What do lambda function closures capture?

Recently I started playing around with Python and I came around something peculiar in the way closures work. Consider the following code:

adders=[None, None, None, None]

for i in [0,1,2,3]:
   adders[i]=lambda a: i+a

print adders[1](3)

It builds a simple array of functions that take a single input and return that input added by a number. The functions are constructed in for loop where the iterator i runs from 0 to 3. For each of these numbers a lambda function is created which captures i and adds it to the function’s input. The last line calls the second lambda function with 3 as a parameter. To my surprise the output was 6.

I expected a 4. My reasoning was: in Python everything is an object and thus every variable is essential a pointer to it. When creating the lambda closures for i, I expected it to store a pointer to the integer object currently pointed to by i. That means that when i assigned a new integer object it shouldn’t effect the previously created closures. Sadly, inspecting the adders array within a debugger shows that it does. All lambda functions refer to the last value of i, 3, which results in adders[1](3) returning 6.

Which make me wonder about the following:

• What do the closures capture exactly?
• What is the most elegant way to convince the lambda functions to capture the current value of i in a way that will not be affected when i changes its value?