Higher Orders and Inductive Structures

Abstract

The design of a cosmic language for interstellar communication should satisfy various significant requirements. Power of expression, the theme of the present chapter, is one of them. This chapter is in a way a continuation of (Appendix), because we present here to begin with interpretations of the combinatory functions I, K and S discussed in that chapter. The interpretations are in terms of LINCOS conventions explained already, notably the concept of inductive definitions. Laws over the combinatory functions are easily constructed using these conventions. This part of the chapter is followed by an in-depth discussion on the concept of recursion, using an important inductive structure, a Matrjoshka—матрёшка -, the well-known Russian doll. Treating this non-elementary case is justified because it illustrates the power of expression using inductive structures. At the same time there are the following considerations.