Why does the doc say `__index` is looked up in the table?

__index: The indexing access table[key]. ... The metamethod is looked up in table.

It says the same thing for __newindex, but not for any other metamethod.

If this were true (which it's not), it would be a major departure from previous versions of Lua. The following code outputs nil, as I would expect, but it's inconsistent with the doc.

#!/usr/bin/env lua5.3

local proto = {a = 54}
local t0 = {__index = proto}
print(t0.a)

To be clear: If the doc was correct, I would expect t0 in the above code to only require an __index field without an actual metatable for t0.a to be 54. So does anyone know what's going on with the doc?

Solution

You are incorrectly interpreting the meaning of the term. To say that it is "metamethod Y is looked up in X" does not mean that it searches the X table for an entry named Y. It means that it gets the metatable for X and looks up an entry named Y, as if by rawget(getmetatable(X) or {}, "Y"), as specified in the docs.

This terminology is repeatedly used in the metamethod descriptions. For example:

First, Lua will check the first operand (even if it is valid). If that operand does not define a metamethod for __add, then Lua will check the second operand.

It's not asking if the first (or second) operand have a method __add; it asks if they have a metamethod __add.

As you can see from the __add example, you have to specify which of the operands it tries to get metamethods from, and in which order. For table[key], the point of the text is that doesn't try to get the metamethod from key, only from table. That may seem a tad bit obvious, but completeness is better than incompleteness.