Process in the World as a Transaction

1
Process in the World as a Transaction

• Nick Rossiter, Michael Heather
• Northumbria University
• nick.rossiter_at_unn.ac.uk
• http//computing.unn.ac.uk/staff/cgnr1/

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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

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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

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But some risk remains

• Strategy A to favour bank
• If ATM crashes before money paid out and after
  last transaction log entry made
• customers 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

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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

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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

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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

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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

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Adjunction Example Mapping Universe to
Information System
A
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Initial State
Blue category/object red functor green
natural transformation
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One cycle -- to right (F) and left (G) -- no
change
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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
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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
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Abstract View of Effect of GF
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Textbook representation of adjunction --
triangle only
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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.

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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
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Adjointness between Customer and Bank
Pin number ?
String match f
Bank
Customer
Access ?
? - f - ?
Better, shows relationships as adjunctions Does
not show state changes
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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
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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
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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

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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.