From Graph Transformation to Algebraic Specification and Back Again

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1 From Grph Trnsformtion to Algebric Specifiction nd Bck Agin Dedicted to 60th Birthdy of HJK Bremen, Hus der Wissenschften, September 2009 Hrtmut Ehrig, TU Berlin Ehrig HJK-Birthdy-Colloquium Sept

2 Wht Cme First? L K R m (1) (2) dt string(dt) G D H nt string(nt) Double Pushout or Prmeter Pssing GRA-GRA or ALG-SPEC? Ehrig HJK-Birthdy-Colloquium Sept

3 Neither GRA-GRA Nor ALG-SPEC S I + l + O M I + [ I +,O ] I + evl CAT AUT Cme First! Ehrig HJK-Birthdy-Colloquium Sept

4 We re in yers fter student movement ginst estblishment t universities ORDINARIEN-UNIVERSITÄT Ehrig HJK-Birthdy-Colloquium Sept

5 We re in 1970 t Mth Dept Seminr Ktegorien und Automten 20 Students 2 Assis No Profs Min Questions Wht is Ctegory? Wht is n Automton? Wht is the Ctegory of Automt? Students Assis Tech HJK HE Ehrig HJK-Birthdy-Colloquium Sept

6 Scientific Opinion in 1970 Optimistic View Ctegory Theory is Hert of Mthemtics Automt Theory is Soul of Computer Science Pessimistic View Ctegory Theory is Abstrct Nonsense Automt Theory is Ded (Hrtmnis) CAT AUT? P = NP? Ehrig HJK-Birthdy-Colloquium Sept

7 Wht is the Outcome in the 70ies? Students receive Seminr Certifictes Students nd Assis become Book Authors Ktegorien und Automten,de Gruyter 1971 Universl Theory of Automt,Teubner 1974 Student HJK receives Dipl. Mth. Degree Theorie von Automten in pseudobgeschlossenen Ktegorien Ehrig HJK-Birthdy-Colloquium Sept

8 We re in 1978 t CS Dept of TUB HJK submits his PhD thesis Mnipultionen von Grphmnipultionen Very strnge title! Wht does it men? Is it Mthemtics or Computer Science? Keywords : Locl Church-Rosser for Grph Trnsformtion Shift Equivlence of Prllel Deriv.Sequences Cnonicl Derivtion Sequences Ehrig HJK-Birthdy-Colloquium Sept

9 Wht does it men? Locl Church-Rosser & Prllelism Prllel nd Sequentil Independence Switch & Shift Equivlence Existence & Uniqueness of Cnonicl Prllel Derivtion Sequences p1 G2 p2 p1 + p2 * * G0 G! G3 G4 p2 G2 p1 Ehrig HJK-Birthdy-Colloquium Sept

10 We re still in 1978 Problem: Cn HJK- PhD-thesis be ccepted? Pper on Locl CR ws rejected by ICALP Referee comment : Result obvious, proof only complicted by use of strnge notion of pushouts Solution: Serch for new referees Result: Acceptnce of pper for MFCS & TCS & Acceptnce of HJK-PhD-thesis t TUB B A PO D E C Ehrig HJK-Birthdy-Colloquium Sept

11 We re in 1982 ACT-project of HE & HJK ccepted by DFG Prm.Spec in Initil Algebr Approch (ADJ et l.) Prmeter Pssing inspired by GRA-GRA (HDEhr) dt string(dt) PO nt string(nt) Alterntives Finl Algebr Approch (Guttg et l.) Loose Semntics with Constrints (Reichel et l.) Ehrig HJK-Birthdy-Colloquium Sept

12 Algebric Spec Lnguges in 1984 CLEAR [BG 77, Sn 81 ] OBJ / OBJ 2 [GT 79, FGJM 85 ] CIP / CIP L [CIP 81, CIP 85 ] ACT ONE / ACT TWO [ACT 83, EM 85,EW 86] ASL [SW 83, Wir 86 ] LARCH [GH 83 ] PLUSS [Gu 84 ] Ehrig HJK-Birthdy-Colloquium Sept

13 Algebric Specifiction Community Since 1974 in USA [Zi 74,Gut 75, ADJ 76 ] Since 1976 in Europe [GGM 76 ] MFCS 76 Since 1978 in Germny [EKW 78] VLDB 78 [EL 79] GRA-GRA 78, [Rei80] MFCS 80, [BW80] CAAP 80 Problem: ACT ONE rejected by ACTA INFORMATICA Referee : ACT ONE cuses hedche becuse of 2 levels of semntics Solution: ACT ONE published in EATCS Monogrphs [EM 85] HJK receives Professorship t Uni Bremen Ehrig HJK-Birthdy-Colloquium Sept

14 10 25 Yers Lter? CAT-AUT UnivTheory of Automt? GRA-GRA Locl CR & Prllelism?? ALG-SPEC ACT-Approch? Ehrig HJK-Birthdy-Colloquium Sept

15 10 25 Yers Lter! CAT-AUT UnivTheory of Automt GRA-GRA Locl CR & Prllelism ALG-SPEC ACT-Approch CAT ALG-SPEC Institutions CAT GRA-TRA Adhesive HLR System GRA-GRA Extensions Constrints & Control GRA-GRA & ALG-SPEC Typed Attributed Gr-Tr Ehrig HJK-Birthdy-Colloquium Sept

16 CAT ALG-SPEC Aim : Institution Independence of Approch Institutions [BG 84] Specifiction Frmes [EM 90] Mod : SPEC op CtCt Model Functor Mod(SPEC) = Ctegory of Algebrs/Models Mod(f) = V f = Forgetful Functor Liberl Institution : Existence of Free Functor F f Amlgmtion & Extension Lemm bsed on POs Min New ALG-SPEC Lnguges MAUDE, SPECTRUM, CASL Ehrig HJK-Birthdy-Colloquium Sept

17 CAT GRA-TRA High-Level Replcement Systems [EHKP91] DPO-Approch bsed on HLR-Conditions Grphs, Hypergrphs, Typed Attributed Grphs Low & High-Level Petri Nets Locl CR, Prllelism, Concurency & Confluence Adhesive Ctegories [LS04] Comptibility of POs & PBs in VK-cube Adhesive HLR Systems [EHPP04] Ctegoricl Theory of GRA-TRA Ehrig HJK-Birthdy-Colloquium Sept

18 GRA-GRA EXTENSIONS Appliction Conditions [EH86] Grph Constrints & Appliction Cond [LKW 95] Control by Trnsformtion Units [KK96] GRA-TRA with Clone & Grph Vribles [Hof06] GRA-TRA with NACs [HW95, Lm08/09 ] GRA-TRA with Nested Appliction Cond [HP05] FOL with Grph Vribles Prllelism & Concurrency for Rules with Nested Appliction Conditions [EHL09, HJK-Festschrift] Ehrig HJK-Birthdy-Colloquium Sept

19 Nested Appliction Conditions List of Exmples: Ehrig HJK-Birthdy-Colloquium Sept

20 GRA-GRA & ALG-SPEC Attributed Grphs [LKW93, HKT02] Attributed Grph AG = (G, D) G = E-Grph with Grph & Dt Nodes D = DSIG-Algebr with D-dt = Dt Nodes Typed Attr.Grphs = Adhesive HLR [EPT 04] DPO-Approch for Typed Attr.Grphs [EEPT06] Applictions Visul Modelling Model Trnsformtion Ehrig HJK-Birthdy-Colloquium Sept

21 Model Trnsformtion bsed on Grph Trnsformtion Attributed grph trnsformtion system AGTS=(ATG,Prod) ATG: ttributed type grph Prod: set of trnsformtion productions Typing for model trnsformtions Ehrig HJK-Birthdy-Colloquium Sept

22 ModTrfo Typegrph `Sttechrts to Petri Nets Ehrig HJK-Birthdy-Colloquium Sept

23 Alterntives for DPO-Approch L K R m (1) (2) G D H NLC, Hyperedge, SPO, Logicl, 2-Struct, Progr. Gr-Gr Hndbook of GRA-GRA [Roz 97] DPO, DPB, DPO-BC, SqPO, MPOC (1) DELETE & (2) ADD Wht bout (1) ADD & (2) DELETE? Ehrig HJK-Birthdy-Colloquium Sept

24 Cospn-DPO Rules & Trfos L K R G m (1) (2) D H Cospn-DPO Trfo G > H vi (p,m) Rules re Cospns p = ( L K R) DPO (1) = ADD & DPO (2) = DELETE Appliction : Reconfigurble Petri Nets Problem : G > H vi (p,m) s Cospn-DPO Trfo? G H vi (p,m) s DPO Trfo Ehrig HJK-Birthdy-Colloquium Sept

25 Proof of Equivlence L K K R G D D H Top PO & PB by Reltionship of p & p Bottom PO & PB by Reltionship of D & D G > H vi (p,m) Front Left & Right PO Bck Left & Right PO G H vi (p,m) Ehrig HJK-Birthdy-Colloquium Sept

26 CONCLUSION : From GRA-GRA to ALG-SPEC & Bck Agin CAT AUT UnivTheory of Automt GRA-GRA Locl CR & Prllelism ALG-SPEC ACT-Approch CAT ALG-SPEC Institutions CAT GRA-TRA Adhesive HLR System GRA-GRA Extensions Constrints & Control GRA-GRA & ALG-SPEC Typed Attr.Gr-Tr Ehrig HJK-Birthdy-Colloquium Sept

27 Joint History of HJK & HE HJK Mth Stud t TU Berlin HJK Ass / AssProf t CS-Dept TUB HJK Prof U Bremen ACT-Project TUB / UB Since 1990 Joint Europen Projects COMPASS COMPUGRAPH GETGRATS APPLIGRAPH SEGRAVIS Ehrig HJK-Birthdy-Colloquium Sept

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