自动化外文翻译.docx
- 文档编号:12679452
- 上传时间:2023-04-21
- 格式:DOCX
- 页数:45
- 大小:56.78KB
自动化外文翻译.docx
《自动化外文翻译.docx》由会员分享,可在线阅读,更多相关《自动化外文翻译.docx(45页珍藏版)》请在冰豆网上搜索。
自动化外文翻译
Automation
TomRidge
April12,2005
Contents
1Introduction...............................................................1
2Requirements..............................................................1
3CurrentAutomationinInteractiveProvers.......................................4
4Techniques...............................................................5
4.1ProofSearch...........................................................6
4.1.1LogicalSystem.....................................................6
4.1.2IntroRules.........................................................6
4.2Equality...............................................................8
4.2.1Rewriting..........................................................8
4.2.2ConditionalSimplification............................................9
4.2.3Completion.......................................................10
4.2.4DynamicCompletion....................................................11
4.2.5EquationalUnification...................................................12
5InterfaceandIntegration......................................................12
6Assessment...............................................................13
6.1Assessmentwrt.Requirements...............................................13
6.2Completeness.............................................................14
6.3Efficiency.............................................................14
6.4InPractice.............................................................15
7Alternative................................................................16
8Conclusion................................................................19
1Introduction
Automationcanbekeytosuccessfulmechanisation.Insomesituations,mechanisationisfeasiblewithoutautomation.Indeed,inhighlyabstractmathematicalareas,mostmechanisedreasoningconsistsoftheuserspellingoutcomplicatedargumentswhicharefarbeyondthosewhichcancurrentlybetackledbyautomation.Inthissetting,automation,ifitisusedatall,isdirectedateasilysolvable,tightlydefinedsubproblems.AtypicalexampleofsuchamechanisationisourformalisationofRamsey'sTheorem[Rid04].Ontheotherhand,automationcanbefruitfullyappliedinverificationstyleproofs,wherethereasoningisrelativelyrestricted,butthesheerlevelofdetailmakesanon-automatedmechanisationinfeasible.
ManymanyearshavebeenspentdevelopingfullyautomaticsystemssuchasVampire[VR]andOtter[McC].Itwouldbefoolishtoimaginethatwecouldcompetewithsuchsystems.Theirperformanceiswaybeyondthatofsystemscurrentlyimplementedininteractivetheoremprovers.Projectsareunderway[MP04]tolinksuchsystemstointeractivetheoremprovers.Thisisextremelyvaluablework:
ifoneknowsthatafirstorderstatementisprovable,thenoneshouldprobablyexpectthatthemachinecanprovideaproof.
Inthissection,weoutlinesometechniqueswehaveappliedinvariouscasestudies.Naturallywedonotseektosolvetheproblemofautomatedreasoningonceandforall.Ratherwefocusontheproblemsthattypicallyariseinthecasestudieswehavebeeninvolvedwith.Westartbyoutliningthefunctionalitywerequireoftheautomatedengine.Wethendescribethetechniquesweapplied,andhowtheywereintegrated.Weevaluatetheresultingenginequalitativelyintermsofourrequirements,andquantitativelywithrespecttoasizablecasestudy.Fewofthesetechniquesarenovel,rather,weseektocombineexistingtechniquesinasuitablefashion.
TheseproceduresweredevelopedintheHOLLighttheoremprover,whichwefoundtobeanexcellentvehicleforprototypingdifferentapproaches.
2Requirements
Whatdowerequireofourautomation?
Letusdistinguishbetweenautomationforfullyautomaticuse,andautomationforinteractiveuse,therequirementsforeachbeingconsiderablydifferent.
Perhapsunexpectedly,failureoftheautomatedproofengineisthenorm,isthesensethatwheninteractivelydevelopingcomplexproofswespendmostofourtimeonobligationsthatare"almost"provable.Thuswewouldliketheprovertogiveusexcellentfeedbackastowhyobligationscouldnotbedischarged.[Sym98]
Thisquoteemphasizesanimportantdifferencebetweenautomaticandinteractiveproof.Inautomaticproof,onetypicallyknowsthatthegoalisprovable(oratleast,suspectsverystrongly,andispreparedtowaitaconsiderableamountoftimebeforeterminatingaproofsearch).Indeed,automaticproversarejudgedonhowmanyprovablegoalstheycanactuallyprove.Ininteractiveproof,"wespendmostofourtimeonobligationsthatarealmostprovable".Thisisthedifferencebetweeninteractiveandautomaticproof.Ifwespendmostofthetimetryingtoprovegoalsthataresimplynotprovable,thencompletenessoftheproofsearchbecomeslessimportant.Thisisnottosaythatitlosesimportancealtogether:
ifasystemlackscompleteness,thenitwillfailtoprovesomeprovablegoals.Itisvitallyimportanttoknowwhatsortofgoalsoneisgivingupon,inorderthatonecanunderstandwhatitmeanswhenaproverfailstoproveagoal.Suchknowledgeisalsousefulwhencombiningsystems:
inordertounderstandthebehaviourofthesystemasawholeone
shouldfirstunderstandthebehaviouroftheparts.
Whatpropertiesmightbepreferred,inaninteractivesetting,overcompleteness?
Forus,themostimportantaspectofautomationissimplicity.Bythiswedonotmeanimplementationsimplicity(howmanylinesdidittaketoimplementthesystem?
etc.),butconceptualsimplicity.Forinstance,simplificationisusedubiquitouslyininteractivetheoremproving.Ifthesetofrewriterulesisnotconfluent,thentounderstandthebehaviourofthesimplifier,onehastounderstandtheorderinwhichtherulesareapplied.Needlesstosay,thisisanextremelycomplexthingtounderstand,andproofswhichdependonthesepropertiesarepresumablyextremelyfragile.Conceptualsimplicityforasimplifieriscloselyboundupwithconfluenceandterminationofthesimpset.Conceptualsimplicityisimportantifauseristounderstandthesystem.Ifasystemisconceptuallysimple,itwillhopefullybesimpletouse.
Inaninteractivesetting,weexpectautomationtofail.Inordertomakeprogress,wemustunderstandwhyaproofattemptfails:
theprovermustprovidefeedback.Resolutionbasedsystemscanprovidefeedback,buttheyaredestructive(inthesensethatthegoalisconvertedintoanormalformbeforetheproofattemptstarts,destroyingtheoriginallogicalstructure),sothatthefeedbackcanbedifficulttounderstand(thepointwheretheprooffailsmaylookverydifferenttotheoriginalgoal).Abetterapproachistoconducttheproofinawaythatisascloseaspossibletohowahumanmightconducttheproof.Werequiretheproofsystemtobenaturalinsomesense.Inthiscase,ifaproofattemptfails,thefailingbranchcanoftenbereturneddirectlytotheuserforinspection.
Feedbackisrelatedtovisibility.Oftenauserwishestoinspectafailedproof,butonlyaprooftraceisavailable,whichcancauseaconceptualmismatch:
theuserisfocusedonsequents,whereasthetracemaybeofadifferentnaturealtogether.Iftherearemanyunprovedbranches,thenausermightnotinspectthemall,butmightwishtostepthroughtheproof.Automaticmethods,suchasJohnHarrison'simplementationofmodelelimination[Har96],oftensearchforaproofinatreemakinguseofglobalinformationaboutnodesvisitedpreviously.Ifthisglobalinformationisnotpresentinthesequenttheuserhasaccessto,itwillbedifficulttostepthroughtheautomaticproofbysimplyinvokingtheautomaticproverastepatatime:
theautomaticproverwillnotmakethesamedecisionsitmadewhenconductingthesearchusingglobalinformationbecauseitonlyhasaccesstothelocalsequent.
Manymethodscurrentlyemployedbyinteractivetheoremprovers,suchasIsabelle'sblast,leavethegoalunchangediftheyfailtoproveit.Naturalmethodsofproofsearchexpecttomakeatleastsomeprogressinallsituations,sothattheycanassistevenifthegoalisnotprovable.Forinstance,safesteps(suchas∧Einmanysystems)shouldbeperformed,simplificationstepsappliedandsoon.
Automationshouldalsobestable.Inlargeproofs,onefrequentlymixesinteractiveandautomaticproof.Ifthegoalsreturnedbyautomationareapttochangeradicallywithslightvariationsinthegoal,thenthedependentinteractiveproofscanberendereduseless,andmu
- 配套讲稿:
如PPT文件的首页显示word图标,表示该PPT已包含配套word讲稿。双击word图标可打开word文档。
- 特殊限制:
部分文档作品中含有的国旗、国徽等图片,仅作为作品整体效果示例展示,禁止商用。设计者仅对作品中独创性部分享有著作权。
- 关 键 词:
- 自动化 外文 翻译