A Graph Transformation-Based Semantics for Deep Metamodelling

Transcription

1 A Graph Transformation-Based Semantics for Deep Metamodelling Alessandro Rossini 1, Juan de Lara 2, Esther Guerra 2, Adrian Rutle 3, Yngve Lamo 3 1 Department of Informatics, University of Bergen, Norway 2 Department of Computer Engineering, Universidad Autónoma de Madrid, Spain 3 Department of Computer Engineering, Bergen University College, Norway 05 October 2011 AGTIVE 2011, Budapest, Hungary

2 Traditional metamodelling

3 i... Traditional metamodelling stack Modelling language metamodel of Linear stack Model conforms to... Metalevel l... conforms to Modelling language metamodel of Model i+1 conforms to Model conforms to... Modelling language metamodel of conforms to Model 1

4 OMG s 4-layer hierarchy 4-layer hiearachy conforms to Metalevel MOF metamodel of Metametamodel M 3 conforms to UML/DSL metamodel of Metamodel M 2 conforms to Model M 1 represented by Original O

5 src * Metamodel Model DSL using traditional metamodelling datalink * trg Component id: String 1 type * trg * CInstance dlinstance name: String visualise: Boolean src * Table src id="fusiontable" geopos profstype UAMProfs name="uamprofs" visualise=false src trg Map id="googlemaps" camptype UAMCamp name="uamcampus" visualise=true trg offices

6 Deep metamodelling

7 Deep metamodelling Originally proposed by Atkinson and Kühne

8 Deep metamodelling Originally proposed by Atkinson and Kühne Deep characterisation Double linguistic/ontological typing

9 Deep characterisation Describe structure and express constraints for metalevels below the adjacent one

10 Model M 1 DSL using deep context Component inv: self.trg-> datalink trg * Component@2 id: String@1 name: String@2 visualise: src * Map id="googlemaps" Table * geopos 0..1 trg src id="fusiontable" Model M 2 UAMCamp name="uamcampus" visualise=true offices trg src UAMProfs name="uamprofs" visualise=false Model M 3

11 Double linguistic/ontological typing Orthogonal linguistic and ontological typing for each model element

12 Metamodelling stack with double typing Linguistic metamodel conforms to (ling.) Ontological stack Model conforms to (onto.) Metalevel 1 DeepElement potency: Int name: String conforms to (ling.)... conforms to (onto.) Model conforms to (onto.) i... Attribute * Clabject 1 1 * Association * conforms to (ling.) Model conforms to (onto.) i+1 conforms to (ling.)... conforms to (onto.) Model l...

13 Diagram Predicate Framework

14 Diagram Predicate Framework (DPF) Formal diagrammatic specification framework founded on category theory and graph transformation diagrammatic modelling metamodelling model transformation model versioning deep metamodelling

15 Diagrammatic models in DPF Specification T = (T, C T :Σ) [irr] id [1..1] datalink Component String

16 Diagrammatic models in DPF Specification T = (T, C T :Σ) Graph T [irr] id id [1..1] datalink Component String datalink Component String

17 Diagrammatic models in DPF Specification T = (T, C T :Σ) Graph T [irr] id id [1..1] datalink Component String datalink Component String Signature Σ = (Π Σ, α Σ ) π Π Σ α Σ (π) Proposed vis. Semantic interpretation [irreflexive] 1 [mult(m, n)] 1 a a 2 X [irr] X f [m..n] f x X : x / f (x) Y x X : m f (x) n, with 0 m n and n 1

18 Diagrammatic models in DPF Specification T = (T, C T :Σ) Graph T [irr] id id [1..1] datalink Component String datalink Component String Atomic constraints C T :Σ a datalink ([irreflexive], δ1) 1 Component a id ([mult(1, 1)], δ2) 1 2 Component String Signature Σ = (Π Σ, α Σ ) π Π Σ α Σ (π) Proposed vis. Semantic interpretation [irreflexive] 1 [mult(m, n)] 1 a a 2 X [irr] X f [m..n] f x X : x / f (x) Y x X : m f (x) n, with 0 m n and n 1

19 Typing and conformance in DPF T [irr] id [1..1] datalink Component String Σ π Π Σ α Σ (π) Proposedvis. Semanticinterpretation [irreflexive] 1 [mult(m, n)] 1 a a 2 X [irr] X f [m..n] f x X : x / f(x) Y x X : m f(x) n, with 0 m nand n 1 S Map idmap Google Maps source Plot S'

20 Formalisation of deep metamodelling

21 Our contribution Distinction of two semantics for potency Syntax of potency Structural semantics of double linguistic/ontological typing Operational semantics of potency

22 Multi-potency Metalevel Clabject Reference i A p A a p N i + 1 B p-1 B b p-1 O..... i + p 1 L 1 L l 1 Y i + p M 0 M m 0 Z

23 Single-potency Metalevel Clabject Reference Attribute i A p A a p N A a p DT i + p B 0 M b 0 Z M b 0 DV

24 Tag signature Ψ for specifying potencies θ Θ Ψ α Ψ (θ) Proposed visual. <multi(p)> 1 1 X p <multi(p)> 2 1 <multi(p)> π 1 a a 2 X 2 X f p f π p <single(p)> 1 1 X p <single(p)> 2 1 <single(p)> π 1 a a 2 X 2 X f p f π p Y Y Y Y

25 Deep metamodelling stack Σ S i C i P i Ψ

26 Deep metamodelling stack S i 1 C i 1 Σ ω i S i P i C i P i 1 Ψ

27 Deep metamodelling stack LM λ i 1 C i 1 S i 1 Σ λ i = ω i S i P i C i P i 1 Ψ

28 Deep metamodelling stack λ 1 LM S 1 C 1 Ω λ i 1 λ i ω 2 ω i 1. C i 1 C i = S i 1 C l λ l ω i S i P 1 ω i+1. P i 1 P i ω l S l P l Ψ

29 DSL using the deep metamodelling stack Clabject Attribute DataType Reference (b)s 1 [0..1] 2 datalink 2 [irr] 2 2 Component Map 1 id 1 name 2 idmap 0 geopos 1 [1..1] 1 [1..1] 2 String Google Maps Table 1 idtable 0 Fusion Table (c)s 2 UAM Campus namemapuam 0 UAMCamp 0 offices 0 (a)lm (d)s 3 UAM Profs nametableuam 0 UAMProfs 0

30 DSL after the transformation Clabject Attribute DataType Reference (b)s 1 (c)s 2 String 1 [0..1] 2 datalink 2 [irr] 2 [1..1] 1 namemap 1 nametable 1 2 Component Map 1 id 1 name 2 idmap 0 geopos 1 [0..1] 1 Table 1 [1..1] 1 [1..1] 2 String Google Maps idtable 0 Fusion Table UAM Campus namemapuam 0 UAMCamp 0 offices 0 (a)lm (d)s 3 UAM Profs nametableuam 0 UAMProfs 0

31 Rules for flattening the semantics of single-potencies ta 1 CL = CK CR a:attribute p a:attribute p A:Clabject DT:DataType A:Clabject DT:DataType ω L i ω L i ω R i ω R i ω R i B:Clabject DT:DataType B:Clabject ab:attribute p-1 DT:DataType tr 1 A:Clabject a:reference p N:Clabject A:Clabject a:reference p N:Clabject ω L i ω L i ω R i ω R i ω R i B:Clabject O:Clabject ab:reference p-1 B:Clabject O:Clabject tacr 2 A:Clabject π p a:reference N:Clabject A:Clabject π p a:reference N:Clabject ω L i ω L i ω L i ω R i ω R i ω R i B:Clabject ab:reference O:Clabject B:Clabject π p-1 ab:reference O:Clabject

32 Rules for flattening the semantics of single-potencies tacr 3 A:Clabject CL π p a:reference N:Clabject A:Clabject CK = CR a:reference N:Clabject ω L i ω L i ω L i ω R i ω R i ω R i tr 4 B:Clabject A:Clabject π p-1 ab:reference a:reference p O:Clabject N:Clabject B:Clabject A:Clabject π p-1 ab:reference O:Clabject N:Clabject ω L i ω L i ω L i ω R i ω R i ab:reference p-1 B:Clabject O:Clabject ab:reference p-1 B:Clabject O:Clabject ta 4 A:Clabject a:attribute p DT:DataType A:Clabject DT:DataType ω L i ω L i ω L i ω R i ω R i B:Clabject ab:attribute p-1 DT:DataType B:Clabject ab:attribute p-1 DT:DataType

33 Conclusion Distinction of multi- and single-potency Syntax of multi- and single-potency Structural semantics of double linguistic/ontological typing Operational semantics of single-potency

34 Related work Multi-level metamodelling [Gitzel et al., 2007] Extension of MOF with multiple metalevels to enable XML-based code generation [Asikainen et al., 2009] Nivel: double metamodelling framework based on the weighted constraint rule language [Clark et al., 2010] XMF: language-driven development framework allowing arbitrary number of metalevels

35 Related work Deep characterisation [Kühne et al., 2007] DeepJava: superset of Java which features an unbounded number of metalevels [Atkinson et al., 2009] Prototype modelling infrastructure with multiple ontological and linguistic metalevels [de Lara et al., 2010] metadepth: deep metamodelling framework which supports potency, double linguistic/ontological typing and linguistic extension

36 Future work Structural semantics of multi- and single-potency (in progress) Structural semantics of linguistic extension (in progress) Investigation of the effects of overriding the potency of a clabject using inheritance

37 Thank you! Questions?