Add functions to test properties of default Lua metamethods

[ligurio]

Lua has a number of default metamethods (Lua 5.3 Manual -> 2.4 – Metatables and Metamethods) that defines an object behaviour for example for default Lua operators. Most of these metamethods can be covered by general properties. For example if a and b have metamethod __eq then (a == b) == (b == a) and (a == b) ~= (a ~= b), for metamethod __lt - (a > b) == (b < a) and so on. I believe it would simplify testing a bit if lua-quickcheck will discover available metamethods and them with such properties.

What do you think, @luc-tielen? I'm ready to spend some time implementing this.

General methods

• __index - none?
• __newindex - none?
• __mode - none?
• __call - none?
• __metatable - none?
• __tostring

type(tostring(a)) == 'string'

• __len

type(#a) == 'number' 

• __pairs - none?
• __ipairs - none?
• __gc - none?
• __name

type(a.__name() == 'string'

• __close

Mathematic Operators

• __unm

-(-a) == a

• __add

a + b == b + a
a + 0 == a

• __sub - none?
• __mul

a * 2 == a + a
a * 1 == a * 1 * 1

• __div - none?
• __idiv - none?
• __mod

a % b == a - math.floor(a / b) * b

• __pow
• __concat - none?

Bitwise Operators

• __band

(a & (a - 1)) == 0, if a is x^2

• __bor

a | 0 == a

• __bxor

a && b == b && a

• __bnot

~(~a) == a

• __shl

a << 0 == a

• __shr

a >> 0 == a

Equivalence Comparison Operators

• __eq

(a == b) == (b == a)
(a == b) ~= (a ~= b)

• __lt

(a > b) == (b < a)

• __le

(a >= b) == (b <= a)

[luc-tielen]

Hi @ligurio , thanks for the suggestion.

I'm not so sure about the general methods, but I think the rest could be interesting to provide.
I wouldn't automatically do it though, since most of these operations might not make sense, and how would users fix it then?
But maybe we could provide some functions that take X generators, and then set up a default property that is often used?
For example: property_commutative_addition(generator1, generator2)?