functional programming - What is the exact definition of a closure?

Question

I've read through previous topics on closures on stackflow and other sources and one thing is still confusing me. From what I've been able to piece together technically a closure is simply the set of data containing the code of a function and the value of bound variables in that function.

In other words technically the following C function should be a closure from my understanding:

int count()
{
    static int x = 0;

    return x++;
}

Yet everything I read seems to imply closures must somehow involve passing functions as first class objects. In addition it usually seems to be implied that closures are not part of procedural programming. Is this a case of a solution being overly associated with the problem it solves or am I misunderstanding the exact definition?

Answer 1

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."