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[Python-Dev] Symmetric vs asymmetric symbols (was PEP 572: Do we really need a ":" in ":="?)


On 06.07.2018 7:02, Chris Angelico wrote:
> On Fri, Jul 6, 2018 at 12:48 PM, Alexander Belopolsky
> <alexander.belopolsky at gmail.com> wrote:
>> Python really has a strong C legacy and this is the area where I agree that
>> C designers made a mistake by picking a symmetric symbol (=) for an
>> asymmetric operation. On top of that, they picked an asymmetric digraph (!=)
>> for a symmetric operation as well and Python (unfortunately) followed the
>> crowd and ditched a much better alternative (<>).  My only hope is that
>> Python 4.0 will allow ? to be used in place of either = or :=. :-)
> Interesting. Looking over Python's binary operators, we have:
>
> |, ^, &, +, *: symmetric (on ints)
> -, /, //, **: asymmetric
> <, >: mirrored operations
> <=, >=: mirrored operations but not reflected
> <<, >>: non-mirrored asymmetric
> and, or: technically asymmetric but often treated as symmetric
> in, not in: asymmetric
> is, is not: symmetric
>
> Which ones ought to have symmetric symbols, in an ideal world? Should
> <= and >= be proper mirrors of each other? Are << and >> confusing? Is
> it a problem that the ** operator is most decidedly asymmetric?
>
> Personally, I'm very happy that the operators use the same symbols
> that they do in other languages - U+002B PLUS SIGN means addition, for
> instance - and everything else is secondary. But maybe this is one of
> those "hidden elegances" that you're generally not *consciously* aware
> of, but which makes things "feel right", like how Disney's "Moana" has
> freedom to the right of the screen and duty to the left. Are there
> languages where symmetric operations are always represented with
> symmetric symbols and vice versa?

Nothing like that.
The connotations for the symbols rather draw from other fields that 
we're familiar with.

Primarily math (that everyone has studied at school -- this is also the 
reason why we use infix notation even though the postfix one allows to 
ditch braces);
in particular, % draws from ? (division sign), / from fraction sign;
& is from English;
!, | and ^ are a mash from "the closest unused symbols on keyboard" to 
symbols from logic algebra:
 ?? ?? (https://en.wikipedia.org/wiki/Negation),? {\displaystyle \lor }
 ? ? (https://en.wikipedia.org/wiki/Logical_disjunction),
 ? ? (https://en.wikipedia.org/wiki/Logical_conjunction),
 ?? or | (https://en.wikipedia.org/wiki/Sheffer_stroke),
 ?? (https://en.wikipedia.org/wiki/Peirce's_arrow);

"!=" reads literally "not equal" ( ! is "not", = is "equal" )
 ?? (while "<>" reads "less or greater" which is mathematically not 
equivalent to that: not everything has a defined ordering relation. "<>" 
draws from BASIC AFAIK which was geared towards regular users who don't 
deal with advanced mathematics.)

> ChrisA
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