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

{snip}

 hi Guido,  thanks for your responses, your candor, and your kindness;  I think 

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?  

Thanks for your consideration,

Sincerely,

Kind regards,

marcus