1. Process in the World as a Transaction
Nick Rossiter, Michael Heather
Northumbria University

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

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.  -| f* -|  Adjointness between Customer and Bank Bank Customer
Pin number 
String match f*
Customer
Bank
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.