An Equational Chase for Path-Conjunctive Queries ...

6 downloads 31 Views 300KB Size Report
Jan 10, 1999 - 1rv Intuitively, wnst(Yx) is the minimal instance that contains ... we can express syntactical conditions ondxas equivalent conditions on wnst(Yx).
University of Pennsylvania

ScholarlyCommons Database Research Group (CIS)

Department of Computer & Information Science

1-10-1999

An Equational Chase for Path-Conjunctive Queries, Constraints, and Views Val Tannen University of Pennsylvania, [email protected]

Lucian Popa University of Pennsylvania

Postprint version. Published in Lecture Notes in Computer Science, International Conference on Database Theory (ICDT), Volume 1580, 1999, pages 39-57. Publisher URL: http://springerlink.metapress.com/link.asp?id=105633 This paper is posted at ScholarlyCommons. http://repository.upenn.edu/db_research/40 For more information, please contact [email protected].

      !#"$%'&!( )*  ,+- ./0 1'2345  6 7 '28 9:2 æ Ó Dè Ô ù Õ|Ö6ù Èë ×+×;× Ó /è Ô4Ø Õ&Ö Øsë Ó Dè Ý Iù Õ&Þ5ù Bë ×+×;× Ó /è Ý4ß ÕìÞ ßDë ÞÙ ù Ù ± Ú Ü è4* ùÕ-,5ù ëÈ×+×;× Ü è4*/. Õ5, .†ëìÙ10'â

1æ†FIEÓH›ØÔ{äUV¿Ò‚Vã'Ò{EÓÔ{EÓHWæ»Ô{äDFOÔ(LWÒ{KWP†ADC·VÕ½Dè HþóÚ 0øIT J ë FIHNPûÔ{äWV½Ô{Ò,FIHWÕÛåeKM҂ÙÖFOÔ{EÓKMH»KIå C,KMHUÕ{Ô{Ò,FIEÓH†Ô{Õ-ãRVIM·AWÕ{Ô-Õ|F7ã4ÙÖF7ݵÕ{VVÙÊÕ{KMÙVã'äDFOÔsÙ#݆ՂÔ{V҂EmKAWÕlØ5×WAWÔ6Ô{äWVÝ3ԂK†K8äDF7çMV(F

*… Yw$´Ivqkhcb[]f7Yqk·jtqkh`a^ 6 Õ{ï'EÓÙ KIãLU؆SmV#C‚äDFIFIHNՂP3EmHUæ C,SÓVlèbFIÔaã'ÒIEƒM,C·AUVlÕ{ë*Ô{Eã'„EÓChÔ{FIä8Ô{EÓèbKúéH3ï'QSEmH30lëԂ؆VÒ{ԂÙäWVÕH(KOã'å1EÓÔ{VläµïADèDFI ԂEÓø8KM7ìHDFOáSRë'҂FIVHDã'PÒ{EÓDÔ{HDEÓHWFOæ SmSÓÝ-èeÕ{ã'VhV8EÓÔ{ä8Õ{VlC·è/ Ô{EÓKMø8HÒ7 M07ëëØí Ô{Ò,FIHWÕÛåeKM҂٠Õ0èDHþóÚ 0øTI J ë!EÓH†Ô{K èeTI'úaQ ë ÓÓ èè#  Õ XX]YWY:ZZ[†[Më ë Ó Ó èè9 Õ ² T;UWT;VU:V>\Ië\Ië Ó Óè/Ý èDÝ!Õ   â R: X]R:Y:X]ZY:[Z\l[ë \lë ² Ý:& Õ â X]Á:º=ÅBT$; â XÕ RBT+U:Vã*´V8T É KM×WEÓHÖÔ,FIý*EÓHWK†Vlþ1PßE/* è/HþóÚé1øTI J ë6åe҂KMÙ è/HþsëêèeՂVV8Õ{V7C‚Ú R€ "‚ è Õ XY:Z[Më R€ ~‚ è Õ ® ‹# RBT;U:Vqë R€ ~‚ Dè Ý Õ :²/RBT;U:V â RWXY:Z[\ ë € ˜ ަ è/Ý á  â XÁWº=ÅBTlë™›š Ž‘œ   œ  ¹$X]Á2* â XÁ:º@ÅBT á ¸Áw*À â ¸@¿B\@VÁ:º@ÅBT á Áz*² RBT+U:V â Y]Á:º=ÅBT º TKWCÒ|C,FIAWHU҂Õ{Ò{SGVFIHDԂEmC·HUVæ(KOèDåRHþ @Xë'EÓH†´Ô{KÖT ý*ã'K†EÓþ0Ô{äE!èÜEÓFOÔ{Õ1Õ P†ãRV-V#NHWP†EÓEGÔ{PEÓKMåeH(KÒFIHDèeéú PïóAWQsՂáEmHUë{ëæ(ØBèÜÔ{FIäWՂVÕ{H½KWCÕ{ëóAUãR×WÕ{V ԂEmKMԂ×UAWÔ|Ô{FIEÓHWEÓHæ(* ԂäWVFNÒ{Õ{Ô É †(‡ˆ‡ èÁ Õ X]Y:Z[M댆(‡ˆ‡ 9è  Õ ® ‹ R T;U:VqŒë †(‡ˆ‡ Dè Ý Õ :²/RBT;U:V â R:XY:Z[:\lë †(‡ˆ‡ è9 Õ € ˜ Ž!¦ è/Ý á  â XÁ:º@ÅBTlë™›š Žœ   œ  ¹$XÁ* â X]Á:º=ÅBT á ¸Áz*! â ¸=¿ \@VÁ:º=Å T á ]Á2*² RBT;UWV â YÁWº=ÅBT º ë †(‡ˆ‡ 9è  Õ @X ´]T É ë € ˜ ަ è â XÁ á  â XÁq ë ™›š Ž‘œ ަ è â ]Á á  â ]Á†ë  ™›¤ ¡‘Ž

'åeԂVÒ(Õ{KÙ V8Ù(FIHWEÓLWAWSGFOÔ{EÓKIHWÕ#KIå#C,KMHDPÏEmԂEÓKMHDFOSmÕ#ã*V3FILWLWSÓ݆Ø!EÓHÕ{VlïAWVHNC,VMØ6èeÙ KHDFMPOÁÚ é›ëØ èeH†AWSÓSGëRFOHDP(èaC,KMHNPÚÜSÓK†KMLNëØWFIHNP K×WÔ|FOEÓH* } ~ € Åè >

…*Yw$´Ivqkhcb[]f7Yqk·jtqkh`a^ ˆ †(‡ˆ‡ èÁ Õ X]Y:Z[M댆(‡ˆ‡ è9 Õ ® ‹ R T;U:Vq댆(‡ˆ‡ èDÝ Õ :²/RBT;U:V â R:XY:Z[:\lŒë †(‡ˆ‡ è  Õ @X ´T É ë € ˜ ަ èDÝ á  â X]Á:º=ÅBTlë ¥ œ ® ަ èÁ â XÁWº=ÅBT á ° â XÁqë™›š Ž‘œ ަ è :² R T;U:V â ]YÁ:º=ÅBT á  â Áqë  ™›¤ ¡‘Ž ã'Ô{ äDEÓFOÔ{Ղä8ÔREÓ٠ԂEÓäWÔ{EÓÕ SGVFIՂP†ÒVV-҂DԂVÒ|HUã'FIEmHUԂÒ{EÓEÓÕaKMÔ{åeEÓKH8HWÒ{æ½ÙÖ݆EÓEÓFOVHûSGÔ{P†EÓKMã'Õ1HUäWԂÕ!äWEGC{V,V#ä»üWP†LWÔ{EÓSGäWÒ{FIVlVµEÓC,H Ô6KMÔ,Ô{Ô{FIäUÒ|×WFOVSÓHWÒ#VlÕ{FOKWSGA(FOCÔ{C,çqEÓAWKMEÓV҂H(Ò{ã VEÓHDH¿1{C·Ò‚V¿ý*VLWKqKOSÓþ0êåEGCEFIKIԂ@EÓå0X KM:HèDH3 ´]þóTíÞ  Ú É 0ø¯J EÓ Õ#TIá7Õ{â{AWí ×WJ ՂëÔ{EÓí>Ô{ïóAUÔ{KMVlԂP V E²Ò{åVLUã*SƒT'VFC,äWã V1V!FOV7åbH†KMïMÔ'Ò{ANÙÅÔ{FIäWSÓÕREÓVH-٠׆ã'Ý#Ò{äWVlVhEGïã'C‚ADäÒ{FOEÓÔ{ã*SÓԂÕ!VRVã'H¿äNEÓF7Ô{×UçMäWAWV*EÓÔ'H#ã'HWÔ{Ò{KMäUEÓÔ0Ô{VsԂE²VÕ,åHC,ã*KMԂLNVäWV V'ã KIC,FOåKMH†HW” Ô'‹ ՂÔ{Ô{‹#Ò,K#• FIèÒ{EӃH†Vhã'Ô{Õ!Ò{ԂEÓÔ{AWzV ë*Ò{HW×WÕZEÓHDKMP†AWEÓÔԂHWäWÔ{æVK ÕlÙ½Ø×NãRí†V V0úaC·HÖKMã'H†KEmçMSÓÒ|SWVP†AUHUVhÒsÕ{EmVhVHqԂKFÔ åeKM҂ÙKIåVlïADFIԂEÓKMHWwÕ 1‚æMADFOÒ|P†VlWP 3#×qÝ#ՂVÔ1ÙVÙ#×NVÒ{ՂäWEÓL C,KMHDÕ&PÏEmÞ Ô‚EÓKMHWÕ*åeKÒRԂäWVçMFOÒ{EGFI×WSÓV;Õ * ƒ ù Õ&Þ ù á;â;â+â-á ƒ ß Õ&Þ ß 9è ƒ ù á+â;â;âçá ƒ ß#Ÿ ù  ë ë à ù 9è ƒ ù á;â+â;â-á ƒ ß ë ãà ± è ƒ ù á;â;â+â á ƒ ß ë T'Ô{äDäWFOV1Ô1C,CKFIHWHµæM҂×DAWV VHDåbKMC,AWV HD҂PêAWSÓEmVH3ÕåeށJKÒ!T1Ô{à äW h?V âu”FI‹'SÓSӋKI•ã C,AWKÕ HWÕ{ԂԂK#Ò{ADÒ{C,VÔ'ã'Ԃ҂KMEmԂæVVÔ{ԂäWäWVhVÒRՂã'VÔ EÓÔ{Ù ä#VՂKMÙ#Ù×NVVÒ{FՂPWäWP†EÓLÖEÓÔ{EÓC,KMKHNHDFIP†S†EÓÔ{Ò{EÓAWKSÓHWVÕÕ ã'EÓÔ{äWEÓH ԂäWV Õ|C,KLDV6KIåq†(‡ˆ‡ FOHDPçqEGC,V·ÚÜçVÒ{Õ,FWíWT'ä†AWÕ'ã*V äDF7çMV ԂäWV0åeKMSÓSÓKIã'EÓHWæ>* 쯥 ··œ«í%î›ïNþFø)ðÈø>§·›ùýéø>§ñNø­ ùjú;§@«:©­üú¾ù°ò;°êóüW51´+A!ø+13?A' õSöBW4 * ñ**ˆ †(‡ˆ‡ è– ÕC7 ÿ ë € ˜ ë ù è–!ë™›š Žœ ŠŒ‹#A-56n4C-bè ,B± 5ë S8C-¾“-5 C+FOFOú;HDÕ{¥ V P#² Ñ3èbEGVRP†Vã*Ù V҂SÓK†V1KMäDLNFOëULWåeLWKMEÓÒ!SÓÝïAWLWEÓÒ{Ô{KIV*ç†Õ{EÓKHWÙ æ VlV!ïԂADEmÙFOSmV!EÓԂ×NEmVhV,ÕåeKMEÓH ҂V'ý*ãRK†V*þ1Ò{E†V7׆FIÝ-SÓEÓéÒ{VlVP-ã'Ô{҂äUEmԂV1EÓHWC,æKMHWã'HUEÓVlÔ{ä#C,Ô{EÓP†KV,H Ú þ WC,F7KçqÔ{ºÏEGÔ'P†«:Ñ3ՂKM­H›V¨ÎEÓØ=HW 1ՂúÀÔ{ûSÓVEÓH «:EÓH›­yþ1ØW·FOVhùLAWHDÔ{Pú+Õ,øbC{Ô{ä5äW†ØWV VÑ3LD҂æMFOV&V LDH†Våb 0V;Ò EE×WÕ1HDEÓÔ{Ò{FOVVhH›×Nçq؆KMEÓVý'AUã*SÜFIØ!VÒ{҂ÙJ5ÕlíVVԂÙêVÒ 0GZFIAWÒ,HWFWVhØ:ÙÖ'KFIH5HDF¦Ø †î8KFLWC‚äWäWEÓV8SÓEmH5ý*ØqSÓþ AWVFIÔlHP¯Ø †ÏADAWC,Õ|EÓFOA›H Ø ®ÓGNGRH#G5Ð nG8Q à …*ÃI[ Ê ›€ Ä y†À5…RÃO[]ca^|Æf7vIjGÀ3…Zj]Äl^,ÃM_{k·[]zÖkhYqk·j]f7Älv^|`#cafgGvMYMw†kr ^,YIc{k·j Yflcb[]f7YM`-fg'´IvM^,_ad¿khYMw wM^,p†^,YMw^|Yz,d#caM^,fl_ad7À›Á$^,z‚MYI[]zk·j›_a^,pqf7_ac,n†Dx •…‡xb…1nW‡ˆ Ê €OÀ à …2UXž7ˆ›Ä …0À:)1ÀW…*Mfn„t*À U5^,^,_b[Gn„khYMwfIÀDoóÀ„Xuj]rìkhYWÀÁZM^ caM^,f7_ad#fg$Âaf[]Y`'[]Y(_a^‚jmkcb[]f7Yqk·j Ã( … g¯)'ˆ 6›Ä wqyIÀ'^,kh§I_ac{¨GÄ7kh§^ÅÃqÉ{kh§;`a…R",^|³-`,ÃO"{AÀ []À†ca»f^,…RÃqw¼!f7wI½¿vI[]jG`aìn f7¾YI#e‡¶e§I¥[]­ z{",q^,§I`bkhj]«_a^|¿w¨Gd7°Ó¬In­ gZ‡"uˆlvIˆ¬Ij6IG@­ n8À À'kh§IYM¨Gšw § ɂ;§)Z"|[]B³ z|caÁÃf7Âjb_ "|¨˜³)ZÆ [mk"‚YIn vU‰ À¸e€7d¹ T } ÅÏÀˆ ¬Ižu¯ÄO­€O‡%I‰§InN¨G°Ó‡·¬Iˆ ­ ž7"ñˆIÀ /¬ Æ Ã … ( üi ‡!ˆOI‡ Äì„ÀW…!9c h7[]Y`aflYUn„t*À ( ^,z{j]v`a^7n„iNÀDiBI[j]ÃM_afh¾'n›kYwÖiN>À ‡5[]z‚qkh_awWÀsoZ^,`b[]ÄlY[]`a`av^|`ó[]YÖk rÎW§Ik­p*ÈIjm¯Mkh§YMÈIÄ7³'vq"ckhÏrÄ7À^lÀ†ÐyxbÇfY Î_Ǧџ#bÒM¬ÓF« nÈM•*/¬ Æk,gG¨]pI©†ja³ []f7ÉYW#{nB%ʆ*w,­†_aM¨^,Ë^|Ç!z,Ì^7n†@¬ …R#t;v"ÜÄl©†v¬‚`a¦sc'¬I‡·J­ ˆ7ˆOÀ'‡l§IÀ ¨G§ É{;§ ",!³ Ǧ#bI¬ È@#b§ ÆÆ °Ó­ È Ã …'yM X žlň Ä …0^,¼I À pM)0_a^,À$`a`b…R[]f7YMfM`,ün 2À Ÿ1ÁÀ „-fl_aÄIkYOD¶ ž'khvIgGrkYYWÀ à t¯ž…)'ˆ ~ Ä yIc{k·\I_afl` yÏÀ¿tfl`arkhwqk!h7[]`,nôi$kh_b[]` t*Àìž'khYM^‚jmkh7[]`,nûkYw „-fl`a^êŸ0À&)kh_awI[GÀ iNÔI¬Ifh¯j]dI#‚YM­†f7§ r1ÇÏ/¬[mk·Æ'j¶e¨²cb©†[]A³r »f^µ¼![]rs½pOnWjÀ€ []zžOk¸acb‡[]d¹f7T]Y÷‡ 6MÄ p‘‰ _aiflÃOn$j]‡^,ˆlrsˆ `-~ À gGf7_vYqkh_ad½[]YMz‚j]vM`b[]f7Y w^|p†^,YMw^,YMz‚[]^,`,À à t ( „ Ê ‡IÄ …0À¾ž0À tuqkhYMwM_{kOng'À@‡*À ( ^,¾[]`,nMkYw’fIÀl…0À¾„#k!h7f¾!`9hId7À>$r0Ãq^,wwM^,w []r pIj[]zkhcb[]flYWk·j wMÁƒ^, p†^,¦qYM;¬ w"|^|°ÓY¯ z‚[]^|`*¬I­#kY¨²ws©†6³ ca¾†^‚©†[]_$³{@¬ []YI#dgGÂs^,_a/¬ ^,ÆfYM¼$z,^!¬ p_a¦Dfl¯MÃO¨Gj]°Ó^|­ r-È7nIÀWpqxbLYkhÄlÇ^,`R#e¬€ «‚‰I³{}³ %IÄM°mÀ€ ­ 6 È;‰ "›n$/¬ ‡·Æ_ˆ »fÊ ‡7¼!À ½Á~w*Û»{¼c¾ à t5j]v†ˆI‡_Ä y†Ð!Àl;§ tÆ "|³j]vM%I^,–³c,Àƒ%IÎWÆ ¬I§I­q­­†ÈI³‚§-³ ÈI"!³-@¬"$#{³°Ó¨_³­†ÜU¨G¦D³,¨Gªa°¬ Æ ÉG®,°³"|¨²§IÀD¨˜°mi$¬IÆ †­oû%I³caM#e³d^,á`b[]¯M`,³nW¨˜X!³-"†YO¦q[]\l¬I^,¯_a#!`b[]Áƒca^ Âj"|wM¨G³ ^1Æ i$³-kh"_b%I[]`b³2¶ÜyIÛ!v³'wW"|n5¨G°Ó‡·¬Iˆ7­ˆI%I‡7À³ à ¯t „’žžÅÄ …*`aMf hst†kYwM_{k kYwi$O[j []z ´I¾†vM©†^,³{_b@¬ []^,#d`Â1[]/¬ Y-Æf_a¼$^‚jm¬ kcb[]¦Df7¯Yq¨Gk·°Ój›‘­ Èwqnkhp†c{k'kÄ7p Æ^,k`„-`a^,ž^,`,žu_bÀ›jÄO[]xbˆYWY ~ À ƒn Ǧƒ*U5#bpMfl¬cb«‚vO[]³{rj]wM³é%Ik·^,jW°Ó_,­n„[]È;r tu"pIf¬/j]j]Æ]^,f7r _{ÑIk¨]^|w©fYIfMc{»f>n khcb¼!„#[]f7½:k·Y#d#Áƒf‡·Âg$ˆ Æ z,žfl¦qžIYh¬;À ÂÜ"|v°Ó¯YMÆz,cb[]¬I\7­^ à ¯t ‡ZÀˆ žÅÄ txb*YCÀWtÎ!ÖfM›^ ¼ hIÁ¨v_bҟ[uÒ*khâ