Order of operations (== vs. not)

Question

Does anyone know why "boolean not" has higher precedence than == in order of operations for most programming languages?

In mathematical logic/model theory, isn't it the other way around? I recently wrote the following in Lua:

if not 1 == 2 then
    print("hi")
end

It wasn't printing "hi" because of the order of operations between not and ==, which seems bizarre to me.

Answer 1

There's never a need to negate a relational operator because each one has an opposite operator. For instance, we have both equality and inequality operators (your example could have been written 1 ~= 2). Unary operators in most programming languages have the highest precedence, because most of the time that results in code that reads more like natural language.

For instance, not green and not blue should mean "neither green nor blue". A very low precedence for not would turn that into something like not (green and not blue) which is a lot harder to make sense of.

Answer 2

You need to distinguish between not 1 == 2 and not (1 == 2). The latter behaves as you expect; the former is a unary not applied to 1 only, which probably produces zero.

This is not different from 'mathematical/model theory'.