Indeed, programming something is a great trick to get a deeper understanding of it. It means writing everythin down to the details that even a dumb machine can understand it.

I guess this is like understanding something better by explaining it to others. Just that this "other person" is a machine. It is also well-known that it even helps to explain it to your own, by writing it down. For example, PG noted that in the introduction of http://paulgraham.com/writing44.html