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Comment by dragonwriter | Hacker News Reader

You provide:

   a+b+c = (a+b)+c = a+(b+c)  // Good!
   f a b = (f a) b != f (a b)  // WTF?

So, I suppose, also:

   a/b/c = (a/b)/c != a/(b/c) // WTF?

> BTW, that's also a good rule of thumb for defining new operators. If your new op ~-^-~ is not associative, don't make it an op!!

Why should associativity be a requirement for a new op? Its not universal among common standard binary operators, after all (particularly division and exponentiation are not associative.)

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I said either associative or parenthesized. People don't write a/b/c because they had 10 years of learning to use parens in arithmetic, but they write f a b all the time. For the same reason, my rule of thumb applies only to operators that you define.

The non-associativity of exponentiation does throw people off sometimes. Not all college students will correctly parse 2^2^2. IMO it's a wart in math notation. It could've been easily avoided by e.g. drawing a box around the exponent, so stacked exponentials would have boxes nesting upward.

Interesting that the two operators that aren't associative are the two that you don't typically write as operators in mathematics.

> Interesting that the two operators that aren't associative are the two that you don't typically write as operators in mathematics.

Sure, for those two examples, but plenty of things that are typically written as operators in math aren't associative (× as the cross product, for instance, which gets bonus points for overloading a symbol that is an associative operator in other contexts.)

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