Proof Assistant Projects
Collection
Digesting proof assistant libraries for AI ingestion. • 84 items • Updated • 3
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 |
|---|---|---|---|---|---|---|
Proc == 1 .. N | definition | aba-asyn-byz | [
"Naturals"
] | aba-asyn-byz/aba_asyn_byz.tla | Proc | null |
Location == { "V0", "V1", "EC", "RD", "AC", "BYZ" } | definition | aba-asyn-byz | [
"Naturals"
] | aba-asyn-byz/aba_asyn_byz.tla | Location | null |
vars == << nSntE, nSntR, nRcvdE, nRcvdR, nByz, pc >> | definition | aba-asyn-byz | [
"Naturals"
] | aba-asyn-byz/aba_asyn_byz.tla | vars | null |
guardE == (N + T + 2) \div 2 | definition | aba-asyn-byz | [
"Naturals"
] | aba-asyn-byz/aba_asyn_byz.tla | guardE | null |
guardR1 == T + 1 | definition | aba-asyn-byz | [
"Naturals"
] | aba-asyn-byz/aba_asyn_byz.tla | guardR1 | null |
guardR2 == 2 * T + 1 | definition | aba-asyn-byz | [
"Naturals"
] | aba-asyn-byz/aba_asyn_byz.tla | guardR2 | null |
Init ==
/\ nSntE = 0
/\ nSntR = 0
/\ nRcvdE = [ i \in Proc |-> 0 ]
/\ nRcvdR = [ i \in Proc |-> 0 ]
/\ nByz = 0
/\ pc \in [ Proc -> { "V0", "V1" } ] | definition | aba-asyn-byz | [
"Naturals"
] | aba-asyn-byz/aba_asyn_byz.tla | Init | null |
Init0 ==
/\ nSntE = 0
/\ nSntR = 0
/\ nRcvdE = [ i \in Proc |-> 0 ]
/\ nRcvdR = [ i \in Proc |-> 0 ]
/\ nByz = 0
/\ pc \in [ i \in Proc |-> "V0" ] | definition | aba-asyn-byz | [
"Naturals"
] | aba-asyn-byz/aba_asyn_byz.tla | Init0 | An encoding of the asynchronous Byzantine consensus protocol in Fig.3 [1]:
[1] Bracha, Gabriel, and Sam Toueg. "Asynchronous consensus and broadcast protocols."
Journal of the ACM (JACM) 32.4 (1985): 824-840.
Thanh Hai Tran, Igor Konnov, Josef Widder, 2016
This file is a subject to the license tha... |
Init1 ==
/\ nSntE = 0
/\ nSntR = 0
/\ nRcvdE = [ i \in Proc |-> 0 ]
/\ nRcvdR = [ i \in Proc |-> 0 ]
/\ nByz = 0
/\ pc \in [ i \in Proc |-> "V1" ] | definition | aba-asyn-byz | [
"Naturals"
] | aba-asyn-byz/aba_asyn_byz.tla | Init1 | An encoding of the asynchronous Byzantine consensus protocol in Fig.3 [1]:
[1] Bracha, Gabriel, and Sam Toueg. "Asynchronous consensus and broadcast protocols."
Journal of the ACM (JACM) 32.4 (1985): 824-840.
Thanh Hai Tran, Igor Konnov, Josef Widder, 2016
This file is a subject to the license tha... |
BecomeByzantine(i) ==
/\ nByz < F
/\ \/ pc[i] = "V1"
\/ pc[i] = "V0"
/\ nByz' = nByz + 1
/\ pc' = [ pc EXCEPT ![i] = "BYZ" ]
/\ UNCHANGED << nSntE, nSntR, nRcvdE, nRcvdR >> | definition | aba-asyn-byz | [
"Naturals"
] | aba-asyn-byz/aba_asyn_byz.tla | BecomeByzantine | An encoding of the asynchronous Byzantine consensus protocol in Fig.3 [1]:
[1] Bracha, Gabriel, and Sam Toueg. "Asynchronous consensus and broadcast protocols."
Journal of the ACM (JACM) 32.4 (1985): 824-840.
Thanh Hai Tran, Igor Konnov, Josef Widder, 2016
This file is a subject to the license tha... |
Receive(i, includeByz) ==
\/ /\ nRcvdE[i] < nSntE + (IF includeByz THEN nByz ELSE 0)
/\ nRcvdE' = [ nRcvdE EXCEPT ![i] = nRcvdE[i] + 1 ]
/\ UNCHANGED << nSntE, nSntR, nRcvdR, nByz, pc >>
\/ /\ nRcvdR[i] < nSntR + (IF includeByz THEN nByz ELSE 0)
/\ nRcvdR' = [ nRcvdR EXCEPT ![i] = nRcvdR[i] + 1 ... | definition | aba-asyn-byz | [
"Naturals"
] | aba-asyn-byz/aba_asyn_byz.tla | Receive | An encoding of the asynchronous Byzantine consensus protocol in Fig.3 [1]:
[1] Bracha, Gabriel, and Sam Toueg. "Asynchronous consensus and broadcast protocols."
Journal of the ACM (JACM) 32.4 (1985): 824-840.
Thanh Hai Tran, Igor Konnov, Josef Widder, 2016
This file is a subject to the license tha... |
SendEcho(i) ==
/\ \/ pc[i] = "V1"
\/ /\ pc[i] = "V0"
/\ \/ nRcvdE[i] >= guardE
\/ nRcvdR[i] >= guardR1
/\ pc' = [ pc EXCEPT ![i] = "EC" ]
/\ nSntE' = nSntE + 1
/\ UNCHANGED << nSntR, nRcvdE, nRcvdR, nByz >> | definition | aba-asyn-byz | [
"Naturals"
] | aba-asyn-byz/aba_asyn_byz.tla | SendEcho | An encoding of the asynchronous Byzantine consensus protocol in Fig.3 [1]:
[1] Bracha, Gabriel, and Sam Toueg. "Asynchronous consensus and broadcast protocols."
Journal of the ACM (JACM) 32.4 (1985): 824-840.
Thanh Hai Tran, Igor Konnov, Josef Widder, 2016
This file is a subject to the license tha... |
SendReady(i) ==
/\ pc[i] = "EC"
/\ \/ nRcvdE[i] >= guardE
\/ nRcvdR[i] >= guardR1
/\ pc' = [ pc EXCEPT ![i] = "RD" ]
/\ nSntR' = nSntR + 1
/\ UNCHANGED << nSntE, nRcvdE, nRcvdR, nByz >> | definition | aba-asyn-byz | [
"Naturals"
] | aba-asyn-byz/aba_asyn_byz.tla | SendReady | An encoding of the asynchronous Byzantine consensus protocol in Fig.3 [1]:
[1] Bracha, Gabriel, and Sam Toueg. "Asynchronous consensus and broadcast protocols."
Journal of the ACM (JACM) 32.4 (1985): 824-840.
Thanh Hai Tran, Igor Konnov, Josef Widder, 2016
This file is a subject to the license tha... |
Decide(i) ==
/\ pc[i] = "RD"
/\ nRcvdR[i] >= guardR2
/\ pc' = [ pc EXCEPT ![i] = "AC" ]
/\ UNCHANGED << nSntE, nSntE, nSntR, nRcvdE, nRcvdR, nByz >> | definition | aba-asyn-byz | [
"Naturals"
] | aba-asyn-byz/aba_asyn_byz.tla | Decide | An encoding of the asynchronous Byzantine consensus protocol in Fig.3 [1]:
[1] Bracha, Gabriel, and Sam Toueg. "Asynchronous consensus and broadcast protocols."
Journal of the ACM (JACM) 32.4 (1985): 824-840.
Thanh Hai Tran, Igor Konnov, Josef Widder, 2016
This file is a subject to the license tha... |
Next ==
/\ \E self \in Proc :
\/ BecomeByzantine(self)
\/ Receive(self, TRUE)
\/ SendEcho(self)
\/ SendReady(self)
\/ Decide(self)
\/ UNCHANGED vars | definition | aba-asyn-byz | [
"Naturals"
] | aba-asyn-byz/aba_asyn_byz.tla | Next | null |
Spec == Init /\ [][Next]_vars
/\ WF_vars(\E self \in Proc : \/ Receive(self, FALSE)
\/ SendEcho(self)
\/ SendReady(self)
\/ Decide(self)) | definition | aba-asyn-byz | [
"Naturals"
] | aba-asyn-byz/aba_asyn_byz.tla | Spec | An encoding of the asynchronous Byzantine consensus protocol in Fig.3 [1]:
[1] Bracha, Gabriel, and Sam Toueg. "Asynchronous consensus and broadcast protocols."
Journal of the ACM (JACM) 32.4 (1985): 824-840.
Thanh Hai Tran, Igor Konnov, Josef Widder, 2016
This file is a subject to the license tha... |
Spec0 == Init0 /\ [][Next]_vars
/\ WF_vars(\E self \in Proc : \/ Receive(self, FALSE)
\/ SendEcho(self)
\/ SendReady(self)
\/ Decide(self)) | definition | aba-asyn-byz | [
"Naturals"
] | aba-asyn-byz/aba_asyn_byz.tla | Spec0 | null |
TypeOK ==
/\ pc \in [ Proc -> Location ]
/\ nSntE \in 0..N
/\ nSntR \in 0..N
/\ nByz \in 0..F
/\ nRcvdE \in [ Proc -> 0..(nSntE + nByz) ]
/\ nRcvdR \in [ Proc -> 0..(nSntR + nByz) ] | definition | aba-asyn-byz | [
"Naturals"
] | aba-asyn-byz/aba_asyn_byz.tla | TypeOK | null |
Unforg_Ltl ==
(\A i \in Proc : pc[i] = "V0") => []( \A i \in Proc : pc[i] # "AC" ) | definition | aba-asyn-byz | [
"Naturals"
] | aba-asyn-byz/aba_asyn_byz.tla | Unforg_Ltl | null |
Corr_Ltl ==
(\A i \in Proc : pc[i] = "V1") => <>( \E i \in Proc : pc[i] = "AC" ) | definition | aba-asyn-byz | [
"Naturals"
] | aba-asyn-byz/aba_asyn_byz.tla | Corr_Ltl | null |
Agreement_Ltl ==
[]((\E i \in Proc : pc[i] = "AC") => <>(\A i \in Proc : pc[i] = "AC" \/ pc[i] = "BYZ" )) | definition | aba-asyn-byz | [
"Naturals"
] | aba-asyn-byz/aba_asyn_byz.tla | Agreement_Ltl | null |
NTF == N \in Nat /\ T \in Nat /\ F \in Nat /\ (N > 3 * T) /\ (T >= F) /\ (F >= 0) | assume | aba-asyn-byz | [
"Naturals"
] | aba-asyn-byz/aba_asyn_byz.tla | NTF | null |
TypeInvParticipantNB == participant \in [
participants -> [
vote : {yes, no},
alive : BOOLEAN,
decision : {undecided, commit, abort},
faulty : BOOLEAN,
... | definition | acp | [
"ACP_SB"
] | acp/ACP_NB.tla | TypeInvParticipantNB | null |
TypeInvNB == TypeInvParticipantNB /\ TypeInvCoordinator | definition | acp | [
"ACP_SB"
] | acp/ACP_NB.tla | TypeInvNB | null |
InitParticipantNB == participant \in [
participants -> [
vote : {yes, no},
alive : {TRUE},
decision : {undecided},
faulty : {FALSE},
voteSent : {FALSE},
... | definition | acp | [
"ACP_SB"
] | acp/ACP_NB.tla | InitParticipantNB | null |
InitNB == InitParticipantNB /\ InitCoordinator | definition | acp | [
"ACP_SB"
] | acp/ACP_NB.tla | InitNB | null |
forward(i,j) == /\ i # j
/\ participant[i].alive
/\ participant[i].forward[i] # notsent
/\ participant[i].forward[j] = notsent
/\ participant' = [participant EXCEPT ![i] =
[@ EXCEPT !.forward =
[@ EXCEPT ![j] =... | definition | acp | [
"ACP_SB"
] | acp/ACP_NB.tla | forward | null |
preDecideOnForward(i,j) == /\ i # j
/\ participant[i].alive
/\ participant[i].forward[i] = notsent
/\ participant[j].forward[i] # notsent
/\ participant' = [participant EXCEPT ![i] =
... | definition | acp | [
"ACP_SB"
] | acp/ACP_NB.tla | preDecideOnForward | null |
preDecide(i) == /\ participant[i].alive
/\ participant[i].forward[i] = notsent
/\ coordinator.broadcast[i] # notsent
/\ participant' = [participant EXCEPT ![i] =
[@ EXCEPT !.forward =
[@ EXCEPT ![i] = coordinator.broadcast[i]]
... | definition | acp | [
"ACP_SB"
] | acp/ACP_NB.tla | preDecide | null |
decideNB(i) == /\ participant[i].alive
/\ \A j \in participants : participant[i].forward[j] # notsent
/\ participant' = [participant EXCEPT ![i] =
[@ EXCEPT !.decision = participant[i].forward[i]]
]
/\ UNCHANGED<<coordinator>> | definition | acp | [
"ACP_SB"
] | acp/ACP_NB.tla | decideNB | null |
abortOnTimeout(i) == /\ participant[i].alive
/\ participant[i].decision = undecided
/\ ~coordinator.alive
/\ \A j \in participants : participant[j].alive => coordinator.broadcast[j] = notsent
/\ \A j,k \in participants : ~participant[j]... | definition | acp | [
"ACP_SB"
] | acp/ACP_NB.tla | abortOnTimeout | null |
parProgNB(i,j) == \/ sendVote(i)
\/ abortOnVote(i)
\/ abortOnTimeoutRequest(i)
\/ forward(i,j)
\/ preDecideOnForward(i,j)
\/ abortOnTimeout(i)
\/ preDecide(i)
\/ decideNB(i) | definition | acp | [
"ACP_SB"
] | acp/ACP_NB.tla | parProgNB | null |
parProgNNB == \E i,j \in participants : parDie(i) \/ parProgNB(i,j) | definition | acp | [
"ACP_SB"
] | acp/ACP_NB.tla | parProgNNB | null |
progNNB == parProgNNB \/ coordProgN | definition | acp | [
"ACP_SB"
] | acp/ACP_NB.tla | progNNB | null |
fairnessNB == /\ \A i \in participants : WF_<<coordinator, participant>>(\E j \in participants : parProgNB(i,j))
/\ WF_<<coordinator, participant>>(coordProgB) | definition | acp | [
"ACP_SB"
] | acp/ACP_NB.tla | fairnessNB | null |
SpecNB == InitNB /\ [][progNNB]_<<coordinator, participant>> /\ fairnessNB | definition | acp | [
"ACP_SB"
] | acp/ACP_NB.tla | SpecNB | null |
AllCommit == \A i \in participants : <>(participant[i].decision = commit \/ participant[i].faulty) | definition | acp | [
"ACP_SB"
] | acp/ACP_NB.tla | AllCommit | null |
AllAbort == \A i \in participants : <>(participant[i].decision = abort \/ participant[i].faulty) | definition | acp | [
"ACP_SB"
] | acp/ACP_NB.tla | AllAbort | null |
AllCommitYesVotes == \A i \in participants :
\A j \in participants : participant[j].vote = yes
~> participant[i].decision = commit \/ participant[i].faulty \/ coordinator.faulty | definition | acp | [
"ACP_SB"
] | acp/ACP_NB.tla | AllCommitYesVotes | null |
Perms == Permutations(participants) | definition | acp | [
"TLC",
"ACP_NB"
] | acp/ACP_NB_TLC.tla | Perms | null |
AC4_alt == [][ /\ (\A i \in participants : participant[i].decision = commit
=> (participant'[i].decision = commit))
/\ (\A j \in participants : participant[j].decision = abort
=> (participant'[j].decision = abort))]_<<participant>> | definition | acp | [
"TLC",
"ACP_NB"
] | acp/ACP_NB_TLC.tla | AC4_alt | null |
TypeInvParticipantNB == participant \in [
participants -> [
vote : {yes, no},
alive : BOOLEAN,
decision : {undecided, commit, abort},
faulty : BOOLEAN,
... | definition | acp | [
"ACP_SB"
] | acp/ACP_NB_WRONG_TLC.tla | TypeInvParticipantNB | null |
TypeInvNB == TypeInvParticipantNB /\ TypeInvCoordinator | definition | acp | [
"ACP_SB"
] | acp/ACP_NB_WRONG_TLC.tla | TypeInvNB | null |
InitParticipantNB == participant \in [
participants -> [
vote : {yes, no},
alive : {TRUE},
decision : {undecided},
faulty : {FALSE},
voteSent : {FALSE},
... | definition | acp | [
"ACP_SB"
] | acp/ACP_NB_WRONG_TLC.tla | InitParticipantNB | null |
InitNB == InitParticipantNB /\ InitCoordinator | definition | acp | [
"ACP_SB"
] | acp/ACP_NB_WRONG_TLC.tla | InitNB | null |
forward(i,j) == /\ i # j
/\ participant[i].alive
/\ participant[i].decision # notsent
/\ participant[i].forward[j] = notsent
/\ participant' = [participant EXCEPT ![i] =
[@ EXCEPT !.forward =
[@ EXCEPT ![j] = p... | definition | acp | [
"ACP_SB"
] | acp/ACP_NB_WRONG_TLC.tla | forward | null |
decideOnForward(i,j) == /\ i # j
/\ participant[i].alive
/\ participant[i].decision = undecided
/\ participant[j].forward[i] # notsent
/\ participant' = [participant EXCEPT ![i] =
[@ EXCEPT !.de... | definition | acp | [
"ACP_SB"
] | acp/ACP_NB_WRONG_TLC.tla | decideOnForward | null |
abortOnTimeout(i) == /\ participant[i].alive
/\ participant[i].decision = undecided
/\ ~coordinator.alive
/\ \A j \in participants : participant[j].alive => coordinator.broadcast[j] = notsent
/\ \A j,k \in participants : ~participant[j]... | definition | acp | [
"ACP_SB"
] | acp/ACP_NB_WRONG_TLC.tla | abortOnTimeout | null |
parProgNB(i,j) == \/ parProg(i)
\/ forward(i,j)
\/ decideOnForward(i,j)
\/ abortOnTimeout(i) | definition | acp | [
"ACP_SB"
] | acp/ACP_NB_WRONG_TLC.tla | parProgNB | null |
parProgNNB == \E i,j \in participants : parDie(i) \/ parProgNB(i,j) | definition | acp | [
"ACP_SB"
] | acp/ACP_NB_WRONG_TLC.tla | parProgNNB | null |
progNNB == parProgNNB \/ coordProgN | definition | acp | [
"ACP_SB"
] | acp/ACP_NB_WRONG_TLC.tla | progNNB | null |
fairnessNB == /\ \A i \in participants : WF_<<coordinator, participant>>(\E j \in participants : parProgNB(i,j))
/\ WF_<<coordinator, participant>>(coordProgB) | definition | acp | [
"ACP_SB"
] | acp/ACP_NB_WRONG_TLC.tla | fairnessNB | null |
SpecNB == InitNB /\ [][progNNB]_<<coordinator, participant>> /\ fairnessNB | definition | acp | [
"ACP_SB"
] | acp/ACP_NB_WRONG_TLC.tla | SpecNB | null |
TypeInvParticipant == participant \in [
participants -> [
vote : {yes, no},
alive : BOOLEAN,
decision : {undecided, commit, abort},
faulty : BOOLEAN,
... | definition | acp | [] | acp/ACP_SB.tla | TypeInvParticipant | null |
TypeInvCoordinator == coordinator \in [
request : [participants -> BOOLEAN],
vote : [participants -> {waiting, yes, no}],
broadcast : [participants -> {commit, abort, notsent}],
decision : {commit, abort, undecided}... | definition | acp | [] | acp/ACP_SB.tla | TypeInvCoordinator | null |
TypeInv == TypeInvParticipant /\ TypeInvCoordinator | definition | acp | [] | acp/ACP_SB.tla | TypeInv | null |
InitParticipant == participant \in [
participants -> [
vote : {yes, no},
alive : {TRUE},
decision : {undecided},
faulty : {FALSE},
voteSent : {FALSE}
]
... | definition | acp | [] | acp/ACP_SB.tla | InitParticipant | null |
InitCoordinator == coordinator \in [
request : [participants -> {FALSE}],
vote : [participants -> {waiting}],
alive : {TRUE},
broadcast : [participants -> {notsent}],
decision : {undecided},
... | definition | acp | [] | acp/ACP_SB.tla | InitCoordinator | null |
Init == InitParticipant /\ InitCoordinator | definition | acp | [] | acp/ACP_SB.tla | Init | null |
request(i) == /\ coordinator.alive
/\ ~coordinator.request[i]
/\ coordinator' = [coordinator EXCEPT !.request =
[@ EXCEPT ![i] = TRUE]
]
/\ UNCHANGED<<participant>> | definition | acp | [] | acp/ACP_SB.tla | request | null |
getVote(i) == /\ coordinator.alive
/\ coordinator.decision = undecided
/\ \A j \in participants : coordinator.request[j]
/\ coordinator.vote[i] = waiting
/\ participant[i].voteSent
/\ coordinator' = [coordinator EXCEPT !.vote =
[@... | definition | acp | [] | acp/ACP_SB.tla | getVote | null |
detectFault(i) == /\ coordinator.alive
/\ coordinator.decision = undecided
/\ \A j \in participants : coordinator.request[j]
/\ coordinator.vote[i] = waiting
/\ ~participant[i].alive
/\ ~participant[i].voteSent
/... | definition | acp | [] | acp/ACP_SB.tla | detectFault | null |
makeDecision == /\ coordinator.alive
/\ coordinator.decision = undecided
/\ \A j \in participants : coordinator.vote[j] \in {yes, no}
/\ \/ /\ \A j \in participants : coordinator.vote[j] = yes
/\ coordinator' = [coordinator EXCEPT !.decision = commit... | definition | acp | [] | acp/ACP_SB.tla | makeDecision | null |
coordBroadcast(i) == /\ coordinator.alive
/\ coordinator.decision # undecided
/\ coordinator.broadcast[i] = notsent
/\ coordinator' = [coordinator EXCEPT !.broadcast =
[@ EXCEPT ![i] = coordinator.decision]
... | definition | acp | [] | acp/ACP_SB.tla | coordBroadcast | null |
coordDie == /\ coordinator.alive
/\ coordinator' = [coordinator EXCEPT !.alive = FALSE, !.faulty = TRUE]
/\ UNCHANGED<<participant>> | definition | acp | [] | acp/ACP_SB.tla | coordDie | null |
sendVote(i) == /\ participant[i].alive
/\ coordinator.request[i]
/\ participant' = [participant EXCEPT ![i] =
[@ EXCEPT !.voteSent = TRUE]
]
/\ UNCHANGED<<coordinator>> | definition | acp | [] | acp/ACP_SB.tla | sendVote | null |
abortOnVote(i) == /\ participant[i].alive
/\ participant[i].decision = undecided
/\ participant[i].voteSent
/\ participant[i].vote = no
/\ participant' = [participant EXCEPT ![i] =
[@ EXCEPT !.decision = abort]
... | definition | acp | [] | acp/ACP_SB.tla | abortOnVote | null |
abortOnTimeoutRequest(i) == /\ participant[i].alive
/\ participant[i].decision = undecided
/\ ~coordinator.alive
/\ ~coordinator.request[i]
/\ participant' = [participant EXCEPT ![i] =
... | definition | acp | [] | acp/ACP_SB.tla | abortOnTimeoutRequest | null |
decide(i) == /\ participant[i].alive
/\ participant[i].decision = undecided
/\ coordinator.broadcast[i] # notsent
/\ participant' = [participant EXCEPT ![i] =
[@ EXCEPT !.decision = coordinator.broadcast[i]]
]
/\ UNCHANGED<<coordinat... | definition | acp | [] | acp/ACP_SB.tla | decide | null |
parDie(i) == /\ participant[i].alive
/\ participant' = [participant EXCEPT ![i] =
[@ EXCEPT !.alive = FALSE, !.faulty = TRUE]
]
/\ UNCHANGED<<coordinator>> | definition | acp | [] | acp/ACP_SB.tla | parDie | null |
parProg(i) == sendVote(i) \/ abortOnVote(i) \/ abortOnTimeoutRequest(i) \/ decide(i) | definition | acp | [] | acp/ACP_SB.tla | parProg | null |
parProgN == \E i \in participants : parDie(i) \/ parProg(i) | definition | acp | [] | acp/ACP_SB.tla | parProgN | null |
coordProgA(i) == request(i) \/ getVote(i) \/ detectFault(i) \/ coordBroadcast(i) | definition | acp | [] | acp/ACP_SB.tla | coordProgA | null |
coordProgB == makeDecision \/ \E i \in participants : coordProgA(i) | definition | acp | [] | acp/ACP_SB.tla | coordProgB | null |
coordProgN == coordDie \/ coordProgB | definition | acp | [] | acp/ACP_SB.tla | coordProgN | null |
progN == parProgN \/ coordProgN | definition | acp | [] | acp/ACP_SB.tla | progN | null |
fairness == /\ \A i \in participants : WF_<<coordinator, participant>>(parProg(i))
/\ WF_<<coordinator, participant>>(coordProgB) | definition | acp | [] | acp/ACP_SB.tla | fairness | null |
Spec == Init /\ [][progN]_<<coordinator, participant>> /\ fairness | definition | acp | [] | acp/ACP_SB.tla | Spec | null |
AC1 == [] \A i, j \in participants :
\/ participant[i].decision # commit
\/ participant[j].decision # abort | definition | acp | [] | acp/ACP_SB.tla | AC1 | null |
AC2 == [] ( (\E i \in participants : participant[i].decision = commit)
=> (\A j \in participants : participant[j].vote = yes)) | definition | acp | [] | acp/ACP_SB.tla | AC2 | null |
AC3_1 == [] ( (\E i \in participants : participant[i].decision = abort)
=> \/ (\E j \in participants : participant[j].vote = no)
\/ (\E j \in participants : participant[j].faulty)
\/ coordinator.faulty) | definition | acp | [] | acp/ACP_SB.tla | AC3_1 | null |
AC4 == [] /\ (\A i \in participants : participant[i].decision = commit
=> [](participant[i].decision = commit))
/\ (\A j \in participants : participant[j].decision = abort
=> [](participant[j].decision = abort)) | definition | acp | [] | acp/ACP_SB.tla | AC4 | null |
AC3_2 == <> \/ \A i \in participants : participant[i].decision \in {abort, commit}
\/ \E j \in participants : participant[j].faulty
\/ coordinator.faulty | definition | acp | [] | acp/ACP_SB.tla | AC3_2 | null |
FaultyStable == /\ \A i \in participants : [](participant[i].faulty => []participant[i].faulty)
/\ [](coordinator.faulty => [] coordinator.faulty) | definition | acp | [] | acp/ACP_SB.tla | FaultyStable | null |
VoteStable == \A i \in participants :
\/ [](participant[i].vote = yes)
\/ [](participant[i].vote = no) | definition | acp | [] | acp/ACP_SB.tla | VoteStable | null |
StrongerAC2 == [] ( (\E i \in participants : participant[i].decision = commit)
=> /\ (\A j \in participants : participant[j].vote = yes)
/\ coordinator.decision = commit) | definition | acp | [] | acp/ACP_SB.tla | StrongerAC2 | null |
StrongerAC3_1 == [] ( (\E i \in participants : participant[i].decision = abort)
=> \/ (\E j \in participants : participant[j].vote = no)
\/ /\ \E j \in participants : participant[j].faulty
/\ coordinator.decision = abort
\/ /\... | definition | acp | [] | acp/ACP_SB.tla | StrongerAC3_1 | null |
NoRecovery == [] /\ \A i \in participants : participant[i].alive <=> ~participant[i].faulty
/\ coordinator.alive <=> ~coordinator.faulty | definition | acp | [] | acp/ACP_SB.tla | NoRecovery | null |
DecisionReachedNoFault == (\A i \in participants : participant[i].alive)
~> (\A k \in participants : participant[k].decision # undecided) | definition | acp | [] | acp/ACP_SB.tla | DecisionReachedNoFault | null |
AbortImpliesNoVote == [] ( (\E i \in participants : participant[i].decision = abort)
=> (\E j \in participants : participant[j].vote = no)) | definition | acp | [] | acp/ACP_SB.tla | AbortImpliesNoVote | null |
AC5 == <> \A i \in participants : \/ participant[i].decision \in {abort, commit}
\/ participant[i].faulty | definition | acp | [] | acp/ACP_SB.tla | AC5 | null |
Perms == Permutations(participants) | definition | acp | [
"ACP_SB",
"TLC"
] | acp/ACP_SB_TLC.tla | Perms | null |
AC4_alt == [][ /\ (\A i \in participants : participant[i].decision = commit
=> (participant'[i].decision = commit))
/\ (\A j \in participants : participant[j].decision = abort
=> (participant'[j].decision = abort))]_<<participant>> | definition | acp | [
"ACP_SB",
"TLC"
] | acp/ACP_SB_TLC.tla | AC4_alt | null |
Sched == INSTANCE SchedulingAllocator | definition | allocator | [
"Naturals",
"FiniteSets",
"Sequences"
] | allocator/AllocatorImplementation.tla | Sched | null |
Messages ==
[type : {"request", "allocate", "return"},
clt : Clients,
rsrc : SUBSET Resources] | definition | allocator | [
"Naturals",
"FiniteSets",
"Sequences"
] | allocator/AllocatorImplementation.tla | Messages | null |
TypeInvariant ==
/\ Sched!TypeInvariant
/\ requests \in [Clients -> SUBSET Resources]
/\ holding \in [Clients -> SUBSET Resources]
/\ network \in SUBSET Messages | definition | allocator | [
"Naturals",
"FiniteSets",
"Sequences"
] | allocator/AllocatorImplementation.tla | TypeInvariant | null |
Init ==
/\ Sched!Init
/\ requests = [c \in Clients |-> {}]
/\ holding = [c \in Clients |-> {}]
/\ network = {} | definition | allocator | [
"Naturals",
"FiniteSets",
"Sequences"
] | allocator/AllocatorImplementation.tla | Init | null |
Request(c,S) ==
/\ requests[c] = {} /\ holding[c] = {}
/\ S # {} /\ requests' = [requests EXCEPT ![c] = S]
/\ network' = network \cup {[type |-> "request", clt |-> c, rsrc |-> S]}
/\ UNCHANGED <<unsat,alloc,sched,holding>> | definition | allocator | [
"Naturals",
"FiniteSets",
"Sequences"
] | allocator/AllocatorImplementation.tla | Request | null |
RReq(m) ==
/\ m \in network /\ m.type = "request"
/\ alloc[m.clt] = {}
/\ unsat' = [unsat EXCEPT ![m.clt] = m.rsrc]
/\ network' = network \ {m}
/\ UNCHANGED <<alloc,sched,requests,holding>> | definition | allocator | [
"Naturals",
"FiniteSets",
"Sequences"
] | allocator/AllocatorImplementation.tla | RReq | null |
Allocate(c,S) ==
/\ Sched!Allocate(c,S)
/\ network' = network \cup {[type |-> "allocate", clt |-> c, rsrc |-> S]}
/\ UNCHANGED <<requests,holding>> | definition | allocator | [
"Naturals",
"FiniteSets",
"Sequences"
] | allocator/AllocatorImplementation.tla | Allocate | null |
End of preview. Expand in Data Studio
TLA+
Structured dataset of TLA+ specifications from the official TLA+ Examples repository.
Schema
| Column | Type | Description |
|---|---|---|
| fact | string | Declaration body |
| type | string | definition, theorem, lemma, assume |
| library | string | Specification name (Paxos, DieHard, etc.) |
| imports | list | EXTENDS statements |
| filename | string | Source file path |
| symbolic_name | string | Declaration identifier |
| docstring | string | Documentation comment (where available) |
Statistics
By Type
| Type | Count |
|---|---|
| definition | 3,511 |
| theorem | 224 |
| lemma | 125 |
| assume | 42 |
By Library (Top 10)
| Library | Count |
|---|---|
| SpecifyingSystems | 681 |
| SDP_Verification | 468 |
| ewd998 | 290 |
| byzpaxos | 172 |
| dijkstra-mutex | 126 |
| FiniteMonotonic | 115 |
| Paxos | 108 |
| byihive | 105 |
| PaxosHowToWinATuringAward | 102 |
| LoopInvariance | 100 |
About TLA+
TLA+ is a formal specification language developed by Leslie Lamport for designing, modeling, and verifying concurrent and distributed systems. It is widely used in industry (Amazon, Microsoft, Oracle) to verify critical system designs before implementation.
Key features:
- Based on set theory and temporal logic
- Model checking via TLC
- Proof system via TLAPS
- Used for consensus protocols, distributed databases, and concurrent algorithms
Use Cases
- Retrieval/RAG for TLA+ specifications
- Learning distributed systems patterns
- Training embeddings for formal specifications
- Semantic search over protocol designs
Related Datasets
- Coq-Verdi - Verified distributed systems in Coq
- Coq-Iris - Concurrent separation logic
- Lean4-Mathlib - Mathematical formalizations
Citation
If you use this dataset, please cite the TLA+ Examples repository:
@software{tlaplus_examples,
title={TLA+ Examples},
url={https://github.com/tlaplus/Examples},
publisher={TLA+ Foundation}
}
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Source:
tlaplus/Examples
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Files processed:
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License:
MIT
Number of rows:
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Total file size:
468 kB