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| In [[computer science]], the '''happened-before''' [[binary relation|relation]] (denoted: <math>\to \;</math>) is a relation between the result of two events, such that if one event should happen before another event, the result must reflect that. Even if those events are in reality executed out of order (usually to optimize program flow). This involves [[partially ordered set|ordering]] events based on the potential [[causal relationships|causal relationship]] of pairs of events in a concurrent system, especially [[asynchronous communication|asynchronous]] [[distributed systems]]. It was formulated by [[Leslie Lamport]].<ref>Lamport, Leslie (1978). [http://research.microsoft.com/en-us/um/people/lamport/pubs/time-clocks.pdf "Time, Clocks and the Ordering of Events in a Distributed System"], ''Communications of the ACM'', 21(7), 558-565.</ref> In Java specifically, a '''happens-before''' relationship is a guarantee that memory written to by statement A is visible to statement B, that is, that statement A completes its write before statement B starts its read.[http://docs.oracle.com/javase/tutorial/essential/concurrency/memconsist.html]
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| The happened-before relation is formally defined as the least [[strict partial order]] on events such that:
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| * If events <math>a \;</math> and <math>b \;</math> occur on the same process, <math>a \to b\;</math> if the occurrence of event <math>a \;</math> preceded the occurrence of event <math>b \;</math>.
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| * If event <math>a \;</math> is the sending of a message and event <math>b \;</math> is the reception of the message sent in event <math>a \;</math>, <math>a \to b\;</math>.
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| If there are other causal relationships between events in a given system, such as between the creation of a process and its first event, these relationships are also added to the definition.
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| Like all strict partial orders, the happened-before relation is ''[[transitive relation|transitive]]'', ''[[irreflexive relation|irreflexive]]'' and ''[[antisymmetric relation|antisymmetric]]'', i.e.:
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| * <math>\forall a, b, c</math>, if <math>a \to b\;</math> and <math>b \to c\;</math>, then <math>a \to c\;</math> (transitivity) ;
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| * <math>\forall a, a \nrightarrow a</math> (irreflexivity) ;
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| * <math>\forall a, b,</math> if <math>a \to b\;</math> then <math>b \nrightarrow a</math> (antisymmetry).
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| The processes that make up a distributed system have no knowledge of the happened-before relation unless they use a [[logical clock]], like a [[Lamport clock]] or a [[vector clock]]. This allows to design algorithms for [[mutual exclusion]] and tasks like debugging or optimising distributed systems.
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| ==See also==
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| * [[Java Memory Model]]
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| * [[Lamport timestamps]]
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| ==References==
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| <references/>
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| {{DEFAULTSORT:Happened-Before}}
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| [[Category:Distributed computing problems]]
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