Promotion

1. Promotion

2. Promotion • Promotion is a structuring technique that may be used whenever the state of a system contains multiple, indexed instances of the same component. • It is most useful when several operations are possible upon the component, and their effect is independent of the index: that is, their effect is the same for each instance.

3. Example1 • The state of a game of trivial pursuit might be described using the following pair of schemas:

4. Example1

5. Example1 • The change in state associated with a single player answering a scoring question correctly could be described by:

6. Example1 • The change in local state - in the individual player's score - could be described by

7. Example1 • The following mixed operation identifies a particular local score; one of the copies indexed by score:

8. Example1 • The following operation describes the change in global state that accompanies such a correct answer: • Removing the extra names from the declaration, we obtain a global operation schema:

9. Promotion Schema • If Local describes a copy of the local state and Global describes a copy of the global state, then a promotion schema Promote will contain decorated and undecorated copies of both Local and Global. • If LocalOperation contains decorated and undecorated copies of Local, then we may promote LocalOperation to the global operation

10. Example2

11. Example2

12. Example2 • Each mailbox is a binding:

13. Example2 • A local operation:

14. Example2 • A promotion schema:

15. Example2 • A global operation:

16. Example2 • A global operation (without promotion):

17. Example3

18. Example3

19. Example3 A local operation:

20. Example3

22. Example • We wish to describe a library of musical recordings on tape or compact disc. We shall call this system as AudioLib. We want to attach a loan category to each recording copy and we want to maintain a record of the date on which the copy was loaned out.

23. Example • For this system the set Recording is defined by a schema so that the members of this set have a particular structure Recording cat : Category loans : seq Date rec : RecordingDetails • Date is a given set and RecordingDetails is either a given set or a schema type defined elseware • Two loan categories: Category ::= Loanable | Restricted

24. Example • A given set of identifiers used to identify uniquely each distinct physical tape or compact disc in AudioLib stock [RecId]

25. Example • We define the abstract state for the AudioLib system AudioLib stock : RecId ↛Recording out : RecId ↛Listener listeners : Listener dom out  dom stock ran out  listeners  r : dom out  (stock r).cat = Loanable

26. Example • The predicate part of this schema says that: - only items of stock can be out on loan - loans can only be made to registered listeners - items out on loan must be loanable and not restricted to the library

27. Example • We define an operation to change the loan category of a Recording ChangeCategory Recording newcat? : Category report! : Report cat ≠ newcat?  (report! = Ok  cat’ = newcat?) cat = newcat?  (report! = NoChange  cat’ = cat?) loans’ = loans rec’ = rec

28. Example • To promote operations on individual Recordings to be operations on the AudioLib abstract state, we factored using promotion; we define a promotion schema Promote AudioLib Recording rcid? : RecId rcid?  dom stock Recording = stock rcid? stock’ = stock  {rcid? ↦ Recording’}

29. Example • The constraint Recording = stock rcid? ensures that Recording concerned is the one corresponding to stock rcid? • The constraint stock’ = stock  {rcid? ↦ Recording’} ensures that stock is unchanged except that rcid? Is now associated with the modified Recording • we could define an operation ChangeRecordingCategas: ChangeRecordingCateg ≙  Recording  ChangeCategory Promote