You Can Program What You Want but You Cannot Compute What You Want

Abstract

Computers are the most fascinating machines ever invented. Virtually everyone uses them in one form or another every day. However, most people only have a vague understanding of how computers work, let alone how to program them. Yet computing has become a commodity almost like energy, food, or water. The question is if the general public, for modern society to work properly, needs to understand computing better than what people generally know about, say, producing electricity or clean water. We argue that the intractability and even undecidability of so many important problems in computer science are the reason that computing is indeed different. It is the limits of computability, not just the capabilities of computers, that is the source of unbounded potential in the automation of everything. The challenge is to teach people not just programming but also how programming is the neverending process of overcoming those limits. We have developed a system called selfie that implements a self-referential compiler, emulator, and hypervisor that can compile, execute, and virtualize itself. We use selfie to teach undergraduate and graduate students computer science from first principles. In particular, we show them how self-referentiality in selfie is capability and limitation of computing at the same time. Here, we discuss ongoing early work on integrating verification technology into selfie as yet another way of exploring what computing is.