Design and Verification of Adaptive Cache Coherence Protocols ...

Base Rule Base Imperative Rule
P1 IP1 (Loadl-on-Clean)
P2 IP2 (Loadl-on-Dirty)
P3
P4
P5 IC3 (C-Send-CacheReq)
P6 IP3 (Storel-on-Clean)
P7 IP4 (Storel-on-Dirty)
P8
P9
P10 IC3 (C-Send-CacheReq)
P11 IP5 (Commit-on-Clean)
P12 IC2 (C-Send-Wb)
P13
P14
P15 IP6 (Commit-on-Invalid)
P16 IC1 (C-Purge)
P17 IP7 (Reconcile-on-Dirty)
P18
P19
P20 IP8 (Reconcile-on-Invalid)
VC1 IC1 (C-Purge)
VC2 IC2 (C-Send-Wb)
VC3 IC3 (C-Send-CacheReq)
MC1 IC4 (C-Receive-Cache)
MC2 IC5 (C-Receive-WbAck)
MM1 IM1 (M-Receive-CacheReq-&-Send-Cache)
MM2 IM2 (M-Receive-Wb-&-Send-WbAck)
Figure 4.7: Derivation of Base from Imperative Rules
If Rule IM1 (M-Receive-CacheReq-&-Send-Cache) applies, then
Cell(a,v) 2 Mem(s1) ^ Msg(id ,H,CacheReq,a) 2 Min(s1) ^
Cell(a,v) 2 Mem(s2) ^ Msg(H,id ,Cache,a,v) 2 Mout(s2)
) Cell(a,v) 2 Mem(dr(s1)) ^ a =2 Cache id(dr(s1)) ^ (Lemmas 5 & 8 )
Cell(a,v) 2 Mem(dr(s2)) ^ Cell(a,v,Clean) 2 Cache id(dr(s2)) (Lemmas 5 & 8 )
) f(s1) ! f(s2) (CRF-Cache )
If Rule IM2 (M-Receive-Wb-&-Send-WbAck) applies, then
Msg(id ,H,Wb,a,v) 2 Min(s1) ^
Cell(a,v) 2 Mem(s2) ^ Msg(H,id ,WbAck,a) 2 Mout(s2)
) Cell(a,v,Dirty) 2 Cache id(dr(s1)) ^ (Lemma 8 )
Cell(a,v) 2 Mem(dr(s2)) ^ Cell(a,v,Clean) 2 Cache id(dr(s2)) (Lemmas 5 & 8 )
) f(s1) ! f(s2) (CRF-Writeback )
Draining Rules
If Rule IC2 (C-Send-Wb), IC3 (C-Send-CacheReq), IC4 (C-Receive-Cache), IC5 (C-Receive-
WbAck), Message-Cache-to-Mem or Message-Mem-to-Cache applies, then
f(s1) =f(s2) (Since the rule or its backward version is a draining rule)
Figure 4.6 summarizes the simulation proof. 2
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