Re: Operator precedence

On 2024-05-24, Janis Papanagnou <janis_papanagnou+ng@hotmail.com> wrote:

After pondering a bit more I think this is my personal resume...
>
On 24.05.2024 01:53, Janis Papanagnou wrote:

[...]
Moreover, what seams reasonable (to me) is that _unary_ operators
should (typically/always?) bind tighter than _binary_ operators!

>
An example may make things probably more apparent; in the expression
>
    5 * -3 ^ 2
>
it would never occur to me to not consider the "-3" as an entity.
Because of the typical inherently tight coupling of unary operators.
>
(Assuming an interpretation of
>
    5 * -(3 ^ 2)
>
would look just wrong to me.)

That interpretation is required if - 3 ^ 2  is to correspond to:

    2
  -3

Indeed the ^ circumflex is intended to mean "we don't have support
for superscripts in this notation, but pretend that the 2 is raised up".

(In TeX/LaTeX, ^ is used for marking up superscripts: x^y.)

Now in the C grammar, we have multiplication also occuping a
precedence rung between unary plus/minus and additive expressions.

Thus -A*B means (-A)*B, whereas X - A*B means X-(A*B).

In this case it doesn't matter because the unary minus is
a kind of product. -A can be regarded as a shorthand for (-1)*A.

More importantly the identity (-A)*B = -(A*B) holds.

This creates a problem if we naively wedge exponentiation into
the grammar, by sticking it into a precedence level above
multiplication, but below unary.

The identity does not hold in exponentiation: (-A)**B
is not -(A**B).

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