We need to talk about parentheses

Re:We need to talk about parentheses by tsimionescu on Monday February 12, 2024 @08:50AM (#39344691)

For expnentiation I was talking about something else:

   1+3
  x    + 4

In this case, the exponent notation makes it unambiguous that this is (x^(1+3))+4, and not x^(1+3+4).

I agree that xy² could mean both (xy)² and x(y²), and that perhaps you need to understand precedence to disbiguate. I would still contend that the notation is defined as "each term has its own exponent, possibly 1 which need not be written" to disambiguate, where terms are separated by parentheses or by other operators.

That is, in my mind, the grammar for usual algebraic notation is something like this:

  expression = term (op term)*
                                                   expression___________ (expression)? 
  term = (num | var | fraction | \( expression \) |        \/expression)

  op = + | - | / | × | ° etc

And the rules are that you first evaluate each term, and then the operators between the terms. You only need to follow precedence rules for those operators between terms, the evaluation of a term is unambiguous.

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Re:We need to talk about parentheses by samatman on Monday February 12, 2024 @04:43PM (#39350932)

You appear to be inventing elaborate ways to talk about precedence without saying "precedence".

Precedence, under the term "order of operations", predates computers by several centuries. Which is not to apply that it was fixed in stone from the beginning, or perfectly consistent, but mathematics agreed on the modern rules universally in the first couple decades of the 20th century.

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