The document describes the MetaL modeling language, which has two layers - MetaL1 and MetaL2. MetaL1 defines a minimal data modeling kernel where all elements are treated as data objects with properties and relationships. MetaL2 provides a formal metamodeling foundation where meta-objects can be extended and refined through multiple inheritance. The language allows for fine-grained sharing and overlapping of meta-models and their elements.

1. MetaL MetaCASE Tools &
Possibilities
Fahad Rafique Golra
19/03/2012 Département Informatique

2. Table of Contents
1. MetaL1
2. MetaL2
3. Examples
4. Benefits
5. Discussion
page 1 Département Informatique Fahad R. Golra

3. MetaL Language
 Two distinct layers
• MetaL 1 (minimal kernel language)
• MetaL 2 (formal foundation)
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4. MetaL 1 Repository
 Everything in the repository is a dataobject (D: set
of all dataobjects)
 Facets of Dataobject
• Object (O: set of all objects)
• Properties (P: set of all properties)
domain : P  O
range : P  O
« facet of » defines the hidden dataobject
fo : O  P  D
A dataobject can be a property, an object or both
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5. Properties & Objects
o1, o2 , o3 , op O
op, q P
 op has both a property and an object facet
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6. Dataobject Types
 The objet type, OT is a subset of O
 The property type, PT is a subset of P
 Instance-type relationship is modeled as
o def
typeo O OT x y typeo x, y
typep P PT p def
x y type p x, y
A property has exactly one property type
 Every object has atleast one object type
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7. Types
 Thedomain (resp. range) of a property must be an
instance of the domain (resp. range) of its property
type.
o
domain( p)  domain( pt )
and
o
range( p)  range( pt )
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8. Object values
 Object values are specialized objects that hold
value
val : OB  OS  O  O  O  B  S      
 If x OT then val ( x) T where T denotes any
type N,B, …
 The object value sets are disjoint and are all
included in O.
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9. Inheritance & Name
 isa relationship isa OT OT
 Objecttypes inherit properties from their
supertypes
typeo (o, t ) t isa* t typeo (o, t )
 Object and property types have unique names
x, y OT : name( x) name( y) x y
p1 , p2 P : name( p1 ) name( p2 )
T
Fam* (domain( p1 )) Fam* (domain( p2 )) p1 p2
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10. MetaL1 Specification
 Root object type ( ) and property type ( )
( ) is an instance of root object type and
supertype of the elementary types
 For example:
TN OT  ON isa(TN , )
typeo (TN , ) typeo (TN , TN )
val (TN ) 0 name(TN ) int
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11. Elementry Types
 Each object value is typed by exactly two types
o ON : typeo (o, TN ) typeo (o, ) 2
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12. Example
 To model: Albert and Bernard are two persons
who have the same age, they are 45 years old.
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13. Integrity
 If some object o O is deleted
- If p P is a property whose domain( p) o typep ( p, pt ) true for some
pt P and if dr kind ( pt ) then range( p) must also be deleted.
T
- If p P is a property whose range( p) o typep ( p, pt ) true for some
pt P and if rd kind ( p ) then domain( p) must also be deleted.
T t
 If some property p P is deleted
- If pd kind ( pt ) , then domain( p) must be deleted
- If pr kind ( pt ) , then range( p) must be deleted
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14. MetaL 2 Metametamodel
 CommonMetaObject
- Default supertype of all other metaclasses
 CommonMetaModel
- Default supertype of all constructs denoting metamodels
- Inherits from CommonMetaObject
 MetaObject
- Key metaclass as main concept
- Generalizes MetaRole, MetaProperty, MetaModel
- Has a unique name
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15. MetaL 2 Metametamodel
 MetaProperty
- Adds slots to metaobjects
- Inherits from MetaObject
- Domain of cardP property which limits the number of concrete
properties
- Cardinality -1 is considered infinite, otherwise ≥ 1
- Must have exactly one cardinality and one type
- Cardinality is the range of exactly one metaproperty
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16. MetaL 2 Metametamodel
 MetaRole
- Both object type and property type
- As object type, subtype of MetaObject
- As property type, has MetaObject object type as domain and
range
- Domain of cardR property, where cardR denotes one-to-
one(0), one-to-many(1), many-to-one(4), many-to-many(5),
manys-to-manys(10).
- Cardinality is the range of exactly one metarole
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17. MetaL 2 Metametamodel
 MetaModel
- Aggregate concept defined by a set of metaobjects
- Inherits from CommonMetaModel
- PartWhole metaRole has CommonMetaObject as domain
and CommonMetaModel as range.
- PartWhole is domain of
– nickname:optional, unicity of name inside a metamodel
– canNotBeShared: allows sharing in metamodels
– isNotDependentOn: dependency of object on metamodel
– isHidden: hiding technical details
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18. Example
 PartWhole
- metametamodel – metaclass
- statechart – state
- coffemachine - IDLE
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19. MetaL 2 Metametamodel
 Inheritence
- MetaObjects can inherit from other MetaObjects
- Multiple inheritance is allowed
- Cycles are forbidden in the generalization graph
- Inheritance between metamodels is allowed
MM typeo ( , MetaModel)
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20. MetaL 2 Metametamodel
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21. MetaL 2 Concrete Layer
 ConcreteObjects
- Instance of metaobject which is instance of MetaObject
- Can belong to several concrete models
- Can not live outside the definition of atleast one concrete
model
 Concrete Property
- Valued slot attached to concrete object
- Can be shared by multiple concrete objects
- As its a metaobject so it can own properties, roles etc
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22. MetaL 2 Concrete Layer
 Concrete Roles
- Has property and object facets
- Links two objects and can be a domain/range of property
- Respects cardinality
 Concrete Models
- Instance of metamodel which is an instance of MetaModel
- Composed of concrete objects that are instance of
metaobjects in metamodel definition.
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23. Example Coffee Machine (state chart)
Redundancy
Properties can have
properties then MetaRoles
are redundant
Instance of/Conforms to
« state name » a property
or an object
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24. General Benefits
- Meta(models) can overlap
- Sharing between (meta)models is fine-grained: (meta)objects,
(meta)models, …
- Multiple instantiation
- Free from instance/type delimitation in modeling layers
- Granularity: meta(models) are meta(objects)
- Metamodel refinement: As metamodels can be extended
further and refined.
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25. Example
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26. Points for discussion
• Having shared objects can help transformations, as
some part of the (meta)model remains constant in
transformation
• Maintaining metamodel families by transformations
without referential redundancies
• As other terminal languages can be defined on top
MetaL1, so a complete family of of DSLs can exist
e.g. for Component Oriented Programming.
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27. References
1. V. Englebert. MetaL1: a formal specification. Technical Report,
University of Namur – PRECISE Research Centre, Belgique,
May 2010.
2. V. Englebert. MetaL2: a formal specification. Technical Report,
University of Namur – PRECISE Research Centre, Belgique,
May 2010.
3. V. Englebert, P. Heymans, “Towards More Extensive
MetaCASE Tools”, In: Proceedings of CAiSE 2007, Springer-
Verlag Berlin Heidelberg, pp 454–468, 2007.
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