Process in the World as a Transaction

1. Process in the World as a Transaction Nick Rossiter, Michael Heather Northumbria University nick.rossiter@unn.ac.uk http://computing.unn.ac.uk/staff/cgnr1/

2. Classical (Database) Transactions • Properties of ACID: • Atomicity • collection of operations viewed as single process • Consistency • rules of organisation obeyed • Isolation • no results released until end • Durability • results are guaranteed to persist

3. Closure is Difficult • For instance in ATM withdrawal: • mixture of physical and logical tasks • once cash given to customer, cannot undo • bank at risk unless results are immediately durable • Notion of Transaction Log: • save results to a number of different targets (disks) • only complete when successfully write to last target disk

4. Recovery • If bank information system crashes; • transaction log can be run through from • last known position (savepoint) to • most recent successful transaction • partial transactions are discarded • So if disk crashes after customer paid £1,000,000 in a suitcase of notes • system will re-run the transaction and customer will have account debited

5. But some risk remains • Strategy A to favour bank: • If ATM crashes before money paid out and after last transaction log entry made: • customer’s account is debited but customer has no cash • Strategy B to favour customer: • If transaction log entry fails after cash paid to customer: • customer has the cash and no debit to account

6. In practice • A bank would probably not adopt strategy B as it could lose money • Strategy A is workable if: • ATM downtimes are accurately recorded • Enables customer accounts to be corrected • Corrections could be made semi-automatically with supervisory control • Recourse to higher level

7. Problem of Physical/Logical Mix • Example of the principle of Landauer • Information cannot exist except in the physical form • All transactions ultimately involve physical objects • need to handle together • physical entities • logic of the information system

8. Parallel processing • Transactions involve a sequence of operations • But often the operations should be in parallel • Sequence is used because of: • von Neumann architecture • locality of view • sequence of operations between fixed cells

9. Theory of Transactions • Need constructions to: • represent changes between states as dynamic relationships • indicate desired change in state • indicate rules controlling change in state • measure changes in state that occur

10. Satisfying Theory - Category Theory • Need constructions to: • represent changes between states as dynamic relationships • adjunctions • indicate desired change in state • free functor (F) • indicate rules controlling change in state • underlying functor (G) • measure changes in state that occur • unit and counit of adjunction (, ) •  from left-adjoint perspective •  from right-adjoint perspective

11. Adjunction Example: Mapping Universe to Information System A

12. Initial State Blue = category/object; red = functor; green = natural transformation

13. One cycle -- to right (F) and left (G) -- no change

14. One cycle -- to right (GF) and left (FG) -- change by  in S and  in A Adjoint if triangles commute If  is or  is , then equivalence relation

15. Two cycles -- to right (GFGF) and left (FGFG) -- change by  in S and  in A Gives symmetry in treatment of S and A Dynamical relationship Perhaps one cycle enforces rules, second cycle commits

16. Abstract View of Effect of GF

17. Textbook representation of adjunction -- triangle only

18. Transactions are Non-local • This banking transaction is typical of any transaction as a non-local process. • The log provides a parallel information system: • looking forward to the sequence • looking back to check that what was expected was achieved.

19. Possible Approaches to Banking ATM Transaction Security Bank Customer Funds-check Grant Cash Simple commutative requirement Grant = Funds-check o Security Does not show state changes or rules

20. Adjointness between Customer and Bank Pin number  String match f* Bank Customer Access   -| f*-| Better, shows relationships as adjunctions Does not show state changes

21. One cycle -- to right (FG) and left (GF) -- change by  in S (Customer) and  in A (Bank) F Funds request (free functor), G Status check (underlying functor applying rules) If  is or  is ,then no change to categories so back to initial state - transaction is aborted

22. Two cycles -- to right (GFGF) and left (FGFG) -- change by  in S and  in A Second cycle acts from banking perspective Introduces g in bank category Commits and releases cash Should be brief in execution for safety

23. Achievement of ACID • A, I are natural, achieved through closure in adjointness • C is natural, achieved through underlying functor in adjointness • D is natural, represented by back and forward components • log file is not represented directly but such a file is an artefact needed in a sequential system

24. Universe Transactions • The universe carries out transactions all the time non-locally • mediating between objects in time and space. • nevertheless still has the forward and back components except that they are non-local.