Kleene, Rogers and Rice Theorems Revisited in C and in Bash

TL;DR

This paper revisits fundamental recursion and Rice theorems, demonstrating their proofs using programs written in C and Bash scripts, highlighting alternative implementation approaches.

Contribution

It provides the first proofs of these theorems using C and Bash, offering new perspectives on classical computability results.

Findings

Proofs of the recursion theorem in C and Bash

Proofs of Rice's theorem in C and Bash

Demonstration of alternative proof methods in scripting languages

Abstract

The recursion theorem in the weak form {e}(z)=x(e,z) (universal function not needed) and in Rogers form {n}(z)={{x}(n)}(z) and Rice theorem are proved a first time using programs in C, and a second time with scripts in Bash.