Volume 6 : Number 1 : Paper 2
December 2003 Special Issue of Best Papers presented at CLEI'2002. Montevideo, Uruguay. Guest Editor: Alfredo Viola.
Title:
Reduction Strategies for Program Extraction

Authors and Affiliations:
Nora Szasz,
Maribel Fernandez,
Ian Mackie, Departament of Computer Science, King's College London, Strand, WC2R 2LS London, U.K.
Paula Severi, Departimento di Informatica, Universita di Torino, Corso Svizzera 185, 10149, Italy.

Abstract:
We introduce Pure Type Systems with Pairs generalising earlier work on program extraction in Typed Lambda Calculus. We model the process of program extraction in these systems by means of a reduction relation called o-reduction, and give strategies for Bo-reduction which will be useful for an implementation of a proof assistant. More precisely, we give an algorithm to compute theo-normal form of a term in Pure Type System with Pairs, and show that this defines a prejection from Pure Type Systems with Pairs to standart Pure Type Systems. This result shows that o-reduction is an operational description of aprgram extraction that is independent of the particular Typed Lambda Calculus specified as a Pure Typoe System. For B-reduction, we define weak and strong reduction strategies using Interaction Nets, generalising well-know efficient strategies for the l-calculus to the general setting of Pure Type Systems.


Received May 2004, Revised , Editor: Alfredo Viola
Full paper, 24 pages [ PDF, 705 Kb ]