Unicode operators and precedence?

[Dominikus Dittes Scherkl]

On Sunday, 1 November 2020 at 20:15:00 UTC, Ola Fosheim Grøstad 
wrote:
> On Sunday, 1 November 2020 at 19:47:33 UTC, Dominikus Dittes 
> Scherkl wrote:
>>> opBinary!"·"
>> I would recommend to refrain from it as it is visual too 
>> similar [to dot].
>
> It is center-dot, multiplication/inner product: vec1·vec2
> IDEs should colour it differently than the regular 
> "vec1.length" operator
Ok, may work, but I still think it's no good idea.

>>> opBinary!"✕"
>>> opBinary!"⊗"
>>> opBinary!"⊘"
>>> opBinary!"⊙"
>> same as *, / ("point" arithmetic)
>
> I wonder if they should be one step higher so that they can be 
> used for linear algebra? But I am not sure.
Yeah, one step higher prio would be good.

>>> opBinary!"∩"
>>> opBinary!"∪"
>> same as &, |, ^ ("set" arithmetic - bitwise is only a special 
>> kind of set)
>
> IIRC D uses the same as C where "&", "|" have higher precedence 
> than "==" which is not good.
>
> I want to be able to say "A∩B == C" and have it parse as "(A∩B) 
> == C".
I don't understand. if & | ^ had higher prio than == everything 
would be good.
SO yes, you are right, the prio of set operation should be higher 
than comparison.

> > !  --> ¬ (logic not)
> > && --> ∨ (logic and)
> > || --> ∧ (logic or)
> I was thinking to use those for bitwise operators in order to 
> overcome the precedence mess that currently exists.

No, they are clearly logic operators and should NOT have set 
semantics.
Bitwise, as I mentioned, is only a special kind of set, so we 
should use the set operators to overload bitwise arithmetic (I 
always think of an unsigned value as a set of bits).
But I agree, logic should have higher prio than comparison, but 
lower prio than set operators.

> > ^  --> ⊻ (xor - and add the missing ⊼ (nand) and ⊽ (nor))
> Also xor makes more sense bitwise.
Hmm. Maybe you are right - Xor, Nand and Nor are more useful as 
additional set operators.
But And, Or and Not should be pure logic.

Ah, i missed one:
~  --> ∁ (complement)
And of course unary operators should have highest priority, no 
matter if they are set, logic or whatever.