The Shape of Code

The size distribution of software components used in building many programs appears to follow a power law. Some researchers have and continue to do little more than fit a straight line to their measurements, while those that have proposed a process driving the behavior (e.g., information content) continue to rely on plenty of arm waving.

I have a very simple, and surprising, explanation for component size distribution following power law-like behavior; when writing new code developers ignore the surrounding context. To be a little more mathematical, I believe code written by developers has the following two statistical properties:

• nesting invariance. That is, the statistical characteristics of code sequences does not depend on how deeply nested the sequence is within if/for/while/switch statements,
• independent of what went immediately before. That is the choice of what statement a developer writes next does not depend on the statements that precede it (alternatively there is no short range correlation).

Measurements of C source show that these two properties hold for some constructs in some circumstances (the measurements were originally made to serve a different purpose) and I have yet to see instances that significantly deviate from these properties.

How does writing code following these two properties generate a power law? The answer comes from the paper Power Laws for Monkeys Typing Randomly: The Case of Unequal Probabilities which proves that Zipf’s law like behavior (e.g., the frequency of any word used by some author is inversely proportional to its rank) would occur if the author were a monkey randomly typing on a keyboard.

To a good approximation every non-comment/blank line in a function body contains a single statement and statements do not often span multiple lines. We can view a function definition as being a sequence of statement kinds (e.g., each kind could be if/for/while/switch/assignment statement or an end-of-function terminator). The number of lines of code in a function is closely approximated by the length of this sequence.

The two statistical properties listed above allow us to treat the selection of which statement kind to write next in a function as mathematically equivalent to a monkey randomly typing on a keyboard. I am not suggesting that developers actually select statements at random, rather that the set of higher level requirements being turned into code are sufficiently different from each other that developers can and do write code having the properties listed.

Switching our unit of measurement from lines of code to number of tokens does not change much. Every statement has a few common forms that occur most of the time (e.g., most function calls contain no parameters and most assignment statements assign a scalar variable to another scalar variable) and there is a strong correlation between lines of code and token count.

What about object-oriented code, do developers follow the same pattern of behavior when creating classes? I am not aware of any set of measurements that might help answer this question, but there have been some measurements of Java that have power law-like behavior for some OO features.