Beware of bugs in the above code; I have only proved it correct, not tried it.
Science is knowledge which we understand so well that we can teach it to a computer; and if we don't fully understand something, it is an art to deal with it.
In fact, my main conclusion after spending ten years of my life working on the TEX project is that software is hard. It’s harder than anything else I’ve ever had to do.
Let us change our traditional attitude to the construction of programs: Instead of imagining that our main task is to instruct a computer what to do, let us concentrate rather on explaining to human beings what we want a computer to do.
The real problem is that programmers have spent far too much time worrying about efficiency in the wrong places and at the wrong times; premature optimization is the root of all evil (or at least most of it) in programming.