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Information to Users INFORMATION TO USERS The most advanced technology has been used to photograph and reproduce this manuscript from the microfilm master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer. The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. Oversize materials (e.g., maps, drawings, charts) are reproduced by sectioning the original, beginning at the upper left-hand corner and continuing from left to right in equal sections with small overlaps. Each original is also photographed in one exposure and is included in reduced form at the back of the book. Photographs included in the original manuscript have been reproduced xerographically in this copy. Higher quality 6" x 9" black and white photographic prints are available for any photographs or illustrations appearing in this copy for an additional charge. Contact UMI directly to order. v.r> University Microlilms International A Beil & Howell Information Company 300 North Zeeb Road. Ann Arbor. Ml 48106-1346 USA 313- 761-4700 800 521-0600 Order Number 9022471 Understanding programs as devices Allemang, Dean Thomas, Ph.D. The Ohio State University, 1990 Copyright ©1990 by Allemang, Dean Thomas. All rights reserved. UMI 300 N. Zeeb Rd. Ann Arbor, MI 48106 U nderstanding P r o g r a m s as D evices DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Dean T. Allemang 3|< jjc jjc The Ohio State University 1990 Dissertation Committee Adviser’s Approval B. Chandrasekaran William Ogden John Josephson Adviser W. Lewis Johnson Computer and Information Sciences ©Copyright by Dean T. Allemang 1990 For Barbara, who taught me the correct use of the word ‘cogno-babble’ A cknowledgements I wish to thank B. Chandrasekaran for providing the framework and environ­ ment that made this work possible. I wish to thank the members of my reading committee, William Ogden, John Josephson and especially W. Lewis Johnson for insightful comments that greatly helped me to understand the nature of this work. For their work on the Functional Representation, which preceded this, I wish to thank my fellow graduate students, Ashok Goel, Anne Keuneke, Bill Punch and Jon Sticklen. I would also like to thank Liz Fannin, Dave Herman, Arun Welch and Mike Tanner for making the LAIR an enjoyable place to work. I would like to thank Mike Weintraub and Richard Fox for actually taking interest in and reading this document. This work was supported in part by DARPA/AFOSR contract #A F F 49620- 89-C-0110, the Air Force Office of Scientific Research grants 87-0090 and 89-0250, and a Presidential Fellowship from The Ohio State University. V it a April 30, 1960 .............................. Born—Columbus, Ohio 1982 ............................................ B.S. Mathematics and Computer Science The Ohio State University Columbus, Ohio 1978-1982 ................................... Systems Programmer (part time) AccuRay Corporation Columbus, Ohio 1982-1984 ................................... Marshall Scholar University of Cambridge, Cambridge, England 1984 ............................................ M. Sc. Pure Mathematics University of Cambridge Cambridge, England 1984-1987 ................................... NSF Graduate Fellow, tenure taken at Computer Science Department The Ohio State University Columbus, Ohio iv 1985 ............................................ M.S. Computer Science The Ohio State University Columbus, Ohio 1989 ............................................ OSU Presidential Fellow The Ohio State University Columbus, Ohio 1987-1988, 1990 ........................ Graduate Research Assistant Laboratory for Artificial Intelligence Research The Ohio State University Columbus, Ohio v PUBLICATIONS D. Allemang and A. Keuneke, “Causal Reasoning at higher levels of abstraction”, Proceedings of IJCAI workshop on Model Based Reasoning, Detroit, 1989, p. 80- 82. A. Keuneke and Dean Allemang, “Exploring the No Function in Structure Princi­ ple”, Journal Expt. Theor. Artif. Intell. 1(1989) 79-89. Tom Bylander, Dean Allemang, M. C. Tanner, and J. Josephson, “Some results concerning the computational complexity of abduction”, First International confer­ ence on Principles of Knowledge Representation and Reasoning, Toronto, Canada, 1989. B. Chandrasekaran, Ashok Goel and Dean Allemang, “Connectionism and In­ formation Processing Abstractions: The Message Still Counts More Than the Medium”. AI Magazine , AMERICAN ASSOCIATION FOR ARTIFICIAL IN­ TELLIGENCE, 1988. The following two papers axe shorter versions of this one. B. Chandrasekaran, Ashok Goel and Dean Allemang, “Information Processing Abstractions: The Message Still Counts More Than the Medium”. Behavioral and Brain Sciences, Stevan Hamad: editor, Cambridge University Press, 1988; This is a commentary on Paul Smolensky’s paper “On the Proper Treatment of Connectionism”. B. Chandrasekaran, Ashok Goel and Dean Allemang, “Connectionism and Infor­ mation Processing Abstractions”. In the Proceedings of the AAAI Spring Sympo­ sium on “Parallel Models of Intelligence: How Can Slow Components Think So Fast?”, Stanford University, Palo Alto, California, March 22-24, 1988, pages 66-85. Tom Bylander, Dean Allemang, Michael C. Tanner, John Josephson, “Some Re­ sults on the Complexity of Abduction”, In the Proceedings of the A A A I Spring Symposium on AI in Medicine, Stanford University, Palo Alto, California, March 22-24, 1988. Dean Allemang, Michael C. Tanner, Tom Bylander, John Josephson, “Computa­ tional Complexity of Hypothesis Assembly.” In Proceedings of the tenth interna­ tional joint conference on artificial intelligence. Milan, Italy, August 1987, pp. 1112. Fields of Study Major field: Computer and Information Sciences Specializations: Artificial Intelligence: Prof. B. Chandrasekaran Theory of Computer Science: Prof. T. Long Cognitive Science: Prof. T. Milburn Table of Contents DEDICATION ..................................................................................................... ii ACKNOWLEDGEMENTS........................................................................... iii VITA ....................................................................................................................... iv LIST OF FIGURES ........................................................................................... xi LIST OF SYMBOLS ....................................................................................... xv ABSTRACT ...................................................................................................... xvi CHAPTER PAGE I Introduction 1 1.1 Necessary Aspects of a Representation ................................... 2 1.2 The Functional Representation Language................................ 3 1.3 Demonstration of the Functional Representation 11 1.4 The Contribution of D udu ........................................................... 12 1.5 The Scope of Dudu .......................................................................... 14 1.6 The Rest of this Work.................................................................... 15 II An Example 16 2.1 Functional Representation........................................................... 19 2.2 Using Correctness Proofs.............................................................. 27 2.3 Modifying Proofs ............................................................................. 32 2.4 Representing a Proof According to Intentions..................... 40 2.5 Consistency of a Functional Representation ......................... 50 2.5.1 Consistency and Different Description Languages 54 2.6 Ramifications of Consistency........................................................ 58 III Generic Representations 64 3.1 Representing Generic Devices..................................................... 66 3.2 Generic Loops.................................................................................... 70 3.3 Generic Data Structures.............................................................. 75 3.4 Other Generic Devices ................................................................. 77 3.5 Example of use of Generic Objects: the shift loop .... 79 viii 3.6 Why Generic Objects? ............................................................. 84 3.6.1 Proof Strategies......................................................... 85 3.6.2 Scope of Constructed Proofs................................ 87 3.6.3 Providing Provisos................................................... 88 3.6.4 Forming Functional Representations................. 88 IV Debugging Using Device Understanding: Dudu 91 4.1 Matching a Functional Representation to Program Code 94 4.2 The Role of FR in Program Debugging.............................. 98 4.3 The Role of Proof in Program Debugging........................ 100 4.3.1 Constructing a Proof of Correctness from the Func­ tional Representation............................................... 101 4.3.2 Constructing an Approximate
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