Proof Assistant Projects
Collection
Digesting proof assistant libraries for AI ingestion.
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84 items
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Updated
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2
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 that is bundled together with this package and can
be found in the file LICENSE.
)
EXTENDS Naturals (*, FiniteSets *)
CONSTANTS N, T, F
VARIABLES nSntE, (* the number of ECHO, READY messages which are sent *)
nSntR,
nRcvdE, (* the number of ECHO, READY messages which are received *)
nRcvdR,
nByz, (* the number of Byzantine processes *)
pc (* program counters *)
ASSUME NTF == N \in Nat /\ T \in Nat /\ F \in Nat /\ (N > 3 * T) /\ (T >= F) /\ (F >= 0)
Proc == 1 .. N
Location == { "V0", "V1", "EC", "RD", "AC", "BYZ" }
vars == << nSntE, nSntR, nRcvdE, nRcvdR, nByz, pc >>
guardE == (N + T + 2) \div 2
guardR1 == T + 1
guardR2 == 2 * T + 1
(* Some processes propose 0 and others propose 1.*)
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. *)
/\ pc \in [ Proc -> { "V0", "V1" } ]
(* All processes propose 0.
|
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 that is bundled together with this package and can
be found in the file LICENSE.
)
EXTENDS Naturals (*, FiniteSets *)
CONSTANTS N, T, F
VARIABLES nSntE, (* the number of ECHO, READY messages which are sent *)
nSntR,
nRcvdE, (* the number of ECHO, READY messages which are received *)
nRcvdR,
nByz, (* the number of Byzantine processes *)
pc (* program counters *)
ASSUME NTF == N \in Nat /\ T \in Nat /\ F \in Nat /\ (N > 3 * T) /\ (T >= F) /\ (F >= 0)
Proc == 1 .. N
Location == { "V0", "V1", "EC", "RD", "AC", "BYZ" }
vars == << nSntE, nSntR, nRcvdE, nRcvdR, nByz, pc >>
guardE == (N + T + 2) \div 2
guardR1 == T + 1
guardR2 == 2 * T + 1
(* Some processes propose 0 and others propose 1.*)
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. *)
/\ pc \in [ Proc -> { "V0", "V1" } ]
(* All processes propose 0. *)
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.
|
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 that is bundled together with this package and can
be found in the file LICENSE.
)
EXTENDS Naturals (*, FiniteSets *)
CONSTANTS N, T, F
VARIABLES nSntE, (* the number of ECHO, READY messages which are sent *)
nSntR,
nRcvdE, (* the number of ECHO, READY messages which are received *)
nRcvdR,
nByz, (* the number of Byzantine processes *)
pc (* program counters *)
ASSUME NTF == N \in Nat /\ T \in Nat /\ F \in Nat /\ (N > 3 * T) /\ (T >= F) /\ (F >= 0)
Proc == 1 .. N
Location == { "V0", "V1", "EC", "RD", "AC", "BYZ" }
vars == << nSntE, nSntR, nRcvdE, nRcvdR, nByz, pc >>
guardE == (N + T + 2) \div 2
guardR1 == T + 1
guardR2 == 2 * T + 1
(* Some processes propose 0 and others propose 1.*)
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. *)
/\ pc \in [ Proc -> { "V0", "V1" } ]
(* All processes propose 0. *)
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. *)
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 *)
(* message counting abstraction.
|
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 << nSntE, nSntR, nRcvdE, nByz, pc >>
\/ /\ UNCHANGED vars
|
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 that is bundled together with this package and can
be found in the file LICENSE.
)
EXTENDS Naturals (*, FiniteSets *)
CONSTANTS N, T, F
VARIABLES nSntE, (* the number of ECHO, READY messages which are sent *)
nSntR,
nRcvdE, (* the number of ECHO, READY messages which are received *)
nRcvdR,
nByz, (* the number of Byzantine processes *)
pc (* program counters *)
ASSUME NTF == N \in Nat /\ T \in Nat /\ F \in Nat /\ (N > 3 * T) /\ (T >= F) /\ (F >= 0)
Proc == 1 .. N
Location == { "V0", "V1", "EC", "RD", "AC", "BYZ" }
vars == << nSntE, nSntR, nRcvdE, nRcvdR, nByz, pc >>
guardE == (N + T + 2) \div 2
guardR1 == T + 1
guardR2 == 2 * T + 1
(* Some processes propose 0 and others propose 1.*)
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. *)
/\ pc \in [ Proc -> { "V0", "V1" } ]
(* All processes propose 0. *)
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. *)
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 *)
(* message counting abstraction. *)
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. Otherwise, only messages from *)
(* correct processes are considered.
|
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 that is bundled together with this package and can
be found in the file LICENSE.
)
EXTENDS Naturals (*, FiniteSets *)
CONSTANTS N, T, F
VARIABLES nSntE, (* the number of ECHO, READY messages which are sent *)
nSntR,
nRcvdE, (* the number of ECHO, READY messages which are received *)
nRcvdR,
nByz, (* the number of Byzantine processes *)
pc (* program counters *)
ASSUME NTF == N \in Nat /\ T \in Nat /\ F \in Nat /\ (N > 3 * T) /\ (T >= F) /\ (F >= 0)
Proc == 1 .. N
Location == { "V0", "V1", "EC", "RD", "AC", "BYZ" }
vars == << nSntE, nSntR, nRcvdE, nRcvdR, nByz, pc >>
guardE == (N + T + 2) \div 2
guardR1 == T + 1
guardR2 == 2 * T + 1
(* Some processes propose 0 and others propose 1.*)
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. *)
/\ pc \in [ Proc -> { "V0", "V1" } ]
(* All processes propose 0. *)
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. *)
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 *)
(* message counting abstraction. *)
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. Otherwise, only messages from *)
(* correct processes are considered. *)
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 << nSntE, nSntR, nRcvdE, nByz, pc >>
\/ /\ UNCHANGED vars
(* Process i will send an ECHO message if it proposed 1 and did not send an ECHO message.
If process i proposed 0, did not send an ECHO message but has received greater than
(N + F) / 2 ECHO messages or (F + 1) READY messages, it will also send an ECHO messages.
|
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 that is bundled together with this package and can
be found in the file LICENSE.
)
EXTENDS Naturals (*, FiniteSets *)
CONSTANTS N, T, F
VARIABLES nSntE, (* the number of ECHO, READY messages which are sent *)
nSntR,
nRcvdE, (* the number of ECHO, READY messages which are received *)
nRcvdR,
nByz, (* the number of Byzantine processes *)
pc (* program counters *)
ASSUME NTF == N \in Nat /\ T \in Nat /\ F \in Nat /\ (N > 3 * T) /\ (T >= F) /\ (F >= 0)
Proc == 1 .. N
Location == { "V0", "V1", "EC", "RD", "AC", "BYZ" }
vars == << nSntE, nSntR, nRcvdE, nRcvdR, nByz, pc >>
guardE == (N + T + 2) \div 2
guardR1 == T + 1
guardR2 == 2 * T + 1
(* Some processes propose 0 and others propose 1.*)
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. *)
/\ pc \in [ Proc -> { "V0", "V1" } ]
(* All processes propose 0. *)
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. *)
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 *)
(* message counting abstraction. *)
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. Otherwise, only messages from *)
(* correct processes are considered. *)
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 << nSntE, nSntR, nRcvdE, nByz, pc >>
\/ /\ UNCHANGED vars
(* Process i will send an ECHO message if it proposed 1 and did not send an ECHO message.
If process i proposed 0, did not send an ECHO message but has received greater than
(N + F) / 2 ECHO messages or (F + 1) READY messages, it will also send an ECHO messages.
)
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 will send a READY messages.
|
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 that is bundled together with this package and can
be found in the file LICENSE.
)
EXTENDS Naturals (*, FiniteSets *)
CONSTANTS N, T, F
VARIABLES nSntE, (* the number of ECHO, READY messages which are sent *)
nSntR,
nRcvdE, (* the number of ECHO, READY messages which are received *)
nRcvdR,
nByz, (* the number of Byzantine processes *)
pc (* program counters *)
ASSUME NTF == N \in Nat /\ T \in Nat /\ F \in Nat /\ (N > 3 * T) /\ (T >= F) /\ (F >= 0)
Proc == 1 .. N
Location == { "V0", "V1", "EC", "RD", "AC", "BYZ" }
vars == << nSntE, nSntR, nRcvdE, nRcvdR, nByz, pc >>
guardE == (N + T + 2) \div 2
guardR1 == T + 1
guardR2 == 2 * T + 1
(* Some processes propose 0 and others propose 1.*)
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. *)
/\ pc \in [ Proc -> { "V0", "V1" } ]
(* All processes propose 0. *)
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. *)
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 *)
(* message counting abstraction. *)
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. Otherwise, only messages from *)
(* correct processes are considered. *)
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 << nSntE, nSntR, nRcvdE, nByz, pc >>
\/ /\ UNCHANGED vars
(* Process i will send an ECHO message if it proposed 1 and did not send an ECHO message.
If process i proposed 0, did not send an ECHO message but has received greater than
(N + F) / 2 ECHO messages or (F + 1) READY messages, it will also send an ECHO messages.
)
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 will send a READY messages.
)
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.
|
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 that is bundled together with this package and can
be found in the file LICENSE.
)
EXTENDS Naturals (*, FiniteSets *)
CONSTANTS N, T, F
VARIABLES nSntE, (* the number of ECHO, READY messages which are sent *)
nSntR,
nRcvdE, (* the number of ECHO, READY messages which are received *)
nRcvdR,
nByz, (* the number of Byzantine processes *)
pc (* program counters *)
ASSUME NTF == N \in Nat /\ T \in Nat /\ F \in Nat /\ (N > 3 * T) /\ (T >= F) /\ (F >= 0)
Proc == 1 .. N
Location == { "V0", "V1", "EC", "RD", "AC", "BYZ" }
vars == << nSntE, nSntR, nRcvdE, nRcvdR, nByz, pc >>
guardE == (N + T + 2) \div 2
guardR1 == T + 1
guardR2 == 2 * T + 1
(* Some processes propose 0 and others propose 1.*)
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. *)
/\ pc \in [ Proc -> { "V0", "V1" } ]
(* All processes propose 0. *)
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. *)
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 *)
(* message counting abstraction. *)
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. Otherwise, only messages from *)
(* correct processes are considered. *)
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 << nSntE, nSntR, nRcvdE, nByz, pc >>
\/ /\ UNCHANGED vars
(* Process i will send an ECHO message if it proposed 1 and did not send an ECHO message.
If process i proposed 0, did not send an ECHO message but has received greater than
(N + F) / 2 ECHO messages or (F + 1) READY messages, it will also send an ECHO messages.
)
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 will send a READY messages.
)
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. *)
Decide(i) ==
/\ pc[i] = "RD"
/\ nRcvdR[i] >= guardR2
/\ pc' = [ pc EXCEPT ![i] = "AC" ]
/\ UNCHANGED << nSntE, nSntE, nSntR, nRcvdE, nRcvdR, nByz >>
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.
|
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,
voteSent : BOOLEAN,
forward : [ participants -> {notsent, commit, abort} ]
]
]
|
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},
forward : [ participants -> {notsent} ]
]
]
|
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] = participant[i].forward[i]]
]
]
/\ UNCHANGED<<coordinator>>
|
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] =
[@ EXCEPT !.forward =
[@ EXCEPT ![i] = participant[j].forward[i]]
]
]
/\ UNCHANGED<<coordinator>>
|
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]]
]
]
/\ UNCHANGED<<coordinator>>
|
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].alive /\ participant[k].alive => participant[j].forward[k] = notsent
/\ participant' = [participant EXCEPT ![i] = [@ EXCEPT !.decision = abort]]
/\ UNCHANGED<<coordinator>>
|
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,
voteSent : BOOLEAN,
forward : [ participants -> {notsent, commit, abort} ]
]
]
|
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},
forward : [ participants -> {notsent} ]
]
]
|
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] = participant[i].decision]
]
]
/\ UNCHANGED<<coordinator>>
|
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 !.decision = participant[j].forward[i]]
]
/\ UNCHANGED<<coordinator>>
|
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].alive /\ participant[k].alive => participant[j].forward[k] = notsent
/\ participant' = [participant EXCEPT ![i] = [@ EXCEPT !.decision = abort]]
/\ UNCHANGED<<coordinator>>
|
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,
voteSent : 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},
alive : BOOLEAN,
faulty : BOOLEAN
]
|
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},
faulty : {FALSE}
]
|
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 =
[@ EXCEPT ![i] = participant[i].vote]
]
/\ UNCHANGED<<participant>>
|
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
/\ coordinator' = [coordinator EXCEPT !.decision = abort]
/\ UNCHANGED<<participant>>
|
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]
\/ /\ \E j \in participants : coordinator.vote[j] = no
/\ coordinator' = [coordinator EXCEPT !.decision = abort]
/\ UNCHANGED<<participant>>
|
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]
]
/\ UNCHANGED<<participant>>
|
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]
]
/\ UNCHANGED<<coordinator>>
|
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] =
[@ EXCEPT !.decision = abort]
]
/\ UNCHANGED<<coordinator>>
|
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<<coordinator>>
|
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
\/ /\ coordinator.faulty
/\ coordinator.decision = undecided)
|
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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License:
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Number of rows:
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