Default initialization of std::array?

By definition, default initialization is the initialization that occurs when no other initialization is specified; the C++ language guarantees you that any object for which you do not provide an explicit initializer will be default initialized (C++11 §8.5/11). That includes objects of type std::array<T, N> and T[N].

Be aware that there are types for which default initialization has no effect and leaves the object's value indeterminate: any non-class, non-array type (§8.5/6). Consequently, a default-initialized array of objects with such types will have indeterminate value, e.g.:

int plain_int;
int c_style_array[13];
std::array<int, 13> cxx_style_array;

Both the c-style array and std::array are filled with integers of indeterminate value, just as plain_int has indeterminate value.

Is there a syntax that will work on all arrays (including zero-sized arrays) to initialize all elements to their default value?

I'm guessing that when you say "to their default value" you really mean "initialize all elements to T{}". That's not default-initialization, it is value-initialization (8.5/7). You can request value initialization quite easily in C++11 by giving each declaration an empty initializer:

int plain_int{};
int c_style_array[13]{};
std::array<int, 13> cxx_style_array{};

Which will value-initialize all of the array elements in turn, resulting in plain_old_int, and all the members of both kinds of arrays, being initialized to zero.

Default-initialization is a term from the Standard potentially meaning no initialization at all, so you probably mean zero-initialization.

The description at cppreference.com is actually a bit misleading. std::array is an aggregate class, and if the element type is primitive, it is POD: "plain old data," with semantics closely matching the C language. The implicitly-defined constructor of std::array< int, N > is a trivial one which does absolutely nothing.

Syntax like std::array< int, 3 >() or std::array< int, 3 > x{} which provide zeroed values do not do so by invoking a constructor. Getting zeroes is part of value-initialization, specified in C++11 §8.5/8:

To value-initialize an object of type T means:

— if T is a (possibly cv-qualified) class type without a user-provided or deleted default constructor, then the object is zero-initialized …, and if T has a non-trivial default constructor, the object is default-initialized;

std::array has no user-provided default constructor, so it gets zero-initialized. It has an implicitly-defined default constructor, but it is trivial, so it is never default-initialized. (But this doesn't make a difference since trivial initialization by definition has no effect at runtime.)

if not, is there a syntax that will work on all arrays (including zero-sized arrays) to initialize all elements to their default value?

C-style arrays and std::array are both aggregates, and the way to completely zero-initialize any aggregate is with the syntax = {}. This works since C++98. Note that C-style arrays cannot have zero extent, and that sizeof (std::array< X, 0 >) is not zero.

Both T x[N]; and std::array<T, N> x; default-initialize every element of the array.

For example, if T = std::string, every element will be an empty string. If T is a class without a default constructor, both will fail to compile. If T = int, every element will have indeterminate value (unless that declaration happens to be at namespace scope)