Experiments with Implementations of Two Theoretical Constructions

This paper reports two experiments with implementations of constructions from theoretical computer science. The first one deals with Kleene’s and Rogers’ second recursion theorems and the second is an implementation of Cook’s linear time simulation of two way deterministic pushdown automata (2DPDAs). Both experiments involve the treatment of programs as data objects and their execution by means of interpreters. For our implementations we have been using a small LISP-like language called Mixwell, originally devised for the partial evaluator MIX used in the second experiment. LISP-like languages are especially suitable since programs are data (S-expressions) so the tedious coding of programs as G¨odel numbers so familiar from recursive function theory is completely avoided. We programmed the constructions in the standard proofs of Kleene’s and Rogers’ recursion theorems and found (as expected) the programs so constructed to be far too inefficient for practical use. We then d...

• Type: Conference
• Year: 1989
• Where: ERSHOV
• Authors: Torben Amtoft Hansen, Thomas Nikolajsen, Jesper Larsson Träff, Neil D. Jones
• Keywords: ERSHOV 1989, Linear Time, Lisp-like Languages, Recursion Theorems, Theoretical Computer Science