On Thursday, March 6, 2014 11:48:53 AM UTC-6, Guido van Rossum wrote:
{snip}

dialogue will work, and I promise to keep the rhetoric to a bare minimum, if at all.    :)

There really are only two questions I am going to try to answer here, and some of
the answer goes back to Stefan's (and others) questions as well, so I hope its helpful.

So, by context you really seem to be referring to some specific state of the program. Perhaps you are even talking about extending the existing notion of numeric context used by Python's Decimal type. But it's not very clear because "you change the context" is also a common term for changing the topic of a discussion.

This is what I mean by "context," for this entire discussion, mostly having to do with
Decimal and the "context manager" and these two lines:

getcontext()

with localcontext(ctx=None) as context_manager

Allow me to back up a bit...  the pdeclib module was not difficult for me because of the
mathematics (no brag) I can code transcendental functions in my sleep. The hard part of
that project last week was coming to grips with the context manger, and the parameterization
of context attributes in the Decimal class. Back in the day when I did this work for Rexx at IBM
I used NUMERIC DIGITS and NUMERIC FUZZ  to emulate (in a crude way) what Decimal is
doing correctly with its context, with the context manager. I credit Oscar Benjamin for helping
me get up to speed with this concept (and I am so glad he did too, because its key for this
entire discussion.

Before we go on, allow me to explain my italics of Number  and  PythonNumber.  These are
each an abstract base class.  They are a class that is never instantiated, but from which all
other "numbers" are derived as objects.   (more below)

I'm sorry, but I am *still* unsure about what you mean by "context". Python does not need a context object to switch between complex and real number processing -- it's all done through operator overloading.

(more on this below, but I am thinking beyond overloading/  actually, virtual functions and templates)

Actually, modern Python is considered object-oriented.

Thank you.  This has everything to do with this discussion, but allow me to take a humorous
break and relate an anecdote... I have had numerous discussions with T.R. and C.A and S.D. and
others where in the end python was object based.  Ha!   Nope, you have seen it right here, the
BDfL says its "object oriented," and that's the end of the argument!   (ok, tiny rhetoric)

Unifying the
number system on a computer does not have to be grounded in paradigms that serviced the
industry (and academy) for the past 40 years;
{snip}

Now you've got a specific proposal and we can discuss pros and cons. This is a topic that comes up occasionally and it is indeed a pretty interesting trade-off. I suspect the large (and fast-growing) SciPy community would prefer to keep binary floating point, because that's what their libraries written in Fortran or C++ want, and extra binary/decimal conversions at the boundaries would just slow things down. But I'm really speculating here -- maybe they don't need high-performance conversion between binary and decimal, since (perhaps) they may do their bulk I/O in C++ anyway. Or maybe it varies per application.

Here is the main response for this discussion, and I will endeavor to keep the
rhetoric down, I promise.
This may even be easier to accomplish in 3.x without breaking anyone, or any third party software either; depends

In my view numbers are objects (like circles, squares and triangles; in polymorphism discussions).
Numbers are nothing more than objects which have "contexts" just like circles and squares and triangles
are nothing more than objects that have "contexts". In the following discussion think in terms of object
oriented (as in Grady Booch) rather than any specific language--- and certainly not python syntax.  um,
think C++ for now, if you must think of any.  A  Number  is an abstract base class with "context" attributes
and pure virtual functions--- it will never be instantiated---and  PythonNumber  will derive from that; also
an abstract base class.   Here is the Class hierarchy I am proposing:

Number

PythonNumber

Decimal

Real         <======= this is the  default

BinaryIEEE85

Real_b

&c (...)   omitted for clarity

Complex

Quaternion

Rational

Fraction

&c--------------------------------------------------

Well, there it is.   The idea is that any function or method that takes a  Number reference
or a  PythonNumber  reference does not have to interrogate what type of Number it is... it just
works (why?) glad you asked, because of polymorphism and a three pointer hop down a virtual
function table!
If a function or method gets a Number parm in as in    method(num)    then to get the pretty
print representation of the number  is simply    num.pretty_print(),   or to get an evaluation
of the number is   num.eval(), or to get the string rep of the number is  num.str()...  and on and on.
The point is that other parts of the system no longer need to know what "type" of number object
it is,  the right code gets called because of virtual functions, operator overloading, and the beautiful
virtual function table (all under the covers, not MAGIC, but polymorphism).
Python at present is disjointed when it comes to number as a concept. In my view numbers
need to be objects, and the Class hierarchy (see my simplified version above) needs to unify numbers
across the python boards (so to speak) so that "types" are only important to the implementors, and
so that adding new "types" is easy, concise, and coherent.

I realize that this suggestion is over the top in terms of size and weight (Stefan's concern above).
But not really, when you think of conceptualizing the unification of numbers  under Number  and
PythonNumber .  There may be other kinds of numbers too, besides these...  like maybe GmpyNumber
of BC_Number, or others.

The bottom line is that we have an object oriented language in front of us that has the
software engineering advantages which would allow this kind of hierarchy and conceptualization
of a unified number system.  Let's leverage our technology for mutual advantage across python
communities?