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Chapter 0: Q1E (page 1)

Give an example in the spirit of the recursion theorem of a program in a real programming language (or a reasonable approximation thereof) that prints itself out.

Short Answer

Expert verified

Example of Recursive Equation: rw=tR.w

Step by step solution

01

Introduction Recursion

Recursion is the phenomena where a particular function repeatedly calls itself until reach to base condition (terminating point).

02

Defining Recurrence relation

First let us assume two Turing Machine T and R such that:

  • T compute a function t:∑*×∑*→∑*
  • R compute a function t:∑*→∑*

We will create TM R based on T :

For every string w ,

rw=tR.w

So, we our recursion program will have to work like:

SELF=onanyinput

  • Obtain own description SELF through recursion theorem
  • Print SELF
03

Writing LISP Program

Use LISP programming language which is compatible for recursion theorem.

Following LISP program is in spirit of recursion:

defineSELFlambdaw

listwlistquotequotew

)

(quote(lambda(w)

(list w(quote quote)w)

))

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