Quotation and Self-Reference

Abstract

Many years ago, kurt godel suggested to the author the idea of formalizing quotation. this paper treats both two-sided and the more bizarre one-sided quotation (used in lisp) with emphasis on fixed-points and self-reference. the recursion and double recursion theorems both leave their analogues in quotational systems. for rather weird reasons, the one-sided systems are particularly suited for double fixed-points.