Are ints always initialized to 0?

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Yes, class instance variables are always initialized to 0 (or nil, NULL, or false, depending on the exact data type). See the Objective-C 2.0 Programming Language:

The alloc method dynamically allocates memory for the new object’s instance variables and initializes them all to 0—all, that is, except the isa variable that connects the new instance to its class.

EDIT 2013-05-08
Apple seems to have removed the above document (now linked to The Wayback Machine). The (currently) active document Programming With Objective-C contains a similar citation:

The alloc method has one other important task, which is to clear out the memory allocated for the object’s properties by setting them to zero. This avoids the usual problem of memory containing garbage from whatever was stored before, but is not enough to initialize an object completely.

However, this is only true for instance variables of a class; it is also true for POD types declared at global scope:

// At global scope
int a_global_var;  // guaranteed to be 0
NSString *a_global_string;  // guaranteed to be nil

With one exception, it is not true for local variables, or for data allocated with malloc() or realloc(); it is true for calloc(), since calloc() explicitly zeros out the memory it allocates.

The one exception is that when Automatic Reference Counting (ARC) is enabled, stack pointers to Objective-C objects are implicitly initialized to nil; however, it’s still good practice to explicitly initialize them to nil. From the Transitioning to to ARC Release Notes:

Stack Variables Are Initialized with nil

Using ARC, strong, weak, and autoreleasing stack variables are now implicitly initialized with nil

In C++ (and C++ objects being used in Objective-C++), class instance variables are also not zero-initialized. You must explicitly initialize them in your constructor(s).

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