Modelling Constraints

Transcription

1 Modelling Constraints by Constraining the Models Gerrit Renker RGU Constraints Group The Robert Gordon University, Aberdeen Modelling Constraints p.1/42

2 Talk Outline 4 Blocks: Purpose and Concept UML and OCL Modelling Example Outlook and Conclusion Modelling Constraints p.2/42

3 Part 1 Purpose and Concept Modelling Constraints p.3/42

4 Project Goals Goals: (1) modelling support for constraint problems (2) suitable reuse of public standards (UML/OCL,... ) Modelling Constraints p.4/42

5 Motivation little modelling support for (re-) formulating CSPs most problems still solved by experts constraint engineering Problem Description model Implementation informal language machineparseable Modelling Constraints p.5/42

6 Motivation little modelling support for (re-) formulating CSPs most problems still solved by experts constraint engineering Problem Description model Implementation informal language machineparseable structure information gained in analysis varying levels of abstraction different degrees of precision Modelling Constraints p.5/42

7 Classical CSP Definition Constraint CSP: 1..* 1..* Variable 1..* 1 value Domain variables X := {x 1,..., x n } domains D := {d 1,..., d n } constraints C d 1 d 2... d n 1 d n Modelling Constraints p.6/42

8 Classical CSP Definition Constraint CSP: 1..* 1..* Variable 1..* 1 value Domain variables X := {x 1,..., x n } domains D := {d 1,..., d n } constraints C d 1 d 2... d n 1 d n Example: X = {a, b}; D = {N, N} C a < 22 a b b > 12 Modelling Constraints p.6/42

9 Purpose: Why use class models objective: complex data in terse format Modelling Constraints p.7/42

10 Purpose: Why use class models objective: complex data in terse format constraint (hyper-) graph inappropriate q1 q8 q2 q7 q3 q6 q4 q5 Modelling Constraints p.7/42

11 Purpose: Why use class models objective: complex data in terse format constraint (hyper-) graph inappropriate q1 q8 q2 q7 q3 q6 q4 q5 no structural abstraction Modelling Constraints p.7/42

12 Purpose: Modelling Support Support In Other Disciplines: Semantic Data Models in Database Design Modelling Constraints p.8/42

13 Purpose: Modelling Support Support In Other Disciplines: Semantic Data Models in Database Design Semantic Networks in Knowledge Engineering Modelling Constraints p.8/42

14 Purpose: Modelling Support Support In Other Disciplines: Semantic Data Models in Database Design Semantic Networks in Knowledge Engineering Ubiquitous modelling in: Software development Hardware development Engineering in general Modelling Constraints p.8/42

15 Concept Problem Specification Conceptual Model Source Code Modelling Constraints p.9/42

16 Concept Problem Specification natural language Conceptual Model Source Code Modelling Constraints p.9/42

17 Concept Problem Specification natural language Conceptual Model UML Structural Model Entities Source Code Modelling Constraints p.9/42

18 Concept Problem Specification natural language Conceptual Model UML Structural Model Entities OCL Source Code code transformation Algebraic Model Constraints Modelling Constraints p.9/42

19 Part 2a: UML Modelling Constraints p.10/42

20 The 4+1 view of UML Vocabulary Functionality System Assembly Configuration Management Behaviour Design View Use Case View Implementation View Process View Deployment View Scalability Performance Distribution Installation System Topology Modelling Constraints p.11/42

21 The 4+1 view of UML Vocabulary Functionality System Assembly Configuration Management Behaviour Design View Use Case View Implementation View Process View Deployment View Scalability Performance Distribution Installation System Topology Modelling Constraints p.11/42

22 Types of UML Diagrams UML diagrams static view dynamic view class diagram object diagram use case diagram activity diagram statechart diagram implementation diagrams interaction diagrams component diagram deployment diagram sequence diagram collaboration diagram Modelling Constraints p.12/42

23 Types of UML Diagrams UML diagrams static view class diagram object diagram Modelling Constraints p.12/42

24 UML Packaging Behavioral Elements Activity Graphs Model Management Collaborations Use Cases State Machines Common Behavior Foundation Core Extension Mechanisms Data Types Modelling Constraints p.13/42

25 UML Packaging Model Management Foundation Core Data Types Modelling Constraints p.13/42

26 Building Blocks (UML) classification Type 1 Type 2 Complex Type Type 3 Modelling Constraints p.14/42

27 Building Blocks (UML) classification Type 1 Type 2 Complex Type Type 3 association A 1..* * B A 1 C * B A * 1..* C B Modelling Constraints p.14/42

28 Building Blocks (UML) classification Type 1 Type 2 Complex Type Type 3 association A 1..* * B A 1 C * B A * 1..* C B aggregation U A 5, * V W X B Z C Modelling Constraints p.14/42

29 Building Blocks (UML) classification Type 1 Type 2 Complex Type Type 3 association A 1..* * B A 1 C * B A * 1..* C B aggregation U A 5, * V W X B Z C attributes Account c: Money MyType time: Date Modelling Constraints p.14/42

30 Building Blocks (UML) classification Type 1 Type 2 Complex Type Type 3 association A 1..* * B A 1 C * B A * 1..* C B aggregation U A 5, * V W X B Z C attributes Account c: Money MyType time: Date ISA (specialization / generalization) A A1 B BC C Modelling Constraints p.14/42

31 Example IS-A Relation properties explained in terms of structural differences 0..* previous Task part start duration resource tag Begin Foundation Masonry End inheritance of: attributes associations constraints Modelling Constraints p.15/42

32 Part 2b: OCL Modelling Constraints p.16/42

33 The Object Constraint Language (OCL) textual complement to UML first order logic with navigation Modelling Constraints p.17/42

34 The Object Constraint Language (OCL) textual complement to UML first order logic with navigation Use of Types basic types: Real, Integer, Boolean container types: Collection, Set, Sequence, Bag user-defined: Tuple{} e.g. Tuple{ Set(1,3,4), Joe Bloggs, 1999, Sequence(Tuple(2,1}, Tuple{2,-1}) } Modelling Constraints p.17/42

35 The Object Constraint Language (OCL) textual complement to UML first order logic with navigation Use of Types basic types: Real, Integer, Boolean container types: Collection, Set, Sequence, Bag user-defined: Tuple{} e.g. Tuple{ Set(1,3,4), Joe Bloggs, 1999, Sequence(Tuple(2,1}, Tuple{2,-1}) } UML model: all classes accessible Modelling Constraints p.17/42

36 Status of the OCL fully integrated into UML 1.4 several implementations (Boldsoft, Argo/UML,...) Modelling Constraints p.18/42

37 A Flavour of OCL: N-queens NQProblem numqueens: Integer * Nqueen row: Integer column: Integer * others Modelling Constraints p.19/42

38 A Flavour of OCL: N-queens NQProblem numqueens: Integer * Nqueen row: Integer column: Integer * others Attribute access context Nqueen inv: column > 0 and column <= N and row > 0 and row <= N Modelling Constraints p.19/42

39 A Flavour of OCL: N-queens NQProblem numqueens: Integer * Nqueen row: Integer column: Integer * others Attribute access context Nqueen inv: column > 0 and column <= N and row > 0 and row <= N Navigation context Nqueen inv: nqproblem.numqueens >= 3 Modelling Constraints p.19/42

40 A Flavour of OCL NQProblem numqueens: Integer * Nqueen row: Integer column: Integer * others Pseudo - attributes --simplifies the other expressions context Nqueen def: attr N : Integer = nqproblem.numqueens Modelling Constraints p.20/42

41 A Flavour of OCL NQProblem numqueens: Integer * Nqueen row: Integer column: Integer * others Pseudo - attributes --simplifies the other expressions context Nqueen def: attr N : Integer = nqproblem.numqueens Set expressions context NQProblem inv: numqueens = nqueen->size() Modelling Constraints p.20/42

42 A Flavour of OCL NQProblem numqueens: Integer * Nqueen row: Integer column: Integer * others Quantification --no two queens attack another: context NQProblem inv: nqueen->forall(q1, q2 : Nqueen not q1.attacks(q2) ) Modelling Constraints p.21/42

43 Pseudo - Operations in OCL NQProblem numqueens: Integer * Nqueen row: Integer column: Integer * others context Nqueen def: oper attacks(other: Nqueen) : Boolean = self.column <> other.column and self.row <> other.row and (self.row - other.row).abs <> (self.column - other.column).abs Modelling Constraints p.22/42

44 Part 3 Modelling Example Modelling Constraints p.23/42

45 The Bridge - Building Problem schedule the setup of a 5 - segment bridge Martin Bartusch 1983, Massimo Paltrinieri 1994 Modelling Constraints p.24/42

46 Bridge - Building: Constraints 11 bridge components, 46 tasks, 7 resources Number of Constraints: Modelling Constraints p.25/42

47 Bridge - Building: Constraints 11 bridge components, 46 tasks, 7 resources Number of Constraints: Resource Constraints: most tasks multiply on n = components n(n 1) 2 constraints each 77 constraints Modelling Constraints p.25/42

48 Bridge - Building: Constraints 11 bridge components, 46 tasks, 7 resources Number of Constraints: Resource Constraints: most tasks multiply on n = components n(n 1) 2 constraints each 77 constraints Precedences among tasks: 66 constraints Modelling Constraints p.25/42

49 Bridge - Building: Constraints 11 bridge components, 46 tasks, 7 resources Number of Constraints: Resource Constraints: most tasks multiply on n = components n(n 1) 2 constraints each 77 constraints Precedences among tasks: 66 constraints Five additional requirements: 25 constraints Modelling Constraints p.25/42

50 Bridge - Building: Constraints 11 bridge components, 46 tasks, 7 resources Number of Constraints: Resource Constraints: most tasks multiply on n = components n(n 1) 2 constraints each 77 constraints Precedences among tasks: 66 constraints Five additional requirements: 25 constraints Sum: 168 constraints Modelling Constraints p.25/42

51 Bridge - Building: Constraint Graph PA UE A2 S1 B1 A1 A3 P1 S3 S2 B2 B3 K1 A6 A4 P2 S4 S6 B6 B4 A5 S5 B5 K2 M2 AB2 L M1 M3 AB3 AB1 V1 T1 T2 M4 M6 AB6 AB4 V2 T3 T4 M5 UA AB5 T5 PE Modelling Constraints p.26/42

52 Bridge - Building: Constraint Graph PA UE A2 S1 B1 A1 A3 P1 S3 S2 B2 B3 K1 A6 A4 P2 S4 S6 B6 B4 A5 S5 B5 K2 M2 AB2 L M1 M3 AB3 AB1 V1 T1 T2 M4 M6 AB6 AB4 V2 T3 T4 M5 UA AB5 T5 PE Modelling Constraints p.26/42

53 Bridge - Building: generic constraints 1/2 Disjunction: Unary Resources Modelling Constraints p.27/42

54 Bridge - Building: generic constraints 1/2 Disjunction: Unary Resources 0..* previous Task resource start duration part context Task inv: Task.allInstances->forAll(a,b: Task a <> b and a.name() = b.name() and a.resource = b.resource implies ( a.start + a.duration <= b.start xor b.start + b.duration <= a.start ) ) Modelling Constraints p.27/42

55 Bridge - Building: generic constraints 2/2 Precedence Constraints 0..* previous Task resource start duration part context Task inv: Task.allInstances->forAll(t: t.previous->forall(prev: prev.start + prev.duration <= t.start ) ) Task Task Modelling Constraints p.28/42

56 Bridge - Building: All Tasks requ4 Stop Positioning Removal Filling Excavation Masonry Costing 0..* previous Task resource start duration part requ2 Begin Setting Delivery Erection Piles Formwork Foundation requ5 requ3 requ1 generic constraints apply to all 14 subtypes 2 instead of 143 Modelling Constraints p.29/42

57 requ3: Erection of temporary housing requ4 Stop Positioning Removal Filling Excavation Masonry Costing 0..* previous Task resource start duration part requ2 Begin Setting Delivery Erection Piles Formwork Foundation requ5 requ3 requ1 context Erection inv: start + 6 <= formwork.start Modelling Constraints p.30/42

58 Part 4 Outlook and Conclusion Modelling Constraints p.31/42

59 Outlook: Application Development <XMI.header> <XMI.documentation> <XMI.exporter>Together</XMI.exporter> <XMI.exporterVersion>4.0</XMI.exporterVersion> </XMI.documentation> <XMI.metamodel xmi.name = UML xmi.version = 1.1 /> </XMI.header> XML & OCL CP Code in Host Language Parser Application CP Code in Host Language class Model { ComponentType pc = new Component;... }; class foo : public baz { //... }; C++ Definitions Modelling Constraints p.32/42

60 Outlook: Distributed CSPs user agent problem specification XML Constraint Repository solutions constraint user fusing agent mediator XML XML XML Constraint Repository Constraint Repository solutions CSP constraint solver Modelling Constraints p.33/42

61 Benefits of using UML & OCL simplified, comprehensible knowledge acquisition seamless integration: constraint-based reasoning software development open to emerging developments (Semantic Web) Modelling Constraints p.34/42

62 Benefits of using UML & OCL simplified, comprehensible knowledge acquisition seamless integration: constraint-based reasoning software development open to emerging developments (Semantic Web) Experiences: UML/OCL in Software Architecture Description Languages (ADL) excellent experiences for configuration KBS Ontology Description CommonKADS, Rule-Based Systems Modelling Constraints p.34/42

63 Problems of UML informal notation informal use semantics in precise English conflicting definitions, ambiguities, imprecision meta-circular: defines itself by itself commercial standard dependent on OMG politics slow adaptation (6-12 months) Modelling Constraints p.35/42

64 Problems of UML informal notation informal use semantics in precise English conflicting definitions, ambiguities, imprecision meta-circular: defines itself by itself commercial standard dependent on OMG politics slow adaptation (6-12 months) modelling relations is awkward, e.g. R A B: ( a A) ( b B) (a, b) R Modelling Constraints p.35/42

65 Problems of UML informal notation informal use semantics in precise English conflicting definitions, ambiguities, imprecision meta-circular: defines itself by itself commercial standard dependent on OMG politics slow adaptation (6-12 months) modelling relations is awkward, e.g. R A B: ( a A) ( b B) (a, b) R A R(A,B) B Modelling Constraints p.35/42

66 Problems of UML informal notation informal use semantics in precise English conflicting definitions, ambiguities, imprecision meta-circular: defines itself by itself commercial standard dependent on OMG politics slow adaptation (6-12 months) modelling relations is awkward, e.g. R A B: ( a A) ( b B) (a, b) R A R(A,B) B Modelling Constraints p.35/42

67 Conclusion Useful for further work intuitively appealing notation informal notation as scratch pad abstraction / generalisation / packaging facilities translation to XML What to do next define a precise UML subset interfacing with eg. Localizer explore model transformation Modelling Constraints p.36/42

68 Fin Thank you for your attention. Modelling Constraints p.37/42

69 Configuration Knowledge Base in UML «RootComponent» PC type = {standard, deluxe} 1 «ComponentType» Motherboard clockrate = {800, 2200} floppy->size() > «ComponentType» HardDrive gig = {20, 40, 80} 1..5 «ComponentType» Floppy size = {3.5, 5.25} 1..4 «ComponentType» CPU «ComponentType» MBoard-1 «ComponentType» MBoard-2 <<incompatible>> «requires» «ComponentType» 486 «ComponentType» Pentium Modelling Constraints p.38/42

70 Additional Information: MOF M3: Meta-metamodel Hard-wired Meta-metamodel M2: Metamodel MetaModel( "RECORD_TYPES", MetaClass("RECORD", [MetaAttr("name", String), [MetaAttr("fields", List<"FIELD">) ]) MetaClass("FIELD", [... ] ) ) M1: User Model RECORD("StockQuote", [ FIELD("company", String) FIELD("price", Real) ] ) M0: User Data StockQuote("Sunbeam Harvesters", 98.88) StockQuote("Ilog PA", ) StockQuote("GreedyDudes", 2.13) Modelling Constraints p.39/42

71 Additional Information: MOF Meta Object Facility (MOF) MOF is a simple language for defining languages UML is a MOF-based metamodel Level MOF Terms Examples M3 meta-metamodel MOF Model M2 meta-metadata UML Metamodel M1 metadata Class Diagram M0 data User Objects Modelling Constraints p.40/42

72 Additional Information: XMI XMI = XML Metadata Interchange (OMG) is a way to save UML models in XML for any MOF-based metamodel ability to move UML models between tools <XMI.header> <XMI.documentation> <XMI.exporter>Together</XMI.exporter> <XMI.exporterVersion>4.0</XMI.exporterVersion> </XMI.documentation> <XMI.metamodel xmi.name = UML xmi.version = 1.1 /> </XMI.header> Modelling Constraints p.41/42

73 Additional Information: What s in XMI? Document Type Definition (DTD) rules for transforming MOF based models into XML DTDs XML Document production rules for MOF based data UML can be regarded as: an XML document conforming to a DTD an XML DTD to which UML models must conform Caveat: version differences between XMI and UML limits tool-to-tool interchange XMI 1.0, 1.1 UML1.1, 1.3, 1.4 Modelling Constraints p.42/42