Recovery, Convergence and Documentation of Languages

Total Page:16

File Type:pdf, Size:1020Kb

Recovery, Convergence and Documentation of Languages Recovery, Convergence and Documentation of Languages by Vadim Zaytsev September 14, 2010 VRIJE UNIVERSITEIT Recovery, Convergence and Documentation of Languages ACADEMISCH PROEFSCHRIFT ter verkrijging van de graad Doctor aan de Vrije Universiteit Amsterdam, op gezag van de rector magnificus prof.dr. L.M. Bouter, in het openbaar te verdedigen ten overstaan van de promotiecommissie van de faculteit der Exacte Wetenschappen op woensdag 27 oktober 2010 om 15.45 uur in de aula van de universiteit, De Boelelaan 1105 door Vadim Valerievich Zaytsev geboren te Rostov aan de Don, Rusland promotoren: prof.dr. R. Lammel¨ prof.dr. C. Verhoef Dit onderzoek werd ondersteund door de Nederlandse Organisatie voor Wetenschappelijk Onderzoek via: This research has been sponsored by the Dutch Organisation of Scientific Research via: NWO 612.063.304 LPPR: Language-Parametric Program Restructuring Acknowledgements Working on a PhD is supposed to be an endeavour completed in seclusion, but in practice one cannot survive without the help and support from others, fruitful scientific discus- sions, collaborative development of tools and papers and valuable pieces of advice. My work was supervised by Prof. Dr. Ralf Lammel¨ and Prof. Dr. Chris Verhoef, who often believed in me more than I did and were always open to questions and ready to give expert advice. They have made my development possible. LPPR colleagues — Jan Heering, Prof. Dr. Paul Klint, Prof. Dr. Mark van den Brand — have been a rare yet useful source of new research ideas. All thesis reading committee members have dedicated a lot of attention to my work and delivered exceptionally useful feedback on the late stage of the research: Prof. Dr. Jean Bezivin,´ Dr. Jean-Marie Favre, Prof. Dr. Willem Jan Fokkink, Prof. Dr. Paul Klint, Dr. Steven Klusener. I am also grateful for Cor-Paul Bezemer and Toon Verwaest who provided proofreading and correcting services for the Dutch part of this thesis. There have been a lot of insightful discussions in the rooms and hallways of the Vrije Universiteit with Dr. Niels Veerman, Ernst-Jan Verhoeven, Łukasz Kwiatkowski and Johan Vincent de Vries. I would like to thank my family that backed me up with complete support and encour- agement through the years of research, especially my mother, Dr.ir. Liudmila Zaytseva; my grandmother, Dr. Svetlana Bocheva; my grandfather, Prof. Dr.ir. Alexander Bochev ; my uncle, Dr. Michael Bochev and my godfather, Prof. Dr. Yuri Bashmakov, MD. My close friends’ understanding, respect and interest in my work was also among the most important things that kept me going: Dr. Alexander Gufan, Dr. Stanislav Tsykavy and Stanislav Rezhabek. I have also been saved many times from depression and writer’s blocks by good mu- sic. I cannot name all the artists responsible for that, but the most credit goes to Huddie Ledbetter, William Broonzy, Fulton Allen, Thomas McClennan and Bruce Springsteen. i Contents Acknowledgementsi Contents ii List of Tables ................................... ix List of Figures................................... x List of Listings .................................. xi 1 Introduction1 1.1 Research context .............................. 1 1.2 Motivation and objectives.......................... 2 1.3 Example scenario.............................. 3 1.4 Thesis outline and contributions ...................... 10 1.4.1 Chapter 2 overview: additional background............ 10 1.4.2 Chapter 3 overview: case study on language recovery . 11 1.4.3 Chapter 4 overview: language convergence............ 12 1.4.4 Chapter 5 overview: case study on recovery and convergence . 13 1.4.5 Chapter 6 overview: language documentation........... 14 1.4.6 Chapter 7 overview: XBGF language manual........... 15 2 Additional background 17 2.1 Terminology................................. 17 2.2 Grammarware................................ 18 2.3 Techniques for grammars.......................... 19 2.4 Language evolution: versions and dialects................. 20 2.5 Grammar levels............................... 22 2.6 Grammar recovery methodology...................... 22 2.7 Grammar definition formalism....................... 23 2.8 Grammar idiosyncrasies and parsing technology.............. 24 2.9 Grammarware and tool generation..................... 25 2.10 Language documentation qualities..................... 27 2.11 Standardisation bodies ........................... 28 2.12 Languages used in the thesis ........................ 31 2.13 Transformations used in the thesis ..................... 34 3 Case study on recovery 37 ii Contents iii 3.1 Contributions................................ 37 3.2 Semi-automated recovery of C# grammar ................. 38 3.2.1 Step 1: Obtaining the standard................... 38 3.2.2 Step 2: Extracting the grammar .................. 39 3.2.3 Step 3: Fixing misprints ...................... 40 3.2.4 Step 4: Completing a formal part ................. 40 3.2.5 Step 5: Relaxation ......................... 40 3.2.6 Step 6: Removing idiosyncrasies from the grammar . 44 3.2.7 Step 7: Resolving conflicts..................... 48 3.2.8 Step 8: Improving the grammar .................. 49 3.2.9 Step 9: Generating the parser.................... 49 3.3 Proposed solution generalisation and evaluation.............. 50 3.4 Conclusion ................................. 54 3.4.1 Discussion on the method automation............... 54 3.4.2 Research objectives revisited.................... 55 4 Language convergence 57 4.1 Motivation.................................. 58 4.2 Contributions................................ 58 4.3 The domain................................. 59 4.3.1 Sources of convergence....................... 61 4.3.2 Targets of convergence....................... 61 4.3.3 BGF — BNF-like Grammar Format................ 63 4.4 Grammar extraction............................. 65 4.4.1 Abstraction by extraction...................... 65 4.4.2 Grammar extractors ........................ 66 4.5 Grammar comparison............................ 68 4.6 Grammar transformation.......................... 73 4.7 Convergence process ............................ 76 4.8 Programmable grammar transformations.................. 79 4.8.1 Transformation properties ..................... 79 4.8.2 Grammar refactoring........................ 79 4.8.3 Grammar editing.......................... 81 4.9 Transformation generators ......................... 83 4.10 Language Convergence Infrastructure ................... 86 4.10.1 Main configuration elements.................... 86 4.10.2 Shortcuts.............................. 87 4.10.3 Generators ............................. 87 4.10.4 Sources............................... 87 4.10.5 Targets ............................... 88 4.10.6 Phases................................ 89 4.10.7 Test sets............................... 89 4.10.8 Tools ................................ 90 4.10.9 xstring ............................... 90 4.11 Related work ................................ 91 iv Contents 4.11.1 Interoperability........................... 91 4.11.2 Testing grammarware........................ 91 4.11.3 Generators and synchronisers ................... 91 4.11.4 Grammar recovery......................... 92 4.11.5 Grammar transformation...................... 92 4.11.6 Grammar convergence....................... 92 4.12 Concluding remarks............................. 93 5 Case study on recovery and convergence 95 5.1 Java is not syntax-safe—apparently .................... 95 5.2 Contributions................................ 97 5.3 The JLS corpus............................... 98 5.3.1 JLS1 ................................ 98 5.3.2 JLS2 ................................ 99 5.3.3 JLS3 ................................ 99 5.3.4 Grammar data............................ 99 5.4 Automated grammar extraction.......................100 5.4.1 Assumed grammar format .....................101 5.4.2 Phase 1 — Preprocessing......................102 5.4.3 Phase 2 — Error recovery .....................104 5.4.4 Phase 3 — Removal of doubles ..................107 5.4.5 Phase 4 — Precise parsing.....................107 5.4.6 Extraction data...........................108 5.5 The convergence graph...........................108 5.6 Grammar transformation ..........................109 5.6.1 Semantics-preserving operators ..................109 5.6.2 Semantics-in/decreasing operators . 110 5.6.3 Semantics-revising operators....................112 5.6.4 Grammar refactoring........................114 5.7 Grammar convergence phases .......................117 5.7.1 Preparation phase: semantic error recovery . 117 5.7.2 Preparation phase: fixing known bugs . 117 5.7.3 Preparation phase: initial correction . 118 5.7.4 Nominal matching phase......................119 5.7.5 Structural matching phase .....................119 5.7.6 Resolution phase: extension ....................119 5.7.7 Resolution phase: relaxation....................120 5.7.8 Resolution phase: correction....................120 5.8 Measuring grammars and transformations . 121 5.9 Related work ................................122 5.9.1 Grammar recovery.........................123 5.9.2 Programmable grammar transformations . 124 5.9.3 Grammar engineering .......................127 5.9.4 Schema/metamodel comparison..................128 5.9.5 Coupled transformations......................128 Contents v 5.10 Concluding remarks.............................129 6 Language documentation 131 6.1 Motivation..................................132 6.2 Contributions ................................133 6.3 Grammar
Recommended publications
  • Cobol/Cobol Database Interface.Htm Copyright © Tutorialspoint.Com
    CCOOBBOOLL -- DDAATTAABBAASSEE IINNTTEERRFFAACCEE http://www.tutorialspoint.com/cobol/cobol_database_interface.htm Copyright © tutorialspoint.com As of now, we have learnt the use of files in COBOL. Now, we will discuss how a COBOL program interacts with DB2. It involves the following terms: Embedded SQL DB2 Application Programming Host Variables SQLCA SQL Queries Cursors Embedded SQL Embedded SQL statements are used in COBOL programs to perform standard SQL operations. Embedded SQL statements are preprocessed by SQL processor before the application program is compiled. COBOL is known as the Host Language. COBOL-DB2 applications are those applications that include both COBOL and DB2. Embedded SQL statements work like normal SQL statements with some minor changes. For example, that output of a query is directed to a predefined set of variables which are referred as Host Variables. An additional INTO clause is placed in the SELECT statement. DB2 Application Programming Following are rules to be followed while coding a COBOL-DB2 program: All the SQL statements must be delimited between EXEC SQL and END-EXEC. SQL statements must be coded in Area B. All the tables that are used in a program must be declared in the Working-Storage Section. This is done by using the INCLUDE statement. All SQL statements other than INCLUDE and DECLARE TABLE must appear in the Procedure Division. Host Variables Host variables are used for receiving data from a table or inserting data in a table. Host variables must be declared for all values that are to be passed between the program and the DB2. They are declared in the Working-Storage Section.
    [Show full text]
  • An Efficient Implementation of the Head-Corner Parser
    An Efficient Implementation of the Head-Corner Parser Gertjan van Noord" Rijksuniversiteit Groningen This paper describes an efficient and robust implementation of a bidirectional, head-driven parser for constraint-based grammars. This parser is developed for the OVIS system: a Dutch spoken dialogue system in which information about public transport can be obtained by telephone. After a review of the motivation for head-driven parsing strategies, and head-corner parsing in particular, a nondeterministic version of the head-corner parser is presented. A memorization technique is applied to obtain a fast parser. A goal-weakening technique is introduced, which greatly improves average case efficiency, both in terms of speed and space requirements. I argue in favor of such a memorization strategy with goal-weakening in comparison with ordinary chart parsers because such a strategy can be applied selectively and therefore enormously reduces the space requirements of the parser, while no practical loss in time-efficiency is observed. On the contrary, experiments are described in which head-corner and left-corner parsers imple- mented with selective memorization and goal weakening outperform "standard" chart parsers. The experiments include the grammar of the OV/S system and the Alvey NL Tools grammar. Head-corner parsing is a mix of bottom-up and top-down processing. Certain approaches to robust parsing require purely bottom-up processing. Therefore, it seems that head-corner parsing is unsuitable for such robust parsing techniques. However, it is shown how underspecification (which arises very naturally in a logic programming environment) can be used in the head-corner parser to allow such robust parsing techniques.
    [Show full text]
  • Modern Programming Languages CS508 Virtual University of Pakistan
    Modern Programming Languages (CS508) VU Modern Programming Languages CS508 Virtual University of Pakistan Leaders in Education Technology 1 © Copyright Virtual University of Pakistan Modern Programming Languages (CS508) VU TABLE of CONTENTS Course Objectives...........................................................................................................................4 Introduction and Historical Background (Lecture 1-8)..............................................................5 Language Evaluation Criterion.....................................................................................................6 Language Evaluation Criterion...................................................................................................15 An Introduction to SNOBOL (Lecture 9-12).............................................................................32 Ada Programming Language: An Introduction (Lecture 13-17).............................................45 LISP Programming Language: An Introduction (Lecture 18-21)...........................................63 PROLOG - Programming in Logic (Lecture 22-26) .................................................................77 Java Programming Language (Lecture 27-30)..........................................................................92 C# Programming Language (Lecture 31-34) ...........................................................................111 PHP – Personal Home Page PHP: Hypertext Preprocessor (Lecture 35-37)........................129 Modern Programming Languages-JavaScript
    [Show full text]
  • The Monad.Reader Issue 6 by Bernie Pope [email protected] and Dan Piponi [email protected] and Russell O’Connor [email protected]
    The Monad.Reader Issue 6 by Bernie Pope [email protected] and Dan Piponi [email protected] and Russell O’Connor [email protected] Wouter Swierstra, editor. 1 Contents Wouter Swierstra Editorial 3 Bernie Pope Getting a Fix from the Right Fold 5 Dan Piponi Adventures in Classical-Land 17 Russell O’Connor Assembly: Circular Programming with Recursive do 35 2 Editorial by Wouter Swierstra [email protected] It has been many months since the last issue of The Monad.Reader. Quite a few things have changed since Issue Five. For better or for worse, we have moved from wikipublishing to LATEX. I, for one, am pleased with the result. This issue consists of three top-notch articles on a variety of subjects: Bernie Pope explores just how expressive foldr is; Dan Piponi shows how to compile proofs in classical logic to Haskell programs; Russell O’Connor has written an embedded assembly language in Haskell. Besides the authors, I would like to acknowledge several other people for their contributions to this issue. Andres L¨oh provided a tremendous amount of TEXnical support and wrote the class files. Peter Morris helped design the logo. Finally, I’d like to thank Shae Erisson for starting up The Monad.Reader – without his limitless enthusiasm for Haskell this magazine would never even have gotten off the ground. 3 Getting a Fix from the Right Fold by Bernie Pope [email protected] What can you do with foldr? This is a seemingly innocent question that will confront most functional programmers at some point in their life.
    [Show full text]
  • Communications/Information
    Communications/Information Volume 7 — November 2008 Issue date: November 7, 2008 Info Update is published by the Canadian Standards Association (CSA) eight times a year. It contains important information about new and existing standards, e.g., recently published standards, and withdrawn standards. It also gives you highlights of other activities and services. CSA offers a free online service called Keep Me Informed that will notify registered users when each new issue of Info Update is published. To register go to http://www.csa-intl.org/onlinestore/KeepMeInformed/PleaseIdentifyYourself.asp?Language=EN. To view the complete issue of Info Update visit http://standardsactivities.csa.ca/standardsactivities/default.asp?language=en. y Completed Projects / Projets terminés New Standards — New Editions — Special Publications Please note: The following standards were developed by the International Organization for Standardization (ISO) and the International Electrotechnical Commission (IEC), and have been adopted by the Canadian Standards Association. These standards are available in Portable Document Format (PDF) only. CAN/CSA-ISO/IEC 7812-2:08, 2nd edition Identification cards — Identification of issuers — Part 2: Application and registration procedures (Adopted ISO/IEC 7812-2:2007).................................................................. $110 CAN/CSA-ISO/IEC 7816-2:08, 1st edition Identification cards — Integrated circuit cards — Part 2: Cards with contacts — Dimensions and location of the contacts (Adopted ISO/IEC 7816-2:2007) ......................... $60 CAN/CSA-ISO/IEC 7816-13:08, 1st edition Identification cards — Integrated circuit cards — Part 13: Commands for application management in a multi-application environment (Adopted ISO/IEC 7816-13:2007)....... $110 CAN/CSA-ISO/IEC 8484:08, 1st edition Information technology — Magnetic stripes on savingsbooks (Adopted ISO/IEC 8484:2007) ......................................................................................
    [Show full text]
  • 10 Programming Languages You Should Learn Right Now by Deborah Rothberg September 15, 2006 8 Comments Posted Add Your Opinion
    10 Programming Languages You Should Learn Right Now By Deborah Rothberg September 15, 2006 8 comments posted Add your opinion Knowing a handful of programming languages is seen by many as a harbor in a job market storm, solid skills that will be marketable as long as the languages are. Yet, there is beauty in numbers. While there may be developers who have had riches heaped on them by knowing the right programming language at the right time in the right place, most longtime coders will tell you that periodically learning a new language is an essential part of being a good and successful Web developer. "One of my mentors once told me that a programming language is just a programming language. It doesn't matter if you're a good programmer, it's the syntax that matters," Tim Huckaby, CEO of San Diego-based software engineering company CEO Interknowlogy.com, told eWEEK. However, Huckaby said that while his company is "swimmi ng" in work, he's having a nearly impossible time finding recruits, even on the entry level, that know specific programming languages. "We're hiring like crazy, but we're not having an easy time. We're just looking for attitude and aptitude, kids right out of school that know .Net, or even Java, because with that we can train them on .Net," said Huckaby. "Don't get fixated on one or two languages. When I started in 1969, FORTRAN, COBOL and S/360 Assembler were the big tickets. Today, Java, C and Visual Basic are. In 10 years time, some new set of languages will be the 'in thing.' …At last count, I knew/have learned over 24 different languages in over 30 years," Wayne Duqaine, director of Software Development at Grandview Systems, of Sebastopol, Calif., told eWEEK.
    [Show full text]
  • Instructions to the Ada Rapporteur Group from SC22/WG9 For
    Work Programme of ISO/IEC JTC1/SC22/WG9 (Ada) For presentation to the SIGAda Conference December 2003 Jim Moore, [The MITRE Corporation] Convener of ISO/IEC JTC1/SC22/WG9 In this presentation, Jim Moore is representing his opinions as an officer of ISO/IEC JTC1/SC22/WG9. His opinions do not necessarily represent those of The MITRE Corporation or any of its sponsors. Goal for the Presentation A quick description of international standardization. An overview of the work programme of the standards committee responsible for Ada. A description of the process and constraints for amending the Ada language standard. Who Makes Standards? De jure standards are formal standards made Today’s by organizations authorized, in some way, to Subject make them. Examples include ISO and IEEE standards. De facto standards (more properly called specifications) are those recognized by the marketplace as important. Examples include OMG CORBA, Windows API. Developers of International Standards ISO IEC ITU ... TC176 JTC1 TC56 SC65A Quality Information Technology Dependability Functional Safety ... SC7 SC22 Software & Systems Languages, OS Engineering WG9 Ada Developers of US Standards ANSI INCITS AIAA ANS ASTM EIA IEEE PMI OMG About 550 organizations in the U. S. make standards. About half of them are accredited by ANSI, allowing them to participate in international standardization activity. Three Ways to Make a US Standard Accredited Standards Organization: An organization that does many things including making standards, e.g. IEEE. Accredited Standards
    [Show full text]
  • Modular Logic Grammars
    MODULAR LOGIC GRAMMARS Michael C. McCord IBM Thomas J. Watson Research Center P. O. Box 218 Yorktown Heights, NY 10598 ABSTRACT scoping of quantifiers (and more generally focalizers, McCord, 1981) when the building of log- This report describes a logic grammar formalism, ical forms is too closely bonded to syntax. Another Modular Logic Grammars, exhibiting a high degree disadvantage is just a general result of lack of of modularity between syntax and semantics. There modularity: it can be harder to develop and un- is a syntax rule compiler (compiling into Prolog) derstand syntax rules when too much is going on in which takes care of the building of analysis them. structures and the interface to a clearly separated semantic interpretation component dealing with The logic grammars described in McCord (1982, scoping and the construction of logical forms. The 1981) were three-pass systems, where one of the main whole system can work in either a one-pass mode or points of the modularity was a good treatment of a two-pass mode. [n the one-pass mode, logical scoping. The first pass was the syntactic compo- forms are built directly during parsing through nent, written as a definite clause grammar, where interleaved calls to semantics, added automatically syntactic structures were explicitly built up in by the rule compiler. [n the two-pass mode, syn- the arguments of the non-terminals. Word sense tactic analysis trees are built automatically in selection and slot-filling were done in this first the first pass, and then given to the (one-pass) pass, so that the output analysis trees were actu- semantic component.
    [Show full text]
  • The Evolution of Lisp
    1 The Evolution of Lisp Guy L. Steele Jr. Richard P. Gabriel Thinking Machines Corporation Lucid, Inc. 245 First Street 707 Laurel Street Cambridge, Massachusetts 02142 Menlo Park, California 94025 Phone: (617) 234-2860 Phone: (415) 329-8400 FAX: (617) 243-4444 FAX: (415) 329-8480 E-mail: [email protected] E-mail: [email protected] Abstract Lisp is the world’s greatest programming language—or so its proponents think. The structure of Lisp makes it easy to extend the language or even to implement entirely new dialects without starting from scratch. Overall, the evolution of Lisp has been guided more by institutional rivalry, one-upsmanship, and the glee born of technical cleverness that is characteristic of the “hacker culture” than by sober assessments of technical requirements. Nevertheless this process has eventually produced both an industrial- strength programming language, messy but powerful, and a technically pure dialect, small but powerful, that is suitable for use by programming-language theoreticians. We pick up where McCarthy’s paper in the first HOPL conference left off. We trace the development chronologically from the era of the PDP-6, through the heyday of Interlisp and MacLisp, past the ascension and decline of special purpose Lisp machines, to the present era of standardization activities. We then examine the technical evolution of a few representative language features, including both some notable successes and some notable failures, that illuminate design issues that distinguish Lisp from other programming languages. We also discuss the use of Lisp as a laboratory for designing other programming languages. We conclude with some reflections on the forces that have driven the evolution of Lisp.
    [Show full text]
  • GNU Cobol FAQ
    GNU Cobol FAQ | Status This is a 2.1 work in progress release of the GNU Cobol FAQ. Sourced at gcfaqrrst. Courtesty of ReStructuredText, Sphinx and Pygments. GNU Cobol 2.1 is not currently rolled out, but is available for testing. GNUCobolFAQppdf is also available, but broken, as a work in progress, with no work done yet, using Texlive and Sphinx. This FAQ is more than a FAQ and less than a FAQ. Someday that will change and this document will be split into a GNU Cobol manual and a simplified Frequently Asked Questions file. Website favicon by Mark James, help.png from the FAMFAMFAM Silk icon set. http://creativecommons.org/licenses/by/2.5/ Banner courtesy of the GIMP, Copyright © 2008-2014 Brian Tif- fin licensed under Creative Commons Attribution-Share Alike 2.0 Generic License http://creativecommons.org/licenses/by-sa/2.0/ Authors Brian Tiffin [btiffin]_ Answers, quotes and contributions: John Ellis [jrls_swla]_, Vincent Coen, Jim Currey, Bill Klein [wmk- lein]_, Ganymede, Simon Sobisch [human]_, Rildo Pragana, Sergey Kashyrin, Federico Priolo, Frank Swarbrick, Angus, DamonH, Parhs, Gerald Chudyk Compiler by: *Roger While* [Roger]_, *Keisuke Nishida* [Keisuke]_, *Ron Norman* [Ron]_, *Sergey Kashyrin* [Sergey]_, (with the invaluable assistance of many others) Special credits to *Gary Cutler* author of the GNU Cobol Programmers Guide Joseph James Frantz for hosting and advocacy [aoirthoir]_ 1 Version 2.1.17, May 24th, 2014 Status never complete; like a limit, limaq→0 f(aq) = 42 Copyright Copyright © 2008-2014 Brian Tiffin ChangeLog ChangeLog_ note Regarding COBOL Standards, Official COBOL Standards: There are many references to standards in this document.
    [Show full text]
  • NINETEENTH PLENARY MEETING of ISO/IEC JTC 1/SC 22 London, United Kingdom September 19-22, 2006 [20060918/22] Version 1, April 17, 2006 1
    NINETEENTH PLENARY MEETING OF ISO/IEC JTC 1/SC 22 London, United Kingdom September 19-22, 2006 [20060918/22] Version 1, April 17, 2006 1. OPENING OF PLENARY MEETING (9:00 hours, Tuesday, September 19) 2. CHAIRMAN'S REMARKS 3. ROLL CALL OF DELEGATES 4. APPOINTMENT OF DRAFTING COMMITTEE 5. ADOPTION OF THE AGENDA 6. REPORT OF THE SECRETARY 6.1 SC 22 Project Information 6.2 Proposals for New Work Items within SC 22 6.3 Outstanding Actions From the Eighteenth Plenary of SC 22 Page 1 of 7 JTC 1 SC 22, 2005 Version 1, April 14, 2006 6.4 Transition to ISO Livelink 6.4.1 SC 22 Transition 7. ACTIVITY REPORTS 7.1 National Body Reports 7.2 External Liaison Reports 7.2.1 ECMA International (Rex Jaeschke) 7.2.2 Free Standards Group (Nick Stoughton) 7.2.2 Austin Joint Working Group (Nick Stoughton) 7.3 Internal Liaison Reports 7.3.1 Liaison Officers from JTC 1/SC 2 (Mike Ksar) 7.3.2 Liaison Officer from JTC 1/SC 7 (J. Moore) Page 2 of 7 JTC 1 SC 22, 2005 Version 1, April 14, 2006 7.3.3 Liaison Officer from ISO/TC 37 (Keld Simonsen) 7.3.5 Liaison Officer from JTC 1 SC 32 (Frank Farance) 7.4 Reports from SC 22 Subgroups 7.4.1 Other Working Group Vulnerabilities (Jim Moore) 7.4.2 SC 22 Advisory Group for POSIX (Stephen Walli) 7.5 Reports from JTC 1 Subgroups 7.5.1 JTC 1 Vocabulary (John Hill) 7.5.2 JTC 1 Ad Hoc Directives (John Hill) 8.
    [Show full text]
  • A Relatively Small Turing Machine Whose Behavior Is Independent of Set Theory
    A Relatively Small Turing Machine Whose Behavior Is Independent of Set Theory Adam Yedidia Scott Aaronson MIT MIT [email protected] [email protected] May 17, 2016 Abstract Since the definition of the Busy Beaver function by Rad´oin 1962, an interesting open question has been the smallest value of n for which BB(n) is independent of ZFC set theory. Is this n approximately 10, or closer to 1,000,000, or is it even larger? In this paper, we show that it is at most 7,910 by presenting an explicit description of a 7,910-state Turing machine Z with 1 tape and a 2-symbol alphabet that cannot be proved to run forever in ZFC (even though it presumably does), assuming ZFC is consistent. The machine is based on work of Harvey Friedman on independent statements involving order-invariant graphs. In doing so, we give the first known upper bound on the highest provable Busy Beaver number in ZFC. To create Z, we develop and use a higher-level language, Laconic, which is much more convenient than direct state manipulation. We also use Laconic to design two Turing machines, G and R, that halt if and only if there are counterexamples to Goldbach’s Conjecture and the Riemann Hypothesis, respectively. 1 Introduction 1.1 Background and Motivation Zermelo-Fraenkel set theory with the axiom of choice, more commonly known as ZFC, is an ax- iomatic system invented in the twentieth which has since been used as the foundation of most of modern mathematics. It encodes arithmetic by describing natural numbers as increasing sets of sets.
    [Show full text]