Recursive Specifications

Abstract

A recursive specification “defines a function in terms of itself.” Recursive definitions occur commonly in the mathematical literature including that prior to the computer age. Here, the art of separating out “improper” recursive definitions was regarded as but one of the many skills necessary to write correct mathematics. But modern computer languages allow recursive specification to be expressed directly. Since the implementation of a programming language must respond to any recursive program, no matter how ill- conceived, we must pay attention to the mathematical question of what an “arbitrary” recursive specification should mean.