Yes, you have associativity right. The question is what kind of price you pay. Allowing a user to type ‘a+b+c’ seems reasonable and forcing them to write ‘a+(b+c)’ seems draconian. But what does ‘a/b/c’ mean? Does your grammar have to have different productions for associative and non-associative binary operators? For general operator support do you have to have productions for every operator, or do you add a little bit of state to your parser outside the grammar to handle the lookback to determine if the same operator is being used? These are ugly decisions to make for the smallish benefit of being able to omit a couple of parentheses. And how often does it really occur outside of heavy numeric computations, which are kind of the minority.

Some APLs go overboard here and just say that everything operates right to left so 2*3+4 is 14. This is super awkward but once you get used to it it’s kind of a relief to not have to think about operator precedence. Similarly RPN and Lisp dodge the issue.

In my experience operator precedence causes actual bugs, but associativity rarely does. So despite all this I’m not firmly against associativity, but I’m getting there.

> These are ugly decisions to make for the smallish benefit of being able to omit a couple of parentheses.

Careful there. We're not talking about one compiler writer and one user. There will be potentially many users. That little benefit of using parentheses will be multiplied across users (and across uses).

Paying a large cost upfront to enjoy small but lasting benefits could very well be worth the cost. (Assuming the benefits are real of course. That would be a separate issue.)

Agreed. And the cost is higher than that even; most people who look at code are not the authors of the code, and presenting people with a snippet that looks like `a + (b + c)` seems like it would always be a stumbling block -- "why not `(a + b) + c`? Is there a reason, or did they just type it that way because that's their style?"

Usually operators are defined as being left-associative, right-associative, or non-associative.

So e.g.,

a + b + c is interpreted as (a + b) + c because + is commonly left-associative

whereas

a ^ b ^ c is a ^ (b ^ c)

because languages that support ^ for exponentiation treat it as right associative.

For non-associative operators, parentheses are required if you have two operators at the same precedence, so I believe the grandparent is arguing that e.g. a + b - c should require parens to disbiguate in a language where + and - have the same precedence.

I'm not sure if this is what the OP meant but floating point addition is not necessarily associative and this can surprise people when the same code can produce different results where evaluation order is not guaranteed. If you require parentheses to determine evaluation order it might reduce surprises.