Decomposing the Read Event Sample Clauses

Decomposing the Read Event sociated with a particular process, which replaces bu f f of the abstrac- tion. The data in bu f f 2 can be added or removed one packet at a time. data2 represents a channel buffer, which replaces data of the abstraction. The data in data2 can be added or removed one packet at a time. Invariants writing ∈ proc >' reading ∈ proc > xxxx xxxx bu f f 2 ∈ proc→Block data2 ∈ chan→Block We ensure processes cannot be reading and writing at the same time with the invariant, dom(writing) ∩ dom(reading) = ∅ However we allow channels to be in the range of both reading and writing simultaneously. The new event StartWrite refines skip. StartWrite , ANY p, c WHERE p ∈ proc A c ∈ chan A p ∈/ dom(writing) A c ∈/ ran(writing) A bu f f 2(p) /= ∅ A data2(c) = ∅A p ∈/ dom(reading) THEN writing := writing ∪ {p '→ c} END '→ '→ The process and channel p c are added to the set of writing pairs. Once a process-channel pair is added to the set of writing pairs we transfer individual packets of data k d, from one to the other. k is the packet identifier and d represents the data. The WritePacket event: WritePacket , ANY p, c, k, d WHERE p '→ c ∈ writing A k ∈ dom(bu f f 2(p)) A d = bu f f 2(p)(k) A k ∈/ dom(data2(c)) THEN data2(c) := data2(c) ∪ {k '→ d} END '→ In the WritePacket event a packet k d is added to the channel buffer data2(c). The EndWrite event refines Write. EndWrite , REFINES Write ANY p, c WHERE p '→ c ∈ writing A c ∈ chan A data2(c) = bu f f 2(p) WITH b = bu f f 2(p) THEN writing := {p} — writing bu f f 2(p) := ∅ END { }— The process p is removed from the set of writers writing := p writing and the local buffer is cleared, bu f f 2(p) := ∅. The witness b = bu f f 2(p) links local variable b of the abstraction to bu f f 2(p) of the refinement. Local variable b does not appear in the refinement and is, instead, re- placed by buff2(p). Both b and bu f f 2(p) represent the process’ block of data. StartRead refines skip: StartRead , ANY p, c WHERE p ∈ proc A c ∈ chan A p ∈/ dom(reading) A c ∈/ ran(reading) A p ∈/ dom(writing) A data2(c) =/ THEN reading ∪ {p '→ c} END ∅ A bu f f 2(p) = ∅ '→ The process and channel pair p c are added to the set of reading pairs. ReadPacket refines skip: ReadPacket , ANY p, c, k WHERE p '→ c ∈ reading A k ∈ dom(data2(c)) A k ∈/ dom(bu f f 2(p))
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