Arithmetic Metamethods Part 1

You've learned how to customize what happens when you print a table using __tostring. Now you'll discover that metatables can also define what happens when you use arithmetic operators like + and - on your tables.

Normally, if you try to add two tables together with the + operator, Lua will give you an error because it doesn't know how to add tables. But with arithmetic metamethods, you can define exactly what addition means for your custom data types.

The __add metamethod controls addition behavior. When Lua encounters the + operator between two values and at least one has a metatable with __add, it calls that function instead of producing an error:

local v1 = {x = 3, y = 4}
local v2 = {x = 1, y = 2}

local meta = {
    __add = function(a, b)
        return {x = a.x + b.x, y = a.y + b.y}
    end
}

setmetatable(v1, meta)
setmetatable(v2, meta)

local v3 = v1 + v2
print(v3.x, v3.y)  -- Output: 4  6

The __add function receives two arguments: the left operand and the right operand. In this example, it creates a new table with x and y values that are the sum of the corresponding values from both input tables.

Similarly, the __sub metamethod controls subtraction with the - operator:

local meta = {
    __sub = function(a, b)
        return {x = a.x - b.x, y = a.y - b.y}
    end
}

setmetatable(v1, meta)
setmetatable(v2, meta)

local v3 = v1 - v2
print(v3.x, v3.y)  -- Output: 2  2

This ability to define custom operator behavior is called operator overloading.