Re: Operator precedence

On 26.05.2024 00:26, Kaz Kylheku wrote:

On 2024-05-25, Janis Papanagnou <janis_papanagnou+ng@hotmail.com> wrote:

(Mind my remark that mathematicians and computer scientists were
involved in the Algol 68 definition, and that this topic had been
discussed there, and despite the old mathematical convention they
decided to consistently streamline the definition. Frank Pagan's
Algol 68 book, for example says that _every_ monadic operator has
higher precedence than any dyadic operator. And that makes sense;
also in my opinion. I consider Algol 68 also a landmark due to its
extraordinary formal definition, that's why I emphasize it here as
an outstanding paragon.)

 
What they are effectively saying is that the dyadic power operator A**B
(or A^B or whatever it is) bears no syntactic relation to the 2D notation
involving a superscript. I.e. it is a completely different syntactic
interface to the same abstract operation. As such, it can have its own
precedence rules, not hinged to the superscript power notation.

There's three power operators in Algol 68 ('UP', '^', '**') each with
the same default precedence (and each individually changeable.

What the Algol 68 report says on priorities is:

 Priority-declarations are used to specify the priority of operators.
 Priorities from 1 to 9 are available.
 Since monadic-operators have effectively only one priority-level, which
 is higher than that of all dyadic-operators, monadic-operators do not
 require priority-declarations.

 Formulas are either dyadic or monadic: e.g., x + i or ABS x. The order
 of elaboration of a formula is determined by the priority of its
 operators; monadic formulas are elaborated first and then the dyadic
 ones from the highest to the lowest priority.

 https://jmvdveer.home.xs4all.nl/en.post.algol-68-revised-report.html

This is IMO a very clear and sensible definition. It resembles the
property that I upthread mentioned as "tight binding" of monadics.
(I know your mileage varies.)

Janis