Introduction Attributed Graphs Rule Specification Implementation Conclusion. AGG and PROGRES. Bernhard Scholz. 27th January 2006.

Transcription

1 AGG and PROGRES 27th January 2006 AGG and PROGRES 1

2 Motivation AGG Attributed Graph Grammar System TU Berlin PROGRES PROgrammed Graph REwriting Systems RTWH Aachen How do these systems work? Graph model Data structures Rule specification Algorithms AGG and PROGRES 2

3 Motivation AGG Attributed Graph Grammar System TU Berlin PROGRES PROgrammed Graph REwriting Systems RTWH Aachen How do these systems work? Graph model Data structures Rule specification Algorithms AGG and PROGRES 2

4 Motivation Introduction Motivation Attributed Graphs Graphs Attributed Graphs Rule Specification General Definition AGG Specific PROGRES Specific Implementation Pattern Matching General Features Screenshots Conclusion Questions AGG and PROGRES 3

5 Graphs Graph A directed, node and edge labelled graph is a system G = (G V, G E, L, s, t, l) of nodes G V, edges G E (G V G E = ), labels (or types) L, mappings s, t : G E G V and l : G V G E L. Definition allows multiple edges between the same nodes. AGG and PROGRES 4

6 Graphs Example Labels L = {Shipping Company, Truck, Container, owns, on} AGG and PROGRES 5

7 Attributed Graphs Approaches to represent additional information Here: The contents of the container e.g. peanuts. By additional nodes and edges Pure graph approaches are not useful. AGG and PROGRES 6

8 Attributed Graphs Approaches to represent additional information Here: The contents of the container e.g. peanuts. By additional nodes and edges Pure graph approaches are not useful. AGG and PROGRES 6

9 Attributed Graphs Approaches to represent additional information Here: The contents of the container e.g. peanuts. By additional nodes and edges Pure graph approaches are not useful. AGG and PROGRES 6

10 Attributed Graphs Attributed Graphs Attributes Each graph object (nodes and edges) can have a list of attributes. Attribute: name, type, value Example: String content = "Peanuts" For all graph objects: same label same attribute declarations (name and type). AGG and PROGRES 7

11 Attributed Graphs Example AGG and PROGRES 8

12 General Definition Graph Rewrite Rule Rule Single pushout approach A (partial) morphism r : L R for graphs L, R. Structure and label (type) preserving. e dom(r E ) : r V (s L (e)) = s R (r E (e)), r V (t L (e)) = t R (r E (e)), o dom(r) : l L (o) = l R (r(o)) Partiality is needed to differ: objects to be deleted / objects to be preserved. AGG and PROGRES 9

13 General Definition Numbers (1:, 2:, 3:, 5:) specify the partial morphism. AGG and PROGRES 10

14 General Definition Attributed Graph Rewrite Rule AGG and PROGRES 11

15 General Definition Rule Application AGG and PROGRES 12

16 AGG Specific AGG Conditions for Rule Application Match conditions A total morphism m : L G that preserves structure e L E : m V (s L (e)) = s G (m E (e)), m V (t L (e)) = t G (m E (e)) and types o L V L E : l L (o) = l G (m(o)) Attribute value conditions (e.g. weight < 10.0) Negative application conditions (NACs) Ability to express which graph objects are not desired in the environment of a match. AGG and PROGRES 13

17 AGG Specific NAC Negative Application Condition AGG and PROGRES 14

18 AGG Specific NAC Negative Application Condition Formal specification NAC: A (partial) morphism l : L N for graphs L, N. An NAC is satisfied by a match m : L G iff we cannot find a total morphism n : N G such that n l = m dom(l) Intuitionally... NAC fails if the graph N can be matched onto G such that the images of L and N are at the same place. AGG and PROGRES 15

19 AGG Specific NAC Negative Application Condition Formal specification NAC: A (partial) morphism l : L N for graphs L, N. An NAC is satisfied by a match m : L G iff we cannot find a total morphism n : N G such that n l = m dom(l) Intuitionally... NAC fails if the graph N can be matched onto G such that the images of L and N are at the same place. AGG and PROGRES 15

20 PROGRES Specific PROGRES Extended Rule Elements PROGRES rules allow the use of nondeterministic and/or partial variables. Cardinality for nodes single node non-empty set of nodes optional node optional set of nodes AGG and PROGRES 16

21 PROGRES Specific Example AGG and PROGRES 17

22 PROGRES Specific PROGRES Production vs. Transaction Production left- and right-hand side graph pattern, in/out parameters. Transaction imperative structure, calls tests and productions. allows (guarded) alternatives, loops,..., for example: AGG and PROGRES 18

23 Pattern Matching PROGRES Pattern Matching with Search Plan Search plan pattern graph, operation graph calculated as soon as the rule has been specified, i.e. at compile time does not account for the current working graph AGG and PROGRES 19

24 Pattern Matching AGG Pattern Matching as CSP Constraint Satisfaction Problem well known from artifical intelligence a lot of implementations (backtracking, backjumping,... ) Variable order / search plan is calculated during application. first-fail principle partial match = partial assignment of CSP variables. frequency of object types? AGG and PROGRES 20

25 General Features AGG Implementation written in Java. 1:1 image of the theoretical formalism. extended by some redundancies. Advantages easy writing, understanding and expanding of the code. easy proof of correctness. easy access by Java API. Disadvantages bad time performance. huge Java overhead. AGG and PROGRES 21

26 General Features AGG Implementation written in Java. 1:1 image of the theoretical formalism. extended by some redundancies. Advantages easy writing, understanding and expanding of the code. easy proof of correctness. easy access by Java API. Disadvantages bad time performance. huge Java overhead. AGG and PROGRES 21

27 General Features PROGRES Implementation written in Modula optimized for performance Advantages performs lots of rule applications in huge graphs very fast. provides sophisticated language constructs. best horror GUI ever :-). Disadvantages has a usability of ± zero. AGG and PROGRES 22

28 General Features PROGRES Implementation written in Modula optimized for performance Advantages performs lots of rule applications in huge graphs very fast. provides sophisticated language constructs. best horror GUI ever :-). Disadvantages has a usability of ± zero. AGG and PROGRES 22

29 General Features PROGRES Implementation written in Modula optimized for performance Advantages performs lots of rule applications in huge graphs very fast. provides sophisticated language constructs. best horror GUI ever :-). Disadvantages has a usability of ± zero. AGG and PROGRES 22

30 Screenshots AGG and PROGRES 23

31 Screenshots AGG and PROGRES 24

32 Questions Thanks for your attention! Any questions? AGG and PROGRES 25