A basis for a mathematical theory of computation, preliminary report

Abstract

Programs that learn to modify their cwn behaviors require a way of representing algorithms so that interesting properties and interesting transformations of algorithms are simply represented. Theories of computability have been based on Turing machines, recursive functions of integers and computer programs. Each of these has artificialities which make it difficult to manipulate algorithms or to prove things about them. The present paper presents a formalism based on conditional forms and recursive functions whereby the functions computable in terms of certain base functions can be simply expressed. We also describe some of the formal properties of conditional forms, and a method called recursion indtiction for proving facts about algorithms.