl> At times, BTW, I am not so sure that is such a good idea, for
piercarl> while the function computed by the "+" procedure usually
piercarl> somewhat resembles the function indicated by "+" in maths, the
piercarl> details (and vital ones) are as a rule grotesquely different
piercarl> (just consider addition of 'real's and of 'R'eals).

jsa> Again - it depends on context.

That's entirely correct, and exactly my point; as I wrote, "usually",
not "always" or "never". However the cases where the function computer
by some "+" procedure are exactly identicaly to the function dinciated
by "+" in some branch of maths would tend to be few; one major factor is
that procedures usually compute functions over finite domains/codomains,
which is almost never the case in [``ordinary''] maths, and even in
``discrete'' maths.

jsa> There are cases where the two will denote identical results.

Well, this is actually quite impossible as literally written :-); the
results of any particular "+" operation are in the domain of
implementation entities, those of any articular "+" function are in the
domain of mathematical entities.

What you probably wanted to say is that it can happen that the function
computed by some particular "+" operation is exactly the same as that
meant by some "+" function in ``ordinary'' maths.

Ues indeed, but I suspect that this is rare, for example for the reason
given above; also given that the levels of discouse of procedures
(implementations) and functions (maths) are so different, I feel that
notational similarity can mislead, and indeed:

piercarl> I often think that the constant attempt to make programming
piercarl> languages resemble maths (and this includes functional
piercarl> languages) are not quite useful: Lisp, properly written, seems
piercarl> rather legible and yet does not quite resemble maths notation,
piercarl> operator symbols and all that.

jsa> Forget about the notation.  That's irrelvant.  The real problem is
jsa> that _often_ (not always) the semantics are all wrong in those cases
jsa> where they are "supposed to be the same or at least similar".

Well, while what I have written expresses a similar sentiment, I would
be so radical in saying that notation is so irrelevant.

Actually it is irrelevant, but it is not _unimportant_, for programs are
about communicating in textual form, and communicating by suggesting
analogies that are more or less subtly flawed (e.g. having a floating
point datatype called 'real' as in many languages) might confuse people.

This is why I have expressed the idea that it might actually be useful
to have rarther different looking notations for procedures and
functions; it should matter, but I must confess that even I am
constantly amazed by the fondness for terminological confusions that
many people display; the major example is "OO", which many people take
literally as being about objects, with dire consequences.

Misnomers such as "OO" and notational devices *are* irrelevant, to those
that see them as mere pointers to the concepts they label; but
unfortunately nominalism is rampant.

[ ... agreement, strangely enough :-). Omitted not to set a bad
precedent :-) ... ]