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TestLinearizability.tla
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------------------------ MODULE TestLinearizability ------------------------
EXTENDS Naturals, Sequences, LinQueue
\* L == INSTANCE Linearizability
H3 == <<
[op|->"E", val|->"x", proc|->"A"],
[op|->"D", proc|-> "B"],
[op|->"Ok", val|->"x", proc|->"B"]
>>
TestCollect == L!Collect({
{[op|->"Ok", proc|->"A"]},
{[op|->"Ok", proc|->"B", val|->"x"], [op|->"Ok", proc|->"B", val|->"y"]}}) =
{
{[op|->"Ok", proc|->"A"], [op|->"Ok", proc|->"B", val|->"x"]},
{[op|->"Ok", proc|->"A"], [op|->"Ok", proc|->"B", val|->"y"]}
}
ASSUME TestCollect
TestInvocationsWithoutResponse == L!InvocationsWithoutResponses(H3) = {[op|->"E", val|->"x", proc|->"A"]}
ASSUME TestInvocationsWithoutResponse
TestExtensions ==
LET H == <<[op|->"E", val|->"x", proc|->"A"],
[op|->"D", proc|-> "B"]>>
IN L!Extensions(H) = {
{[op|->"Ok", proc|->"A"], [op|->"Ok", proc|->"B", val|->"x"]},
{[op|->"Ok", proc|->"A"], [op|->"Ok", proc|->"B", val|->"y"]},
{[op|->"Ok", proc|->"A"], [op|->"Ok", proc|->"B", val|->"z"]}
}
ASSUME TestExtensions
TestExtendedHistories ==
LET H == <<[op|->"E", val|->"x", proc|->"A"], [op|->"D", proc|-> "B"]>>
IN L!ExtendedHistories(H) = {
<< [op |-> "E", val |-> "x", proc |-> "A"],
[op |-> "D", proc |-> "B"],
[op |-> "Ok", proc |-> "A"] >>,
<< [op |-> "E", val |-> "x", proc |-> "A"],
[op |-> "D", proc |-> "B"],
[op |-> "Ok", val |-> "x", proc |-> "B"] >>,
<< [op |-> "E", val |-> "x", proc |-> "A"],
[op |-> "D", proc |-> "B"],
[op |-> "Ok", val |-> "y", proc |-> "B"] >>,
<< [op |-> "E", val |-> "x", proc |-> "A"],
[op |-> "D", proc |-> "B"],
[op |-> "Ok", val |-> "z", proc |-> "B"] >>,
<< [op |-> "E", val |-> "x", proc |-> "A"],
[op |-> "D", proc |-> "B"],
[op |-> "Ok", proc |-> "A"],
[op |-> "Ok", val |-> "x", proc |-> "B"] >>,
<< [op |-> "E", val |-> "x", proc |-> "A"],
[op |-> "D", proc |-> "B"],
[op |-> "Ok", proc |-> "A"],
[op |-> "Ok", val |-> "y", proc |-> "B"] >>,
<< [op |-> "E", val |-> "x", proc |-> "A"],
[op |-> "D", proc |-> "B"],
[op |-> "Ok", proc |-> "A"],
[op |-> "Ok", val |-> "z", proc |-> "B"] >>,
<< [op |-> "E", val |-> "x", proc |-> "A"],
[op |-> "D", proc |-> "B"],
[op |-> "Ok", val |-> "x", proc |-> "B"],
[op |-> "Ok", proc |-> "A"] >>,
<< [op |-> "E", val |-> "x", proc |-> "A"],
[op |-> "D", proc |-> "B"],
[op |-> "Ok", val |-> "y", proc |-> "B"],
[op |-> "Ok", proc |-> "A"] >>,
<< [op |-> "E", val |-> "x", proc |-> "A"],
[op |-> "D", proc |-> "B"],
[op |-> "Ok", val |-> "z", proc |-> "B"],
[op |-> "Ok", proc |-> "A"] >> }
ASSUME TestExtendedHistories
TestSubseq == L!Subseq(<<"a", "b", "c", "d", "e">>, {2,3,5}) = <<"b", "c", "e">>
ASSUME TestSubseq
TestSubsequences == L!Subsequences(<<"a", "b", "c">>) = {
<< >>,
<<"a">>,
<<"b">>,
<<"c">>,
<<"a","b">>,
<<"a","c">>,
<<"b","c">>,
<<"a","b","c">>
}
ASSUME TestSubsequences
TestComplete == L!Complete(
<< [op |-> "E", val |-> "x", proc |-> "A"], [op |-> "D", proc |-> "B"], [op |-> "Ok", proc |-> "A"] >>)
ASSUME TestComplete = <<[op |-> "E", val |-> "x", proc |-> "A"], [op |-> "Ok", proc |-> "A"]>>
TestAreEquivalentTrue == L!AreEquivalent(
<< [op |-> "E", val |-> "x", proc |-> "A"], [op |-> "D", proc |-> "B"], [op |-> "Ok", proc |-> "A"], [op |-> "Ok", val |-> "x", proc |-> "B"] >>,
<< [op |-> "E", val |-> "x", proc |-> "A"], [op |-> "Ok", proc |-> "A"], [op |-> "D", proc |-> "B"], [op |-> "Ok", val |-> "x", proc |-> "B"] >>
)
ASSUME TestAreEquivalentTrue
TestAreEquivalentFalse == L!AreEquivalent(
<< [op |-> "E", val |-> "x", proc |-> "A"], [op |-> "D", proc |-> "B"], [op |-> "Ok", proc |-> "A"], [op |-> "Ok", val |-> "x", proc |-> "B"] >>,
<< [op |-> "E", val |-> "x", proc |-> "A"], [op |-> "Ok", proc |-> "A"], [op |-> "D", proc |-> "B"], [op |-> "Ok", val |-> "y", proc |-> "B"] >>
)
ASSUME ~TestAreEquivalentFalse
TestPrecedes ==
LET H == <<
[op |-> "E", val |-> "x", proc |-> "A"], [op |-> "Ok", proc |-> "A"],
[op |-> "D", proc |-> "B"], [op |-> "Ok", val |-> "x", proc |-> "B"],
[op |-> "E", val |-> "x", proc |-> "A"], [op |-> "Ok", proc |-> "A"]>>
e1 == <<H[1], H[2]>>
e2 == <<H[3], H[4]>>
e3 == <<H[5], H[6]>>
IN /\ L!Precedes(H, e1, e2)
/\ L!Precedes(H, e2, e3)
ASSUME TestPrecedes
TestOperations ==
LET H == <<
[op |-> "E", val |-> "x", proc |-> "A"], [op |-> "Ok", proc |-> "A"],
[op |-> "D", proc |-> "B"], [op |-> "Ok", val |-> "x", proc |-> "B"],
[op |-> "E", val |-> "x", proc |-> "A"], [op |-> "Ok", proc |-> "A"]>>
IN L!Operations(H) = {
<<[op |-> "E", val |-> "x", proc |-> "A"], [op |-> "Ok", proc |-> "A"]>>,
<<[op |-> "D", proc |-> "B"], [op |-> "Ok", val |-> "x", proc |-> "B"]>>}
ASSUME TestOperations
Test == TestOperations
ASSUME Test
\* The only possible extension for H3 is completing the enqueue
ExtH3 == L!Extensions(H3) = {{[op|->"Ok", proc|->"A"]}}
ASSUME ExtH3
=============================================================================
\* Modification History
\* Last modified Sun Oct 21 10:18:05 PDT 2018 by lhochstein
\* Created Sat Oct 20 13:43:05 PDT 2018 by lhochstein