1. Chess Review May 11, 2005 Berkeley, CA Formal Semantics of Metamodeling Frameworks Ethan Jackson ISIS, Vanderbilt University Semantic Anchoring Infrastructure Kai Chen ISIS, Vanderbilt University Semantics of Metamodeling

2. Chess Review, May 11, 2005 2 Metamodels As Formal Objects Pumping Lemma If it is accepted by the DFA ? ? If Graph structure, type structure, containment, aspects, etc… are valid Is a string in the language? Is a model well-formed?

3. Chess Review, May 11, 2005 3 Denotational Structural Semantics Set of all Realizations 1.Define an algebraic structure that is rich enough to express all of the modeling concepts. (e.g. a graph with typed vertices and edges). All realizations form a set. 2.Define constraints on this set so that only valid models are included 3.A metamodel carves out a subset of this valid space. Valid Model Invalid Model 4.A meta-metamodel exists if it is a metamodel that carves out the set of all metamodels

4. Chess Review, May 11, 2005 4 Tailoring the Semantics Topological Layer Object Instantiation Layer Extension Layer Metamodel Constraints Metamodeling constraints

5. Chess Review, May 11, 2005 5 The Layered Approach By choosing a layer, one chooses the set of concepts that naturally suite the semantic domain. 1 2 3 4 5 1 Start 2 3 Accept 4 5 a/b c/d e/f a/f 1 Start 2 3 Accept a/b c/d e/f 4 5 a/f

6. Chess Review, May 11, 2005 6 Layer Preservation Layers progressively adds information. This is stated formally as layer preservation.

7. Chess Review, May 11, 2005 7 Applications Giotto Metamodel is a formal object that simultaneously describes a modeling environment and a structural semantics. Automatically generated Trivial bijective mapping Automatically generated Environment is expressive MoC is descriptive, yet “baggage-free” because it builds off of the formal definition of the metamodel. The semantics of the metamodeling framework need not be reproduced, but just referenced. Additional semantics that utilize the formal structures, Proofs Additional semantics that utilize the formal structures, Proofs ASML Textual

8. Chess Review, May 11, 2005 8 Semantic Anchoring Infrastructure Semantic Unit –A well-defined DSML that captures the semantics of a particular model of computation. Semantic Anchoring –Define the semantics of a DSML through the transformational specification to a semantic unit. AsmL Behavioral Semantic Spec Transformational Specification Transition Engine DSML MetamdoelGMEToolset GReAT Tool Model Checker Model Simulator Test Case Generator Mc XML Parser AsmL Spec AsmL Tools Instance Generate Domain Model AsmL Model (XML Format) AsmL Metamodel AsmL Data Model

9. Chess Review, May 11, 2005 9 A Semantic Unit for Timed Automata Based Modeling Language Common semantic domain for varied timed automata based modeling languages. –Guard –Priority –Synchronization S C A M C M S Timed Automata (AsmL Supported Semantics) MoC Variants Model Checker Model Simulator Test Case Generator AsmL Tools IF Lang. Transformation T Semantic Anchoring U PPAAL Lang. Kronos Lang. MoC Semantic Unit GReAT Tool GMEToolset S C A M C M S

10. Chess Review, May 11, 2005 10 FSM Metamodel

11. Chess Review, May 11, 2005 11 FSM Model

12. Chess Review, May 11, 2005 12 Metamodel for AsmL Abstract Data Model

13. Chess Review, May 11, 2005 13 AsmL Abstract Data Model

14. Chess Review, May 11, 2005 14 AsmL Behavioral Semantic Specifications

15. Chess Review, May 11, 2005 15 Transformational Specifications

16. Chess Review, May 11, 2005 16 AsmL Data Model in XML Format

17. Chess Review, May 11, 2005 17 AsmL Data Model

18. Chess Review, May 11, 2005 18 Distributed Real-time System (1) Abstract Syntax (1) Component Interactions

19. Chess Review, May 11, 2005 19 Distributed Real-time System (2) Abstract Syntax (2) Component Behaviors

20. Chess Review, May 11, 2005 20 Distributed Real-time System (3) AsmL Abstract Data Structure class State id as String option as STATEOPTION class Transition id as String option as TRANSITIONOPTION abstract class TimeAutomata var currentState as State? = null abstract property states as Set of State abstract property transitions as Set of Transition abstract property localClocks as Set of Clock abstract property outTransitions as Map of abstract property srcState as Map of abstract property dstState as Map of abstract property syns as Map of abstract class DRTSystem abstract property timeAutomatas as Set of TimeAutomata abstract property signalChannels as Set of SignalChannel abstract property signalRouters as Set of SignalRouter var activeAutomatas as Set of TimeAutomata = {}

21. Chess Review, May 11, 2005 21 Distributed Real-time System (4) AsmL Behavior Semantics Specification //In the current clock time, whether the time guard of an transition is true IsTimeGuardTrueNow (t as Transition) as Boolean require t in me.transitions step return TimeGuard (t) //In the next clock time, whether the time guard of an transition is true IsTimeGuardTureNext (t as Transition) as Boolean require t in me.transitions step forall c in globalClocks c.Go () forall c in me.localClocks c.Go () step let next = IsTimeGuardTrueNow (t) step forall c in globalClocks c.Back () forall c in localClocks c.Back () step return next

22. Chess Review, May 11, 2005 22 IF Asynchronous Component Interaction Simulation Verification

23. Chess Review, May 11, 2005 23 U PPAAL Synchronous Component Interaction Simulation Verification

24. Chess Review, May 11, 2005 24 The End Questions?