fact stringlengths 6 24.9k | type stringclasses 4
values | library stringclasses 77
values | imports listlengths 0 8 | filename stringclasses 299
values | symbolic_name stringlengths 1 46 | docstring stringclasses 186
values |
|---|---|---|---|---|---|---|
RAlloc(m) ==
/\ m \in network /\ m.type = "allocate"
/\ holding' = [holding EXCEPT ![m.clt] = @ \cup m.rsrc]
/\ requests' = [requests EXCEPT ![m.clt] = @ \ m.rsrc]
/\ network' = network \ {m}
/\ UNCHANGED <<unsat,alloc,sched>> | definition | allocator | [
"Naturals",
"FiniteSets",
"Sequences"
] | allocator/AllocatorImplementation.tla | RAlloc | null |
Return(c,S) ==
/\ S # {} /\ S \subseteq holding[c]
/\ holding' = [holding EXCEPT ![c] = @ \ S]
/\ network' = network \cup {[type |-> "return", clt |-> c, rsrc |-> S]}
/\ UNCHANGED <<unsat,alloc,sched,requests>> | definition | allocator | [
"Naturals",
"FiniteSets",
"Sequences"
] | allocator/AllocatorImplementation.tla | Return | null |
RRet(m) ==
/\ m \in network /\ m.type = "return"
/\ alloc' = [alloc EXCEPT ![m.clt] = @ \ m.rsrc]
/\ network' = network \ {m}
/\ UNCHANGED <<unsat,sched,requests,holding>> | definition | allocator | [
"Naturals",
"FiniteSets",
"Sequences"
] | allocator/AllocatorImplementation.tla | RRet | null |
Schedule ==
/\ Sched!Schedule
/\ UNCHANGED <<requests,holding,network>> | definition | allocator | [
"Naturals",
"FiniteSets",
"Sequences"
] | allocator/AllocatorImplementation.tla | Schedule | null |
Next ==
\/ \E c \in Clients, S \in SUBSET Resources :
Request(c,S) \/ Allocate(c,S) \/ Return(c,S)
\/ \E m \in network :
RReq(m) \/ RAlloc(m) \/ RRet(m)
\/ Schedule | definition | allocator | [
"Naturals",
"FiniteSets",
"Sequences"
] | allocator/AllocatorImplementation.tla | Next | null |
vars == <<unsat,alloc,sched,requests,holding,network>> | definition | allocator | [
"Naturals",
"FiniteSets",
"Sequences"
] | allocator/AllocatorImplementation.tla | vars | null |
Liveness ==
/\ \A c \in Clients : WF_vars(requests[c]={} /\ Return(c,holding[c]))
/\ \A c \in Clients : WF_vars(\E S \in SUBSET Resources : Allocate(c, S))
/\ WF_vars(Schedule)
/\ \A m \in Messages :
/\ WF_vars(RReq(m))
/\ WF_vars(RAlloc(m))
/\ WF_vars(RRet(m)) | definition | allocator | [
"Naturals",
"FiniteSets",
"Sequences"
] | allocator/AllocatorImplementation.tla | Liveness | null |
Specification == Init /\ [][Next]_vars /\ Liveness | definition | allocator | [
"Naturals",
"FiniteSets",
"Sequences"
] | allocator/AllocatorImplementation.tla | Specification | null |
RequestsInTransit(c) ==
{ msg.rsrc : msg \in {m \in network : m.type = "request" /\ m.clt = c} } | definition | allocator | [
"Naturals",
"FiniteSets",
"Sequences"
] | allocator/AllocatorImplementation.tla | RequestsInTransit | null |
AllocsInTransit(c) ==
{ msg.rsrc : msg \in {m \in network : m.type = "allocate" /\ m.clt = c} } | definition | allocator | [
"Naturals",
"FiniteSets",
"Sequences"
] | allocator/AllocatorImplementation.tla | AllocsInTransit | null |
ReturnsInTransit(c) ==
{ msg.rsrc : msg \in {m \in network : m.type = "return" /\ m.clt = c} } | definition | allocator | [
"Naturals",
"FiniteSets",
"Sequences"
] | allocator/AllocatorImplementation.tla | ReturnsInTransit | null |
Invariant ==
/\ Sched!AllocatorInvariant
/\ \A c \in Clients :
/\ Cardinality(RequestsInTransit(c)) <= 1
/\ requests[c] = unsat[c]
\cup UNION RequestsInTransit(c)
\cup UNION AllocsInTransit(c)
/\ alloc[c] = holding[c]
\cup UN... | definition | allocator | [
"Naturals",
"FiniteSets",
"Sequences"
] | allocator/AllocatorImplementation.tla | Invariant | null |
ResourceMutex ==
\A c1,c2 \in Clients : holding[c1] \cap holding[c2] # {} => c1 = c2 | definition | allocator | [
"Naturals",
"FiniteSets",
"Sequences"
] | allocator/AllocatorImplementation.tla | ResourceMutex | null |
ClientsWillReturn ==
\A c \in Clients: (requests[c]={} ~> holding[c]={}) | definition | allocator | [
"Naturals",
"FiniteSets",
"Sequences"
] | allocator/AllocatorImplementation.tla | ClientsWillReturn | null |
ClientsWillObtain ==
\A c \in Clients, r \in Resources : r \in requests[c] ~> r \in holding[c] | definition | allocator | [
"Naturals",
"FiniteSets",
"Sequences"
] | allocator/AllocatorImplementation.tla | ClientsWillObtain | null |
InfOftenSatisfied ==
\A c \in Clients : []<>(requests[c] = {}) | definition | allocator | [
"Naturals",
"FiniteSets",
"Sequences"
] | allocator/AllocatorImplementation.tla | InfOftenSatisfied | null |
SchedAllocator == Sched!Allocator | definition | allocator | [
"Naturals",
"FiniteSets",
"Sequences"
] | allocator/AllocatorImplementation.tla | SchedAllocator | null |
Specification => []TypeInvariant | theorem | allocator | [
"Naturals",
"FiniteSets",
"Sequences"
] | allocator/AllocatorImplementation.tla | Specification | null |
Specification => []ResourceMutex | theorem | allocator | [
"Naturals",
"FiniteSets",
"Sequences"
] | allocator/AllocatorImplementation.tla | Specification | null |
Specification => []Invariant | theorem | allocator | [
"Naturals",
"FiniteSets",
"Sequences"
] | allocator/AllocatorImplementation.tla | Specification | null |
Specification => ClientsWillReturn | theorem | allocator | [
"Naturals",
"FiniteSets",
"Sequences"
] | allocator/AllocatorImplementation.tla | Specification | null |
Specification => ClientsWillObtain | theorem | allocator | [
"Naturals",
"FiniteSets",
"Sequences"
] | allocator/AllocatorImplementation.tla | Specification | null |
Specification => InfOftenSatisfied | theorem | allocator | [
"Naturals",
"FiniteSets",
"Sequences"
] | allocator/AllocatorImplementation.tla | Specification | null |
Specification => SchedAllocator | theorem | allocator | [
"Naturals",
"FiniteSets",
"Sequences"
] | allocator/AllocatorImplementation.tla | Specification | null |
Simple == INSTANCE SimpleAllocator | definition | allocator | [
"SchedulingAllocator"
] | allocator/AllocatorRefinement.tla | Simple | null |
SimpleAllocator == Simple!SimpleAllocator | definition | allocator | [
"SchedulingAllocator"
] | allocator/AllocatorRefinement.tla | SimpleAllocator | null |
Allocator => SimpleAllocator | theorem | allocator | [
"SchedulingAllocator"
] | allocator/AllocatorRefinement.tla | Allocator | null |
TypeInvariant ==
/\ unsat \in [Clients -> SUBSET Resources]
/\ alloc \in [Clients -> SUBSET Resources]
/\ sched \in Seq(Clients) | definition | allocator | [
"TLC",
"Naturals",
"FiniteSets",
"Sequences"
] | allocator/SchedulingAllocator.tla | TypeInvariant | null |
PermSeqs(S) ==
LET perms[ss \in SUBSET S] ==
IF ss = {} THEN { << >> }
ELSE LET ps == [ x \in ss |->
{ Append(sq,x) : sq \in perms[ss \ {x}] } ]
IN UNION { ps[x] : x \in ss }
IN perms[S] | definition | allocator | [
"TLC",
"Naturals",
"FiniteSets",
"Sequences"
] | allocator/SchedulingAllocator.tla | PermSeqs | null |
Drop(seq,i) == SubSeq(seq, 1, i-1) \circ SubSeq(seq, i+1, Len(seq)) | definition | allocator | [
"TLC",
"Naturals",
"FiniteSets",
"Sequences"
] | allocator/SchedulingAllocator.tla | Drop | null |
available == Resources \ (UNION {alloc[c] : c \in Clients}) | definition | allocator | [
"TLC",
"Naturals",
"FiniteSets",
"Sequences"
] | allocator/SchedulingAllocator.tla | available | null |
Range(f) == { f[x] : x \in DOMAIN f } | definition | allocator | [
"TLC",
"Naturals",
"FiniteSets",
"Sequences"
] | allocator/SchedulingAllocator.tla | Range | null |
toSchedule == { c \in Clients : unsat[c] # {} /\ c \notin Range(sched) } | definition | allocator | [
"TLC",
"Naturals",
"FiniteSets",
"Sequences"
] | allocator/SchedulingAllocator.tla | toSchedule | null |
Init ==
/\ unsat = [c \in Clients |-> {}]
/\ alloc = [c \in Clients |-> {}]
/\ sched = << >> | definition | allocator | [
"TLC",
"Naturals",
"FiniteSets",
"Sequences"
] | allocator/SchedulingAllocator.tla | Init | null |
Request(c,S) ==
/\ unsat[c] = {} /\ alloc[c] = {}
/\ S # {} /\ unsat' = [unsat EXCEPT ![c] = S]
/\ UNCHANGED <<alloc,sched>> | definition | allocator | [
"TLC",
"Naturals",
"FiniteSets",
"Sequences"
] | allocator/SchedulingAllocator.tla | Request | null |
Allocate(c,S) ==
/\ S # {} /\ S \subseteq available \cap unsat[c]
/\ \E i \in DOMAIN sched :
/\ sched[i] = c
/\ \A j \in 1..i-1 : unsat[sched[j]] \cap S = {}
/\ sched' = IF S = unsat[c] THEN Drop(sched,i) ELSE sched
/\ alloc' = [alloc EXCEPT ![c] = @ \cup S]
/\ unsat' = [unsat EXCEPT ![c... | definition | allocator | [
"TLC",
"Naturals",
"FiniteSets",
"Sequences"
] | allocator/SchedulingAllocator.tla | Allocate | null |
Return(c,S) ==
/\ S # {} /\ S \subseteq alloc[c]
/\ alloc' = [alloc EXCEPT ![c] = @ \ S]
/\ UNCHANGED <<unsat,sched>> | definition | allocator | [
"TLC",
"Naturals",
"FiniteSets",
"Sequences"
] | allocator/SchedulingAllocator.tla | Return | null |
Schedule ==
/\ toSchedule # {}
/\ \E sq \in PermSeqs(toSchedule) : sched' = sched \circ sq
/\ UNCHANGED <<unsat,alloc>> | definition | allocator | [
"TLC",
"Naturals",
"FiniteSets",
"Sequences"
] | allocator/SchedulingAllocator.tla | Schedule | null |
Next ==
\/ \E c \in Clients, S \in SUBSET Resources :
Request(c,S) \/ Allocate(c,S) \/ Return(c,S)
\/ Schedule | definition | allocator | [
"TLC",
"Naturals",
"FiniteSets",
"Sequences"
] | allocator/SchedulingAllocator.tla | Next | null |
vars == <<unsat,alloc,sched>> | definition | allocator | [
"TLC",
"Naturals",
"FiniteSets",
"Sequences"
] | allocator/SchedulingAllocator.tla | vars | null |
Liveness ==
/\ \A c \in Clients : WF_vars(unsat[c]={} /\ Return(c,alloc[c]))
/\ \A c \in Clients : WF_vars(\E S \in SUBSET Resources : Allocate(c, S))
/\ WF_vars(Schedule) | definition | allocator | [
"TLC",
"Naturals",
"FiniteSets",
"Sequences"
] | allocator/SchedulingAllocator.tla | Liveness | null |
Allocator == Init /\ [][Next]_vars /\ Liveness | definition | allocator | [
"TLC",
"Naturals",
"FiniteSets",
"Sequences"
] | allocator/SchedulingAllocator.tla | Allocator | null |
ResourceMutex ==
\A c1,c2 \in Clients : c1 # c2 => alloc[c1] \cap alloc[c2] = {} | definition | allocator | [
"TLC",
"Naturals",
"FiniteSets",
"Sequences"
] | allocator/SchedulingAllocator.tla | ResourceMutex | null |
UnscheduledClients ==
Clients \ Range(sched) | definition | allocator | [
"TLC",
"Naturals",
"FiniteSets",
"Sequences"
] | allocator/SchedulingAllocator.tla | UnscheduledClients | null |
PrevResources(i) ==
available
\cup (UNION {unsat[sched[j]] \cup alloc[sched[j]] : j \in 1..i-1})
\cup (UNION {alloc[c] : c \in UnscheduledClients}) | definition | allocator | [
"TLC",
"Naturals",
"FiniteSets",
"Sequences"
] | allocator/SchedulingAllocator.tla | PrevResources | null |
AllocatorInvariant ==
/\
\A i \in DOMAIN sched : unsat[sched[i]] # {}
/\
\A c \in toSchedule : unsat[c] # {}
/\
\A i \in DOMAIN sched : \A j \in 1..i-1 :
alloc[sched[i]] \cap unsat[sched[j]] = {}
/\
\A i \in DOMAIN sched : unsat[sched[i]] \subseteq PrevResources(i) | definition | allocator | [
"TLC",
"Naturals",
"FiniteSets",
"Sequences"
] | allocator/SchedulingAllocator.tla | AllocatorInvariant | null |
ClientsWillReturn ==
\A c \in Clients: (unsat[c]={} ~> alloc[c]={}) | definition | allocator | [
"TLC",
"Naturals",
"FiniteSets",
"Sequences"
] | allocator/SchedulingAllocator.tla | ClientsWillReturn | null |
ClientsWillObtain ==
\A c \in Clients, r \in Resources : r \in unsat[c] ~> r \in alloc[c] | definition | allocator | [
"TLC",
"Naturals",
"FiniteSets",
"Sequences"
] | allocator/SchedulingAllocator.tla | ClientsWillObtain | null |
InfOftenSatisfied ==
\A c \in Clients : []<>(unsat[c] = {}) | definition | allocator | [
"TLC",
"Naturals",
"FiniteSets",
"Sequences"
] | allocator/SchedulingAllocator.tla | InfOftenSatisfied | null |
Symmetry == Permutations(Resources) | definition | allocator | [
"TLC",
"Naturals",
"FiniteSets",
"Sequences"
] | allocator/SchedulingAllocator.tla | Symmetry | null |
Allocator => []TypeInvariant | theorem | allocator | [
"TLC",
"Naturals",
"FiniteSets",
"Sequences"
] | allocator/SchedulingAllocator.tla | Allocator | null |
Allocator => []ResourceMutex | theorem | allocator | [
"TLC",
"Naturals",
"FiniteSets",
"Sequences"
] | allocator/SchedulingAllocator.tla | Allocator | null |
Allocator => []AllocatorInvariant | theorem | allocator | [
"TLC",
"Naturals",
"FiniteSets",
"Sequences"
] | allocator/SchedulingAllocator.tla | Allocator | null |
Allocator => ClientsWillReturn | theorem | allocator | [
"TLC",
"Naturals",
"FiniteSets",
"Sequences"
] | allocator/SchedulingAllocator.tla | Allocator | null |
Allocator => ClientsWillObtain | theorem | allocator | [
"TLC",
"Naturals",
"FiniteSets",
"Sequences"
] | allocator/SchedulingAllocator.tla | Allocator | null |
Allocator => InfOftenSatisfied | theorem | allocator | [
"TLC",
"Naturals",
"FiniteSets",
"Sequences"
] | allocator/SchedulingAllocator.tla | Allocator | null |
TypeInvariant ==
/\ unsat \in [Clients -> SUBSET Resources]
/\ alloc \in [Clients -> SUBSET Resources] | definition | allocator | [
"TLC",
"FiniteSets"
] | allocator/SimpleAllocator.tla | TypeInvariant | null |
available == Resources \ (UNION {alloc[c] : c \in Clients}) | definition | allocator | [
"TLC",
"FiniteSets"
] | allocator/SimpleAllocator.tla | available | null |
Init ==
/\ unsat = [c \in Clients |-> {}]
/\ alloc = [c \in Clients |-> {}] | definition | allocator | [
"TLC",
"FiniteSets"
] | allocator/SimpleAllocator.tla | Init | null |
Request(c,S) ==
/\ unsat[c] = {} /\ alloc[c] = {}
/\ S # {} /\ unsat' = [unsat EXCEPT ![c] = S]
/\ UNCHANGED alloc | definition | allocator | [
"TLC",
"FiniteSets"
] | allocator/SimpleAllocator.tla | Request | null |
Allocate(c,S) ==
/\ S # {} /\ S \subseteq available \cap unsat[c]
/\ alloc' = [alloc EXCEPT ![c] = @ \cup S]
/\ unsat' = [unsat EXCEPT ![c] = @ \ S] | definition | allocator | [
"TLC",
"FiniteSets"
] | allocator/SimpleAllocator.tla | Allocate | null |
Return(c,S) ==
/\ S # {} /\ S \subseteq alloc[c]
/\ alloc' = [alloc EXCEPT ![c] = @ \ S]
/\ UNCHANGED unsat | definition | allocator | [
"TLC",
"FiniteSets"
] | allocator/SimpleAllocator.tla | Return | null |
Next ==
\E c \in Clients, S \in SUBSET Resources :
Request(c,S) \/ Allocate(c,S) \/ Return(c,S) | definition | allocator | [
"TLC",
"FiniteSets"
] | allocator/SimpleAllocator.tla | Next | null |
vars == <<unsat,alloc>> | definition | allocator | [
"TLC",
"FiniteSets"
] | allocator/SimpleAllocator.tla | vars | null |
SimpleAllocator ==
/\ Init /\ [][Next]_vars
/\ \A c \in Clients: WF_vars(Return(c, alloc[c]))
/\ \A c \in Clients: SF_vars(\E S \in SUBSET Resources: Allocate(c,S)) | definition | allocator | [
"TLC",
"FiniteSets"
] | allocator/SimpleAllocator.tla | SimpleAllocator | null |
ResourceMutex ==
\A c1,c2 \in Clients : c1 # c2 => alloc[c1] \cap alloc[c2] = {} | definition | allocator | [
"TLC",
"FiniteSets"
] | allocator/SimpleAllocator.tla | ResourceMutex | null |
ClientsWillReturn ==
\A c \in Clients : unsat[c]={} ~> alloc[c]={} | definition | allocator | [
"TLC",
"FiniteSets"
] | allocator/SimpleAllocator.tla | ClientsWillReturn | null |
ClientsWillObtain ==
\A c \in Clients, r \in Resources : r \in unsat[c] ~> r \in alloc[c] | definition | allocator | [
"TLC",
"FiniteSets"
] | allocator/SimpleAllocator.tla | ClientsWillObtain | null |
InfOftenSatisfied ==
\A c \in Clients : []<>(unsat[c] = {}) | definition | allocator | [
"TLC",
"FiniteSets"
] | allocator/SimpleAllocator.tla | InfOftenSatisfied | null |
Symmetry == Permutations(Clients) \cup Permutations(Resources) | definition | allocator | [
"TLC",
"FiniteSets"
] | allocator/SimpleAllocator.tla | Symmetry | null |
SimpleAllocator2 ==
/\ Init /\ [][Next]_vars
/\ \A c \in Clients: WF_vars(unsat[c] = {} /\ Return(c, alloc[c]))
/\ \A c \in Clients: SF_vars(\E S \in SUBSET Resources: Allocate(c,S)) | definition | allocator | [
"TLC",
"FiniteSets"
] | allocator/SimpleAllocator.tla | SimpleAllocator2 | null |
SimpleAllocator => []TypeInvariant | theorem | allocator | [
"TLC",
"FiniteSets"
] | allocator/SimpleAllocator.tla | SimpleAllocator | null |
SimpleAllocator => []ResourceMutex | theorem | allocator | [
"TLC",
"FiniteSets"
] | allocator/SimpleAllocator.tla | SimpleAllocator | null |
SimpleAllocator => ClientsWillReturn | theorem | allocator | [
"TLC",
"FiniteSets"
] | allocator/SimpleAllocator.tla | SimpleAllocator | null |
SimpleAllocator2 => ClientsWillReturn | theorem | allocator | [
"TLC",
"FiniteSets"
] | allocator/SimpleAllocator.tla | SimpleAllocator2 | null |
SimpleAllocator => ClientsWillObtain | theorem | allocator | [
"TLC",
"FiniteSets"
] | allocator/SimpleAllocator.tla | SimpleAllocator | null |
SimpleAllocator => InfOftenSatisfied | theorem | allocator | [
"TLC",
"FiniteSets"
] | allocator/SimpleAllocator.tla | SimpleAllocator | null |
Procs == 1..N
a \prec b == \/ a[1] < b[1]
\/ (a[1] = b[1]) /\ (a[2] < b[2]) | definition | Bakery-Boulangerie | [
"Naturals",
"TLAPS"
] | Bakery-Boulangerie/Bakery.tla | Procs | null |
vars == << num, flag, pc, unchecked, max, nxt >> | definition | Bakery-Boulangerie | [
"Naturals",
"TLAPS"
] | Bakery-Boulangerie/Bakery.tla | vars | null |
ProcSet == (Procs) | definition | Bakery-Boulangerie | [
"Naturals",
"TLAPS"
] | Bakery-Boulangerie/Bakery.tla | ProcSet | null |
Init ==
/\ num = [i \in Procs |-> 0]
/\ flag = [i \in Procs |-> FALSE]
/\ unchecked = [self \in Procs |-> {}]
/\ max = [self \in Procs |-> 0]
/\ nxt = [self \in Procs |-> 1]
/\ pc = [self \in ProcSet |-> "ncs"] | definition | Bakery-Boulangerie | [
"Naturals",
"TLAPS"
] | Bakery-Boulangerie/Bakery.tla | Init | null |
ncs(self) == /\ pc[self] = "ncs"
/\ pc' = [pc EXCEPT ![self] = "e1"]
/\ UNCHANGED << num, flag, unchecked, max, nxt >> | definition | Bakery-Boulangerie | [
"Naturals",
"TLAPS"
] | Bakery-Boulangerie/Bakery.tla | ncs | null |
e1(self) == /\ pc[self] = "e1"
/\ \/ /\ flag' = [flag EXCEPT ![self] = ~ flag[self]]
/\ pc' = [pc EXCEPT ![self] = "e1"]
/\ UNCHANGED <<unchecked, max>>
\/ /\ flag' = [flag EXCEPT ![self] = TRUE]
/\ unchecked' = [unchecked EXCEPT ![self] =... | definition | Bakery-Boulangerie | [
"Naturals",
"TLAPS"
] | Bakery-Boulangerie/Bakery.tla | e1 | null |
e2(self) == /\ pc[self] = "e2"
/\ IF unchecked[self] # {}
THEN /\ \E i \in unchecked[self]:
/\ unchecked' = [unchecked EXCEPT ![self] = unchecked[self] \ {i}]
/\ IF num[i] > max[self]
THEN /\ max' = [... | definition | Bakery-Boulangerie | [
"Naturals",
"TLAPS"
] | Bakery-Boulangerie/Bakery.tla | e2 | null |
e3(self) == /\ pc[self] = "e3"
/\ \/ /\ \E k \in Nat:
num' = [num EXCEPT ![self] = k]
/\ pc' = [pc EXCEPT ![self] = "e3"]
\/ /\ \E i \in {j \in Nat : j > max[self]}:
num' = [num EXCEPT ![self] = i]
/\ pc' = [pc ... | definition | Bakery-Boulangerie | [
"Naturals",
"TLAPS"
] | Bakery-Boulangerie/Bakery.tla | e3 | null |
e4(self) == /\ pc[self] = "e4"
/\ \/ /\ flag' = [flag EXCEPT ![self] = ~ flag[self]]
/\ pc' = [pc EXCEPT ![self] = "e4"]
/\ UNCHANGED unchecked
\/ /\ flag' = [flag EXCEPT ![self] = FALSE]
/\ unchecked' = [unchecked EXCEPT ![self] = Procs \... | definition | Bakery-Boulangerie | [
"Naturals",
"TLAPS"
] | Bakery-Boulangerie/Bakery.tla | e4 | null |
w1(self) == /\ pc[self] = "w1"
/\ IF unchecked[self] # {}
THEN /\ \E i \in unchecked[self]:
nxt' = [nxt EXCEPT ![self] = i]
/\ ~ flag[nxt'[self]]
/\ pc' = [pc EXCEPT ![self] = "w2"]
ELSE /\ pc' = [p... | definition | Bakery-Boulangerie | [
"Naturals",
"TLAPS"
] | Bakery-Boulangerie/Bakery.tla | w1 | null |
w2(self) == /\ pc[self] = "w2"
/\ \/ num[nxt[self]] = 0
\/ <<num[self], self>> \prec <<num[nxt[self]], nxt[self]>>
/\ unchecked' = [unchecked EXCEPT ![self] = unchecked[self] \ {nxt[self]}]
/\ pc' = [pc EXCEPT ![self] = "w1"]
/\ UNCHANGED << num, flag, max,... | definition | Bakery-Boulangerie | [
"Naturals",
"TLAPS"
] | Bakery-Boulangerie/Bakery.tla | w2 | null |
cs(self) == /\ pc[self] = "cs"
/\ TRUE
/\ pc' = [pc EXCEPT ![self] = "exit"]
/\ UNCHANGED << num, flag, unchecked, max, nxt >> | definition | Bakery-Boulangerie | [
"Naturals",
"TLAPS"
] | Bakery-Boulangerie/Bakery.tla | cs | null |
exit(self) == /\ pc[self] = "exit"
/\ \/ /\ \E k \in Nat:
num' = [num EXCEPT ![self] = k]
/\ pc' = [pc EXCEPT ![self] = "exit"]
\/ /\ num' = [num EXCEPT ![self] = 0]
/\ pc' = [pc EXCEPT ![self] = "ncs"]
/\ UNCH... | definition | Bakery-Boulangerie | [
"Naturals",
"TLAPS"
] | Bakery-Boulangerie/Bakery.tla | exit | null |
p(self) == ncs(self) \/ e1(self) \/ e2(self) \/ e3(self) \/ e4(self)
\/ w1(self) \/ w2(self) \/ cs(self) \/ exit(self) | definition | Bakery-Boulangerie | [
"Naturals",
"TLAPS"
] | Bakery-Boulangerie/Bakery.tla | p | null |
Next == (\E self \in Procs: p(self)) | definition | Bakery-Boulangerie | [
"Naturals",
"TLAPS"
] | Bakery-Boulangerie/Bakery.tla | Next | null |
Spec == /\ Init /\ [][Next]_vars
/\ \A self \in Procs : WF_vars((pc[self] # "ncs") /\ p(self)) | definition | Bakery-Boulangerie | [
"Naturals",
"TLAPS"
] | Bakery-Boulangerie/Bakery.tla | Spec | null |
MutualExclusion == \A i,j \in Procs : (i # j) => ~ /\ pc[i] = "cs"
/\ pc[j] = "cs" | definition | Bakery-Boulangerie | [
"Naturals",
"TLAPS"
] | Bakery-Boulangerie/Bakery.tla | MutualExclusion | null |
TypeOK == /\ num \in [Procs -> Nat]
/\ flag \in [Procs -> BOOLEAN]
/\ unchecked \in [Procs -> SUBSET Procs]
/\ max \in [Procs -> Nat]
/\ nxt \in [Procs -> Procs]
/\ pc \in [Procs -> {"ncs", "e1", "e2", "e3",
"e4", "w1", "w2", "cs", "exit"}... | definition | Bakery-Boulangerie | [
"Naturals",
"TLAPS"
] | Bakery-Boulangerie/Bakery.tla | TypeOK | null |
Before(i,j) == /\ num[i] > 0
/\ \/ pc[j] \in {"ncs", "e1", "exit"}
\/ /\ pc[j] = "e2"
/\ \/ i \in unchecked[j]
\/ max[j] >= num[i]
\/ /\ pc[j] = "e3"
/\ max[j] >= num[i]
\/ /\ pc[j] \in... | definition | Bakery-Boulangerie | [
"Naturals",
"TLAPS"
] | Bakery-Boulangerie/Bakery.tla | Before | null |
IInv == \A i \in Procs :
/\ (pc[i] \in {"e4", "w1", "w2", "cs"}) => (num[i] # 0)
/\ (pc[i] \in {"e2", "e3"}) => flag[i]
/\ (pc[i] = "w2") => (nxt[i] # i)
/\ pc[i] \in {"w1", "w2"} => i \notin unchecked[i]
/\ (pc[i] \in {"w1", "w2"}) =>
\A j \in ... | definition | Bakery-Boulangerie | [
"Naturals",
"TLAPS"
] | Bakery-Boulangerie/Bakery.tla | IInv | null |
Inv == TypeOK /\ IInv | definition | Bakery-Boulangerie | [
"Naturals",
"TLAPS"
] | Bakery-Boulangerie/Bakery.tla | Inv | null |
Trying(i) == pc[i] = "e1" | definition | Bakery-Boulangerie | [
"Naturals",
"TLAPS"
] | Bakery-Boulangerie/Bakery.tla | Trying | null |
InCS(i) == pc[i] = "cs" | definition | Bakery-Boulangerie | [
"Naturals",
"TLAPS"
] | Bakery-Boulangerie/Bakery.tla | InCS | null |
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