HaloO,
Larry Wall wrote:

That interpretation doesn't help me solve my generic parsing problems,
which is about the relationship of op1 to op2 and op3 in

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op1 a() op2 b() op3 c()
and presumably the same thing for postfixes in the other order.

My idea is to have a term re-writing stage before the precedence
parser does its job. I assume that "chalkboard mathematics" means
term re-writing. Which sort of means that infix:<->($x,$y) is a macro
that expands to infix:<+>($x,prefix:<->($y)).

So here's another question in the same vein. How would mathematicians
read these (assuming Perl has a factorial postfix operator):

Without implying to actually being a mathematician I'll
give my thoughts on the subject.

1 + a(x)**2!

That is a poor version the the version below and obviously
depends on the precedence that ! has relative to **.

1 + a(x)²!

This means to me to square the return value of a(x), then
take the factorial and then add 1. Getting a(x) raised to
2! would require the ! to be superscripted as well. Its ASCII
version would explicitly require a(x)**(2!). So a(x)**2! is
either ambiguous or requires lower precedence for !. My actual
reading of the ASCII version picks a(x) as the operation with
highest precedence and going from there outwards encountering
+ to the left and ** to the right with ** being of higher
precedence. Then I'm left with + to the left and ! to the right
with precedence of ! higher than +.
I hope that helps, TSa.
--
The Angel of Geometry and the Devil of Algebra fight for the soul
of any mathematical being. -- Attributed to Hermann Weyl