Fundamentals of algebraic graph transformation:
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2006
|
| Schriftenreihe: | Monographs in theoretical computer science
|
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis Inhaltsverzeichnis |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | XIII, 388 S. Ill., graph. Darst. |
| ISBN: | 3540311874 9783540311874 9783642068317 |
Internformat
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| 245 | 1 | 0 | |a Fundamentals of algebraic graph transformation |c H. Ehrig ... |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2006 | |
| 300 | |a XIII, 388 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 0 | |a Monographs in theoretical computer science | |
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 650 | 4 | |a Grammaires de graphes | |
| 650 | 4 | |a Informatique - Mathématiques | |
| 650 | 4 | |a Categories (Mathematics) | |
| 650 | 4 | |a Graph grammars | |
| 650 | 4 | |a Graph theory | |
| 650 | 4 | |a Morphisms (Mathematics) | |
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Datensatz im Suchindex
| _version_ | 1804135344872882176 |
|---|---|
| adam_text | H. EHRIG YY K. EHRIG
U. PRANGE YY G. TAENTZER
FUNDAMENTALS
OF ALGEBRAIC
GRAPH TRANSFORMATION
WITH 41 FIGURES
4U SPRINGER
CONTENTS
PART I INTRODUCTIO
N T
O GRAPH TRANSFORMATION SYSTEM
S
1 GENERAL INTRODUCTIO
N
5
1.1 GENERAL OVERVIEW OF GRAPH GRAMMARS AND GRAPH
TRANSFORMATION 5
1.1.1 WHAT IS GRAPH TRANSFORMATION? 6
1.1.2 AIMS AND PARADIGMS OF GRAPH TRANSFORMATION 6
1.1.3 OVERVIEW OF VARIOUS APPROACHES 9
1.2 THE MAIN IDEAS OF THE ALGEBRAIC GRAPH TRANSFORMATION
APPROACH 10
1.2.1 THE DPO APPROACH 11
1.2.2 THE ALGEBRAIC ROOTS 12
1.2.3 PROM THE DPO TO THE SPO APPROACH 13
1.2.4 FROM GRAPHS T
O HIGH-LEVEL STRUCTURES 14
1.3 THE CHAPTERS OF THIS BOOK AND THE MAIN RESULTS 15
1.3.1 PAR
T I: INTRODUCTION T
O GRAPH TRANSFORMATION SYSTEMS . 15
1.3.2 PART II: ADHESIVE HLR CATEGORIES AND SYSTEMS 15
1.3.3 PAR
T
III:
TYPED ATTRIBUTED GRAPH TRANSFORMATION
SYSTEMS 16
1.3.4 PAR
T IV: CASE STUDY AND TOOL SUPPORT 17
1.3.5 APPENDICES 17
1.3.6 HINTS FOR READING THIS BOOK 17
1.4 BIBLIOGRAPHIC NOTES AND FURTHER TOPICS 17
1.4.1 CONCEPTS OF GRAPH GRAMMARS AND GRAPH
TRANSFORMATION SYSTEMS 17
1.4.2 APPLICATION AREAS OF GRAPH TRANSFORMATION SYSTEMS ..
. 19
1.4.3 LANGUAGES AND TOOLS FOR GRAPH TRANSFORMATION SYSTEMS 19
1.4.4 FUTURE WORK 20
X CONTENTS
2 GRAPHS
, TYPE
D GRAPHS
, AN
D TH
E GLUIN
G CONSTRUCTIO
N
21
2.1 GRAPHS AND TYPED GRAPHS 21
2.2 INTRODUCTION TO CATEGORIES 25
2.3 PUSHOUTS AS A GLUING CONSTRUCTION 29
2.4 PULLBACKS AS THE DUAL CONSTRUCTION OF PUSHOUTS 33
3 GRAP
H TRANSFORMATIO
N SYSTEM
S
37
3.1 BASIC DEFINITIONS FOR GT SYSTEMS 37
3.2 CONSTRUCTION OF GRAPH TRANSFORMATIONS 43
3.3 LOCAL (PHURCH-ROSSER AND PARALLELISM THEOREMS FOR GT
SYSTEMS 47
3.4 OVERVIEW OF SOME OTHER MAIN RESULTS FOR GT SYSTEMS 53
3.4.1 CONCURRENCY THEOREM 54
3.4.2 EMBEDDING AND EXTENSION THEOREMS 56
3.4.3 CONFLUENCE, LOCAL CONFLUENCE, TERMINATION, AND
CRITICAL PAIRS 59
3.4.4 FUNCTIONAL BEHAVIOR OF GT SYSTEMS AND TERMINATION
ANALYSIS 62
3.5 GRAPH CONSTRAINTS AND APPLICATION CONDITIONS 64
PAR
T II ADHESIV
E HIGH-LEVE
L REPLACEMEN
T CATEGORIE
S AN
D SYSTEM
S
4 ADHESIV
E HIGH-LEVE
L REPLACEMEN
T CATEGORIE
S
77
4.1 VAN KAMPEN SQUARES AND ADHESIVE CATEGORIES 77
4.2 ADHESIVE HLR CATEGORIES 86
4.3 HLR PROPERTIES OF ADHESIVE HLR CATEGORIES 96
5 ADHESIV
E HIGH-LEVE
L REPLACEMEN
T SYSTEM
S
101
5.1 BASIC CONCEPTS OF ADHESIVE HLR SYSTEMS 101
5.2 INSTANTIATION OF ADHESIVE HLR SYSTEMS 105
5.2.1 GRAPH AND TYPED GRAPH TRANSFORMATION SYSTEMS 106
5.2.2 HYPERGRAPH TRANSFORMATION SYSTEMS 106
5.2.3 PETR
I NET TRANSFORMATION SYSTEMS 107
5.2.4 ALGEBRAIC SPECIFICATION TRANSFORMATION SYSTEMS 108
5.2.5 TYPED ATTRIBUTED GRAPH TRANSFORMATION SYSTEMS 108
5.3 THE LOCAL CHURCH-ROSSER AND PARALLELISM THEOREMS 109
5.4 CONCURRENCY THEOREM AND PAIR FACTORIZATION
117
6 EMBEDDIN
G AN
D LOCA
L CONFLUENC
E
125
6.1 INITIAL PUSHOUTS AND THE GLUING CONDITION 125
6.2 EMBEDDING AND EXTENSION THEOREMS 130
6.3 CRITICAL PAIRS 140
6.4 LOCAL CONFLUENCE THEOREM 144
CONTENTS XI
CONSTRAINT
S AND APPLICATIO
N CONDITION
S
151
7.1 DEFINITION OF CONSTRAINTS AND APPLICATION CONDITIONS 152
7.2 CONSTRUCTION OF APPLICATION CONDITIONS FROM CONSTRAINTS 156
7.3 CONSTRUCTION OF LEFT FROM RIGHT APPLICATION CONDITIONS 160
7.4 GUARANTEEING AND PRESERVATION OF CONSTRAINTS 164
PART II
I TYPE
D ATTRIBUTE
D GRAPH TRANSFORMATION SYSTEM
S
8 TYPE
D ATTRIBUTE
D GRAPHS
171
8.1 ATTRIBUTED GRAPHS AND TYPING 172
8.2 PUSHOUTS AS A GLUING CONSTRUCTION OF ATTRIBUTED GRAPHS 177
8.3 PULLBACKS OF ATTRIBUTED GRAPHS 178
9 TYPE
D ATTRIBUTE
D GRAPH TRANSFORMATION SYSTEM
S
181
9.1 BASIC CONCEPTS FOR TYPED AGT SYSTEMS 181
9.2 CONSTRUCTION OF TYPED ATTRIBUTED GRAPH TRANSFORMATIONS ...
. 188
9.3 LOCAL CHURCH-ROSSER AND PARALLELISM THEOREM FOR TYPED
AGT SYSTEMS 190
9.4 CONCURRENCY THEOREM AND PAIR FACTORIZATION FOR TYPED
AGT SYSTEMS 194
9.4.1 PAIR FACTORIZATIONS 194
9.4.2 CONCURRENCY THEOREM 201
10 EMBEDDIN
G AND LOCAL CONFLUENCE FOR TYPE
D AG
T SYSTEM
S
207
10.1 EMBEDDING AND EXTENSION THEOREMS FOR TYPED AGT SYSTEMS 207
10.2 CRITICAL PAIRS FOR TYPED AGT SYSTEMS 215
10.3 LOCAL CONFLUENCE THEOREM FOR TYPED AGT SYSTEMS 218
11 ADHESIV
E HLR CATEGORIE
S FOR TYPE
D ATTRIBUTE
D GRAPHS
..
. 221
11.1 ATTRIBUTED GRAPH STRUCTURE SIGNATURES AND TYPED ATTRIBUTED
GRAPHS 222
11.2 DEFINITION OF CONCRETE ADHESIVE HLR CATEGORIES 225
11.3 VERIFICATION OF THE MAIN RESULTS FOR TYPED AGT SYSTEMS 232
12 CONSTRAINTS
, APPLICATIO
N CONDITION
S AND TERMINATIO
N FOR
TAG
T SYSTEM
S
237
12.1 CONSTRAINTS AND APPLICATION CONDITIONS FOR TYPED AGT
SYSTEMS 237
12.2 EQUIVALENCE OF CONSTRAINTS AND APPLICATION CONDITIONS 242
12.3 TERMINATION CRITERIA FOR LAYERED TYPED ATTRIBUTED GRAPH
GRAMMARS 249
XII CONTENTS
13 TYPE
D ATTRIBUTE
D GRAPH TRANSFORMATION WIT
H INHERITANCE
. 259
13.1 ATTRIBUTED TYPE GRAPHS WITH INHERITANCE 260
13.2 ATTRIBUTED CLAN MORPHISMS 265
13.3 PRODUCTIONS AND ATTRIBUTED GRAPH TRANSFORMATION WITH
INHERITANCE 271
13.4 EQUIVALENCE OF CONCEPTS WITH AND WITHOUT INHERITANCE 278
PART IV CASE STUD
Y O
N MODE
L TRANSFORMATION, AND
TOOL SUPPORT
PR
AGG
I
14 CASE STUD
Y O
N MODE
L TRANSFORMATION
287
14.1 MODEL TRANSFORMATION BY TYPED ATTRIBUTED GRAPH
TRANSFORMATION 287
14.2 MODEL TRANSFORMATION FROM STATECHARTS T
O PETRI NETS 288
14.2.1 SOURCE MODELING LANGUAGE: SIMPLE VERSION OF UML
STATECHARTS 289
14.2.2 TARGET MODELING LANGUAGE: PETRI NETS 290
14.2.3 MODEL TRANSFORMATION 293
14.2.4 TERMINATION ANALYSIS OF THE MODEL TRANSFORMATION ...
. 301
14.3 FURTHER CASE STUDIES 303
14.3.1 FROM THE GENERAL RESOURCE MODEL TO PETRI NETS 303
14.3.2 FROM PROCESS INTERACTION DIAGRAMS TO TIMED PETRI NETS 304
14.4 CONCLUSION 304
15 IMPLEMENTATIO
N OF TYPE
D ATTRIBUTE
D GRAPH
TRANSFORMATION BY AGG
305
15.1 LANGUAGE CONCEPTS OF AGG 305
15.1.1 GRAPHS 306
15.1.2 TYPING FACILITIES 306
15.1.3 NODE AND EDGE ATTRIBUTES 307
15.1.4 RULES AND MATCHES 308
15.1.5 GRAPH TRANSFORMATIONS 310
15.1.6 GRAPH GRAMMARS 312
15.2 ANALYSIS TECHNIQUES IMPLEMENTED IN AGG 312
15.2.1 GRAPH CONSTRAINTS 312
15.2.2 CRITICAL PAIR ANALYSIS 313
15.2.3 GRAPH PARSING 317
15.2.4 TERMINATION 318
15.3 TOOL ENVIRONMENT OF AGG 318
15.3.1 VISUAL ENVIRONMENT 320
15.3.2 GRAPH TRANSFORMATION ENGINE 321
15.3.3 TOOL INTEGRATION 322
15.4 CONCLUSION 322
CONTENTS
XIII
APPENDICE
S
A A SHORT INTRODUCTIO
N T
O CATEGOR
Y THEOR
Y
329
A.I CATEGORIES 329
A.2 CONSTRUCTION OF CATEGORIES, AND DUALITY 330
A.3 MONOMORPHISMS, EPIMORPHISMS, AND ISOMORPHISMS 332
A.4 PUSHOUTS AND PULLBACKS 334
A.5 BINARY COPRODUCTS AND INITIAL OBJECTS 340
A.6 FUNCTORS, FUNCTOR CATEGORIES, AND COMMA CATEGORIES 344
A.7 ISOMORPHISM AND EQUIVALENCE OF CATEGORIES 350
B A SHORT INTRODUCTIO
N T
O SIGNATURE
S AND ALGEBRA
S
353
B.I
ALGEBRAIC SIGNATURES 353
B.2 ALGEBRAS 355
B.3 TERMS AND TERM EVALUATION 357
C DETAILE
D PROOF
S
359
C.I COMPLETION OF PROOF OF FACT 4.24 359
C.2 PROOF OF LEMMA 6.25 361
C.3 COMPLETION OF PROOF OF THEOREM 11.3 362
C.3.1 WELL-DEFINEDNESS 362
C.3.2 FUNCTORS 364
C.3.3 ISOMORPHISM 365
C.4 PROOF OF LEMMA 11.17 366
C.4.1 WELL-DEFINEDNESS 366
C.4.2 PUSHOUT PROPERTY 367
C.4.3 INITIAL PUSHOUT 368
C.5 PROOF OF THEOREM 13.12 370
C.6 PROOF OF LEMMA 13.20 373
REFERENCES
377
INDE
X
385
|
| adam_txt |
H. EHRIG YY K. EHRIG
U. PRANGE YY G. TAENTZER
FUNDAMENTALS
OF ALGEBRAIC
GRAPH TRANSFORMATION
WITH 41 FIGURES
4U SPRINGER
CONTENTS
PART I INTRODUCTIO
N T
O GRAPH TRANSFORMATION SYSTEM
S
1 GENERAL INTRODUCTIO
N
5
1.1 GENERAL OVERVIEW OF GRAPH GRAMMARS AND GRAPH
TRANSFORMATION 5
1.1.1 WHAT IS GRAPH TRANSFORMATION? 6
1.1.2 AIMS AND PARADIGMS OF GRAPH TRANSFORMATION 6
1.1.3 OVERVIEW OF VARIOUS APPROACHES 9
1.2 THE MAIN IDEAS OF THE ALGEBRAIC GRAPH TRANSFORMATION
APPROACH 10
1.2.1 THE DPO APPROACH 11
1.2.2 THE ALGEBRAIC ROOTS 12
1.2.3 PROM THE DPO TO THE SPO APPROACH 13
1.2.4 FROM GRAPHS T
O HIGH-LEVEL STRUCTURES 14
1.3 THE CHAPTERS OF THIS BOOK AND THE MAIN RESULTS 15
1.3.1 PAR
T I: INTRODUCTION T
O GRAPH TRANSFORMATION SYSTEMS . 15
1.3.2 PART II: ADHESIVE HLR CATEGORIES AND SYSTEMS 15
1.3.3 PAR
T
III:
TYPED ATTRIBUTED GRAPH TRANSFORMATION
SYSTEMS 16
1.3.4 PAR
T IV: CASE STUDY AND TOOL SUPPORT 17
1.3.5 APPENDICES 17
1.3.6 HINTS FOR READING THIS BOOK 17
1.4 BIBLIOGRAPHIC NOTES AND FURTHER TOPICS 17
1.4.1 CONCEPTS OF GRAPH GRAMMARS AND GRAPH
TRANSFORMATION SYSTEMS 17
1.4.2 APPLICATION AREAS OF GRAPH TRANSFORMATION SYSTEMS .
. 19
1.4.3 LANGUAGES AND TOOLS FOR GRAPH TRANSFORMATION SYSTEMS 19
1.4.4 FUTURE WORK 20
X CONTENTS
2 GRAPHS
, TYPE
D GRAPHS
, AN
D TH
E GLUIN
G CONSTRUCTIO
N
21
2.1 GRAPHS AND TYPED GRAPHS 21
2.2 INTRODUCTION TO CATEGORIES 25
2.3 PUSHOUTS AS A GLUING CONSTRUCTION 29
2.4 PULLBACKS AS THE DUAL CONSTRUCTION OF PUSHOUTS 33
3 GRAP
H TRANSFORMATIO
N SYSTEM
S
37
3.1 BASIC DEFINITIONS FOR GT SYSTEMS 37
3.2 CONSTRUCTION OF GRAPH TRANSFORMATIONS 43
3.3 LOCAL (PHURCH-ROSSER AND PARALLELISM THEOREMS FOR GT
SYSTEMS 47
3.4 OVERVIEW OF SOME OTHER MAIN RESULTS FOR GT SYSTEMS 53
3.4.1 CONCURRENCY THEOREM 54
3.4.2 EMBEDDING AND EXTENSION THEOREMS 56
3.4.3 CONFLUENCE, LOCAL CONFLUENCE, TERMINATION, AND
CRITICAL PAIRS 59
3.4.4 FUNCTIONAL BEHAVIOR OF GT SYSTEMS AND TERMINATION
ANALYSIS 62
3.5 GRAPH CONSTRAINTS AND APPLICATION CONDITIONS 64
PAR
T II ADHESIV
E HIGH-LEVE
L REPLACEMEN
T CATEGORIE
S AN
D SYSTEM
S
4 ADHESIV
E HIGH-LEVE
L REPLACEMEN
T CATEGORIE
S
77
4.1 VAN KAMPEN SQUARES AND ADHESIVE CATEGORIES 77
4.2 ADHESIVE HLR CATEGORIES 86
4.3 HLR PROPERTIES OF ADHESIVE HLR CATEGORIES 96
5 ADHESIV
E HIGH-LEVE
L REPLACEMEN
T SYSTEM
S
101
5.1 BASIC CONCEPTS OF ADHESIVE HLR SYSTEMS 101
5.2 INSTANTIATION OF ADHESIVE HLR SYSTEMS 105
5.2.1 GRAPH AND TYPED GRAPH TRANSFORMATION SYSTEMS 106
5.2.2 HYPERGRAPH TRANSFORMATION SYSTEMS 106
5.2.3 PETR
I NET TRANSFORMATION SYSTEMS 107
5.2.4 ALGEBRAIC SPECIFICATION TRANSFORMATION SYSTEMS 108
5.2.5 TYPED ATTRIBUTED GRAPH TRANSFORMATION SYSTEMS 108
5.3 THE LOCAL CHURCH-ROSSER AND PARALLELISM THEOREMS 109
5.4 CONCURRENCY THEOREM AND PAIR FACTORIZATION
117
6 EMBEDDIN
G AN
D LOCA
L CONFLUENC
E
125
6.1 INITIAL PUSHOUTS AND THE GLUING CONDITION 125
6.2 EMBEDDING AND EXTENSION THEOREMS 130
6.3 CRITICAL PAIRS 140
6.4 LOCAL CONFLUENCE THEOREM 144
CONTENTS XI
CONSTRAINT
S AND APPLICATIO
N CONDITION
S
151
7.1 DEFINITION OF CONSTRAINTS AND APPLICATION CONDITIONS 152
7.2 CONSTRUCTION OF APPLICATION CONDITIONS FROM CONSTRAINTS 156
7.3 CONSTRUCTION OF LEFT FROM RIGHT APPLICATION CONDITIONS 160
7.4 GUARANTEEING AND PRESERVATION OF CONSTRAINTS 164
PART II
I TYPE
D ATTRIBUTE
D GRAPH TRANSFORMATION SYSTEM
S
8 TYPE
D ATTRIBUTE
D GRAPHS
171
8.1 ATTRIBUTED GRAPHS AND TYPING 172
8.2 PUSHOUTS AS A GLUING CONSTRUCTION OF ATTRIBUTED GRAPHS 177
8.3 PULLBACKS OF ATTRIBUTED GRAPHS 178
9 TYPE
D ATTRIBUTE
D GRAPH TRANSFORMATION SYSTEM
S
181
9.1 BASIC CONCEPTS FOR TYPED AGT SYSTEMS 181
9.2 CONSTRUCTION OF TYPED ATTRIBUTED GRAPH TRANSFORMATIONS .
. 188
9.3 LOCAL CHURCH-ROSSER AND PARALLELISM THEOREM FOR TYPED
AGT SYSTEMS 190
9.4 CONCURRENCY THEOREM AND PAIR FACTORIZATION FOR TYPED
AGT SYSTEMS 194
9.4.1 PAIR FACTORIZATIONS 194
9.4.2 CONCURRENCY THEOREM 201
10 EMBEDDIN
G AND LOCAL CONFLUENCE FOR TYPE
D AG
T SYSTEM
S
207
10.1 EMBEDDING AND EXTENSION THEOREMS FOR TYPED AGT SYSTEMS 207
10.2 CRITICAL PAIRS FOR TYPED AGT SYSTEMS 215
10.3 LOCAL CONFLUENCE THEOREM FOR TYPED AGT SYSTEMS 218
11 ADHESIV
E HLR CATEGORIE
S FOR TYPE
D ATTRIBUTE
D GRAPHS
.
. 221
11.1 ATTRIBUTED GRAPH STRUCTURE SIGNATURES AND TYPED ATTRIBUTED
GRAPHS 222
11.2 DEFINITION OF CONCRETE ADHESIVE HLR CATEGORIES 225
11.3 VERIFICATION OF THE MAIN RESULTS FOR TYPED AGT SYSTEMS 232
12 CONSTRAINTS
, APPLICATIO
N CONDITION
S AND TERMINATIO
N FOR
TAG
T SYSTEM
S
237
12.1 CONSTRAINTS AND APPLICATION CONDITIONS FOR TYPED AGT
SYSTEMS 237
12.2 EQUIVALENCE OF CONSTRAINTS AND APPLICATION CONDITIONS 242
12.3 TERMINATION CRITERIA FOR LAYERED TYPED ATTRIBUTED GRAPH
GRAMMARS 249
XII CONTENTS
13 TYPE
D ATTRIBUTE
D GRAPH TRANSFORMATION WIT
H INHERITANCE
. 259
13.1 ATTRIBUTED TYPE GRAPHS WITH INHERITANCE 260
13.2 ATTRIBUTED CLAN MORPHISMS 265
13.3 PRODUCTIONS AND ATTRIBUTED GRAPH TRANSFORMATION WITH
INHERITANCE 271
13.4 EQUIVALENCE OF CONCEPTS WITH AND WITHOUT INHERITANCE 278
PART IV CASE STUD
Y O
N MODE
L TRANSFORMATION, AND
TOOL SUPPORT
\PR
AGG
I
14 CASE STUD
Y O
N MODE
L TRANSFORMATION
287
14.1 MODEL TRANSFORMATION BY TYPED ATTRIBUTED GRAPH
TRANSFORMATION 287
14.2 MODEL TRANSFORMATION FROM STATECHARTS T
O PETRI NETS 288
14.2.1 SOURCE MODELING LANGUAGE: SIMPLE VERSION OF UML
STATECHARTS 289
14.2.2 TARGET MODELING LANGUAGE: PETRI NETS 290
14.2.3 MODEL TRANSFORMATION 293
14.2.4 TERMINATION ANALYSIS OF THE MODEL TRANSFORMATION .
. 301
14.3 FURTHER CASE STUDIES 303
14.3.1 FROM THE GENERAL RESOURCE MODEL TO PETRI NETS 303
14.3.2 FROM PROCESS INTERACTION DIAGRAMS TO TIMED PETRI NETS 304
14.4 CONCLUSION 304
15 IMPLEMENTATIO
N OF TYPE
D ATTRIBUTE
D GRAPH
TRANSFORMATION BY AGG
305
15.1 LANGUAGE CONCEPTS OF AGG 305
15.1.1 GRAPHS 306
15.1.2 TYPING FACILITIES 306
15.1.3 NODE AND EDGE ATTRIBUTES 307
15.1.4 RULES AND MATCHES 308
15.1.5 GRAPH TRANSFORMATIONS 310
15.1.6 GRAPH GRAMMARS 312
15.2 ANALYSIS TECHNIQUES IMPLEMENTED IN AGG 312
15.2.1 GRAPH CONSTRAINTS 312
15.2.2 CRITICAL PAIR ANALYSIS 313
15.2.3 GRAPH PARSING 317
15.2.4 TERMINATION 318
15.3 TOOL ENVIRONMENT OF AGG 318
15.3.1 VISUAL ENVIRONMENT 320
15.3.2 GRAPH TRANSFORMATION ENGINE 321
15.3.3 TOOL INTEGRATION 322
15.4 CONCLUSION 322
CONTENTS
XIII
APPENDICE
S
A A SHORT INTRODUCTIO
N T
O CATEGOR
Y THEOR
Y
329
A.I CATEGORIES 329
A.2 CONSTRUCTION OF CATEGORIES, AND DUALITY 330
A.3 MONOMORPHISMS, EPIMORPHISMS, AND ISOMORPHISMS 332
A.4 PUSHOUTS AND PULLBACKS 334
A.5 BINARY COPRODUCTS AND INITIAL OBJECTS 340
A.6 FUNCTORS, FUNCTOR CATEGORIES, AND COMMA CATEGORIES 344
A.7 ISOMORPHISM AND EQUIVALENCE OF CATEGORIES 350
B A SHORT INTRODUCTIO
N T
O SIGNATURE
S AND ALGEBRA
S
353
B.I
ALGEBRAIC SIGNATURES 353
B.2 ALGEBRAS 355
B.3 TERMS AND TERM EVALUATION 357
C DETAILE
D PROOF
S
359
C.I COMPLETION OF PROOF OF FACT 4.24 359
C.2 PROOF OF LEMMA 6.25 361
C.3 COMPLETION OF PROOF OF THEOREM 11.3 362
C.3.1 WELL-DEFINEDNESS 362
C.3.2 FUNCTORS 364
C.3.3 ISOMORPHISM 365
C.4 PROOF OF LEMMA 11.17 366
C.4.1 WELL-DEFINEDNESS 366
C.4.2 PUSHOUT PROPERTY 367
C.4.3 INITIAL PUSHOUT 368
C.5 PROOF OF THEOREM 13.12 370
C.6 PROOF OF LEMMA 13.20 373
REFERENCES
377
INDE
X
385 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author_GND | (DE-588)107905582 |
| building | Verbundindex |
| bvnumber | BV021575831 |
| callnumber-first | Q - Science |
| callnumber-label | QA267 |
| callnumber-raw | QA267.3 |
| callnumber-search | QA267.3 |
| callnumber-sort | QA 3267.3 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 890 ST 130 |
| ctrlnum | (OCoLC)181533205 (DE-599)BVBBV021575831 |
| dewey-full | 511/.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511/.5 |
| dewey-search | 511/.5 |
| dewey-sort | 3511 15 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| discipline_str_mv | Informatik Mathematik |
| format | Book |
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| id | DE-604.BV021575831 |
| illustrated | Illustrated |
| index_date | 2024-07-02T14:40:00Z |
| indexdate | 2024-07-09T20:39:01Z |
| institution | BVB |
| isbn | 3540311874 9783540311874 9783642068317 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014791577 |
| oclc_num | 181533205 |
| open_access_boolean | |
| owner | DE-703 DE-29T DE-706 DE-384 DE-634 DE-83 DE-473 DE-BY-UBG DE-898 DE-BY-UBR |
| owner_facet | DE-703 DE-29T DE-706 DE-384 DE-634 DE-83 DE-473 DE-BY-UBG DE-898 DE-BY-UBR |
| physical | XIII, 388 S. Ill., graph. Darst. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Springer |
| record_format | marc |
| series2 | Monographs in theoretical computer science |
| spelling | Fundamentals of algebraic graph transformation H. Ehrig ... Berlin [u.a.] Springer 2006 XIII, 388 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Monographs in theoretical computer science Hier auch später erschienene, unveränderte Nachdrucke Grammaires de graphes Informatique - Mathématiques Categories (Mathematics) Graph grammars Graph theory Morphisms (Mathematics) Graphersetzungssystem (DE-588)4274073-3 gnd rswk-swf Formale Spezifikationstechnik (DE-588)4299725-2 gnd rswk-swf Graphersetzungssystem (DE-588)4274073-3 s Formale Spezifikationstechnik (DE-588)4299725-2 s DE-604 Ehrig, Hartmut 1944-2016 Sonstige (DE-588)107905582 oth Erscheint auch als Online-Ausgabe 978-3-540-31188-1 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=2760853&prov=M&dok_var=1&dok_ext=htm Inhaltstext http://www3.ub.tu-berlin.de/ihv/001708242.pdf Inhaltsverzeichnis DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014791577&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Fundamentals of algebraic graph transformation Grammaires de graphes Informatique - Mathématiques Categories (Mathematics) Graph grammars Graph theory Morphisms (Mathematics) Graphersetzungssystem (DE-588)4274073-3 gnd Formale Spezifikationstechnik (DE-588)4299725-2 gnd |
| subject_GND | (DE-588)4274073-3 (DE-588)4299725-2 |
| title | Fundamentals of algebraic graph transformation |
| title_auth | Fundamentals of algebraic graph transformation |
| title_exact_search | Fundamentals of algebraic graph transformation |
| title_exact_search_txtP | Fundamentals of algebraic graph transformation |
| title_full | Fundamentals of algebraic graph transformation H. Ehrig ... |
| title_fullStr | Fundamentals of algebraic graph transformation H. Ehrig ... |
| title_full_unstemmed | Fundamentals of algebraic graph transformation H. Ehrig ... |
| title_short | Fundamentals of algebraic graph transformation |
| title_sort | fundamentals of algebraic graph transformation |
| topic | Grammaires de graphes Informatique - Mathématiques Categories (Mathematics) Graph grammars Graph theory Morphisms (Mathematics) Graphersetzungssystem (DE-588)4274073-3 gnd Formale Spezifikationstechnik (DE-588)4299725-2 gnd |
| topic_facet | Grammaires de graphes Informatique - Mathématiques Categories (Mathematics) Graph grammars Graph theory Morphisms (Mathematics) Graphersetzungssystem Formale Spezifikationstechnik |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=2760853&prov=M&dok_var=1&dok_ext=htm http://www3.ub.tu-berlin.de/ihv/001708242.pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014791577&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT ehrighartmut fundamentalsofalgebraicgraphtransformation |