Understanding Computation

Chapter 2. The Meaning of Programs

Don’t think, feel! It is like a finger pointing away to the moon. Don’t concentrate on the finger or you will miss all that heavenly glory.

—Bruce Lee

Programming languages, and the programs we write in them, are fundamental to our work as software engineers. We use them to clarify complex ideas to ourselves, communicate those ideas to each other, and, most important, implement those ideas inside our computers. Just as human society couldn’t operate without natural languages, so the global community of programmers relies on programming languages to transmit and implement our ideas, with each successful program forming part of a foundation upon which the next layer of ideas can be built.

Programmers tend to be practical, pragmatic creatures. We often learn a new programming language by reading documentation, following tutorials, studying existing programs, and tinkering with simple programs of our own, without giving much thought to what those programs mean. Sometimes the learning process feels a lot like trial and error: we try to understand a piece of a language by looking at examples and documentation, then we try to write something in it, then everything blows up and we have to go back and try again until we manage to assemble something that mostly works. As computers and the systems they support become increasingly complex, it’s tempting to think of programs as opaque incantations that represent only themselves and work only by chance.

But computer ...