Postfix evaluating incorrectly - lua

Question

-2^2 (infix notation) should translate to -2 2 ^ (postfix notation). It does as expected however when evaluating that postfix it evaluates to 4 not -4 which is what is expected.
I'm using Lua and here's my precedence & associativity tables:
-- Precedence table for different operators
local PRECEDENCE = {
[Token.Type.MINUS] = 0,
[Token.Type.PLUS] = 0,
[Token.Type.ASTERIK] = 1,
[Token.Type.SLASH] = 1,
[Token.Type.CARET] = 2,
[Token.Type.UMINUS] = 3
}
-- Associativity table for different operators
-- 0 = LTR (Left To Right)
-- 1 = RTL (Right To Left)
local ASSOCIATIVITY = {
[Token.Type.MINUS] = 0,
[Token.Type.PLUS] = 0,
[Token.Type.ASTERIK] = 0,
[Token.Type.SLASH] = 0,
[Token.Type.CARET] = 1,
[Token.Type.UMINUS] = 1
}
When trying to evaluate -2^2 my output queue looks like this:
{
2,
UMINUS,
2,
CARET
}
Here's my parser. It's worth noting that queue and stack are "classes" with their respective functionality.
--[[
Parse tokens
]]
function Parser:parse()
self:preprocess() -- Convert valid MINUS tokens into UMINUS
while (self.token) do
local token = self.token
if (token.type == Token.Type.NUMBER) then
self.queue:enqueue(tonumber(token.value))
elseif (isOperator(token)) then -- PLUS, MINUS, SLASH, ASTERIK, UMINUS, CARET
while (not self.stack:isEmpty()
and ASSOCIATIVITY[token.type]
and PRECEDENCE[token.type]
and ASSOCIATIVITY[self.stack:top().type]
and PRECEDENCE[self.stack:top().type]
and ((ASSOCIATIVITY[token.type] == 0 and PRECEDENCE[token.type] <= PRECEDENCE[self.stack:top().type])
or (ASSOCIATIVITY[token.type] == 1 and PRECEDENCE[token.type] < PRECEDENCE[self.stack:top().type]))) do
self.queue:enqueue(self.stack:pop())
end
self.stack:push(token)
elseif (token.type == Token.Type.LPAREN) then
self.stack:push(token)
elseif (token.type == Token.Type.RPAREN) then
while (self.stack:top().type ~= Token.Type.LPAREN) do
self.queue:enqueue(self.stack:pop())
end
self.stack:pop()
end
self:next() -- Move to the next token
end
while (not self.stack:isEmpty()) do
self.queue:enqueue(self.stack:pop())
end
return self.queue
end
What am I doing wrong? I tried an online calculator here and I also get 4 yet I know the correct output should be -4 for that expression.

Answer 1

To get the result you expect, the carat must have a higher precedence than unary minus. That's how it works in Lua's operator precedence. The postfix notation for -2^2 should actually be 2 2 ^ UMINUS. Remember that the square of any real number is always positive. You could just swap the precedence levels:
[Token.Type.CARET] = 3,
[Token.Type.UMINUS] = 2,