For nearly a quarter of a century, one of the responsibilities that I’ve taken most seriously is the shepherding of the design of Mathematica. Partly that has involved establishing foundational principles, and maintaining unity and consistency across the system. But at some point all the capabilities of Mathematica must get expressed in the individual built-in functions—like Table or NestList—that ultimately make up the system.
Each one of those functions encapsulates some piece of repeated computational work—often implemented by some deep tower of algorithms. And each one of those now 3000 or so functions requires a name.
We’re currently in the closing weeks of a (spectacular!) new version of Mathematica, and I spent part of last week doing final design reviews for some fascinating new areas of the system. And as part of those design reviews, we were confirming and tweaking some of the names we’re going to use for new functions.
The naming of functions is a strange and difficult art—a bit like an ultimately abstracted form of poetry. The goal is to take the concept and functionality of a function, and capture the essence of it in one, or two, or perhaps three, words (like Riffle, or DeleteCases, or FixedPointList)—chosen so that when someone sees those words, they immediately get the right idea about the function. In even the most succinct forms of ordinary poetry, you get at least a handful of words to communicate with. In function names, you typically get at most perhaps three.