Function Prototype Narrowing with nils

How are you using the lua-language-server?

Visual Studio Code Extension (sumneko.lua)

Which OS are you using?

Windows

What is the issue affecting?

Type Checking

Expected Behaviour

Foo.Bar('Baz', 'Qux') -- **string**
Foo.Bar('Baz', nil) -- nil
Foo.Bar('Baz') -- nil
Foo.Bar(nil, 'Qux') -- nil
Foo.Bar(nil, nil) -- nil
Foo.Bar() -- nil

Actual Behaviour

Foo.Bar('Baz', 'Qux') -- **string|nil**
Foo.Bar('Baz', nil) -- nil
Foo.Bar('Baz') -- nil
Foo.Bar(nil, 'Qux') -- nil
Foo.Bar(nil, nil) -- nil
Foo.Bar() -- nil

Reproduction steps

---@param baz string|number
---@param qux string|number
---@return string
---@overload fun(text: string|number, title: nil):nil
---@overload fun(text: nil, title: string|number):nil
---@overload fun(text: nil, title: nil):nil
function Foo.Bar(baz, qux)
	if not baz or not qux then
		return nil
	end
	return 'SomeString'
end

Additional Notes

It seems to match the 'strings' can be nil

First input example

Last input example

Log File

No response

Start by running the Lua reproduction from the issue and compare the inferred return types for each argument combination. Trace the type-checking and overload-resolution paths involved in function prototypes, then add coverage for the expected narrowing behavior and verify that the non-nil overload resolves to string while the nil cases resolve to nil.