occurrence
Part I, The Sentence and the Kernel · defined in Chapter I, The Founding Sentence
One lawful event. It makes one distinction and leaves records.
Chapter I defines it as one application of a law to named inputs, and a history as a finite admitted sequence of occurrences. Read on the world side the first clause gives a partial order and no clock. An occurrence precedes another when the second reads a record the first wrote; independent occurrences, which read and write disjoint records, commute; and records are permanent, so alternatives that write different records are different histories. A shared occurrence is one occurrence in the world and one entry in each participant’s log.
A register’s time is the number of occurrences committed to its own log, its age. Every age is the same in every sequential presentation of the history, the ages add up to the number of private occurrences plus twice the number of shared ones, and the age of a register at an occurrence is its component of that occurrence’s vector clock.
As mathematics
In the minimal register an occurrence is a transition of the automaton, and the symbol it writes is its record. In the world, histories up to the commutation of independent occurrences are Mazurkiewicz traces: if histories agree on the complete past of every occurrence they share, the local orders glue into one partial order, every history is a downward-closed part of it, and the admitted schedules are its linear extensions, connected by exchanges of adjacent independent occurrences.
If every exchange is recorded by both participants, each naming the other, the complete logs determine the read/write order uniquely: the vector-clock theorem of Fidge and Mattern in the program’s setting. Without the names, reconstruction first fails with four registers after three occurrences.
| Its name in another field | Bridge |
|---|---|
| a transition of the minimal automaton | built |
| an event of a Mazurkiewicz trace | built |
| an event with its vector clock, after Fidge and Mattern | classical |
| one update of a Wolfram model | type |
| an event | a reading |