Re: Operator precedence

On 2024-05-23, Axel Reichert <mail@axel-reichert.de> wrote:

Kaz Kylheku <643-408-1753@kylheku.com> writes:
>

Furthermore exponentation between on an intermediate precedence level
between unary minus and regular minus is simply insane.

>
This is a very good argument! Prior to reading it I was kind of
indifferent (at least in infix programming languages, but not in typeset
mathematics).
>

I made it n-ary in TXR Lisp:
>
1> (expt 5 2)
25
2> (expt 5 2 3)
390625

>
... so conforming to the habit of typeset mathematics, which is based on
the fact that
>
    c
   b
  a
>
could be written as
>
   bc
  a
>
if meant to be left-associative. So having it right associative is the
more terse convention.

Yes. Also, in the left associative semantics, we have a choice. We can
do the exponentation earnestly as if by:

  (expt (expt 5 2) 3)

Or we can take advantage of the identity:

  (expt 5 (* 2 3))

The former could be important in some situation involving
floating-point: you can't always use simplifying identities.

The latter is favored when efficiency is more important.

A left associative n-ary expt function would have to make one of those
two choices: either doggedly do the exponentiations (such that the
function would be avoided by anyone looking for efficiency), or else
serve as a syntactic sugar for the exponent raised to the product
of the remaining arguments (which provides low value as a syntactic
sugar, and yet has to be avoided by someone who can't use that identity
for whatever reason).

I felt that the n-ary semantics of expt provided the best value
when right associative. It's not something obtainable by a ready
identity, and there is one obvious way to do it.

--
TXR Programming Language: http://nongnu.org/txr
Cygnal: Cygwin Native Application Library: http://kylheku.com/cygnal
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