Three dimensions of formal languages

1. Three dimensions of formal languages Arve Meisingset Telenor R&D

2. Dimensions 3. Implementation 1. Denotation But first, the language itself 2. Instantiation

3. The languageas a syntax tree Population Name 1 Company Name Telenor Employee Number 017976 <> Employee ’ Company ’ Population Person Name Arve Meisingset Person Name Arve Meisingset Labels are local to the superior node Superior nodes provide the context in an attachment grammar

4. Population Emplyee Company Person Company Person Graphic notationisomorphic to alphanumerical notation Simplification Emplyee

5. Even labels and tokensare syntax trees Population Name 1 Company Name : T e l e n o r Provides lists of significant duplicates

6. Algorithmic and navigating functionsare subordinate to dataref. UML class diagrams Population Company Name Telenor Employee Number 017976 <>Employee ’ Company ’ Population Person Name Example Arve Meisingset PS. Subordinate, Sequence and Operator form a threedimensional tree; ie. <> and ’ are not needed with navigating references between the nodes – as an alternative to the Turing tape

7. 1. Denotations Population English Company Name Telenor Denotation <> Denotation ’ Company ’ English ’ Population Phenomena Bedrift Phenomena Bedrift Explisit Isomorphic mappingfrom Terminologies to Phenomena The isomorphic mapping is made between inscriptions; there is no need for strings Phenomena are themselves data inside some observer

8. Cir. group Circuit Cable pair Note on modelling Provides overview of Circuits terminated in the same two Exchanges 1 Is a Cable pair a physical entity? Is a Circuit a physical entity Is Circuit group a physical entity? Or are they just data providing overview of other data – to serve some tasks? Do most data model nothing?

9. 2. Instatiations System Schema P <> ’ System (Population Company Name Population S <> ’ System (Schema Company Name Telenor Company Name Telia Schema and Population references Mappings from instances to classes Enforced implicitHomomorphic mappingfrom Instances to Classes

10. System Schema Company Company Population Company Company Company Company Company Graphic notationwith recursion S S Homomorphic dotted implicit moppings Note that class labels are copied into every instance, but not every (subordinate) detail needs be instantiated

11. System Schema Company Company Population Company Company Company Company Company Detailed Graphic notation S S The syntax tree is made up of lists of lists with significant duplicates

12. Company Company Company Company Note on homomorphism Implementation cOMPANY Instantiation Languages not satisfying the homomorphism requirement are translated to implementations before instantiation Ie. Not Class Company Better Company Class Best Company

13. Company Employee Person Note on Subclasses Phenomena acting as roles of other phenomena is replacing the subclass notion The Schema-Population references are more generic than and replacing nheritance Also Contents schemata providing views of Application schemata, have a similar effect Also Access control must be much more powerfull than hiding by classes

14. LS CS ETS OS ITS DS PS 3. Implementationby the Data transformation architecture Schemata and mappings between schemata state the rules for transformation of data between two media External schemata Application schema Internal schemata Processes state abstract implementations HCI DB • Compiler architecture • The Application schema provides the domain model inside the implementation; implementation specifications are added and do not replace the Application schema

15. ImplementationSystem schema External schema LS Layout schema CS Contents schema Application schema ETS External terminology schema OS Concept schema ITS Internal terminology schema Internal schema DS Distribution schema PS Physical schema

16. Implementationon multiple media Tape Graphic Alfa DB SG10 ? Reports Process Tele

17. ImplementationNote on partial reuseof more central schemata Tape Graphic Alfa DB Reports Process Tele

18. Company C1-record C2-record ImplementationMapping from External terminology schemata to Internal terminology schemata C1-C2-set If a Specification is a Model of an Implementation, then the Specification has to be Isomorphic to the Implementation Only change of labels and details are permitted. Often, as examplified, the mapping is not isomorphic. We do not require an isomorphic mapping from Application schemata to Internal schemata, but the Application schema must itself be in the running implementation

19. Schematacan themselves be stored in a database.Hence, you can have external and internal forms of each schema LS CS ETS CS ITS DS PS External form, presented to developers and users SG10 ? Internal executable form

20. Conclusions UML does neither Model implementations nor anything else SG10 languages are neither Description techniques for implementations nor of anything else Process and Block are internal implementation notions External HCI aspects are not addressed by SG10 Data(base) aspects are not addressed by SG10 Will competition come from these domains, and is UML such an approach?