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Types for Proofs and Programs
International Workshop, TYPES '98, Kloster Irsee, Germany, March 27-31, 1998, Selected Papers
Häftad, Engelska, 1999
551 kr
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Thisbookcontainsaselectionofpaperspresentedatthesecondannualworkshop heldundertheauspicesoftheEspritWorkingGroup21900Types. Theworkshop tookplaceinIrsee,Germany,from27to31ofMarch1998andwasattendedby 89researchers. Ofthe25submissions,14wereselectedforpublicationafteraregularref- eeingprocess. The?nalchoicewasmadebytheeditors. Thisvolumeisasequeltotheproceedingsfromthe?rstworkshopofthe workinggroup,whichtookplaceinAussois,France,inDecember1996. The proceedingsappearedinvol. 1512oftheLNCSseries,editedbyChristinePaulin- MohringandEduardoGim'enez. Theseworkshopsare,inturn,acontinuationofthemeetingsorganizedin 1993,1994,and1995undertheauspicesoftheEspritBasicResearchAction 6453 Types for Proofs and Programs. Thoseproceedingswerealsopublished intheLNCSseries,editedbyHenkBarendregtandTobiasNipkow(vol. 806, 1993),byPeterDybjer,BengtNordstr..omandJanSmith(vol. 996,1994)and byStefanoBerardiandMarioCoppo(vol. 1158,1995). TheEspritBRA6453 wasacontinuationoftheformerEspritAction3245Logical Frameworks: - sign,ImplementationandExperiments.Thearticlesfromtheannualworkshops organizedunderthatActionwereeditedbyGerardHuetandGordonPlotkin inthebooksLogical FrameworksandLogicalEnvironments,bothpublishedby CambridgeUniversityPress. Acknowledgments WewouldliketothankIrmgardMignaniandAgnesSzabo-Lackingerforhelping uswithprocessingtheregistrations,andRalphMatthesandMarkusWenzelfor organizationalsupportduringthemeeting. Weareindebtedtotheorganizersof theWorkingGroupTypesandalsotoPeterClote,TobiasNipkowandMartin Wirsingforgivingustheopportunitytoorganizethisworkshopandfortheir support. WewouldalsoliketoacknowledgefundingbytheEuropeanUnion. Thisvolumewouldnothavebeenpossiblewithouttheworkofthereferees. Theyarelistedonthenextpageandwethankthemfortheirinvaluablehelp. June1999 ThorstenAltenkirch WolfgangNaraschewski BernhardReus VI List of Referees PeterAczel PetriMa..enp..a..a ThorstenAltenkirch RalphMatthes GillesBarthe MichaelMendler HenkBarendregt WolfgangNaraschewski UliBerger TobiasNipkow MarcBezem SaraNegri VenanzioCapretta ChristinePaulin-Mohring MarioCoppo HenrikPersson CatarinaCoquand RandyPollack RobertoDiCosmo DavidPym GillesDowek ChristopheRa?alli MarcDymetman AarneRanta Jean-ChristopheFilliatre BernhardReus NeilGhani EikeRitter MartinHofmann GiovanniSambin MonikaSeisenberger FurioHonsell AntonSetzer PaulJackson JanSmith FelixJoachimski FlorianKammuller .. SergeiSoloview JamesMcKinna MakotoTakeyama Sim"aoMelodeSousa SilvioValentini ThomasKleymann MarkusWenzel HansLeiss BenjaminWerner Table of Contents OnRelatingTypeTheoriesandSetTheories...1 PeterAczel CommunicationModellingandContext-DependentInterpretation: AnIntegratedApproach...19 Ren'eAhn,TijnBorghuis Grobner .. BasesinTypeTheory ...33 ThierryCoquand,HenrikPersson AModalLambdaCalculuswithIterationandCaseConstructs...47 Jo..elleDespeyroux,PierreLeleu ProofNormalizationModulo ...62 GillesDowek,BenjaminWerner ProofofImperativeProgramsinTypeTheory...78 Jean-ChristopheFilliatre AnInterpretationoftheFanTheoreminTypeTheory ...93 DanielFridlender ConjunctiveTypesandSKInT...106 JeanGoubault-Larrecq ModularStructuresasDependentTypesinIsabelle ...121 FlorianKammul ..ler MetatheoryofVeri?cationCalculiinLEGO...133 ThomasKleymann BoundedPolymorphismforExtensibleObjects ...149 LuigiLiquori AboutE?ectiveQuotientsinConstructiveTypeTheory ...164 MariaEmiliaMaietti VIII AlgorithmsforEqualityandUni?cationinthePresenceof NotationalDe?nitions...179 FrankPfenning,CarstenSch..urmann APreviewoftheBasicPicture:ANewPerspectiveonFormalTopology. .194 GiovanniSambin,SilviaGebellato On Relating TypeTheories and Set Theories PeterAczel Departments of Mathematics and Computer Science Manchester University petera@cs. man. ac. uk Introduction 1 The original motivation for the work described in this paper was to det- minetheprooftheoreticstrengthofthetypetheoriesimplementedintheproof developmentsystemsLegoandCoq,[12,4]. Thesetypetheoriescombinetheim- 2 predicativetype of propositions , from the calculus of constructions,[5], with theinductivetypesandhierarchyoftypeuniversesofMartin-Lo..f'sconstructive typetheory,[13]. Intuitivelythereisaneasywaytodetermineanupperbound ontheprooftheoreticstrength. Thisistousethe'obvious'types-as-sets- terpretation of these type theories in a strong enough classical axiomatic set theory.
Types for Proofs and Programs
International Workshop, TYPES 2006, Nottingham, UK, April 18-21, 2006, Revised Selected Papers
Häftad, Engelska, 2007
551 kr
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The refereed post-proceedings of the International Workshop of the Types Working Group are presented in this volume. The 17 papers address all current issues in formal reasoning and computer programming based on type theory, including languages and computerized tools for reasoning; applications in several domains, such as analysis of programming languages; certified software; formalization of mathematics; and mathematics education.