Is std::is_unsigned<bool>::value well defined?

Question

I am wondering whether

std::is_unsigned<bool>::value

is well defined according to the standard or not?

I ask the question because typename std::make_unsigned<bool>::type is not well defined.

Answer 1

There is no concept of signedness for bool. From [basic.fundamental]/6:

Values of type bool are either true of false. [Note: There are no signed, unsigned, short, or long bool types or values. — end note] Values of type bool participate in integral promotions (4.5).

By contrast, signedness is explicitly called out for the signed integer types (paragraph 2) and unsigned integer types (paragraph 3).

Now for the is_signed and is_unsigned traits. First off, the traits are always well-defined, but only interesting for arithmetic types. bool is an arithmetic type, and is_signed<T>::value is defined (see Table 49) as T(-1) < T(0). By using the rules of boolean conversion and standard arithmetic conversions, we see that this is is false for T = bool (because bool(-1) is true, which converts to 1). Similarly, is_unsigned<T>::value is defined as T(0) < T(-1), which is true for T = bool.