a diagrammatic formalisation of mof-based modelling languages

Formalisation of MOF-based Modelling Languages

A Diagrammatic Formalisation of MOF-BasedModelling Languages

Adrian Rutle1, Alessandro Rossini2, Yngve Lamo1, Uwe Wolter2

1Faculty of Engineering, Bergen University College, Norway

2Department of Informatics, University of Bergen, Norway

30 June 2009TOOLS Europe, Zurich


Introduction and Motivation

Outline

1 Introduction and MotivationMotivating Example

2 Diagram Predicate Framework (DPF)SyntaxSemantics

3 MOF-based Modelling LanguagesThe 4-Layered Modelling Architecture

4 Case-Study: Formalisation of EMF

5 Summary and Future Work



Model-Driven Engineering (MDE)

Primary artefacts of the software development process: models

Model: abstract specification of a software system

Usually graph-based structures

Model Transformation: generation of target models fromsource models

Model to modelModel to code

Metamodelling: specification of modelling languages

A metamodel defines abstract syntaxA model conforms to the metamodel of its language



MDE standards: state-of-the-art

Modelling languages

Unified Modeling Language (UML)Eclipse Modeling Framework (EMF)

Usually graph-based languages

Constraint languages

Object Constraint Language (OCL)

Usually text-based languages

Metamodelling frameworks

Meta-Object Facility (MOF)



MOF-based modelling hierarchy

Modelling layers Standards and examples

M3: Meta-metamodel MOF

M2: Metamodel UML language: Class, Attribute

M1: Model A UML model: Class Person with At-tributes name and address

M0: Instance An instance of Person: “OlaNordmann” living in “Sotraveien 1,Bergen”



(Meta)modelling challenges

Increase the expressive power of diagrammatic modelling:

Need for additional languages to define constraints

Mixture of different technical spacesDomain experts do not understand code

Formalise modelling and metamodelling:

Formalisation attempts not reflected in the standards

Constraints not reflected in the metamodelling hierarchyLack of diagrammatic formalisation



Remarks on terminology

Diagrammatic 6= Visual

Diagrammatic modelling: techniques targetting graph-basedstructures

Visualisation: rendering a model perceptible and intuitive forhumans

Graph-based structures: often easily visualised

Not necessarily always



Motivating Example

Outline








Motivating Example

Motivating example

Requirements

1 An employee must work for at least one department.

2 A department may have none or many employees.



Motivating Example

Motivating example

UML class diagram

Requirements

1 An employee must work for at least one department.

2 A department may have none or many employees.



Motivating Example

Motivating example

UML class diagram

Requirements

3 An employee may be enrolled in none or many projects.



Motivating Example

Motivating example

UML class diagram

Requirements

4 A department may control none or many projects.

5 A project must be controlled by exactly one department.



Motivating Example

Motivating example

UML class diagram

Requirements

6 An employee enrolled in a project must work in the controlling department.

7 A set of employees working for a controlling department must not be enrolled in

the same controlled project more than once.



Motivating Example

Motivating example

UML class diagram OCL1 context Enrolment

2 inv rule6 : self . department .employees ->

3 includesAll (self . employee )

4 inv rule7 : Let enrolments :Set ( Enrolment )=

5 Enrolment . allInstances in

6 ( not enrolment -> exists (enr |

7 enr. project =self . project

8 and enr .department =self . department

9 and enr .employees =self . employees ))

Requirements

6 An employee enrolled in a project must work in the controlling department.

7 A set of employees working for a controlling department must not be enrolled in

the same controlled project more than once.



Motivating Example

Proposed solution: constraints integrated



Motivating Example

Our contribution

Diagrammatic modelling framework

Integration of constraints in models

Formalisation of the 4-layered modelling hierarchy

Formal description of the relationship between models atdifferent modelling levelsIntegration of constraints in metamodelling


Diagram Predicate Framework (DPF)

Outline








Formalisation approach


Based on category theory

Generalized sketches formalism

models: graphsconstraints: user-defined diagrammatic predicate signatures



Syntax

Diagrammatic specification

S = (GS ,ΓS)



Syntax


S = (GS ,ΓS) GS



Syntax


S = (GS ,ΓS) GS

ΓS



Syntax


S = (GS ,ΓS)

Σ = Π, α

GS

ΓS



Syntax

Signature Σ

p α(p) Proposed visualisat. Intended semantics

[total] 1x // 2 A •

f // B ∀a ∈ A : |f (a)| ≥ 1

[single-

valued]1

x // 2 Af [1]// B ∀a ∈ A : |f (a)| ≤ 1

[cover] 1x // 2 A

f� ,2 B ∀b ∈ B : ∃a ∈ A | b ∈ f (a)

[inverse] 1

x

##2

y

cc A

f

''[INV] B

g

gg ∀a ∈ A , ∀b ∈ B : b ∈ f (a) iff a ∈ g(b)

[subset] 1

x

##

y

;; 2 A

f

''

g

77[⊑]

��B ∀a ∈ A : f (a) ⊆ g(a)

[jointly-

key]1

x //y

��??

?

?

?

?

?

z

��

2

4 3

Af //

g

��??

?

?

?

?

?

h

��

[JK]3

B

D C

∀a, a′ ∈ A : a 6= a′ implies f (a) 6=f (a′) or g(a) 6= g(a′) or h(a) 6= h(a′)



Semantics

Outline








Semantics

Semantics of a diagrammatic specification

Given by the set of its instances

An instance (I , ιI ) of S is

a graph homomorphism ιI : I → GS

i.e. elements of I typed over elements of GS

and constraints ([p], δ) in ΓS are satisfiedi.e. (I , ιs) |= ΓS

Remark

Nodes in GS : interpreted as sets

Arrows Af−→ B in GS : interpreted as

multi-valued functions f : A→ ℘(B)

ΠΓ

S

//___ GS

I

ιI

OO


MOF-based Modelling Languages

Outline







MOF-based Modelling Languages

The 4-Layered Modelling Architecture

MOF-based metamodelling hierarchy and DPF

MOF DPF


Case-Study: Formalisation of EMF

Outline








What is EMF?

Java open source framework for modelling, data integrationand code-generation

Implements Essential MOF (a subset of MOF 2.0)

Its metamodel called Ecore – to avoid confusion with MOF

Considered a low cost entry to the employment of MDE

Several MDE-tools built on EMF



Formalisation of EMF hierarchy

Ecore

conformsTo

��

Model

conformsTo

OO

Instance

conformsTo

OO

ΠEcore

ΓEEcore //______ GE

ιE

��

ΠCore

ΓMCore //______ GM

ιM

OO

I

ιI

OO



E and ιE


Summary and Future Work

Outline








Related work

Graph theory Hartmut Ehrig et al

models: graphs and graph constraintsconformance: typing morphism

Constructive type theory Poernomo

models: terms (token models)metamodels: types (type models)correct typing insures correct models and metamodels

Algebraic specifications Boronat et al, Meseguer et al andRomero et al

models: graphs, nodes : attributed objects, arrows : referencesgraphs repr. by specs. in Membership Equational Logic (MEL)roles of metamodels: as data, as type or as theory

roles formally expressed by metamodel definition, model type,and metamodel realisation



Summary

DPF as a formal diagrammatic specification framework

Integration of constraints in modelling

Presentation of a generic and flexible scheme for theformalisation of metamodelling

Application of the scheme to MOF modelling hierarchy

Integration of constraints in metamodelling

Formalisation of EMF hierarchy as a case-study



Applications of DPF

Formalisation of UML, ER, Relational Data Models

Formalisation of copy-modify-merge approach to versioncontrol

Formalisation of constraint-aware model transformation rules



Future work

Transformation of UML/OCL to DPF

Dependency between predicates

Prototype tool

Comparison to Epsilon, Fujaba etc

Real-size case study: noark (Norwegian Archive standard)



Thank you!

Questions?



Instances

Instances of PredicatesA semantic interpretation of a signature Σ = (Π, α) is given by amapping that assigns to each p ∈ Π a set [[p]] of graphhomomorphisms τ : O → α(p) called valid instances of p, writtenτ � p, where O may vary over all graphs.

Instance of Specification

An instance of a diagrammatic specification S = (GS ,ΓS) is agraph I together with a graph homomorphism ι : I → GS , written(I , ι), such that for each constraint (p, δ) ∈ ΓS we have ι∗ ∈ [[p]],where ι∗ : O∗ → α(p) is given by the following pullback diagram

α(p)δ

// GS

O∗δ∗

//

ι∗

OO

P.B.

I

ι

OO



Semantics of diagrammatic specification



Challenges in modelling

Mixing graph-based structures with textual constraintsDifferent technical spaces

checking models in two different engines/stepsmodel-constraint synchronisation problemviolation of “everything-is-a-model” vision of MDE

Challenge for domain experts who do not understand OCL



Formalisation approach

Based on category theorySketches formalism: define semantics of diagrams (thusgraph-based models)

models: graphs (nodes and edges)model properties: universal properties (limit, colimit,commutative diagrams)

Generalized sketches formalism

not only universal propertiesuser-defined diagrammatic predicate signatures

DPF: specification formalism based on generalized sketches

a diagrammatic formalisation of mof-based modelling languages

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