Proof Assistant Projects
Collection
Digesting proof assistant libraries for AI ingestion. • 103 items • Updated • 3
statement stringlengths 1 146k | proof stringlengths 0 10.9k | type stringclasses 5
values | symbolic_name stringlengths 1 46 | library stringclasses 99
values | filename stringclasses 346
values | imports listlengths 0 8 | deps listlengths 0 45 | docstring stringclasses 1
value | source_url stringclasses 1
value | commit stringclasses 1
value |
|---|---|---|---|---|---|---|---|---|---|---|
NTF == N \in Nat /\ T \in Nat /\ F \in Nat /\ (N > 3 * T) /\ (T >= F) /\ (F >= 0) | assume | NTF | aba-asyn-byz | specifications/aba-asyn-byz/aba_asyn_byz.tla | [
"Naturals"
] | [
"Nat"
] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | ||
Proc | == 1 .. N | definition | Proc | aba-asyn-byz | specifications/aba-asyn-byz/aba_asyn_byz.tla | [
"Naturals"
] | [] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
Location | == { "V0", "V1", "EC", "RD", "AC", "BYZ" } | definition | Location | aba-asyn-byz | specifications/aba-asyn-byz/aba_asyn_byz.tla | [
"Naturals"
] | [] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
vars | == << nSntE, nSntR, nRcvdE, nRcvdR, nByz, pc >> | definition | vars | aba-asyn-byz | specifications/aba-asyn-byz/aba_asyn_byz.tla | [
"Naturals"
] | [
"pc"
] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
guardE | == (N + T + 2) \div 2 | definition | guardE | aba-asyn-byz | specifications/aba-asyn-byz/aba_asyn_byz.tla | [
"Naturals"
] | [] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
guardR1 | == T + 1 | definition | guardR1 | aba-asyn-byz | specifications/aba-asyn-byz/aba_asyn_byz.tla | [
"Naturals"
] | [] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
guardR2 | == 2 * T + 1
(* Some processes propose 0 and others propose 1.*) | definition | guardR2 | aba-asyn-byz | specifications/aba-asyn-byz/aba_asyn_byz.tla | [
"Naturals"
] | [] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
Init | ==
/\ nSntE = 0 (* Neither ECHO nor READY messages are sent. *)
/\ nSntR = 0
/\ nRcvdE = [ i \in Proc |-> 0 ] (* Neither ECHO nor READY messages are received. *)
/\ nRcvdR = [ i \in Proc |-> 0 ]
/\ nByz = 0 (* No processes are faulty. ... | definition | Init | aba-asyn-byz | specifications/aba-asyn-byz/aba_asyn_byz.tla | [
"Naturals"
] | [
"Proc",
"pc"
] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
Init0 | ==
/\ nSntE = 0
/\ nSntR = 0
/\ nRcvdE = [ i \in Proc |-> 0 ]
/\ nRcvdR = [ i \in Proc |-> 0 ]
/\ nByz = 0
/\ pc \in [ i \in Proc |-> "V0" ]
(* All processes propose 1. *) | definition | Init0 | aba-asyn-byz | specifications/aba-asyn-byz/aba_asyn_byz.tla | [
"Naturals"
] | [
"Proc",
"pc"
] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
Init1 | ==
/\ nSntE = 0
/\ nSntR = 0
/\ nRcvdE = [ i \in Proc |-> 0 ]
/\ nRcvdR = [ i \in Proc |-> 0 ]
/\ nByz = 0
/\ pc \in [ i \in Proc |-> "V1" ]
(* If there are less than F Byzantine processes, process i becomes faulty. *)
(* We requite i to be in an initial state (V0 or V1) to not break the *)
... | definition | Init1 | aba-asyn-byz | specifications/aba-asyn-byz/aba_asyn_byz.tla | [
"Naturals"
] | [
"Proc",
"pc"
] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
BecomeByzantine(i) | ==
/\ nByz < F
/\ \/ pc[i] = "V1"
\/ pc[i] = "V0"
/\ nByz' = nByz + 1
/\ pc' = [ pc EXCEPT ![i] = "BYZ" ]
/\ UNCHANGED << nSntE, nSntR, nRcvdE, nRcvdR >>
(* Process i receives a new message. If includeByz is TRUE, then messages from both *)
(* correct and Byzantine processes are considered. Otherw... | definition | BecomeByzantine | aba-asyn-byz | specifications/aba-asyn-byz/aba_asyn_byz.tla | [
"Naturals"
] | [
"pc"
] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
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 ]
/\ UNCHANGED << ... | definition | Receive | aba-asyn-byz | specifications/aba-asyn-byz/aba_asyn_byz.tla | [
"Naturals"
] | [
"pc",
"vars"
] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
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 >>
(* If process i sent an ECHO message and has received enough ECHO or READY messages,
it... | definition | SendEcho | aba-asyn-byz | specifications/aba-asyn-byz/aba_asyn_byz.tla | [
"Naturals"
] | [
"guardE",
"guardR1",
"pc"
] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
SendReady(i) | ==
/\ pc[i] = "EC"
/\ \/ nRcvdE[i] >= guardE
\/ nRcvdR[i] >= guardR1
/\ pc' = [ pc EXCEPT ![i] = "RD" ]
/\ nSntR' = nSntR + 1
/\ UNCHANGED << nSntE, nRcvdE, nRcvdR, nByz >>
(* If process has received READY messages from a majority of processes, it will accept. *) | definition | SendReady | aba-asyn-byz | specifications/aba-asyn-byz/aba_asyn_byz.tla | [
"Naturals"
] | [
"guardE",
"guardR1",
"pc"
] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
Decide(i) | ==
/\ pc[i] = "RD"
/\ nRcvdR[i] >= guardR2
/\ pc' = [ pc EXCEPT ![i] = "AC" ]
/\ UNCHANGED << nSntE, nSntE, nSntR, nRcvdE, nRcvdR, nByz >> | definition | Decide | aba-asyn-byz | specifications/aba-asyn-byz/aba_asyn_byz.tla | [
"Naturals"
] | [
"guardR2",
"pc"
] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
Next | ==
/\ \E self \in Proc :
\/ BecomeByzantine(self)
\/ Receive(self, TRUE)
\/ SendEcho(self)
\/ SendReady(self)
\/ Decide(self)
\/ UNCHANGED vars
(* Add weak fairness condition since we want to check liveness properties. *) | definition | Next | aba-asyn-byz | specifications/aba-asyn-byz/aba_asyn_byz.tla | [
"Naturals"
] | [
"BecomeByzantine",
"Decide",
"Proc",
"Receive",
"SendEcho",
"SendReady",
"vars"
] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
Spec | == Init /\ [][Next]_vars
/\ WF_vars(\E self \in Proc : \/ Receive(self, FALSE)
\/ SendEcho(self)
\/ SendReady(self)
\/ Decide(self)) | definition | Spec | aba-asyn-byz | specifications/aba-asyn-byz/aba_asyn_byz.tla | [
"Naturals"
] | [
"Decide",
"Init",
"Next",
"Proc",
"Receive",
"SendEcho",
"SendReady"
] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
Spec0 | == Init0 /\ [][Next]_vars
/\ WF_vars(\E self \in Proc : \/ Receive(self, FALSE)
\/ SendEcho(self)
\/ SendReady(self)
\/ Decide(self)) | definition | Spec0 | aba-asyn-byz | specifications/aba-asyn-byz/aba_asyn_byz.tla | [
"Naturals"
] | [
"Decide",
"Init0",
"Next",
"Proc",
"Receive",
"SendEcho",
"SendReady"
] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
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 | TypeOK | aba-asyn-byz | specifications/aba-asyn-byz/aba_asyn_byz.tla | [
"Naturals"
] | [
"Location",
"Proc",
"pc"
] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
Unforg_Ltl | ==
(\A i \in Proc : pc[i] = "V0") => []( \A i \in Proc : pc[i] # "AC" ) | definition | Unforg_Ltl | aba-asyn-byz | specifications/aba-asyn-byz/aba_asyn_byz.tla | [
"Naturals"
] | [
"Proc",
"pc"
] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
Corr_Ltl | ==
(\A i \in Proc : pc[i] = "V1") => <>( \E i \in Proc : pc[i] = "AC" ) | definition | Corr_Ltl | aba-asyn-byz | specifications/aba-asyn-byz/aba_asyn_byz.tla | [
"Naturals"
] | [
"Proc",
"pc"
] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
Agreement_Ltl | ==
[]((\E i \in Proc : pc[i] = "AC") => <>(\A i \in Proc : pc[i] = "AC" \/ pc[i] = "BYZ" )) | definition | Agreement_Ltl | aba-asyn-byz | specifications/aba-asyn-byz/aba_asyn_byz.tla | [
"Naturals"
] | [
"Proc",
"pc"
] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
TypeInvParticipantNB | == participant \in [
participants -> [
vote : {yes, no},
alive : BOOLEAN,
decision : {undecided, commit, abort},
faulty : BOOLEAN,
v... | definition | TypeInvParticipantNB | acp | specifications/acp/ACP_NB.tla | [
"ACP_SB"
] | [
"forward"
] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
TypeInvNB | == TypeInvParticipantNB /\ TypeInvCoordinator | definition | TypeInvNB | acp | specifications/acp/ACP_NB.tla | [
"ACP_SB"
] | [
"TypeInvCoordinator",
"TypeInvParticipantNB"
] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
InitParticipantNB | == participant \in [
participants -> [
vote : {yes, no},
alive : {TRUE},
decision : {undecided},
faulty : {FALSE},
voteSent : {FALSE},
for... | definition | InitParticipantNB | acp | specifications/acp/ACP_NB.tla | [
"ACP_SB"
] | [
"forward"
] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
InitNB | == InitParticipantNB /\ InitCoordinator | definition | InitNB | acp | specifications/acp/ACP_NB.tla | [
"ACP_SB"
] | [
"InitCoordinator",
"InitParticipantNB"
] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
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] = participant[... | definition | forward | acp | specifications/acp/ACP_NB.tla | [
"ACP_SB"
] | [] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
preDecideOnForward(i,j) | == /\ i # j
/\ participant[i].alive
/\ participant[i].forward[i] = notsent
/\ participant[j].forward[i] # notsent
/\ participant' = [participant EXCEPT ![i] =
[@ EXCEPT !.forward ... | definition | preDecideOnForward | acp | specifications/acp/ACP_NB.tla | [
"ACP_SB"
] | [
"forward"
] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
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 | preDecide | acp | specifications/acp/ACP_NB.tla | [
"ACP_SB"
] | [
"forward"
] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
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>>
\* abortOnTimeout(i... | definition | decideNB | acp | specifications/acp/ACP_NB.tla | [
"ACP_SB"
] | [
"forward"
] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
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].alive /\ particip... | definition | abortOnTimeout | acp | specifications/acp/ACP_NB.tla | [
"ACP_SB"
] | [
"forward"
] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
parProgNB(i,j) | == \/ sendVote(i)
\/ abortOnVote(i)
\/ abortOnTimeoutRequest(i)
\/ forward(i,j)
\/ preDecideOnForward(i,j)
\/ abortOnTimeout(i)
\/ preDecide(i)
\/ decideNB(i) | definition | parProgNB | acp | specifications/acp/ACP_NB.tla | [
"ACP_SB"
] | [
"abortOnTimeout",
"abortOnTimeoutRequest",
"abortOnVote",
"decideNB",
"forward",
"preDecide",
"preDecideOnForward",
"sendVote"
] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
parProgNNB | == \E i,j \in participants : parDie(i) \/ parProgNB(i,j) | definition | parProgNNB | acp | specifications/acp/ACP_NB.tla | [
"ACP_SB"
] | [
"parDie",
"parProgNB"
] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
progNNB | == parProgNNB \/ coordProgN | definition | progNNB | acp | specifications/acp/ACP_NB.tla | [
"ACP_SB"
] | [
"coordProgN",
"parProgNNB"
] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
fairnessNB | == /\ \A i \in participants : WF_<<coordinator, participant>>(\E j \in participants : parProgNB(i,j))
/\ WF_<<coordinator, participant>>(coordProgB) | definition | fairnessNB | acp | specifications/acp/ACP_NB.tla | [
"ACP_SB"
] | [
"coordProgB",
"parProgNB"
] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
SpecNB | == InitNB /\ [][progNNB]_<<coordinator, participant>> /\ fairnessNB | definition | SpecNB | acp | specifications/acp/ACP_NB.tla | [
"ACP_SB"
] | [
"InitNB",
"fairnessNB",
"progNNB"
] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
AllCommit | == \A i \in participants : <>(participant[i].decision = commit \/ participant[i].faulty) | definition | AllCommit | acp | specifications/acp/ACP_NB.tla | [
"ACP_SB"
] | [] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
AllAbort | == \A i \in participants : <>(participant[i].decision = abort \/ participant[i].faulty) | definition | AllAbort | acp | specifications/acp/ACP_NB.tla | [
"ACP_SB"
] | [] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
AllCommitYesVotes | == \A i \in participants :
\A j \in participants : participant[j].vote = yes
~> participant[i].decision = commit \/ participant[i].faulty \/ coordinator.faulty | definition | AllCommitYesVotes | acp | specifications/acp/ACP_NB.tla | [
"ACP_SB"
] | [] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
Perms | == Permutations(participants) \* to benefit from symmetries | definition | Perms | acp | specifications/acp/ACP_NB_TLC.tla | [
"ACP_NB",
"TLC"
] | [] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
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 | AC4_alt | acp | specifications/acp/ACP_NB_TLC.tla | [
"ACP_NB",
"TLC"
] | [] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
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] = participant[i]... | definition | forward | acp | specifications/acp/ACP_NB_WRONG_TLC.tla | [
"ACP_SB"
] | [] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
decideOnForward(i,j) | == /\ i # j
/\ participant[i].alive
/\ participant[i].decision = undecided
/\ participant[j].forward[i] # notsent
/\ participant' = [participant EXCEPT ![i] =
[@ EXCEPT !.decision = participant[... | definition | decideOnForward | acp | specifications/acp/ACP_NB_WRONG_TLC.tla | [
"ACP_SB"
] | [
"forward"
] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
parProgNB(i,j) | == \/ parProg(i)
\/ forward(i,j)
\/ decideOnForward(i,j)
\/ abortOnTimeout(i) | definition | parProgNB | acp | specifications/acp/ACP_NB_WRONG_TLC.tla | [
"ACP_SB"
] | [
"abortOnTimeout",
"decideOnForward",
"forward",
"parProg"
] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
TypeInvParticipant | == participant \in [
participants -> [
vote : {yes, no},
alive : BOOLEAN,
decision : {undecided, commit, abort},
faulty : BOOLEAN,
voteSent : B... | definition | TypeInvParticipant | acp | specifications/acp/ACP_SB.tla | [] | [] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
TypeInvCoordinator | == coordinator \in [
request : [participants -> BOOLEAN],
vote : [participants -> {waiting, yes, no}],
broadcast : [participants -> {commit, abort, notsent}],
decision : {commit, abort, undecided},
... | definition | TypeInvCoordinator | acp | specifications/acp/ACP_SB.tla | [] | [
"request"
] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
TypeInv | == TypeInvParticipant /\ TypeInvCoordinator | definition | TypeInv | acp | specifications/acp/ACP_SB.tla | [] | [
"TypeInvCoordinator",
"TypeInvParticipant"
] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
InitParticipant | == participant \in [
participants -> [
vote : {yes, no},
alive : {TRUE},
decision : {undecided},
faulty : {FALSE},
voteSent : {FALSE}
]
... | definition | InitParticipant | acp | specifications/acp/ACP_SB.tla | [] | [] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
InitCoordinator | == coordinator \in [
request : [participants -> {FALSE}],
vote : [participants -> {waiting}],
alive : {TRUE},
broadcast : [participants -> {notsent}],
decision : {undecided},
faulty ... | definition | InitCoordinator | acp | specifications/acp/ACP_SB.tla | [] | [
"request"
] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
Init | == InitParticipant /\ InitCoordinator | definition | Init | acp | specifications/acp/ACP_SB.tla | [] | [
"InitCoordinator",
"InitParticipant"
] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
request(i) | == /\ coordinator.alive
/\ ~coordinator.request[i]
/\ coordinator' = [coordinator EXCEPT !.request =
[@ EXCEPT ![i] = TRUE]
]
/\ UNCHANGED<<participant>>
\* getVote(i):
\* IF
\* coordinator is alive
\* coordinator is still undecided
\* ... | definition | request | acp | specifications/acp/ACP_SB.tla | [] | [] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
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 =
[@ EXCEPT ![i... | definition | getVote | acp | specifications/acp/ACP_SB.tla | [] | [
"request"
] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
detectFault(i) | == /\ coordinator.alive
/\ coordinator.decision = undecided
/\ \A j \in participants : coordinator.request[j]
/\ coordinator.vote[i] = waiting
/\ ~participant[i].alive
/\ ~participant[i].voteSent
/\ coordinator' ... | definition | detectFault | acp | specifications/acp/ACP_SB.tla | [] | [
"request"
] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
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 | makeDecision | acp | specifications/acp/ACP_SB.tla | [] | [] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
coordBroadcast(i) | == /\ coordinator.alive
/\ coordinator.decision # undecided
/\ coordinator.broadcast[i] = notsent
/\ coordinator' = [coordinator EXCEPT !.broadcast =
[@ EXCEPT ![i] = coordinator.decision]
]
... | definition | coordBroadcast | acp | specifications/acp/ACP_SB.tla | [] | [] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
coordDie | == /\ coordinator.alive
/\ coordinator' = [coordinator EXCEPT !.alive = FALSE, !.faulty = TRUE]
/\ UNCHANGED<<participant>> | definition | coordDie | acp | specifications/acp/ACP_SB.tla | [] | [] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
sendVote(i) | == /\ participant[i].alive
/\ coordinator.request[i]
/\ participant' = [participant EXCEPT ![i] =
[@ EXCEPT !.voteSent = TRUE]
]
/\ UNCHANGED<<coordinator>>
\* abortOnVote(i):
\* IF
\* participant is alive
\* participant is undeci... | definition | sendVote | acp | specifications/acp/ACP_SB.tla | [] | [
"request"
] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
abortOnVote(i) | == /\ participant[i].alive
/\ participant[i].decision = undecided
/\ participant[i].voteSent
/\ participant[i].vote = no
/\ participant' = [participant EXCEPT ![i] =
[@ EXCEPT !.decision = abort]
]
... | definition | abortOnVote | acp | specifications/acp/ACP_SB.tla | [] | [] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
abortOnTimeoutRequest(i) | == /\ participant[i].alive
/\ participant[i].decision = undecided
/\ ~coordinator.alive
/\ ~coordinator.request[i]
/\ participant' = [participant EXCEPT ![i] =
[@ EXCEPT !.de... | definition | abortOnTimeoutRequest | acp | specifications/acp/ACP_SB.tla | [] | [
"request"
] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
decide(i) | == /\ participant[i].alive
/\ participant[i].decision = undecided
/\ coordinator.broadcast[i] # notsent
/\ participant' = [participant EXCEPT ![i] =
[@ EXCEPT !.decision = coordinator.broadcast[i]]
]
/\ UNCHANGED<<coordinator>>
\* ... | definition | decide | acp | specifications/acp/ACP_SB.tla | [] | [] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
parDie(i) | == /\ participant[i].alive
/\ participant' = [participant EXCEPT ![i] =
[@ EXCEPT !.alive = FALSE, !.faulty = TRUE]
]
/\ UNCHANGED<<coordinator>> | definition | parDie | acp | specifications/acp/ACP_SB.tla | [] | [] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
parProg(i) | == sendVote(i) \/ abortOnVote(i) \/ abortOnTimeoutRequest(i) \/ decide(i) | definition | parProg | acp | specifications/acp/ACP_SB.tla | [] | [
"abortOnTimeoutRequest",
"abortOnVote",
"decide",
"sendVote"
] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
parProgN | == \E i \in participants : parDie(i) \/ parProg(i) | definition | parProgN | acp | specifications/acp/ACP_SB.tla | [] | [
"parDie",
"parProg"
] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
coordProgA(i) | == request(i) \/ getVote(i) \/ detectFault(i) \/ coordBroadcast(i) | definition | coordProgA | acp | specifications/acp/ACP_SB.tla | [] | [
"coordBroadcast",
"detectFault",
"getVote",
"request"
] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
coordProgB | == makeDecision \/ \E i \in participants : coordProgA(i) | definition | coordProgB | acp | specifications/acp/ACP_SB.tla | [] | [
"coordProgA",
"makeDecision"
] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
coordProgN | == coordDie \/ coordProgB | definition | coordProgN | acp | specifications/acp/ACP_SB.tla | [] | [
"coordDie",
"coordProgB"
] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
progN | == parProgN \/ coordProgN
\* Death transitions are left outside of fairness | definition | progN | acp | specifications/acp/ACP_SB.tla | [] | [
"coordProgN",
"parProgN"
] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
fairness | == /\ \A i \in participants : WF_<<coordinator, participant>>(parProg(i))
/\ WF_<<coordinator, participant>>(coordProgB) | definition | fairness | acp | specifications/acp/ACP_SB.tla | [] | [
"coordProgB",
"parProg"
] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
Spec | == Init /\ [][progN]_<<coordinator, participant>> /\ fairness | definition | Spec | acp | specifications/acp/ACP_SB.tla | [] | [
"Init",
"fairness",
"progN"
] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
AC1 | == [] \A i, j \in participants :
\/ participant[i].decision # commit
\/ participant[j].decision # abort
\* If any participant decides commit, then all participants must have votes YES | definition | AC1 | acp | specifications/acp/ACP_SB.tla | [] | [] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
AC2 | == [] ( (\E i \in participants : participant[i].decision = commit)
=> (\A j \in participants : participant[j].vote = yes))
\* If any participant decides abort, then:
\* at least one participant voted NO, or
\* at least one participant is faulty, or
\* coordinator is faulty | definition | AC2 | acp | specifications/acp/ACP_SB.tla | [] | [] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
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)
\* Each participant decides at most once | definition | AC3_1 | acp | specifications/acp/ACP_SB.tla | [] | [] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
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 | AC4 | acp | specifications/acp/ACP_SB.tla | [] | [] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
AC3_2 | == <> \/ \A i \in participants : participant[i].decision \in {abort, commit}
\/ \E j \in participants : participant[j].faulty
\/ coordinator.faulty | definition | AC3_2 | acp | specifications/acp/ACP_SB.tla | [] | [] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
FaultyStable | == /\ \A i \in participants : [](participant[i].faulty => []participant[i].faulty)
/\ [](coordinator.faulty => [] coordinator.faulty) | definition | FaultyStable | acp | specifications/acp/ACP_SB.tla | [] | [] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
VoteStable | == \A i \in participants :
\/ [](participant[i].vote = yes)
\/ [](participant[i].vote = no) | definition | VoteStable | acp | specifications/acp/ACP_SB.tla | [] | [] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
StrongerAC2 | == [] ( (\E i \in participants : participant[i].decision = commit)
=> /\ (\A j \in participants : participant[j].vote = yes)
/\ coordinator.decision = commit) | definition | StrongerAC2 | acp | specifications/acp/ACP_SB.tla | [] | [] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
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
\/ /\ coordinator.f... | definition | StrongerAC3_1 | acp | specifications/acp/ACP_SB.tla | [] | [] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
NoRecovery | == [] /\ \A i \in participants : participant[i].alive <=> ~participant[i].faulty
/\ coordinator.alive <=> ~coordinator.faulty | definition | NoRecovery | acp | specifications/acp/ACP_SB.tla | [] | [] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
DecisionReachedNoFault | == (\A i \in participants : participant[i].alive)
~> (\A k \in participants : participant[k].decision # undecided) | definition | DecisionReachedNoFault | acp | specifications/acp/ACP_SB.tla | [] | [] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
AbortImpliesNoVote | == [] ( (\E i \in participants : participant[i].decision = abort)
=> (\E j \in participants : participant[j].vote = no))
\* The following is the termination property that this SB algorithm doesn't have | definition | AbortImpliesNoVote | acp | specifications/acp/ACP_SB.tla | [] | [] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
AC5 | == <> \A i \in participants : \/ participant[i].decision \in {abort, commit}
\/ participant[i].faulty | definition | AC5 | acp | specifications/acp/ACP_SB.tla | [] | [] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
participantsVal | == { "p1_OF_PARTICIPANT", "p2_OF_PARTICIPANT", "p3_OF_PARTICIPANT" } | definition | participantsVal | acp | specifications/acp/APACP_SB.tla | [] | [] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
IsFiniteSet(Resources) | assume | IsFiniteSet | allocator | specifications/allocator/AllocatorImplementation.tla | [
"FiniteSets",
"Sequences",
"Naturals"
] | [
"IsFiniteSet"
] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | ||
Sched | == INSTANCE SchedulingAllocator | definition | Sched | allocator | specifications/allocator/AllocatorImplementation.tla | [
"FiniteSets",
"Sequences",
"Naturals"
] | [] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
Messages | ==
[type : {"request", "allocate", "return"},
clt : Clients,
rsrc : SUBSET Resources] | definition | Messages | allocator | specifications/allocator/AllocatorImplementation.tla | [
"FiniteSets",
"Sequences",
"Naturals"
] | [] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
TypeInvariant | ==
/\ Sched!TypeInvariant
/\ requests \in [Clients -> SUBSET Resources]
/\ holding \in [Clients -> SUBSET Resources]
/\ network \in SUBSET Messages | definition | TypeInvariant | allocator | specifications/allocator/AllocatorImplementation.tla | [
"FiniteSets",
"Sequences",
"Naturals"
] | [
"Messages",
"Sched",
"network"
] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
Init | ==
/\ Sched!Init
/\ requests = [c \in Clients |-> {}]
/\ holding = [c \in Clients |-> {}]
/\ network = {}
(* A client c may request a set of resources provided that it has *)
(* neither pending requests nor holds any resources. The request is *)
(* put into the network for delivery to the allocator. ... | definition | Init | allocator | specifications/allocator/AllocatorImplementation.tla | [
"FiniteSets",
"Sequences",
"Naturals"
] | [
"Sched",
"network"
] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
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>>
(* Reception of a request message from a client by the allocator. *)
(* The allocator updates it... | definition | Request | allocator | specifications/allocator/AllocatorImplementation.tla | [
"FiniteSets",
"Sequences",
"Naturals"
] | [
"network"
] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
RReq(m) | ==
/\ m \in network /\ m.type = "request"
/\ alloc[m.clt] = {} \** don't handle request messages prematurely(!)
/\ unsat' = [unsat EXCEPT ![m.clt] = m.rsrc]
/\ network' = network \ {m}
/\ UNCHANGED <<alloc,sched,requests,holding>>
(* Allocation of a set of available resources to a client that has *)
(*... | definition | RReq | allocator | specifications/allocator/AllocatorImplementation.tla | [
"FiniteSets",
"Sequences",
"Naturals"
] | [
"network"
] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
Allocate(c,S) | ==
/\ Sched!Allocate(c,S)
/\ network' = network \cup {[type |-> "allocate", clt |-> c, rsrc |-> S]}
/\ UNCHANGED <<requests,holding>>
(* Reception of an allocation message by a client. *) | definition | Allocate | allocator | specifications/allocator/AllocatorImplementation.tla | [
"FiniteSets",
"Sequences",
"Naturals"
] | [
"Sched",
"network"
] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
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>>
(* Client c returns a set of resources that it holds. It may do so *)
(* even before its... | definition | RAlloc | allocator | specifications/allocator/AllocatorImplementation.tla | [
"FiniteSets",
"Sequences",
"Naturals"
] | [
"network"
] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
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>>
(* Reception of a return message by the allocator. *) | definition | Return | allocator | specifications/allocator/AllocatorImplementation.tla | [
"FiniteSets",
"Sequences",
"Naturals"
] | [
"network"
] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
RRet(m) | ==
/\ m \in network /\ m.type = "return"
/\ alloc' = [alloc EXCEPT ![m.clt] = @ \ m.rsrc]
/\ network' = network \ {m}
/\ UNCHANGED <<unsat,sched,requests,holding>>
(* The allocator extends its schedule by adding the processes from *)
(* the pool (that have outstanding requests but that have not yet been *)... | definition | RRet | allocator | specifications/allocator/AllocatorImplementation.tla | [
"FiniteSets",
"Sequences",
"Naturals"
] | [
"network"
] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
Schedule | ==
/\ Sched!Schedule
/\ UNCHANGED <<requests,holding,network>>
(* The next-state relation per client and set of resources. *) | definition | Schedule | allocator | specifications/allocator/AllocatorImplementation.tla | [
"FiniteSets",
"Sequences",
"Naturals"
] | [
"Sched",
"network"
] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
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 | Next | allocator | specifications/allocator/AllocatorImplementation.tla | [
"FiniteSets",
"Sequences",
"Naturals"
] | [
"Allocate",
"RAlloc",
"RReq",
"RRet",
"Request",
"Return",
"Schedule",
"network"
] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
vars | == <<unsat,alloc,sched,requests,holding,network>> | definition | vars | allocator | specifications/allocator/AllocatorImplementation.tla | [
"FiniteSets",
"Sequences",
"Naturals"
] | [
"network"
] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
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))
(* The specification of the entire s... | definition | Liveness | allocator | specifications/allocator/AllocatorImplementation.tla | [
"FiniteSets",
"Sequences",
"Naturals"
] | [
"Allocate",
"Messages",
"RAlloc",
"RReq",
"RRet",
"Return",
"Schedule"
] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
Specification | == Init /\ [][Next]_vars /\ Liveness | definition | Specification | allocator | specifications/allocator/AllocatorImplementation.tla | [
"FiniteSets",
"Sequences",
"Naturals"
] | [
"Init",
"Liveness",
"Next"
] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 | |
RequestsInTransit(c) | == \** requests sent by c but not yet received
{ msg.rsrc : msg \in {m \in network : m.type = "request" /\ m.clt = c} } | definition | RequestsInTransit | allocator | specifications/allocator/AllocatorImplementation.tla | [
"FiniteSets",
"Sequences",
"Naturals"
] | [
"network"
] | https://github.com/tlaplus/Examples | 47b0e2cc0268836b89f5ce451f38e5df5f1cf773 |
Structured dataset of TLA+ specifications from the official TLA+ Examples repository.
47b0e2cc0268836b89f5ce451f38e5df5f1cf773| Column | Type | Description |
|---|---|---|
| statement | string | Declaration signature/claim with the leading keyword removed (verbatim slice); the full declaration minus its proof |
| proof | string | Verbatim proof/body, empty if the declaration has none |
| type | string | Declaration keyword |
| symbolic_name | string | Declaration identifier |
| library | string | Sub-library |
| filename | string | Repository-relative source path |
| imports | list[string] | File-level Require/Import modules |
| deps | list[string] | Intra-corpus identifiers referenced |
| docstring | string | Preceding documentation comment, empty if absent |
| source_url | string | Upstream repository |
| commit | string | Upstream commit extracted |
| Type | Count |
|---|---|
| definition | 3,767 |
| assume | 311 |
| theorem | 255 |
| lemma | 218 |
| corollary | 3 |
Init0
==
/\ nSntE = 0
/\ nSntR = 0
/\ nRcvdE = [ i \in Proc |-> 0 ]
/\ nRcvdR = [ i \in Proc |-> 0 ]
/\ nByz = 0
/\ pc \in [ i \in Proc |-> "V0" ]
(* All processes propose 1. *)
Init0 | specifications/aba-asyn-byz/aba_asyn_byz.tlaEach declaration is split into a statement (signature/claim) and a proof (body) that are disjoint
and together form the complete declaration, for proof modeling, autoformalization, retrieval, and
dependency analysis via deps.
@misc{tla_plus_dataset,
title = {TLA-Plus},
author = {Norton, Charles},
year = {2026},
note = {Extracted from https://github.com/tlaplus/Examples, commit 47b0e2cc0268},
url = {https://huggingface.co/datasets/phanerozoic/TLA-Plus}
}