Recursive programs as functions in a first order theory

Pure Lisp style recursive function programs are represented in a new way by sentences and schemata of first order logic. This permits easy and natural proofs of extensional properties of such programs by methods that generalize structural induction. It also systematizes known methods such as recursion induction, subgoal induction, inductive assertions by interpreting them as first order axiom schemata. We discuss the metatheorems justifying the representation and techniques for proving facts about specific programs. We also give a simpler version of the Godel-Kleene way of representing computable functions by first order sentences.

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