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    <p>Whew. All right, here we go!</p> <p>First, you have a function, any function. In your case, that's <code>fib()</code>. Now, in python, functions are also objects, and they can be created in runtime, so we can actually do this:</p> <pre><code>def give_me_a_function(): def f(x): return x return f </code></pre> <p>(Warning: horrible repetition of the word 'function' for the rest of this answer).</p> <p>Well, we defined a function that takes no arguments and returns,... another function? That's right! Functions are objects! You can create them in runtime! So we defined a second function inside our original one, and returned it, as we would any other object.</p> <p>Now, let's do something a tad more complicated:</p> <pre><code>def alter(other_function): def altered(x): return other_function(x) + 1 return altered </code></pre> <p>What the hell was that? </p> <p>Well, we defined a function, <code>alter()</code>. Just as in the example above, it creates a function in run-time and returns it, as the object it is. That much we already covered.</p> <p>Now, if functions are objects, and can be created and returned, why wouldn't you be able to pass one as argument? And call it, while it you're at it! That's right: <code>alter()</code> takes a function as argument(*), and uses it.</p> <p>All it takes to have <code>alter()</code> is combining the above magic with this new magic: we receive a function as an argument, create another one on the fly that makes use of it, and return this new function-object!</p> <p>Let's try it.</p> <pre><code>&gt;&gt;&gt; def f(x): ... return 2*x &gt;&gt;&gt; new_function = alter(f) &gt;&gt;&gt; f(2) 4 &gt;&gt;&gt; new_function(2) 5 </code></pre> <p>There it goes! <code>alter()</code> takes my <code>f()</code>, creates a new function that will return <code>f() + 1</code>, and gives that to me as a return value. I assign it to <code>new_function</code>, and I have a new, home-brewed, run-time created function.</p> <p>(I did warn you about the use of the word 'function', did I not?)</p> <p>Now, to your piece of code. You're doing something more complicated than just <code>f() + 1</code>. Or not? Well, you're creating a new function that takes the original one, calls it, and prints some data. That's not much more magical than what we just did. Where's the big difference?</p> <p>Well, there is one detail: fib() is recursive, so it calls itself, right? Nope! Not <strong>itself</strong>. It calls <code>fib()</code>, and you happened to do this:</p> <pre><code>fib = trace(fib) </code></pre> <p><strong>WHAM. <code>fib()</code> is not itself anymore!</strong> Now <code>fib()</code> is <code>trace(fib)</code>! So when <code>fib()</code> goes into recursion, it's not calling itself, it's calling the wrapped version of itself we created.</p> <p>That's why the indentation is handled like that. Look at <code>trace()</code> again, now knowing it's actually recursively indenting, and it makes sense, doesn't it? You want to have one indentation per level of recursion, so increment it, call <code>fib()</code> (which, remember, is now <code>trace(fib)</code>), and then when we're back (so the recursion went and came, and we're about to return to a previous step in the calling chain) we decrement it.</p> <p>If you still don't see it, try moving all the functionality to fib(). Forget about the decorating function, that's plain confusing.</p> <p>Ah. I really hope this helps, and that the 2.000 guys that beat me to the answer didn't already make this question obsolete.</p> <p>Cheers!</p> <p>(*) Yeah yeah duck typing yadda yadda callable objects bla bla irrelevant.</p>
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    1. COThanks for sparing your time, Santiago Lezica.
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    2. COWhen I say alter(f(4)), I get <function altered at 0x000000000240A248>. So what is the exact difference between that and first assigning it to new_function (as in your example: new_function = alter(f)) ?
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    3. COUhm... when you do alter(f(4)) you are not even passing a function as argument for alter(). alter(f)(4) would be the same as assigning and calling new_function, though it would create the function every time you called it.
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