Dynamic Metamodel and Statecharts

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Dynamic Metamodel and Statecharts

• Contents of
• A Proposal of a Dynamic Core for UML
  Metamodelling with MML by G. Reggio and E.
  Astesiano
• Metamodelling Behavioral Aspects the Case of the
  UML State Machines by G. Reggio
• Available at ftp.disi.unige.it/persons/ReggioG

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Differences from Other Proposals

• Influenced by work from labeled transition
  systems.
• Has influenced the work of Warmer-Kleppe
  metamodel.
• Builds on a (hacked) version of the pUML
  metamodel.
• More closer to standard logical descriptions.

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• All objects have identities
• Expressions
• not instances (as in MML).
• a separate package.
• not necessarily constraints
• Two new packages
• Local Actions
• To model messages
• Labeled Tran. Diagrams
• to model Statecharts and use cases
• no sequence diagrams

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• Makes a difference between virtual objects and
  instantiable objects
• Classes and attributes are the only instantiable
  objects.
• Attribute is a specialization of container, but
  not classifier

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Semantics Well-formedness

• Two object values are different if their names
  are different
• All states of a life must be from the same object
• All instances of StaticObjectState must be lives
  of objects of the same class.

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core.semantics Package

• Use state instead of instance (only a naming
  difference)
• Object state is a mapping of attributes to slots,
  and slots have value, a virtual entity.
• Authors claim that instance of an attribute is
  not clear.
• StaticObjectMeaning
• all possible lives of some object
• a single life is an ordered sequence
• Hence
• meaning of an object collection of all possible
  lives
• Next diagram show how an object can go from any
  state to any other state without further
  constraints.

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Semantics

• Stereotype ltltinductivegtgt means
• association between attribute and slot is a
  specialization of the one between classifier and
  meaning
• Associations are commutative. I.e.
• c.attributes.semantics c.semantics.attributes
• Methods
• attribute gives all methods of a class

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Differences

• DataValue is a refinement of Value, instead of
  instance
• Admits bags, sets and sequences
• Sets and bags must be constructed from the same
  type of objects.
• Have an expression package to evaluate (MML/OCL)
  expressions.

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Notes on Expressions

• Every expression is evaluated in a context
• ltltmonotonicgtgt requires that the context of every
  sub-expression is the same as an expression
• Why association has multiplicity 1 at the
  classifier end.
• Have well-formedness rules to ensure type
  correctness

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Differences

• Semantic interpretations of expression associates
  bindings of free variables with values
• Calc is evaluating the value of the expression
  taking
• ltbinding, states, valuegt
• Calc is a refinement of meaning and not a
  refinement of instance.

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The Dynamic Core Package

• Earlier stuff were changes made to the Static
  Core so that Dynamic Core can be defined

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Semantic Domains

• Active object one that has a unique thread
• The meaning of an active object is a labeled
  transition system (LTS)
• LTS is characterized by
• States (states of active objects)
• Labels (not further specified)
• Transitions
• (source state, label, target state)

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dynamic.core.semantics
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Issues

• Generalization of LTSs are problematic
• Minimally can
• refine state
• add labels
• Add transitions
• Refine attributes
• Add communication
• Constraints on active classes
• Liveliness properties are problematic

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Local Actions Package
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Local Action Domains
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Labeled Transition Diagrams (LTD)

• Used in semantics of active classes
• A specialization of the meta-class
  BehaviorDescription
• An arrow describes as labeled transition as
• Starting state whose control part is source and
  attributes satisfy the guard
• Reaching states whose control part is the target
  and attributes values modified as described in
  intra part
• Labeled by the evaluation of the inter part, that
  is an interaction.
• Interaction is an abstract class refined whenever
  LTD is used.

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LTD.semantics Package
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LTD

• Transitions can be non-deterministic
• Semantics of LTDs are labeled trans. systems
• Semantics of arrows are transition calculations
  (TransCal)
• Semantics of interactions are interaction
  calculations (InterCal) whose values are labels.
• State is not interpreted.

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Example LTD-an active class-
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Example LTD-Its LTD-
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Extreme Metamodelling GML

• Simplified meta modeling language with
• Classes
• Operations
• (characterized by pre and post conditions)
• Associations
• Subtype assertions
• Constraints
• Predefined types

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GML Meanings I

• Object set of all its states
• State characterized by
• Identity
• Type
• Value of all attributes
• Values returned by operations
• Class meanings of all its instantiations
• Association pairs of object identities
  participating in the association

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GML Meanings II

• Subtype pairs of types satisfying the subtype
  assumption
• Model set of objects (OIDs) and associations
  defined by it.
• Data type standard
• Constraints sets of objects /associations
  satisfying them

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GML Extensibility Macros

• To extend GML need to
• Abstract syntax
• Static correctness conditions
• Visual representation
• Provide a translation of any model fragment of
  any instance of a new construct into a model
  fragment of GML

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Labeled Transition Systems (LTS)
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Labeled Transition Diagrams (LTD)

• LTDs provide semantics for LTSs.
• Oriented arcs in LTDs are decorated with
• condition 1 Label / condition 2
• These are GML expressions (like OCL) with
  appropriate type
• At most one free variable of type State may be
  Condition 1 and Label, but only two in Condition 2

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LTD

• LTDs enrich LTSs with control information
  enough to formally specify execution of states
  diagrams.
• Add contexts as a string

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Metamodels for Statecharts

• Add run-to-completion semantics to formalize
  Statechart executions.
• Every object has an event queue and look for
  events in own queue, take one and execute

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Machinery Needed
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Machinery Needed II
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Machinery Needed II
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Event Execution Machine