What is the exact definition of a closure?

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No, that’s not a closure. Your example is simply a function that returns the result of incrementing a static variable.

Here’s how a closure would work:

function makeCounter( int x )
{
  return int counter() {
    return x++;
  }
}

c = makeCounter( 3 );
printf( "%d" c() ); => 4
printf( "%d" c() ); => 5
d = makeCounter( 0 );
printf( "%d" d() ); => 1
printf( "%d" c() ); => 6

In other words, different invocations of makeCounter() produce different functions with their own binding of variables in their lexical environment that they have “closed over”.

Edit: I think examples like this make closures easier to understand than definitions, but if you want a definition I’d say, “A closure is a combination of a function and an environment. The environment contains the variables that are defined in the function as well as those that are visible to the function when it was created. These variables must remain available to the function as long as the function exists.”

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