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Format Title Artist Label Model Number Release Press 12 ラストエンペラー(white) K DUB SHINE CUTTING EDGE,RHYTHM REPUBLIC RR12-88045 1997/--/-- - bf7540a84d1911e3849812006f78d5fc_8.jpg Side Track Title Produce A 1 ラストエンペラー K DUB SHINE 2 ラストエンペラー(Inst) K DUB SHINE 3 ラストエンペラー(Acap) K DUB SHINE B 4 機能停止(REMIX)(宣戦布告VERSION) DJ KENSEI 5 機能停止(REMIX)(宣戦布告VERSION)(Inst) DJ KENSEI PERTAIN CD 現在時刻
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Achim KleinleinAdalbert KrausAleksandra KurzakAlexander KaimbacherAlexander KipnisAlexandra Pawlowna KrutikowaAlfred KaseAlfredo KrausAngelika KirchschlagerAnja KampeAnna KasyanAnna KraujaAnna Maria KaufmannAnnelies KupperAnny KonetzniAnu KomsiAugust KindermannAxel KöhlerBenno KuscheBogomir KorsowCamilla KallfaßCarlos KrauseCharles KullmanChristiane KargChristiane KohlClara Louise KelloggDawn KotoskiDenis Alexandrowitsch KoroljowDirk KleinkeDmitri KhvorostovskiDong-Won KimDora KomarDorothy KirstenEdit KarolyEgon KarterElisabeth Kales-WallnerElisabeth KulmanElizabeth KingdonEmilie KrallEmma KirkbyErich KunzErik KurmangalievErika KöthErnst KozubEtsuko KanohFlorence KirkFrank KelleyFranz KalchmairFranz KelchFranz KlarweinFranz KollFranz KrolopFranziska Romana KochGenia KühmeierGladys KuchtaGregory KundeGreta KlingsbergHanne-Lore KuhseHarry van der KampHeinrich KnoteHeinz KruseHellen KwonHelmut KrebsHelmut KretschmarHiba KawasHilde KonetzniHiroko KashiwagiHiroko KoudaIngrid KaiserfeldIngrid KremlingIrene KurkaIrma KolassiIsabelle KabatuIwan Semjonowitsch KoslowskiJan KiepuraJan KobowJan KullmannJean KraftJochen KowalskiJochen KupferJohannes KalpersJohn KeyesJohn van KesterenJonas KaufmannThe Puccini AlbumVerdi AlbumJosef KrägelJulia KleiterJulia KoganJulie KaufmannKanae KushimaKarl-Christian KohnKatarina KarnéusKathleen KimKathrin KochKatrina KrumpaneKetevan KemoklidzeKlaus KönigKuniko KikkawaKyle KetelsenKyoko KaritaLana KosLjubow Jurjewna KasarnowskajaLucy KelstonLudwig KneissMagdalena KoženáMaija KovalevskaMarek KalbusMargarete KloseMarguerite KrullMariusz KwiecieńMartin KremerMartin KrumbiegelMaría Cristina KiehrMatthias KlinkMax KuttnerMayuko KarasawaMegan KahtsMelanie KurtMichael KellyMichael KupferMichaela KauneMichaela KlarweinMihoko KinoshitaMika KanekoMila Kupfer-BergerMiliza KorjusMlada KhudoleyNorman KelleyOtakar KrausOtto KöhlerPaul Austin KellyPaul KalischPaul KuënPeter KajlingerPeter KleinPeter KooijPhilip KrausPolly KossRajna KabaiwanskaRanko KuranoRené KolloRita KapfhammerRobert KernsRoberta KnieRoland KunzRosemary KuhlmannRuth KobartSachiko KawashimaSalome KammerSalome KruschelnytskaSara KobayashiSelma KurzSibongile KhumaloSigrid KehlSimon KeenlysideSimone KermesSissel KyrkjebøSonja KnittelSophie KarthäuserSophie KochStefanie KunschkeStella KleindienstSándor KónyaTaras KonoshchenkoTeruhiko KomoriThomas KiesslingTom KrauseTomasz KaluznyTomasz KoniecznyTorsten KerlVarduhi KhachatryanVeronika KincsesVesselina KasarovaVitalij KowaljowVuokko KekäläinenWaldemar KmenttWilhelm KrauseWilli Kaiser-HeylWoo-Kyung KimYuko KakutaYumi KoyamaYusuke KoboriZoltán KelemenZoryana Kushpler total 186singers ページ先頭へ
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・ANALOG [ALBUM] 1990 CHECK YOUR MIKE 1992 CHECK YOUR MIKE(promo) 1993 OMNIBUS #1 +玄人はだし+(promo) 1995 悪名 THE BEST OF JAPANESE HIP HOP THE BEST OF JAPANESE HIP HOP VOL.2 THE BEST OF JAPANESE HIP HOP VOL.3(promo) 1996 THE BEST OF JAPANESE DJ VOL.1 THE BEST OF JAPANESE HIP HOP VOL.5 THE BEST OF JAPANESE HIP HOP VOL.4 THE BEST OF JAPANESE DJ VOL.2 THE BEST OF JAPANESE HIP HOP VOL.6 THE BEST OF JAPANESE HIP HOP VOL.7 さんピンCAMP Instrumental(promo) 1997 悪名 Instrumental Acapella THE BEST OF JAPANESE DJ VOL.3 THE BEST OF JAPANESE HIP HOP VOL.8 2000 MAD MAXX WiRED 2-STILL IN THE GROOVE-(white) WiRED 2-STILL IN THE GROOVE- 2002 凶気の桜 ORIGINAL SOUNDTRACK Instrumental(promo) 凶気の桜 ORIGINAL SOUNDTRACK 2011 THE VISIONARIES 2020 Oto No Wa(Selected Sounds of Japan 1988-2018) [SINGLE] 1995 状態のハイウェイ ／ MERRY-GO-ROUND - TOKYO NO.1 SOUL SET - PSYCHEDELIX 1997 FLAVA RECORDS SAMPLE PROMO(promo) - OZROSAURUS - Sugar Soul 1998 'hood SAMPLER - V.A. VIBE - SOUL SCREAM - JIGMASTAS SOUTHPAWFLOW - DESPERADO - OZROSAURUS 1999 DANCEHALL CHECKER(promo type A) DANCEHALL CHECKER(promo type B) DANCEHALL CHECKER DANCEHALL CHECKER(box) DOH KOH HOH / OHYES! - DOHZI-T KOHEI - INNOSENCE 2000 BAY SQUAD 001 BAY SQUAD 002 BAY SQUAD 003 BAY SQUAD 004 PLAYER'S DELIGHT(promo) DRUM,PROGRAM,ANAGRAM EP(promo)(white) DRUM,PROGRAM,ANAGRAM EP(promo) LYRICAL TERRORISTS - SUBSTANTIAL - L UNIVERSE JAKU-NEN - ASA - DAIKEI 2002 HARLEM VER.1.0 0002(promo) HARLEM VER.1.7 0011 2004 HARLEM VER.3.0 ANALOG1 HARLEM VER.3.0 ANALOG2 ナンパスタジアム / VITAL CHILDREN PT.2 - SHIBA-YANKEE - LIKKLE MAI BABY DANCER／星降る夜 - KREVA - KOHEY YAGI WHAT'S UP!(dubplate) 2005 BREAKS BEATS DISNEY(BEAUTY THE BEAST "BEATS AND THE BEAST" E.P.) PRIMAL WALK,SOURCE,I JUDGE(white) - O.N.O - JUN-GOLD PRIMAL WALK,SOURCE,I JUDGE - O.N.O - JUN-GOLD 2006 手を出すな！ - GAKU-MC - 桜井和寿 暴言(promo) 2009 つつみ込むように… - DJ WATARAI - COMA-CHI 2013 UNDER THRONE jojnt DA BEATMINERZ CRAWL EP1 UNDER THRONE jojnt DA BEATMINERZ CRAWL EP2 2014 MALTINE GIRLS WAVE EP EyeSheTell BEATS 'N' LOW LIFE(promo) - PIGEONDUST - BUGSEED スペース★ダンディ DO THE RIGHT THING GET FUNKY／SHADOW OF SUMMER - DJ FUMIYA - DORIAN 2015 A RAPPER GOT KILLED AGAIN - dj honda - BLAHRMY SOUND OF FELICITY - カジヒデキ × やけのはら 7SPACE - MOROHA - STERUSS UNFINISHED CONNECTION - dj honda - B.I.G. JOE I REP - DABO,ANARCHY,KREVA UMUI - RITTO - FReECOol RELIEF EP - NAGAN SERVER MANTIS 2016 U BELONG TO ME／DON’T LEAVE ME - meg - SWEEP F.L.A.Me - DINARY DELTA FORCE×MARCO POLO 2017 BORDER 7INCH BOX SET - B.D.,MR.ITAGAKI a.k.a. ITA-CHO
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Chevrolet Nova and Geo Prizm 1985-90 Automotive Repair Manual Haynes? Jon LaCourse? J H Haynes? Haynes? JonLaCourse? JHHaynes? ユーズドブック(洋書)-Engineering Subjects-Engineering-General? Subjects-Nonfiction-Automotive-Repair? Subjects-Professional&Technical-Engineering-General World Industrial Standards Speedy Finder Astm Intl? AstmIntl? ユーズドブック(洋書)-Engineering Substores-UnknownASINs-57? Subjects-Engineering-Reference? Subjects-Professional&Technical-Engineering-Reference? Honda CB/CD125T and CM125C Twins 1977-88 Owner's Workshop Manual (Motorcycle Manuals) Haynes Publishing? Jeremy Churchill? HaynesPublishing? JeremyChurchill? ユーズドブック(洋書)-Engineering Subjects-Engineering-Automotive? Subjects-Nonfiction-Automotive-Repair? Subjects-Professional&Technical-Engineering-Automotive? Volkswagen Passat (Petrol) 1781cc and 1984cc, 1988-91 Owner's Workshop Manual (Service Repair Manuals) Haynes Publishing? Ian Coomber? HaynesPublishing? IanCoomber? ユーズドブック(洋書)-Engineering Subjects-Engineering-Automotive? Subjects-Nonfiction-Automotive-Repair? Subjects-Professional&Technical-Engineering-Automotive? Haynes' Automotive Electrical Manual (Hayne's Automotive Repair Manual) Haynes Pubns? Jon Lacourse? Mike Stubblefield? Bob Worthy? John Haynes? Ken Freund? HaynesPubns? JonLacourse? MikeStubblefield? BobWorthy? JohnHaynes? KenFreund? ユーズドブック(洋書)-Engineering Subjects-Engineering-General? Subjects-Nonfiction-Transportation-General? Subjects-Nonfiction-Automotive-General? Subjects-Nonfiction-Automotive-Repair? Subjects-Nonfiction-Automotive-Mechanics-ElectricalSystems? Subjects-Professional&Technical-Engineering-General Ford Pick-ups and Bronco 2 and 4 W.D. 1980-90 Owner's Workshop Manual Haynes Publishing? John B. Raffa? J.H. Haynes? HaynesPublishing? JohnB.Raffa? J.H.Haynes? ユーズドブック(洋書)-Engineering Subjects-Engineering-General? Subjects-Nonfiction-Automotive-Repair? Subjects-Professional&Technical-Engineering-General Testing of Peats and Organic Soils Astm Intl? P. M. Jarretl? AstmIntl? P.M.Jarretl? ユーズドブック(洋書)-Engineering Substores-UnknownASINs-57? Subjects-Engineering-Materials-Testing? Subjects-Professional&Technical-Engineering-Materials-Testing? Dodge Caravan and Plymouth Voyager Mini-vans 1984-89 Owner's Workshop Manual Haynes? Curt Choate? J H Haynes? Haynes? CurtChoate? JHHaynes? ユーズドブック(洋書)-Engineering Subjects-Engineering-General? Subjects-Nonfiction-Automotive-Repair? Subjects-Professional&Technical-Engineering-General Buick, Oldsmobile, Pontiac Full-Size Models Owners Workshop Manual, 1970-1990 (Haynes Repair Manual Series) Haynes Pubns? Ken Freund? John H. Haynes? HaynesPubns? KenFreund? JohnH.Haynes? ユーズドブック(洋書)-Engineering Subjects-Engineering-General? Subjects-Nonfiction-Transportation-General? Subjects-Nonfiction-Automotive-Trucks&Vans? Subjects-Nonfiction-Automotive-Repair-General? Subjects-Professional&Technical-Engineering-General Chevrolet and GMC Pick-ups Automotive Repair Manual Haynes? Ken Freund? J H Haynes? Haynes? KenFreund? JHHaynes? ユーズドブック(洋書)-Engineering Subjects-Engineering-General? Subjects-Nonfiction-Automotive-Repair? Subjects-Professional&Technical-Engineering-General The Haynes Small Engine Repair Manual (Hayne's Automotive Repair Manual) Haynes Pubns? Curt Choate? John Harold Haynes? HaynesPubns? CurtChoate? JohnHaroldHaynes? ユーズドブック(洋書)-Engineering Subjects-Engineering-Automotive? Subjects-Engineering-Mechanical-General? Subjects-Nonfiction-Transportation-General? Subjects-Nonfiction-Automotive-General? Subjects-Nonfiction-Automotive-Repair? Subjects-Nonfiction-Automotive-Mechanics-General? Subjects-Professional&Technical-Engineering-Automotive? Subjects-Professional&Technical-Engineering-Mechanical-General? Subjects-Science-Physics-Applied? Haynes Automotive Emissions Control Manual Domestic and Imported Models (Haynes Techbooks) Haynes Pubns? Mike Stubblefield? HaynesPubns? MikeStubblefield? ユーズドブック(洋書)-Engineering Subjects-Engineering-Aerospace? Subjects-Engineering-Automotive? Subjects-Engineering-General? Subjects-Engineering-Mechanical-General? Subjects-Nonfiction-Transportation-General? Subjects-Nonfiction-Automotive-General? Subjects-Nonfiction-Automotive-Repair? Subjects-Professional&Technical-Engineering-Aerospace? Subjects-Professional&Technical-Engineering-Automotive? Subjects-Professional&Technical-Engineering-Mechanical-General? Subjects-Professional&Technical-Engineering-General Dodge Dakota Pick-ups 2WD and 4WD (1987-1990) Automotive Repair Manual Haynes? Brian Styve? J H Haynes? Haynes? BrianStyve? JHHaynes? ユーズドブック(洋書)-Engineering Subjects-Engineering-General? Subjects-Nonfiction-Automotive-Repair? Subjects-Professional&Technical-Engineering-General Mitsubishi Automotive Repair Manual Cordia, Tredia, Precis, Mirage, Galant, 1983 Thru 1993, All Models Haynes Pubns? Larry Warren? John Harold Haynes? HaynesPubns? LarryWarren? JohnHaroldHaynes? ユーズドブック(洋書)-Engineering Substores-UnknownASINs-38? Subjects-Engineering-General? Subjects-Nonfiction-Automotive-Repair? Subjects-Professional&Technical-Engineering-General General Motors Buick Regal, Chevrolet Lumina, Pontiac Grand Prix, Olds Cutlass Supreme Automotive Repair Manual, 1988 Through 1990 (Hayne's Automotive Repair Manual) Haynes Pubns? Robert Maddox? John Harold Haynes? HaynesPubns? RobertMaddox? JohnHaroldHaynes? ユーズドブック(洋書)-Engineering Substores-UnknownASINs-38? Subjects-Engineering-General? Subjects-Nonfiction-Automotive-Trucks&Vans? Subjects-Nonfiction-Automotive-Repair-General? Subjects-Professional&Technical-Engineering-General Mazda Pick-ups 1972-90 Automotive Repair Manual Haynes? J H Haynes? P B Ward? Haynes? JHHaynes? PBWard? ユーズドブック(洋書)-Engineering Subjects-Engineering-General? Subjects-Nonfiction-Automotive-Repair? Subjects-Professional&Technical-Engineering-General Nissan Stanza Automotive Repair Manual 1982 Thru 1990 (Book #981) Haynes Pubns? Peter G. Strasman? P. G. Strasman? John Harold Haynes? HaynesPubns? PeterG.Strasman? P.G.Strasman? JohnHaroldHaynes? ユーズドブック(洋書)-Engineering Subjects-Engineering-General? Subjects-Nonfiction-Transportation-General? Subjects-Nonfiction-Automotive-General? Subjects-Nonfiction-Automotive-Repair? Subjects-Professional&Technical-Engineering-General Rover 213 and 216 1984-89 Owner's Workshop Manual (Service Repair Manuals) Haynes Publishing? Peter G. Strasman? HaynesPublishing? PeterG.Strasman? ユーズドブック(洋書)-Engineering Subjects-Engineering-Automotive? Subjects-Nonfiction-Automotive-Repair? Subjects-Professional&Technical-Engineering-Automotive? MZ ETZ Models Owners Workshop Manual Haynes Publishing? Mark Coombs? HaynesPublishing? MarkCoombs? ユーズドブック(洋書)-Engineering Subjects-Engineering-Automotive? Subjects-Nonfiction-Automotive-Repair? Subjects-Professional&Technical-Engineering-Automotive? Toyota Corolla 1987-92 Owner's Workshop Manual (Service Repair Manuals) Haynes Publishing? T.H.Robert Jones? H. Robert? HaynesPublishing? T.H.RobertJones? H.Robert? ユーズドブック(洋書)-Engineering Subjects-Engineering-Automotive? Subjects-Nonfiction-Automotive-Repair? Subjects-Professional&Technical-Engineering-Automotive? Rover 214 and 414 Owners Workshop Manual (Service Repair Manuals) Haynes Publishing? Mark Coombs? HaynesPublishing? MarkCoombs? ユーズドブック(洋書)-Engineering Subjects-Engineering-Automotive? Subjects-Nonfiction-Automotive-Repair? Subjects-Professional&Technical-Engineering-Automotive? Volvo 440, 460 and 480 Owners Workshop Manual (Service Repair Manuals) Haynes Publishing? A.K. Legg? HaynesPublishing? A.K.Legg? ユーズドブック(洋書)-Engineering Subjects-Engineering-Automotive? Subjects-Nonfiction-Automotive-Repair? Subjects-Professional&Technical-Engineering-Automotive? Land Drilling and Oilwell Servicing Contractors Directory, 1984 Pennwell Corp? PennwellCorp? ユーズドブック(洋書)-Engineering Subjects-Engineering-Petroleum,Mining&Geological-Petroleum? Subjects-Professional&Technical-Engineering-Petroleum,Mining&Geological-Petroleum? Subjects-Reference-Catalogs&Directories-Directories? Subjects-Reference-General? Peugeot/Talbot Diesel Engine Owner's Workshop Manual Haynes Publishing? A.K. Legg? HaynesPublishing? A.K.Legg? ユーズドブック(洋書)-Engineering Subjects-Engineering-Automotive? Subjects-Nonfiction-Automotive-Repair? Subjects-Professional&Technical-Engineering-Automotive? Mechanics of Composite Materials 1983 Amer Society of Mechanical? G. J. Dvorak? AmerSocietyofMechanical? G.J.Dvorak? ユーズドブック(洋書)-Engineering Substores-UnknownASINs-57? Subjects-Engineering-Materials-Composites? Subjects-Engineering-MaterialsScience-MechanicalPropertiesofSolids? Subjects-Professional&Technical-Engineering-MaterialsScience-MechanicalPropertiesofSolids? Subjects-Professional&Technical-Engineering-Materials-Composites? Subaru 1600 and 1800 1980 Thru 1989 Automotive Repair Manual (Book No 681) Motorbooks Intl? Haynes? MotorbooksIntl? Haynes? ユーズドブック(洋書)-Engineering Subjects-Engineering-General? Subjects-Nonfiction-Transportation-General? Subjects-Nonfiction-Automotive-Repair? Subjects-Professional&Technical-Engineering-General Dodge Aries and Plymouth Reliant 1981 Thru 1989 All K-Car Models Owners Workshop Manual (Book No 723) Haynes Pubns? J.H. Haynes? Larry Warren? HaynesPubns? J.H.Haynes? LarryWarren? ユーズドブック(洋書)-Engineering Substores-UnknownASINs-38? Subjects-Engineering-General? Subjects-Nonfiction-Automotive-Repair? Subjects-Professional&Technical-Engineering-General Chevrolet Astro and GMC Safari Mini-vans 1985-90 Automotive Repair Manual Haynes? Ken Freund? J H Haynes? Haynes? KenFreund? JHHaynes? ユーズドブック(洋書)-Engineering Subjects-Engineering-General? Subjects-Nonfiction-Automotive-Repair? Subjects-Professional&Technical-Engineering-General Chevrolet and G.M.C. 510 and 515 Pick-ups 1982-90 Automotive Repair Manual Haynes Publishing? David Hayden? J.H. Haynes? HaynesPublishing? DavidHayden? J.H.Haynes? ユーズドブック(洋書)-Engineering Subjects-Engineering-General? Subjects-Nonfiction-Automotive-Repair? Subjects-Professional&Technical-Engineering-General Dodge Daytona and Chrysler Laser 1984 Thru 1989 All Models Automotive Repair Manual (1140) Haynes Pubns? Haynes Editors? Larry Warren? John Harold Haynes? HaynesPubns? HaynesEditors? LarryWarren? JohnHaroldHaynes? ユーズドブック(洋書)-Engineering Subjects-Engineering-General? Subjects-Engineering-Industrial,Manufacturing&OperationalSystems-Manufacturing? Subjects-Nonfiction-Transportation-General? Subjects-Nonfiction-Automotive-General? Subjects-Nonfiction-Automotive-Repair? Subjects-Professional&Technical-Engineering-Industrial,Manufacturing&OperationalSystems-Manufacturing? Subjects-Professional&Technical-Engineering-General Ford Taurus and Mercury Sable 1986-90 Automotive Repair Manual Haynes? Bob Henderson? J H Haynes? Haynes? BobHenderson? JHHaynes? ユーズドブック(洋書)-Engineering Subjects-Engineering-General? Subjects-Nonfiction-Automotive-Repair? Subjects-Professional&Technical-Engineering-General Ford Aerostar Mini-vans 1986-90 Automobile Repair Manual Haynes? Larry Warren? J H Haynes? Haynes? LarryWarren? JHHaynes? ユーズドブック(洋書)-Engineering Subjects-Engineering-General? Subjects-Nonfiction-Automotive-Repair? Subjects-Professional&Technical-Engineering-General Rover Metro 1990-91 Owner's Workshop Manual (Service Repair Manuals) Haynes Publishing? Jeremy Churchill? HaynesPublishing? JeremyChurchill? ユーズドブック(洋書)-Engineering Subjects-Engineering-Automotive? Subjects-Nonfiction-Automotive-Repair? Subjects-Professional&Technical-Engineering-Automotive? Yugo/Zastava All Models 1981-90 Owners Workshop Manual (Service Repair Manuals) Haynes Publishing? Colin Brown? HaynesPublishing? ColinBrown? ユーズドブック(洋書)-Engineering Subjects-Engineering-Automotive? Subjects-Nonfiction-Automotive-Repair? Subjects-Professional&Technical-Engineering-Automotive? Audi 100 1982-90 and 200 1984-89 Owner's Workshop Manual (Service Repair Manuals) Haynes Publishing? John S. Mead? HaynesPublishing? JohnS.Mead? ユーズドブック(洋書)-Engineering Subjects-Engineering-Automotive? Subjects-Nonfiction-Automotive-Repair? Subjects-Professional&Technical-Engineering-Automotive? Standard Fire Prevention Code 1994 Southern Building Code? Southern Building Code Congress International? SouthernBuildingCode? SouthernBuildingCodeCongressInternational? ユーズドブック(洋書)-Engineering Substores-UnknownASINs-57? Subjects-Engineering-Civil-Construction-BuildingCodes&Laws? Subjects-Professional&Technical-Engineering-Civil-Construction-BuildingCodes&Laws? Subjects-Professional&Technical-CivilService-Firefighting&Prevention? Ford Thunderbird Mercury Cougar Automotive Repair Manual Models Covered All Ford Thunderbird and Mercury Cougar Models 1989 and 1990 (Hayne's Automotive Repair Manual) Haynes Pubns? Ken Freund? John Harold Haynes? HaynesPubns? KenFreund? JohnHaroldHaynes? ユーズドブック(洋書)-Engineering Substores-UnknownASINs-38? Subjects-Engineering-General? Subjects-Nonfiction-Automotive-Trucks&Vans? Subjects-Nonfiction-Automotive-Repair-General? Subjects-Professional&Technical-Engineering-General Chevrolet Sprint Geo Metro Automotive Repair Manual Models Covered Chevrolet Sprint-1985 Through 1988, Geo Metro-1989 Through 1991 (Hayne's Automotive Repair Manual) Haynes Pubns? Larry Warren? John Harold Haynes? HaynesPubns? LarryWarren? JohnHaroldHaynes? ユーズドブック(洋書)-Engineering Substores-UnknownASINs-38? Subjects-Engineering-General? Subjects-Nonfiction-Automotive-Trucks&Vans? Subjects-Nonfiction-Automotive-Repair-General? Subjects-Professional&Technical-Engineering-General Vw Beetle Karmann Ghia Automotive Repair Manual (Hayne's Automotive Repair Manual) Haynes Pubns? John Harold Haynes? Ken Freund? Mike Stubblefield? John Harold Hayne? HaynesPubns? JohnHaroldHaynes? KenFreund? MikeStubblefield? JohnHaroldHayne? ユーズドブック(洋書)-Engineering Subjects-Engineering-General? Subjects-Nonfiction-Transportation-General? Subjects-Nonfiction-Automotive-General? Subjects-Nonfiction-Automotive-Repair? Subjects-Professional&Technical-Engineering-General Honda Cbr600 1000 Fours Owners Workshop Manual (Hayne's Automotive Repair Manual) Haynes Pubns? Mark Coombs? HaynesPubns? MarkCoombs? ユーズドブック(洋書)-Engineering Subjects-Engineering-Automotive? Subjects-Nonfiction-Transportation-General? Subjects-Nonfiction-Automotive-Motorcycles-General? Subjects-Nonfiction-Automotive-Motorcycles-Repair&Performance? Subjects-Nonfiction-Automotive-Repair? Subjects-Professional&Technical-Engineering-Automotive? Subaru 1600 and 1800, 1979-90 Owner's Workshop Manual (Service Repair Manuals) Haynes Publishing? Larry Holt? J.H. Haynes? HaynesPublishing? LarryHolt? J.H.Haynes? ユーズドブック(洋書)-Engineering Subjects-Engineering-Automotive? Subjects-Nonfiction-Automotive-Repair? Subjects-Professional&Technical-Engineering-Automotive? Diesel Engine Repair Manual General Motors and Ford V8 Diesel Engines Gm 350 Cu in (Hayne's Automotive Repair Manual) Haynes Pubns? Ken Freund? John Harold Haynes? HaynesPubns? KenFreund? JohnHaroldHaynes? ユーズドブック(洋書)-Engineering Substores-UnknownASINs-38? Subjects-Engineering-Automotive? Subjects-Engineering-General? Subjects-Nonfiction-Automotive-General? Subjects-Nonfiction-Automotive-Trucks&Vans? Subjects-Nonfiction-Automotive-Repair-General? Subjects-Professional&Technical-Engineering-Automotive? Subjects-Professional&Technical-Engineering-General Ford Escort and Orion 1990-92 Owner's Workshop Manual Haynes Publishing? Ian Coomber? HaynesPublishing? IanCoomber? ユーズドブック(洋書)-Engineering Subjects-Engineering-Automotive? Subjects-Nonfiction-Automotive-Repair? Subjects-Professional&Technical-Engineering-Automotive? Chevrolet and GMC Vans 1968-91 Automotive Repair Manual Haynes? J H Haynes? Peter G Strasman? Haynes? JHHaynes? PeterGStrasman? ユーズドブック(洋書)-Engineering Subjects-Engineering-General? Subjects-Nonfiction-Automotive-Repair? Subjects-Professional&Technical-Engineering-General Dodge and Plymouth Vans 1971 Thru 1991 All Full Size Models Six-Cylinder Inline, V6 and V8 Engines Automotive Repair Manual (349) Motorbooks Intl? John Harold Haynes? MotorbooksIntl? JohnHaroldHaynes? ユーズドブック(洋書)-Engineering Substores-UnknownASINs-38? Subjects-Engineering-Automotive? Subjects-Engineering-General? Subjects-Nonfiction-Automotive-Repair? Subjects-Nonfiction-Automotive-Trucks&Vans? Subjects-Professional&Technical-Engineering-Automotive? Subjects-Professional&Technical-Engineering-General Chevrolet Camaro 1982-90 All Models Automotive Repair Manual Haynes? J H Haynes? John B Raffa? Haynes? JHHaynes? JohnBRaffa? ユーズドブック(洋書)-Engineering Subjects-Engineering-General? Subjects-Nonfiction-Automotive-Repair? Subjects-Professional&Technical-Engineering-General Dodge Omni Plymouth Horizon Automotive Repair Manual 1978 Through 1990 (Haynes Automotive Repair Manual) Haynes Pubns? Larry Warren? Mike Stubblefield? John Harold Haynes? HaynesPubns? LarryWarren? MikeStubblefield? JohnHaroldHaynes? ユーズドブック(洋書)-Engineering Subjects-Engineering-General? Subjects-Nonfiction-Transportation-General? Subjects-Nonfiction-Automotive-General? Subjects-Nonfiction-Automotive-Repair? Subjects-Professional&Technical-Engineering-General Haynes Yamaha Xt,Tt, and Sr 500 Singles Owners Workshop Manual, No 342 '75-83' (Haynes Yamaha XT, Tt, Sr 500 Singles Owners Workshop Manua) Haynes Pubns? Mansur Darlington? HaynesPubns? MansurDarlington? ユーズドブック(洋書)-Engineering Subjects-Engineering-Automotive? Subjects-Engineering-Industrial,Manufacturing&OperationalSystems-Manufacturing? Subjects-Nonfiction-Automotive-General? Subjects-Nonfiction-Automotive-Motorcycles-General? Subjects-Nonfiction-Automotive-Repair? Subjects-Professional&Technical-Engineering-Industrial,Manufacturing&OperationalSystems-Manufacturing? Subjects-Professional&Technical-Engineering-Automotive? Subjects-Science-General Volkswagen Polo 1982-90 Owner's Workshop Manual (Service Repair Manuals) Haynes Publishing? A.K. Legg? HaynesPublishing? A.K.Legg? ユーズドブック(洋書)-Engineering Subjects-Engineering-Automotive? Subjects-Nonfiction-Automotive-Repair? Subjects-Professional&Technical-Engineering-Automotive? Small Engine Repair Manual Haynes Publishing? Curt Choate? J.H. Haynes? Robert Jex? HaynesPublishing? CurtChoate? J.H.Haynes? RobertJex? ユーズドブック(洋書)-Engineering Substores-UnknownASINs-38? Subjects-Engineering-Automotive? Subjects-Nonfiction-Automotive-Repair? Subjects-Professional&Technical-Engineering-Automotive? ユーズドブック(洋書)-Engineering 洋書
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for THINK TANK,CUATRO CIENAGAS ・A.K.A. KILLER BONG LORD PUFF ・ANALOG [WORKS] 1998 THE★GRAFFTTI ROCK '98 - YOU THE ROCK 1999 そっと目を閉じて(white sleeve) - KAANA そっと目を閉じて(black sleeve) - KAANA 2001 SAD SONG - KAANA SPACE FUNK 2001／GALAXY PIMP(promo) - MURO,NIPPS 2002 DELTA EXPRESS(black box) - DELI 2004 BE QUIET(white) - DJ QUIETSTORM BE QUIET - DJ QUIETSTORM ON THE WHEELZ OF STEEL(WHAT'S MY NAME?)(promo) - DJ HAZIME 2006 鋼鉄のBLACK(white) - D.L 鋼鉄のBLACK - D.L THE ALBUM(ADMONITIONS) - D.L 2012 ILLSON EP(white) - B.D. ILLSON EP - B.D. 2013 FAR FROM YESTERDAY EP - OLIVE OIL 2015 甘い魔者 - RUMI 雨衣ルミ TOUCH N GO - BUDDHA MAFIA
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Kahanamoku Duke Kahanamoku (USA, 2002) Surfer, swimmer Kahlo Frida Kahlo (USA, 2001) Painter Kalākaua King Kalākaua (Hawaii, 1875) Hawaiian King Kamāmalu Crown Princess Victoria Kamāmalu (Hawaii, 1871) Hawaiian Crown Princess Kamehameha King Kamehameha I (Hawaii, 1883 USA, 1937) Hawaiian King King Kamehameha III (Hawaii, 1853) Hawaiian King King Kamehameha IV (Hawaii, 1861) Hawaiian King King Kamehameha V (Hawaii, 1866) Hawaiian King Kane Elisha Kent Kane (USA, 1986) Arctic explorer Kapiolani Queen Kapiolani (Hawaii, 1882) Hawaiian Queen Karloff Boris Karloff (USA, 1997) Actor Kármán Theodore von Kármán (USA, 1992) Aerospace scientist Käsebier Gertrude Käsebier (USA, 2002) Photographer Katsushika 葛飾 Katsushika Hokusai (USA, 1974) Painter Kearny Stephen Watts Kearny (USA, 1946) Mexican American War officer Keaton Buster Keaton (USA, 1994) Actor Keats John Keats (United Kingdom, 1971) Poet Kekūanāoa Governor Mataio Kekūanāoa of Oʻahu (Hawaii, 1871) Hawaiian Governor Keller Helen Keller (USA, 1980) Author, disability advocate Kelly Grace Kelly (USA, 1993) Actress and Princess of Monaco Kennaugh Peter Kennaugh (United Kingdom, 2012) Manx professional racing cyclist Kennedy John Fitzgerald Kennedy (USA, 1964) 35th President Robert F. Kennedy (1979) Attorney General Kenny Jason Kenny (United Kingdom, 2012) English track cyclist Kent Rockwell Kent (USA, 2001) Illustrator Keppel Alice Keppel (United Kingdom, 1983) Mistress of Edward VII, great-grandmother of Camilla Parker-Bowles Violet Keppel (United Kingdom, 1983) Novelist Kern Jerome Kern (USA, 1985) Composer Kertész André Kertész (USA, 2002) Hungarian photographer Key Francis Scott Key (USA, 1948) Star-Spangled Banner composer King Danielle King (United Kingdom, 2012) English track cyclist Martin Luther King, Jr. (USA, 1979) Civil Rights advocate Kline Franz Kline (USA, 1998) Painter Knox Henry Knox (USA, 1985) Revolutionary War General Korngold Erich Korngold (USA, 1999) Composer Kościuszko Tadeusz Kościuszko (USA, 1933) Polish-Lithuanian patriot Kossuth Lajos Kossuth (USA, 1958) Hungarian patriot
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(96p) SIEGE MACHINES No besieging army would be complete without siege towers and rams with which to pound the enemy’s fortress to pieces. Some races have developed their own versions of these devices but all function in more or less the same fashion and have equal effectiveness. Concerning Victory Points, destroyed or lost Siege Machines immediately give the opponent their victory points no matter if the unit carrying them is destroyed or not. Siege Machines like Siege Towers, Battering Rams or Sows may use initiative to attack the nearest wall section (towers may be ignored). Siege Towers Troop/Type/Attack/Hits/Armour/Command/Unit Size/Points per Unit/ Min/Max Siege Town/M/0/3/3+/-/1/20/ -/- A Siege Tower is a massive wooden tower that rolls forward on huge wheels. It is pushed to the enemу’ s fortress by troops who are protected by its stout timbers. Once the tower reaches its target, a ramp descends allowing the sheltering troops to swarm over the walls. A Siege Tower is a unique kind of machine. Its sole purpose is to deliver troops onto the enemу’ s walls. A Siege Tower must be assigned to a unit of infantry. To represent the fact that they are really inside the Siege Tower, the unit is arranged directly behind in column. A UNIT WITH A SIEGE TOWER The unit is arranged in column behind the Siege Tower. As Siege Towers are such huge constructions the same shooting rules apply to them as to wall sections. All shooting enemy units within reach of Siege Towers may choose which Tower they want to shoot at (but if they choose to shoot at units without Siege Towers they still have to shoot at the next visible unit). All enemy shots against the unit are assumed to hit the Siege Tower because the troops are actually inside it. A Siege Tower and the unit inside it cannot be driven back by missile fire. Should a Siege Tower be destroyed by shooting, its accompanying infantry will abandon it and may continue to fight normally. The Siege Tower has no value in close combat. If the unit is attacked, the Tower is simply ignored. If the unit is forced to retreat, the Siege Tower is destroyed. Units in Siege Towers may pursue or advance in combat leaving their machine behind which effectively means the Siege Tower is destroyed. The Siege Tower can be pushed forward at a speed of 15cm. As it is an incredible effort to move a massive construction like a Siege Tower, command rolls get an extra -1 from second command onward (so the second command would work at a -3 instead of -2). A unit accompanying a Siege Tower cannot make way for other units. If all its accompanying infantry are killed in combat before it reaches the walls, the Siege Tower is considered to have been immobilized or destroyed. Once the Siege Tower reaches the enemy s walls it has effectively done its job. As soon as the walls are reached, the accompanying infantry can assault the defenders or, if there are no defenders, they can occupy the wall as described below. A Siege Tower is usually not tall enough to reach a tower. However, if there is doubt because a tower is especially low, the players should agree before the game whether it can be assaulted like this. Troops making an assault from a Siege Tower cancel out the advantage of fortifications. Both sides count as being in the open (4+ to hit) and the assaulting stand gets the usual +1 bonus for charging. The assaulting unit fights with only one stand (the warriors at the top of the Siege Tower) whilst the defenders fight with all stands that would theoretically be touching were it possible to move all the stands properly into place! As stands touching corner-to-corner would normally fight, defending stands adjacent to the stand directly facing the Siege Tower will fight, assuming they are otherwise free to do so. Once a Siege Tower has reached the walls and is not destroyed, up to three stands of infantry can move up (97p) it and onto the walls in subsequent turns, assuming that there is room for them to spread out whilst remaining in physical contact with each other. (Once stands have moved onto the ramparts they cannot move further that turn, even if unopposed). If a unit assaulting walls via Siege Tower loses the combat and retreats 4cm or less, it still counts as being in the tower and can assault again in the next turn. If the unit retreats more than 4cm and the wall section it faces is subsequently occupied by the enemy, it is automatically destroyed. They push it over! Troops defending walls from a counter attack cannot retreat down a Siege Tower and enemy cannot pursue or advance using a Siege Tower. If the unit pushing the Siege Tower consists of missile armed troops, all stands can shoot as if they were positioned on top of the tower. This brings them up to the same height as the walls. Targets on the ramparts of walls count as being defended from a Siege Tower rather than being fortified. Targets in higher towers still count as being fortified. Battering Rams Troop/Type/Attack/Hits/Armour/Command/Unit Size/Points per Unit/ Min/Max Ram/M/0/3/3+/-/1/10/ -/- Battering Rams are mounted on a wheeled chassis and protected by a wooden roof so that troops inside can push the ram forward under cover. A Battering Ram can be incorporated into a Siege Tower in which case it simply combines the attributes of both. A Battering Ram’s purpose is to affect a breach in the enemy s gate or walls. A UNIT WITH A BATTERING RAM The unit is arranged in column behind the battering ram A Battering Ram must be assigned to a unit of infantry. To represent the fact that they are inside the covered frame the unit is arranged directly behind in column. All enemy shots against the unit are assumed to hit the Battering Ram because the troops are actually inside it. A Battering Ram and the unit inside it cannot be driven back by missile fire. Should a Battering Ram be destroyed by shooting, its accompanying infantry will abandon it and may continue to fight normally. The Battering Ram has no value in close combat. If the unit is attacked, the Ram is simply ignored. If the unit is forced to retreat, the Ram is destroyed. If units with Battering Rams pursue or advance in combat they leave their machine behind which effectively means it is destroyed. The Battering Ram can be pushed forward at 15cm. A unit accompanying a Battering Ram cannot make way for other units. If all its accompanying infantry stands are killed before it reaches the walls, the Ram is abandoned and is considered to have been immobilized or destroyed. Once the Ram reaches the enemy s walls it can begin to batter! The rules for battering are described above. The Ram must be accompanied by a unit of infantry of at least one stand in order for it to batter (they provide the muscle). A unit may not batter and assault at the same time. Sows Troop/Type/Attack/Hits/Armour/Command/Unit Size/Points per Unit/ Min/Max Sows/M/0/3/3+/-/1/5/ -/- These are roofed and wheeled structures that offer protection to troops as they advance towards a castle. A Sow is very much like a big shed on wheels or, to put it another way, a Battering Ram without a ram. A Sow is represented by the same rules as a Battering Ram except that it cannot batter. Sows have no value in close combat. If the unit is attacked it is simply ignored. If the unit is forced to retreat, the Sow is destroyed. Units with Sows may pursue or advance in combat leaving their machine behind which effectively means the Sow counts as destroyed. (98p) Mantlets These are large mobile shields made from stout wood. They offer protection to troops behind them and can gradually be shuffled forward without exposing the sheltering troops to enemy fire. They are used by infantry units and are provided with arrow slits through which missile armed units can shoot. In a siege game, units of infantry can have Mantlets for +10 points per unit. This is enough to cover the unit’s frontage and the unit is considered to be in a defended position. If it charges, it must abandon its Mantlets. If the unit suffers casualties, it automatically abandons any unnecessary Mantlets (these cannot be used by other troops). If retreating or pursuing in combat its Mantlets are abandoned if they haven’t been already. If a unit equipped with Mantlets is driven back by shooting it will carry its Mantlets with it. However, if driven back more than its half pace move (10cm for standard infantry), the unit automatically abandons its Mantlets as it moves. As units carrying Mantlets count as occupying defended positions, they deduct one dice from their drive back distance. A unit can abandon its Mantlets at any time during the Command phase, in which case it is not restricted to one move that Command phase. In this case, the Mantlets are overturned or cast aside and removed from the battle. Boiling Oil or Rock Droppers Defenders are liable to throw anything they can get their hands on at enemies trying to scale the castle walls. Well prepared defenders will have amassed numerous large rocks, prodigious amounts of garbage, masonry, furniture, statuary, dead horses, stone sinks, anvils and the like. Of course, the professional choice is boiling oil but scalding water and hot sand are also used to good effect. We won’t worry much about the exact type of missile. For our purposes it’s enough to assume that the defenders have something appropriate to hand. For the sake of explanation, we’ll assume that Boiling Oil is our preferred option. A 40 to 50mm wide section of wall may be provisioned with Boiling oil or Rock Droppers. This may be used by any unit of troops manning that section. If an assault is launched against a fortress section which is provisioned with Boiling Oil or Rock Dropper units on this and any adjacent sections may use their equipment against the assaulting enemy. Boiling Oil or Rock Droppers can also be used against units making an assault via Siege Tower or Sow but the attackers may use the 3+ armour save of their Siege equipment instead their own. Note that a unit may only use one Stand and Shoot attack. So units equipped with bows or similar have to choose if they use Boiling Oil or their bows when they are assaulted. They may never use both. Boiling Oil or Rock Dropper attacks are worked out immediately before normal combat at the same time, as shots at chargers. A unit can pour oil or shoot with its own weapons at the same time. Any hits inflicted are carried over into the combat and count as having been struck in the first round. Roll a dice and consult the chart below. D6/Result 1/No effect, you miss or the enemy successfully protect themselves from your barrage. 2-3/The enemy unit suffers 1 attack with a -1 on armour saves. 4-5/The enemy unit suffers 2 attacks with a -1 on armour saves. 6/The enemy unit suffers 3 attacks with a -1 on armour saves. (99p) Tribock When helping a Bretonnian army in the Border Princes two empire engineers encountered a massive Bretonnian machine called “Trebuchet”. It was used to reoccupy a fortress treacherous greenlings had taken and proved very useful there. Otto Ressel and his assistant Fritz Hobel further developed the concept of this siege machine, made it bigger and even more effective and gave it the Reikspiel name “Tribock”. Most Empire generals despise this “woodwork” and prefer massive cannons when it comes to sieges. But in the Border Princes black powder is expensive and good iron hard to get and so Warlords there often choose the Tribock at Sieges. Some even say it is more effective than the bombard. Troop/Type/Attack/Hits/Armour/Command/Unit Size/Points per Unit/ Min/Max Tribock/Art/ 1/6 /4/0/-/1/120/ -/1 Range 20-120cm Attack Close Combat 1 / Shooting 6 As the Tribock is such a giant machine it has to be placed on a special stand with a front edge of 40mm and flank edges of 60mm. For siege use only! May not move once it is deployed. Must be deployed before any other unit. Shooting straight ahead Other than normal shooting units the Tribock has a very restricted view. It can only draw line of sight to targets that lie in the corridor that extends straight ahead from the front edge. So the Tribock only has a 4cm wide corridor of sight. For targets outside this corridor it must be ordered to turn. If the order is failed it does not fire that turn. Any Hits caused by the Tribock allow no save. Because of its immense size the Tribock has a range of 120cm but a minimum range of 20cm as the slingshot like nature of the weapon makes it impossible to shoot at closer targets. This obviously makes units that are under 20cm ineligible as potential targets; thus they are ignored as far as the rules for firing at the closest target are concerned. The Tribock may not shoot at enemy units that charge it. Bombard Troop/Type/Attack/Hits/Armour/Command/Unit Size/Points per Unit/ Min/Max Bombard/Art/ 0/4+bounce /3/0/-/1/130/ -/1 Range 90cm Attack Close Combat 0 / Shooting 4+bounce For siege use only! May not move once it is deployed. Must be deployed before any other unit. Shooting straight ahead Other than normal shooting units the bombard has a very restricted view. It can only draw line of sight to targets that lie in the corridor that extends straight ahead from the front edge. So the bombard only has a 2cm wide corridor of sight. For targets outside this corridor it must be ordered to turn. If the order is failed it does not fire that turn. Any Hits caused by the Bombard allow no save. In addition, fortified targets only count as being defended (5+ to hit) and defended targets count as being in the open (4+ to hit). The Bombards shot bounce like a normal cannon’s. This does not apply when shooting at walls/towers as the stonework will obviously stop the cannon ball and prevent it bouncing. Bombards cannot shoot at charging enemy units. Bombards may not be used by Elves or Bretonnians. (100p) Mangonel Troop/Type/Attack/Hits/Armour/Command/Unit Size/Points per Unit/ Min/Max Mangonel/Art/ 0/4 /3/0/-/1/80/ -/1 Range 20-90cm Attack Close Combat 0 / Shooting 4 For siege use only! Mangonels must be deployed before any other unit and cannot move once it is deployed. If firing it fires “straight ahead”. This means it can only draw a line of sight to targets that lie in the corridor that extends straight ahead from the front edge. So the Mangonel only has a 2cm wide corridor of sight. For targets outside this corridor it must be ordered to turn. If the order is failed it does not fire that turn. Any Hits caused by the Mangonel allow no save. The Mangonel has a minimum range of 20cm as it is impossible to adjust its mechanism to shoot at closer target. Mangonels can’t shoot at charging enemy units. Earthworks These are defensive works built by both defending and attacking forces in a siege and sometimes in other situations as well. These are usually hastily constructed out of earth, log barricades, upturned carts, barrels and whatever else comes to hand. Each section of earthworks purchased is 40mm long and 10mm wide, half the size of a standard Warmaster base. Unless otherwise specified in a particular scenario, earthworks are always deployed before the armies set up in the relevant deployment zones, starting with the defender deploying all his earthworks first, or dice off to decide if for some reason there is no defined attacker or defender. Earthworks can be arranged together in whatever formation is desired by the purchasing player. Earthworks count as a linear feature that confers fortified status against missile fire and defended status against any close combat attacks. To remove earthworks to make way for your siege towers and battering rams, a unit of infantry (and only infantry) must be adjacent to the earthworks. If the unit is not in combat at the beginning of the combat phase each stand in contact with an earthwork section gets its basic attacks against it (no charge bonuses, as what the troops are doing is getting their entrenching tools out). Any 6’s that are rolled will destroy the earthwork that is attacked in this way. It is important that you declare exactly which earthwork sections each stand is attacking, as each 40x10mm section is effectively counted as a separate unit for these purposes. Log Rams Log rams are effectively Battering rams but without the added protection of an armoured covering to shield the battering unit. Log rams can be brought to bear much more rapidly than a Battering ram can be. The main disadvantage is, of course, the lack of protection, especially against boiling oil poured on the battering unit by troops on the ramparts above or stand and fire from these units. Attacking infantry units may be equipped with Log rams. A unit that is equipped with Log rams may abandon its Log rams at any point and is then unrestricted by this. Also, when equipped with Log rams a unit may not cross or move through any terrain which is classed as difficult for movement purposes, such as forests or earthworks. If a unit equipped with Log rams is driven back by enemy shooting or magic and is forced to enter difficult terrain it loses its log rams and moves on. When a unit with a Log ram makes contact with a fortress wall it will commence battering in much the same way as a Battering ram. However, if as a result of a boiling oil attack or stand and fire from units on the walls enough hits are inflicted to remove a whole stand then the battering attempt fails. For every wound the unit has to retreat 1cm. Ladders Infantry units may only assault the walls of a fortress with a siege tower or by using ladders. It costs +5 points to equip all stands of a unit with ladders. Infantry units based as cavalry cannot climb ladders.
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IBM Research Laboratory, San Jose, California Future users of large data banks must be protected from having to know how the data is organized in the machine (the internal representation). A prompting service which supplies such information is not a satisfactory solution. Activities of users at terminals and most application programs should remain unaffected when the internal representation of data is changed and even when some aspects of the external representation are changed. Changes in data representation will often be needed as a result of changes in query, update, and report traffic and natural growth in the types of stored information. Existing noninferential, formatted data systems provide users with tree-structured files or slightly more general network models of the data. In Section 1, inadequacies of these models are discussed. A model based on n-ary relations, a normal form for data base relations, and the concept of a universal data sublanguage are introduced. In Section 2, certain operations on relations (other than logical inference) are discussed and applied to the problems of redundancy and consistency in the user’s model. KEY WORDS AND PHRASES data bank, data base, data structure, data organization, hierarchies of data, networks of data, relations, derivability, redundancy, consistency, composition, join, retrieval language, predicate calculus, security, data integrity CR CATEGORIES 3.70, 3.73, 3.75, 4.20, 4.22, 4.29 1. Relational Model and Normal Form 1 .I. INTR~xJ~TI~N This paper is concerned with the application of elementary relation theory to systems which provide shared access to large banks of formatted data. Except for a paper by Childs [l], the principal application of relations to data systems has been to deductive question-answering systems. Levein and Maron [2] provide numerous references to work in this area. In contrast, the problems treated here are those of data independence-the independence of application programs and terminal activities from growth in data types and changes in data representation-and certain kinds of data inconsistency which are expected to become troublesome even in nondeductive systems. Volume 13 / Number 6 / June, 1970 The relational view (or model) of data described in Section 1 appears to be superior in several respects to the graph or network model [3,4] presently in vogue for noninferential systems. It provides a means of describing data with its natural structure only-that is, without superimposing any additional structure for machine representation purposes. Accordingly, it provides a basis for a high level data language which will yield maximal independence between programs on the one hand and machine representation and organization of data on the other. A further advantage of the relational view is that it forms a sound basis for treating derivability, redundancy, and consistency of relations-these are discussed in Section 2. The network model, on the other hand, has spawned a number of confusions, not the least of which is mistaking the derivation of connections for the derivation of relations (see remarks in Section 2 on the “connection trap”). Finally, the relational view permits a clearer evaluation of the scope and logical limitations of present formatted data systems, and also the relative merits (from a logical standpoint) of competing representations of data within a single system. Examples of this clearer perspective are cited in various parts of this paper. Implementations of systems to support the relational model are not discussed. 1.2. DATA DEPENDENCIESIN PRESENTS YSTEMS The provision of data description tables in recently developed information systems represents a major advance toward the goal of data independence [5,6,7]. Such tables facilitate changing certain characteristics of the data representation stored in a data bank. However, the variety of data representation characteristics which can be changed without logically impairing some application programs is still quite limited. Further, the model of data with which users interact is still cluttered with representational properties, particularly in regard to the representation of collections of data (as opposed to individual items). Three of the principal kinds of data dependencies which still need to be removed are ordering dependence, indexing dependence, and access path dependence. In some systems these dependencies are not clearly separable from one another. 1.2.1. Ordering Dependence. Elements of data in a data bank may be stored in a variety of ways, some involving no concern for ordering, some permitting each element to participate in one ordering only, others permitting each element to participate in several orderings. Let us consider those existing systems which either require or permit data elements to be stored in at least one total ordering which is closely associated with the hardware-determined ordering of addresses. For example, the records of a file concerning parts might be stored in ascending order by part serial number. Such systems normally permit application programs to assume that the order of presentation of records from such a file is identical to (or is a subordering of) the Communications of the ACM 377 stored ordering. Those application programs which take advantage of the stored ordering of a file are likely to fail to operate correctly if for some reason it becomes necessary to replace that ordering by a different one. Similar remarks hold for a stored ordering implemented by means of pointers. It is unnecessary to single out any system as an example, because all the well-known information systems that are marketed today fail to make a clear distinction between order of presentation on the one hand and stored ordering on the other. Significant implementation problems must be solved to provide this kind of independence. 1.2.2. Indexing Dependence. In the context of formatted data, an index is usually thought of as a purely performance-oriented component of the data representation. It tends to improve response to queries and updates and, at the same time, slow down response to insertions and deletions. From an informational standpoint, an index is a redundant component of the data representation. If a system uses indices at all and if it is to perform well in an environment with changing patterns of activity on the data bank, an ability to create and destroy indices from time to time will probably be necessary. The question then arises Can application programs and terminal activities remain invariant as indices come and go? Present formatted data systems take widely different approaches to indexing. TDMS [7] unconditionally provides indexing on all attributes. The presently released version of IMS [5] provides the user with a choice for each file a choice between no indexing at all (the hierarchic sequential organization) or indexing on the primary key only (the hierarchic indexed sequent,ial organization). In neither case is the user’s application logic dependent on the existence of the unconditionally provided indices. IDS [8], however, permits the fle designers to select attributes to be indexed and to incorporate indices into the file structure by means of additional chains. Application programs taking advantage of the performance benefit of these indexing chains must refer to those chains by name. Such programs do not operate correctly if these chains are later removed. 1.2.3. Access Path Dependence. Many of the existing formatted data systems provide users with tree-structured files or slightly more general network models of the data. Application programs developed to work with these systems tend to be logically impaired if the trees or networks are changed in structure. A simple example follows. Suppose the data bank contains information about parts and projects. For each part, the part number, part name, part description, quantity-on-hand, and quantity-on-order are recorded. For each project, the project number, project name, project description are recorded. Whenever a project makes use of a certain part, the quantity of that part committed to the given project is also recorded. Suppose that the system requires the user or file designer to declare or define the data in terms of tree structures. Then, any one of the hierarchical structures may be adopted for the information mentioned above (see Structures l-5). 378 Communications of the ACM Structure 1. Projects Subordinate to Parts File Segment Fields F PART part # part name part description quantity-on-hand quantity-on-order PROJECT project # project name project description quantity committed Structure 2. Parts Subordinate to Projects File Sqmeut Fields F PROJECT project # project name project description PART part # part name part description quantity-on-hand quantity-on-order quantity committed Structure 3. Parts and Projects as Peers Commitment Relationship Subordinate to Projects File Segment Fields F PART part # part name part description quantity-on-hand quantity-on-order G PROJECT project # project name project description PART part # quantity committed Structure 4. Parts and Projects as Peers Commitment Relationship Subordinate to Parts File Segnren1 Fields F PART part # part description quantity-on-hand quantity-on-order PROJECT project # quantity committed G PROJECT project # project name project description Structure 5. Parts, Projects, and Commitment Relationship as Peers FCZC .% -,,ZC,,t Ficlds F PART part # part name part description quantity-on-hand quantity-on-order G PROJECT project # project name project description H COMMIT part # project # quantity committed Volume 13 / Number 6 / June, 1970 Now, consider the problem of printing out the part number, part name, and quantity committed for every part used in the project whose project name is “alpha.” The following observations may be made regardless of which available tree-oriented information system is selected to tackle this problem. If a program P is developed for this problem assuming one of the five structures above-that is, P makes no test to determine which structure is in effect- then P will fail on at least three of the remaining structures. More specifically, if P succeeds with structure 5, it will fail with all the others; if P succeeds with structure 3 or 4, it will fail with at least 1,2, and 5; if P succeeds with 1 or 2, it will fail with at least 3, 4, and 5. The reason is simple in each case. In the absence of a test to determine which structure is in effect, P fails because an attempt is made to exceute a reference to a nonexistent file (available systems treat this as an error) or no attempt is made to execute a reference to a file containing needed information. The reader who is not convinced should develop sample programs for this simple problem. Since, in general, it is not practical to develop application programs which test for all tree structurings permitted by the system, these programs fail when a change in ructure becomes necessary. Systems which provide users with a network model of the data run into similar difficulties. In both the tree and network cases, the user (or his program) is required to exploit a collection of user access paths to the data. It does not matter whether these paths are in close correspondence with pointer-defined paths in the stored representation-in IDS the correspondence is extremely simple, in TDMS it is just the opposite. The consequence, regardless of the stored representation, is that terminal activities and programs become dependent on the continued existence of the user access paths. One solution to this is to adopt the policy that once a user access path is defined it will not be made obsolete until all application programs using that path have become obsolete. Such a policy is not practical, because the number of access paths in the total model for the community of users of a data bank would eventually become excessively large. 1.3. A RELATIONAL VIEW OF DATA The term relation is used here in its accepted mathematical sense. Given sets X1 , S, , . . . , S, (not necessarily distinct), R is a relation on these n sets if it is a set of ntuples each of which has its first element from S1, its second element from Sz , and so on.’ We shall refer to Si as the jth domain of R. As defined above, R is said to have degree n. Relations of degree 1 are often called unary, degree 2 binary, degree 3 ternary, and degree n n-ary. For expository reasons, we shall frequently make use of an array representation of relations, but it must be remembered that this particular representation is not an essential part of the relational view being expounded. An ar- 1 More concisely, R is a subset of the Cartesian product 81 X sz x *.* x 87%. ray which represents an n-ary relation R has the following properties (1) Each row represents an n-tuple of R. (2) The ordering of rows is immaterial. (3) All rows are distinct. (4) The ordering of columns is significant-it corresponds to the ordering S1, Sz , . . . , S, of the domains on which R is defined (see, however, remarks below on domain-ordered and domain-unordered relations ) . (5) The significance of each column is partially conveyed by labeling it with the name of the corresponding domain. The example in Figure 1 illustrates a relation of degree 4, called supply, which reflects the shipments-in-progress of parts from specified suppliers to specified projects in specified quantities. supply (supplier part project quantity) 1 2 5 17 1 3 5 23 2 3 7 9 2 7 5 4 4 1 1 12 FIG. 1. A relation of degree 4 One might ask If the columns are labeled by the name of corresponding domains, why should the ordering of columns matter? As the example in Figure 2 shows, two columns may have identical headings (indicating identical domains) but possessd istinct meanings with respect to the relation. The relation depicted is called component. It is a ternary relation, whose first two domains are called part and third domain is called quantity. The meaning of component (2, y, z) is that part x is an immediate component (or subassembly) of part y, and z units of part 5 are needed to assemble one unit of part y. It is a relation which plays a critical role in the parts explosion problem. component (part part quantity) 1 5 9 2 5 7 3 5 2 2 6 12 3 6 3 4 7 1 6 7 1 FIG. 2. A relation with-two identical domains It is a remarkable fact that several existing information systems (chiefly those based on tree-structured files) fail to provide data representations for relations which have two or more identical domains. The present version of IMS/360 [5] is an example of such a system. The totality of data in a data bank may be viewed as a collection of time-varying relations. These relations are of assorted degrees. As time progresses, each n-ary relation may be subject to insertion of additional n-tuples, deletion of existing ones, and alteration of components of any of its existing n-tuples. Volume 13 / Number 6 / June, 1970 Communications of the ACM 379 In many commercial, governmental, and scientific data banks, however, some of the relations are of quite high degree (a degree of 30 is not at all uncommon). Users should not normally be burdened with remembering the domain ordering of any relation (for example, the ordering supplier, then part, then project, then quantity in the relation supply). Accordingly, we propose that users deal, not with relations which are domain-ordered, but with relationships which are their domain-unordered counterparts.2 To accomplish this, domains must be uniquely identifiable at least within any given relation, without using position. Thus, where there are two or more identical domains, we require in each case that the domain name be qualified by a distinctive role name, which serves to identify the role played by that domain in the given relation. For example, in the relation component of Figure 2, the first domain part might be qualified by the role name sub, and the second by super, so that users could deal with the relationship component and its domains-sub.part super.part, quantity-without regard to any ordering between these domains. To sum up, it is proposed that most users should interact with a relational model of the data consisting of a collection of time-varying relationships (rather than relations). Each user need not know more about any relationship than its name together with the names of its domains (role qualified whenever necessary) Even this information might be offered in menu style by the system (subject to security and privacy constraints) upon request by the user. There are usually many alternative ways in which a relational model may be established for a data bank. In order to discuss a preferred way (or normal form), we must first introduce a few additional concepts (active domain, primary key, foreign key, nonsimple domain) and establish some links with terminology currently in use in information systems programming. In the remainder of this paper, we shall not bother to distinguish between relations and relationships except where it appears advantageous to be explicit. Consider an example of a data bank which includes relations concerning parts, projects, and suppliers. One relation called part is defined on the following domains (1) part number (2) part name (3) part color (4) part weight (5) quantity on hand (6) quantity on order and possibly other domains as well. Each of these domains is, in effect, a pool of values, some or all of which may be represented in the data bank at any instant. While it is conceivable that, at some instant, all part colors are present, it is unlikely that all possible part weights, part 2 In mathematical terms, a relationship is an equivalence class of those relations that are equivalent under permutation of domains (see Section 2.1.1). * Naturally, as with any data put into and retrieved from a computer system, the user will normally make far more effective use of the data if he is aware of its meaning. names, and part numbers are. We shall call the set of values represented at some instant the active domain at that instant. Normally, one domain (or combination of domains) of a given relation has values which uniquely identify each element (n-tuple) of that relation. Such a domain (or combination) is called a primary key. In the example above, part number would be a primary key, while part color would not be. A primary key is nonredundant if it is either a simple domain (not a combination) or a combination such that none of the participating simple domains is superfluous in uniquely identifying each element. A relation may possess more than one nonredundant primary key. This would be the case in the example if different parts were always given distinct names. Whenever a relation has two or more nonredundant primary keys, one of them is arbitrarily selected and called the primary key of that relation. A common requirement is for elements of a relation to cross-reference other elements of the same relation or elements of a different relation. Keys provide a user-oriented means (but not the only means) of expressing such crossreferences. We shall call a domain (or domain combmation) of relation R a foreign key if it is not the primary key of R but its elements are values of the primary key of some relation S (the possibility that S and R are identical is not excluded). In the relation supply of Figure 1, the combination of supplier, part, project is the primary key, while each of these three domains taken separately is a foreign key. In previous work there has been a strong tendency to treat the data in a data bank as consisting of two parts, one part consisting of entity descriptions (for example, descriptions of suppliers) and the other part consisting of relations between the various entities or types of entities (for example, the supply relation). This distinction is difficult to maintain when one may have foreign keys in any relation whatsoever. In the user’s relational model there appears to be no advantage to making such a distinction (there may be some advantage, however, when one applies relational concepts to machine representations of the user’s set of relationships). So far, we have discussed examples of relations which are defined on simple domains-domains whose elements are atomic (nondecomposable) values. Nonatomic values can be discussed within the relational framework. Thus, some domains may have relations as elements. These relations may, in turn, be defined on nonsimple domains, and so on. For example, one of the domains on which the relation employee is defined might be salary history. An element of the salary history domain is a binary relation defined on the domain date and the domain salary. The salary history domain is the set of all such binary relations. At any instant of time there are as many instances of the salary history relation in the data bank as there are employees. In contrast, there is only one instance of the employee relation. The terms attribute and repeating group in present data base terminology are roughly analogous to simple domain 380 Communications of the ACM Volume 13 / Number 6 / June, 1970 and nonsimple domain, respectively. Much of the confusion in present terminology is due to failure to distinguish between type and instance (as in “record”) and between components of a user model of the data on the one hand and their machine representation counterparts on the other hand (again, we cite “record” as an example). 1.4. NORMAL FORM A relation whose domains are all simple can be represented in storage by a two-dimensional column-homogeneous array of the kind discussed above. Some more complicated data structure is necessary for a relation with one or more nonsimple domains. For this reason (and others to be cited below) the possibility of eliminating nonsimple domains appears worth investigating! There is, in fact, a very simple elimination procedure, which we shall call normalization. Consider, for example, the collection of relations exhibited in Figure 3 (a). Job history and children are nonsimple domains of the relation employee. Salary history is a nonsimple domain of the relation job history. The tree in Figure 3 (a) shows just these interrelationships of the nonsimple domains. employee I jobhistory I salaryhistory children employee (man#, name, birthdate, jobhistory, children) jobhistory (jobdate, title, salaryhistory) salaryhistory (salarydate, salary) children (childname, birthyear) FIG. 3(a). Unnormalized set employee’ (man#, name, birthdate) jobhistory’ (man#, jobdate, title) salaryhistory’ (man#, jobdate, salarydate, salary) children’ (man#, childname, birthyear) FIG. 3(b). Normalized set Normalization proceeds as follows. Starting with the relation at the top of the tree, take its primary key and expand each of the immediately subordinate relations by inserting this primary key domain or domain combination. The primary key of each expanded relation consists of the primary key before expansion augmented by the primary key copied down from the parent relation. Now, strike out from the parent relation all nonsimple domains, remove the top node of the tree, and repeat the same sequence of operations on each remaining subtree. The result of normalizing the collection of relations in Figure 3 (a) is the collection in Figure 3 (b). The primary key of each relation is italicized to show how such keys are expanded by the normalization. 4 M. E. Sanko of IBM, San Jose, independently recognized the desirability of eliminating nonsimple domains. If normalization as described above is to be applicable, the unnormalized collection of relations must satisfy the following conditions (1) The graph of interrelationships of the nonsimple domains is a collection of trees. (2) No primary key has a component domain which is nonsimple. The writer knows of no application which would require any relaxation of these conditions. Further operations of a normalizing kind are possible. These are not discussed in this paper. The simplicity of the array representation which becomes feasible when all relations are cast in normal form is not only an advantage for storage purposes but also for communication of bulk data between systems which use widely different representations of the data. The communication form would be a suitably compressed version of the array representation and would have the following advantages (1) It would be devoid of pointers (address-valued or displacement-valued ) . (2) It would avoid all dependence on hash addressing schemes. (3) It would contain no indices or ordering lists. If the user’s relational model is set up in normal form, names of items of data in the data bank can take a simpler form than would otherwise be the case. A general name would take a form such as R (g).r.d where R is a relational name; g is a generation identifier (optional); r is a role name (optional); d is a domain name. Since g is needed only when several generations of a given relation exist, or are anticipated to exist, and r is needed only when the relation R has two or more domains named d, the simple form R.d will often be adequate. 1.5. SOME LINGUISTIC ASPECTS The adoption of a relational model of data, as described above, permits the development of a universal data sublanguage based on an applied predicate calculus. A firstorder predicate calculus s ices if the collection of relations is in normal form. Such a language would provide a yardstick of linguistic power for all other proposed data Ianguages, and would itself be a strong candidate for embedding (with appropriate syntactic modification) in a variety of host Ianguages (programming, command- or problemoriented). While it is not the purpose of this paper to describe such a language in detail, its salient features would be as follows. Let us denote the data sublanguage by R and the host language by H. R permits the declaration of relations and their domains. Each declaration of a relation identifies the primary key for that relation. Declared relations are added to the system catalog for use by any members of the user community who have appropriate authorization. H permits supporting declarations which indicate, perhaps less permanently, how these relations are represented in stor- Volume 13 / Number 6 / June, 1970 Communications of the ACM 381 age. R permits the specification for retrieval of any subset of data from the data bank. Action on such a retrieval request is subject to security constraints. The universality of the data sublanguage lies in its descriptive ability (not its computing ability). In a large data bank each subset of the data has a very large number of possible (and sensible) descriptions, even when we assume (as we do) that there is only a finite set of function subroutines to which the system has access for use in qualifying data for retrieval. Thus, the class of qualification expressions which can be used in a set specification must have the descriptive power of the class of well-formed formulas of an applied predicate calculus. It is well known that to preserve this descriptive power it is unnecessary to express (in whatever syntax is chosen) every formula of the selected predicate calculus. For example, just those in prenex normal form are adequate [9]. Arithmetic functions may be needed in the qualification or other parts of retrieval statements. Such functions can be defined in H and invoked in R. A set so specified may be fetched for query purposes only, or it may be held for possible changes. Insertions t,ake the form of adding new elements to declared relations without regard to any ordering that may be present in their machine representation. Deletions which are effective for the community (as opposed to the individual user or subcommunities) take the form of removing elements from declared relations. Some deletions and updates may be triggered by others, if deletion and update dependencies between specified relations are declared in R. One important effect that the view adopted toward data has on the language used to retrieve it is in the naming of data elements and sets. Some aspects of this have been discussed in the previous section. With the usual network view, users will often be burdened with coining and using more relat,ion names than are absolutely necessary, since names are associated with paths (or path types) rather than with relations. Once a user is aware that a certain relation is stored, he will expect to be able to exploit5 it using any combination of its arguments as “knowns” and the remaining arguments as “unknowns,” because the information (like Everest) is there. This is a system feature (missing from many current informat.ion systems) which we shall call (logically) symmetric expZoitation of relations. Naturally, symmetry in performance is not to be expected. To support symmetric exploitation of a single binary relation, two directed paths are needed. For a relation of degree n, the number of paths to be named and controlled is n factorial. Again, if a relational view is adopted in which every nary relation (n 2) has to be expressed by the user as a nested expression involving only binary relations (see Feldman’s LEAP System [lo], for example) then 2n - 1 names have to be coined instead of only n + 1 with direct n-ary notation as described in Section 1.2. For example, the 6 Exploiting a relation includes query, update, and delete. 4-ary relation supply of Figure 1, which entails 5 names in n-ary notation, would be represented in the form P (supplier, (part, R (project, quantity))) in nested binary notation and, thus, employ 7 names. -4 further disadvantage of this kind of expression is its asymmetry. Although this asymmetry does not prohibit symmetric exploitation, it certainly makes some bases of interrogation very awkward for the user to express (consider, for example, a query for those parts and quantities related to certain given projects via and R). 1.6. EXPRESSIBLE, NAMED, AND STORED RELATIONS Associated with a data bank are two collections of relations the named set and the expressible set. The named set is the collection of all those relations that the community of users can identify by means of a simple name (or identifier). A relation R acquires membership in the named set when a suitably authorized user declares R; it loses membership when a suitably authorized user cancels the declaration of R. The expressible set is the total collection of relations that can be designated by expressions in the data language. Such expressions are constructed from simple names of relations in the named set; names of generations, roles and domains; logical connectives; the quantifiers of the predicate calcu- 1~s;~ and certain constant relation symbols such as = , . The named set is a subset of the expressible set-usually a very small subset. Since some relations in the named set may be time-independent combinations of others in that set, it is useful to consider associating with the named set a collection of statements that define these time-independent constraints. We shall postpone further discussion of this until we have introduced several operations on relations (see Section 2). One of the major problems confronting the designer of a data system which is to support a relational model for its users is that of determining the class of stored representations to be supported. Ideally, the variety of permitted data representations should be just adequate to cover the spectrum of performance requirements of the total collection of installations. Too great a variety leads to unnecessary overhead in storage and continual reinterpretation of descriptions for the structures currently in effect. For any selected class of stored representations the data system must provide a means of translating user requests expressed in the data language of the relational model into corresponding-and elhcient-actions on the current stored representation. For a high level data language this presents a challenging design problem. Nevertheless, it is a problem which must be solved-as more users obtain concurrent access to a large data bank, responsibility for providing efficient response and throughput shifts from the individual user to the data system. 6 Because each relation in a practical data bank is a finite set at every instant of time, the existential and universal quantifiers can be expressed in terms of a function that counts the number of elements in any finite set. 382 Communications of the ACM Volume 13 / Number 6 / June, 1970 2. Redundancy and Consistency 2.1. OPERATIONS ON RELATIONS Since relations are sets, all of the usual set operations are applicable to them. Nevertheless, the result may not be a relation; for example, the union of a binary relation and a ternary relation is not a relation. The operations discussed below are specifically for relations. These operations are introduced because of their key role in deriving relations from other relations. Their principal application is in noninferential information systems- systems which do not provide logical inference services-although their applicability is not necessarily destroyed when such services are added. Most users would not be directly concerned with these operations. Information systems designers and people concerned with data bank control should, however, be thoroughly familiar with them. 2.1.1. Permutation. A binary relation has an array representation with two columns. Interchanging these columns yields the converse relation. More generally, if a permutation is applied to the columns of an n-ary relation, the resulting relation is said to be a permutation of the given relation. There are, for example, 4! = 24 permutations of the relation supply in Figure 1, if we include the identity permutation which leaves the ordering of columns unchanged. Since the user’s relational model consists of a collection of relationships (domain-unordered relations), permutation is not relevant to such a model considered in isolation. It is, however, relevant to the consideration of stored representations of the model. In a system which provides symmetric exploitation of relations, the set of queries answerable by a stored relation is identical to the set answerable by any permutation of that relation. Although it is logically unnecessary to store both a relation and some permutation of it, performance considerations could make it advisable. 2.1.2. Projection. Suppose now we select certain columns of a relation (striking out the others) and then remove from the resulting array any duplication in the rows. The final array represents a relation which is said to be a projection of the given relation. A selection operator ?r is used to obtain any desired permutation, projection, or combination of the two operations. Thus, if L is a list of lc indices7 L = i1, ii, - . - , ik and R is an n-ary relation (n 2 k ), then rrL (R ) is the k-ary relation whose jth column is column ii of R (j = 1,2, * * . ,k) except that duplication in resulting rows is removed. Consider the relation supply of Figure 1. A permuted projection of this relation is exhibited in Figure 4. Note that, in this particular case, the projection has fewer n-tuples than the relation from which it is derived. 2.1.3. Join. Suppose we are given two binary relations, which have some domain in common. Under what circumstances can we combine these relations to form a 7 When dealing with relationships, we use domain names (rolequalified whenever necessary) instead of domain positions. ternary relation which preserves all of the information in the given relations? The example in Figure 5 shows two relations R, S, which are joinable without loss of information, while Figure 6 shows a join of R with S. A binary relation R is joinable with a binary relation S if there exists a ternary relation U such that 7r1(2U ) = R and ‘1~23 (U) = S. Any such ternary relation is called a join of R with S. If R, S are binary relations such that ~2 (R) = ~1 (S), then R is joinable with S. One join that always exists in such a case is the natural join of R with S defined by R*S = {(a, b, c) R(a, b) A S(b, c)) where R (a, b) has the value true if (a, b) is a member of R and similarly for S(b, c). It is immediate that and TB(R*S) = R T33(R*S) = S. Note that the join shown in Figure 6 is the natural join of R with S from Figure 5. Another join is shown in Figure 7. II31 hPPb/) (project supplier) 5 1 5 2 1 4 7 2 FIG. 4. A permuted projection of the relation in Figure 1 R (supplier Part) S (part project) 1 1 1 1 2 1 1 2 2 2 2 1 FIG. 5. Two joinable relations R*S (supplier part project) 1 1 1 1 1 2 2 1 1 2 1 2 2 2 1 FIG. 6. The natural join of R with S (from Figure 5) U (supplier part project) 1 1 2 2 1 1 2 2 1 FIG. 7. Another join of R with S (from Figure 5) Inspection of these relations reveals an element (element 1) of the domain part (the domain on which the join is to be made) with the property that it possessesm ore than one relative under R and also under S. It is this ele- Volume 13 / Number 6 / June, 1970 Communications of the ACM 383 ment which gives rise to the plurality of joins. Such an element in the joining domain is called a point of ambiguity with respect to the joining of R with S. If either ~1 (R) or S is a function no point of ambiguity can occur in joining R with S. In such a case, the natural join of R with S is the only join of R with S. Note that the reiterated qualification “of R with S” is necessary, because S might be joinable with R (as well as R with S), and this join would be an entirely separate consideration. In Figure 5, none of the relations R, 7r21(R), S, ?rzl(S) is a function. Ambiguity in the joining of R with S can sometimes be resolved by means of other relations. Suppose we are given, or can derive from sources independent of R and S, a relation T on the domains project and supplier with the following properties (1) m(T) = m(S), (2) m(T) = al(R), (3) T(i s +~P(R( P A S(P,~))~ (4) R(s, P -+ 3j(Soj\,.i) * T(.A s)), (5) S@,.i) + 3s(T(.?, s A R(s, P , then we may form a three-way join of R, S, T; that is, a ternary relation such that mz(U) = R, 7r23(U) = s, ml(U) = T. Such a join will be called a cyclic 3-join to distinguish it from a linear S-join which would be a quaternary relation V such that m(V) = R, lr23W) = s, lr34(V) = T. While it is possible for more than one cyclic 3-join to exist (see Figures 8,9, for an example), the circumstances under which this can occur entail much more severe constraints R (s P) s (P 23 T 0’ s) 1 a a d d 1 2 a 2 b b Ii d 2 e 2 b e e 2 FIG. 8. Binary relations with a plurality of cyclic 3-joins u b P 8 TJ’ (s P i) 1 a d 1 a d 2 a e 2 a d 2 b d 2 a e 2 b e 2 b d 2 b e FIG. 9. Two cyclic 3-joins of the relations in Figure 8 than those for a plurality of 2-joins. To be specific, the relations R, S, T must possess points of ambiguity with respect to joining R with S (say point x), S with T (say 8 A function is a binary relation, which is one-one or many-one, but not one-many. y), and T with R (say a), and, furthermore, y must be a relative of x under S, z a relative of y under T, and x a relative of z under R. Note that in Figure 8 the points 2 = a; y = d; x = 2 have this property. The natural linear 3-join of three binary relations R, S, T is given by R*S*T = { (a, b, c, d) R (a, b) A S (b, c) A T (c, d)} where parentheses are not needed on the left-hand side because the natural 2-join (*) is associative. To obtain the cyclic counterpart, we introduce the operator y which produces a relation of degree n - 1 from a relation of degree n by tying its ends together. Thus, if R is an n-ary relation (n 2 2), the tie of R is defined by the equation r(R) = {(a~, a2, .-. , a,-l) R(ul, az, ... , a,-~, a,) A al = a,). We may now represent the natural cyclic S-join of R, S, T by the expression y (R*S*T). Extension of the notions of linear and cyclic S-join and their natural counterparts to the joining of n binary relations (where n 2 3) is obvious. A few words may be appropriate, however, regarding the joining of relations which are not necessarily binary. Consider the case of two relations R (degree r ), S (degree s) which are to be joined on p of their domains (p T, p s). For simplicity, suppose these p domains are the last p of the r domains of R, and the first p of the s domains of S. If this were not so, we could always apply appropriate permutations to make it so. Now, take the Cartesian product of the first r-p domains of R, and call this new domain A. Take the Cartesian product of the last p domains of R, and call this B. Take the Cartesian product of the last s-p domains of S and call this C. We can treat R as if it were a binary relation on the domains A, B. Similarly, we can treat S as if it were a binary relation on the domains B, C. The notions of linear and cyclic S-join are now directly applicable. A similar approach can be taken with the linear and cyclic n-joins of n relations of assorted degrees. 2.1.4. Composition. The reader is probably familiar with the notion of composition applied to functions. We shall discuss a generalization of that concept and apply it first to binary relations. Our definitions of composition and composability are based very directly on the definitions of join and joinability given above. Suppose we are given two relations R, S. T is a camposition of R with S if there exists a. join U of R with S such that T = aI3 (U) . Thus, two relations are composable if and only if they are joinable. However, the existence of more than one join of R with S does not imply the existence of more than one composition of R with S. Corresponding to the natural join of R with S is the 384 Communications of the ACM Volume 13 / Number 6 / June, 1970 ndural composition9 of R with S defined by R.S = TH(R*S). Taking the relations R, S from Figure 5, their natural composition is exhibited in Figure 10 and another composition is exhibited in Figure 11 (derived from the join exhibited in Figure 7). R. S (project supplier) 1 1 1 2 2 1 FIG. 10. The natural composition of R with S (from Figure 5) T (project supplier) 1 2 2 1 FIQ. 11. Another composition of R with S (from Figure 5) When two or more joins exist, the number of distinct compositions may be as few as one or as many as the number of distinct joins. Figure 12 shows an example of two relations which have several joins but only one composition. Note that the ambiguity of point c is lost in composing R with S, because of unambiguous associations made via the points a, b, d, e. R (supplier part) S (part project) 1 1 z ; ; 1 c c f 2 2 8 is 2 e e f FICA 12. Many joins, only one composition Extension of composition to pairs of relations which are not necessarily binary (and which may be of different degrees) follows the same pattern as extension of pairwise joining to such relations. A lack of understanding of relational composition has led several systems designers into what may be called the connection trap. This trap may be described in terms of the following example. Suppose each supplier description is linked by pointers to the descriptions of each part supplied by that supplier, and each part description is similarly linked to the descriptions of each project which uses that part. A conclusion is now drawn which is, in general, erroneous namely that, if all possible paths are followed from a given supplier via the parts he supplies to the projects using those parts, one will obtain a valid set of all projects supplied by that supplier. Such a conclusion is correct only in the very special case that the target relation between projects and suppliers is, in fact, the natural composition of the other two relations-and we must normally add the phrase “for all time,” because this is usually implied in claims concerning path-following techniques. 0 Other writers tend to ignore compositions other than the natural one, and accordingly refer to this particular composition as the composition-see, for example, Kelley’s “General Topology.” 2.1.5. Restriction. A subset of a relation is a relation. One way in which a relation S may act on a relation R to generate a subset of R is through the operation restriction of R by S. This operation is a generalization of the restriction of a function to a subset of its domain, and is defined as follows. Let L, M be equal-length lists of indices such that L = iI, ., *** ,ik,M = jI,j2, e-s , jk where k 5 degree of R and k 6 degree of S. Then the L, M restriction of R by S denoted RLIMS is the maximal subset R’ of R such that ?rL(R’) = TM(S). The operation is defined only if equality is applicable between elements of ?T+(,R ) on the one hand and rjh (S) on the other for all h = 1, 2, . . . , k. The three relations R, S, R’ of Figure 13 satisfy the equation R = Rw~wsS. R (8 P ~3 s (P 8 R (8 P 3 1aA a A 1aA 2 a A c B 2 a A 2 a B b B 2 b B 2bA 2 b B FIG. 13. Example of restriction We are now in a position to consider various applications of these operations on relations. 2.2. REDUNDANCY Redundancy in the named set of relations must be distinguished from redundancy in the stored set of representations. We are primarily concerned here with the former. To begin with, we need a precise notion of derivability for relations. Suppose 0 is a collection of operations on relations and each operation has the property that from its operands it yields a unique relation (thus natural join is eligible, but join is not ). A relation R is O-derivable from a set S of relations if there exists a sequence of operations from the collection 0 which, for all time, yields R from members of S. The phrase “for all time” is present, because we are dealing with time-varying relations, and our interest is in derivability which holds over a significant period of time. For the named set of relationships in noninferential systems, it appears that an adequate collection contains the following operations projection, natural join, tie, and restriction. Permutation is irrelevant and natural composition need not be included, because it is obtainable by taking a natural join and then a projection. For the stored set of representations, an adequate collection e2 of operations would include permutation and additional operations concerned with subsetting and merging relations, and ordering and connecting their elements. 2.2.1. Strong Redundancy. A set of relations is strongly redundant if it contains at least one relation that possesses a projection which is derivable from other projections of relations in the set. The following two examples are intended to explain why strong redundancy is defined this way, and to demonstrate its practical use. In the first ex- Volume 13 / Number 6 / June, 1970 Communications of the ACM 385 ample the collection of relations consists of just the following relation employee (serial #, name, manager#, managername) with serial# as the primary key and manager# as a foreign key. Let us denote the active domain by A,, and suppose that A, (munuger#) c A, (serial#) and At (managername) C At (name) for all time t. In this case the redundancy is obvious the domain managername is unnecessary. To see that it is a strong redundancy as defined above, we observe that m4 (employee) = ~12 (empZoyee) r3 (employee). In the second example the collection of relations includes a relation S describing suppliers with primary key s#, a relation D describing departments with primary key d#, a relation J describing projects with primary key j#, and the following relations lJ (s#, d#, - * * t Q(s#,j#, .-- , R(d#,j#, **- , where in each case - - - denotes domains other than s#, d#, j#. Let us suppose the following condition C is known to hold independent of time supplier s supplies department d (relation P ) if and only if supplier s supplies some project j (relation Q) to which d is assigned (relation R). Then, we can write the equation m(P) = m(Q)-w(R) and thereby exhibit a strong redundancy. An important reason for the existence of strong redundancies in the named set of relationships is user convenience. A particular case of this is the retention of semiobsolete relationships in the named set so that old programs that refer to them by name can continue to run correctly. Knowledge of the existence of strong redundancies in the named set enables a system or data base administrator greater freedom in the selection of stored representations to cope more efficiently with current traffic. If the strong redundancies in the named set are directly reflected in strong redundancies in the stored set (or if other strong redundancies are introduced into the stored set), then, generally speaking, extra storage space and update time are consumed with a potential drop in query time for some queries and in load on the central processing units. 2.2.2. Weak Redundancy. A second type of redundancy may exist. In contrast to strong redundancy it is not characterized by an equation. A colIection of relations is weakly redundant if it contains a relation that has a projection which is not derivable from other members but is at all times a projection of some join of other projections of relations in the collection. We can exhibit a weak redundancy by taking the second example (cited above) for a strong redundancy, and assuming now that condition C does not hold at all times. The relations al2 (P), 7r1(2Q ), 7r1(2R ) are complexlo relations with the possibility of points of ambiguity occurring from time to time in the potential joining of any two. Under these circumstances, none of them is derivable from the other two. However, constraints do exist between them, since each is a projection of some cyclic join of the three of them. One of the weak redundancies can be characterized by the statement for all time, 1r1(2P ) is somec omposition of ~12(Q ) with ‘~~1(R ). The composition in question might be the natural one at some instant and a nonnatural one at another instant. Generally speaking, weak redundancies are inherent in the logical needs of the community of users. They are not removable by the system or data base administrator. If they appear at all, they appear in both the named set and the stored set of representations. 2.3. CONSISTENCY Whenever the named set of relations is redundant in either sense, we shall associate with that set a collection of statements which define all of the redundancies which hold independent of time between the member relations. If the information system lacks-and it most probably will-detailed semantic information about each named relation, it cannot deduce the redundancies applicable to the named set. It might, over a period of time, make attempts to induce the redundancies, but such attempts would be fallible. Given a collection C of time-varying relations, an associated set Z of constraint statements and an instantaneous value V for C, we shall call the state (C, 2, V) consistent or inconsistent according as V does or does not satisfy 2. For example, given stored relations R, S, T together with the constraint statement “nlz(T) is a composition of 5~1(R2 ) with ~12(X )“, we may check from time to time that the values stored for R, S, T satisfy this constraint. An algorithm for making this check would examine the first two columns of each of R, S, T (in whatever way they are represented in the system) and determine whether (1) ?rl(T) = rl(R), (2) ?rz(T) = 7r2@), (3) for every element pair (a, c) in the relation al2 (T) there is an element b such that (a, b) is in a12(R) and (b, c) is in 7r12(S). There are practica1 problems (which we shall not discuss here) in taking an instantaneous snapshot of a collection of relations, some of which may be very large and highly variable. It is important to note that consistency as defined above is a property of the instantaneous state of a data bank, and is independent of how that state came about. Thus, in particular, there is no distinction made on the basis of whether a user generated an inconsistency due to an act of omission or an act of commission. Examination of a simple IO A binary relation is complex if neither it nor its converse is a function. 386 Communications of the AMC Volume 13 / Number 6 / June, 1970 example will show the reasonableness of this (possibly unconventional) approach to consistency. Suppose the named set C includes the relations S, J, D, P, Q, R of the example in Section 2.2 and that P, Q, R possess either the strong or weak redundancies described therein (in the particular case now under consideration, it does not matter which kind of redundancy occurs). Further, suppose that at some time t the data bank state is consistent and contains no project j such that supplier 2 supplies project j and j is assigned to department 5. Accordingly, there is no element (2,5) in ~12 (P). Now, a user introduces the element (2, 5) into 7~1(2P ) by inserting some appropriate element into P. The data bank state is now inconsistent. The inconsistency could have arisen from an act of omission, if the input (2, 5) is correct, and there does exist a project j such that supplier 2 supplies j and j is assigned to department 5. In this case, it is very likely that the user intends in the near future to insert elements into Q and R which will have the effect of introducing (2, j) into al2 (Q) and (5, j) in W(R). On the other hand, the input (2, 5) might have been faulty. It could be the case that the user intended to insert some other element into P-an element whose insertion would transform a consistent state into a consistent state. The point is that the system will normally have no way of resolving this question without interrogating its environment (perhaps the user who created the inconsistency ). There are, of course, several possible ways in which a system can detect inconsistencies and respond to them. In one approach the system checks for possible inconsistency whenever an insertion, deletion, or key update occurs. Naturally, such checking will slow these operations down. If an inconsistency has been generated, details are logged internally, and if it is not remedied within some reasonable time interval, either the user or someone responsible for the security and integrity of the data is notified. Another approach is to conduct consistency checking as a batch operation once a day or less frequently. Inputs causing the inconsistencies which remain in the data bank state at checking time can be tracked down if the system maintains a journal of all state-changing transactions. This latter approach would certainly be superior if few nontransitory inconsistencies occurred. 2.4. SUMMARY In Section 1 a relational model of data is proposed as a basis for protecting users of formatted data systems from the potentially disruptive changes in data representation caused by growth in the data bank and changes in traffic. A normal form for the time-varying collection of relationships is introduced. In Section 2 operations on relations and two types of redundancy are defined and applied to the problem of maintaining the data in a consistent state. This is bound to become a serious practical problem as more and more different types of data are integrated together into common data banks. Many questions are raised and left unanswered. For example, only a few of the more important properties of the data sublanguage in Section 1.4 are mentioned. Neither the purely linguistic details of such a language nor the implementation problems are discussed. Nevertheless, the material presented should be adequate for experienced systems programmers to visualize several approaches. It is also hoped that this paper can contribute to greater precision in work on formatted data systems. Acknowledgment. It was C. T. Davies of IBM Poughkeepsie who convinced the author of the need for data independence in future information systems. The author wishes to thank him and also F. P. Palermo, C. P. Wang, E. B. Altman, and M. E. Senko of the IBM San Jose Research Laboratory for helpful discussions. RECEIVED SEPTEMBER, 1969; REVISED FEBRUARY, 1970 REFERENCES 1. CHILDS, D. L. Feasibility of a set-theoretical data structure -a general structure based on a reconstituted definition of relation. Proc. IFIP Cong., 1968, North Holland Pub. Co., Amsterdam, p. 162-172. 2. LEVEIN, R. E., AND MARON, M. E. A computer system for inference execution and data retrieval. Comm. ACM 10, 11 (Nov. 1967), 715-721. 3. BACHMAN, C. W. Software for random access processing. Datumation (Apr. 1965), 3641. 4. MCGEE, W. C. Generalized file processing. In Annual Review in Automatic Programming 6, 13, Pergamon Press, New York, 1969, pp. 77-149. 5. Information Management System/360, Application Description Manual H20-0524-1. IBM Corp., White Plains, N. Y., July 1968. 6. GIS (Generalized Information System), Application Description Manual H20-0574. IBM Corp., White Plains, N. Y., 1965. 7. BLEIER, R. E. Treating hierarchical data structures in the SDC time-shared data management system (TDMS). Proc. ACM 22nd Nat. Conf., 1967, MD1 Publications, Wayne, Pa., pp. 41-49. 8. IDS Reference Manual GE 625/635, GE Inform. Sys. Div., Pheonix, Ariz., CPB 1093B, Feb. 1968. 9. CHURCH, A. An Introduction to Mathematical Logic I. Princeton U. Press, Princeton, N.J., 1956. 10. FELDMAN, J. A., AND ROVNER, P. D. An Algol-based associative language. Stanford Artificial Intelligence Rep. AI-66, Aug. 1, 1968. Volume 13 / Number 6 / June, 1970 Communications of the ACM 38’7