Title: Types for proofs and programs : international workshop, TYPES '98, Kloster Irsee, Germany, March 27-31, 1998 : selected papers /
Authors: Altenkirch, Thorsten, 1962-; Naraschewski, Wolfgang, 1970-; Reus, Bernhard, 1965-
Publisher: Springer,
Year: 1999
Subjects: Automatic theorem proving Congresses.; Computer programming Congresses; Type theory Congresses.; Computer science.; Logic design.; Artificial intelligence.
Abstract: 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-ChristopheFilliˆatre 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-ChristopheFilliˆatre 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.
Contents: On Relating Type Theories and Set Theories -- Communication Modelling and Context-Dependent Interpretation: An Integrated Approach -- Gröbner Bases in Type Theory -- A Modal Lambda Calculus with Iteration and Case Constructs -- Proof Normalization Modulo -- Proof of Imperative Programs in Type Theory -- An Interpretation of the Fan Theorem in Type Theory -- Conjunctive Types and SKInT -- Modular Structures as Dependent Types in Isabelle -- Metatheory of Verification Calculi in LEGO -- Bounded Polymorphism for Extensible Objects -- About Effective Quotients in Constructive Type Theory -- Algorithms for Equality and Unification in the Presence of Notational Definitions -- A Preview of the Basic Picture: A New Perspective on Formal Topology.