I agree, although I suppose different operators could still have different associativity in a language without precedence. I took that phrasing from the “Puffs the Language” documentation.

> I suppose different operators could still have different associativity in a language without precedence

That… is true, and I have a hard time computing how it would even work.

One way to do it would be to have a default associativity between different operators, but chains of the same operator can override it, e.g. suppose “⧺” means concatenation (rightward), “×” means repetition (leftward), and the default is leftward:

      [1, 2] ⧺  [3, 4] ⧺ [5, 6]   × 2  × 3
    (([1, 2] ⧺ ([3, 4] ⧺ [5, 6])) × 2) × 3

    [ [ [1…6], [1…6] ],
      [ [1…6], [1…6] ],
      [ [1…6], [1…6] ] ]

I dunno how good an idea that would be in practice, though.

Think exponentiation, where 2^3^4 might be 2^(3^4), but where subtraction 2-3-4 is (2-3)-4.

Consider:

  2-3^4

Since there is no precedence in this (hypothetical) language that would be an invalid expression.

What I mean is that you can't write "2 + 3 * 4", not even with implicit LTR, you have to write either "(2 + 3) * 4" or "2 + (3 * 4)".

See e.g the "precedence bug" comment I wrote elsewhere on this page.

My point is that's not "equal precedence". Smalltalk has equal precedence, "2 + 3 * 4" parses as "(2 + 3) * 4". If you reject the expression entirely you don't have equal precedences, you have unmixable operators or precedences (the latter being if "2 + 3 - 4" is still allowed).

OK, I'll change the wording. Thanks.