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understanding how the liveness checking algorithm works
understand how the code for the liveness checking works
Produce documentation or else to help other people understand it.

TODOS:

this naturals has unused code copied from Integers module: /home/fponzi/dev/tlaplus/tlatools/org.lamport.tlatools/src/tlc2/module/Naturals.java

java -agentlib:jdwp=transport=dt_socket,server=y,suspend=y,address=*:5005 \
-jar ./dist/tla2tools.jar \
-lncheck final -fpmem 0.65 -fp 120 \
-seed -8286054000752913025  \
-workers 1 \
-config /tmp/elevator.cfg \
/tmp/simple.tla

---- MODULE simple ----
EXTENDS Naturals
VARIABLE x
Init == x = 1
Next ==
  IF x = 5 THEN UNCHANGED x
  ELSE x' = x + 1
Spec == Init ∧ □[Next]_x ∧ WF_x(Next)
\*Liveness == (x = 1) ⇒ ◇□(x = 5)
Liveness2 == <>[](x = 5)
====
----- CONFIG simple -----
SPECIFICATION Spec
PROPERTIES Liveness2
======

TODO: Explore the implementation by using some new tests.

unit tests are completely lacking apparently

TLC:

<HTML><ul></HTML> <HTML><li></HTML>Initializes Model checker <HTML><ul></HTML> <HTML><li></HTML>Calls Abstract Checker <HTML><ul></HTML> <HTML><li></HTML>Initializes CostModelCreator<HTML></li></HTML> <HTML><li></HTML>Initializes LiveCheck if liveness is requested. if (this.checkLiveness) { <HTML><ul></HTML> <HTML><li></HTML><HTML></HTML>LiveCheck constructor will call Liveness.processLiveness(tool) to generate the OrderOfSolution.<HTML></HTML> <HTML><ul></HTML> <HTML><li></HTML>*The method processLiveness normalizes the list of temporals and * impliedTemporals to check their validity, and to figure out the order and * manner in which things should ultimately be checked. This method returns * a handle, which can subsequently be passed to the other liveness things.*<HTML></li></HTML> <HTML><li></HTML>First, this method calls parseLiveness. <HTML><ul></HTML> <HTML><li></HTML>ParseLiveness returns a LiveExprNode in the form of liveness(fairness) / ~livecheck <HTML><ul></HTML> <HTML><li></HTML>where liveness(fairness) is basically the WF_vars(Next)<HTML></li></HTML> <HTML><li></HTML>livecheck are the actions used to check for liveness, as defined for config file.<HTML></li></HTML><HTML></ul></HTML> <HTML></li></HTML><HTML></ul></HTML> <HTML></li></HTML> <HTML><li></HTML>Then: *Give tags to all action and state predicates, for equality// checking (tlc2.tool.liveness.LiveExprNode.equals(LiveExprNode)).// We tag them here so that, if disjunct normal form (DNF) should happen to// duplicate expressions, then they will still have the same tag.*<HTML></li></HTML> <HTML><li></HTML>And then: *Converting the formula to DNF pushes negation inside (see// LiveExprNode#pushNeg). This is important later when the promises are extracted (see LiveExprNode#extractPromises).*<HTML></li></HTML> <HTML><li></HTML>Then:<HTML></li></HTML><HTML></ul></HTML>

        // IV:
        // Now we will turn DNF into a format that can be tested by the
        // tableau method. The first step is to collect everything into
        // pems+lexps: listof-(listof-<>[],[]<> /\ tf).
        //
        // "pems":  Possible Error Models
        // "lexps": Liveness expressions ?
        //
        // In other words, for each junction of the disjunct normal form, classify DNF
        // into four Vects in OSExprPem with A an action and S a state-predicate:
        //
        // 1) <>[]A: "Eventually Always Actions"        OSExprPem#AEAction
        // 2) []<>A: "Always Eventually Actions"        OSExprPem#EAAction
        // 3) <>[]S: "Eventually Always States"         OSExprPem#AEState
        // 4) tf:   "temporal formulae with no actions" OSExprPem#tfs
        //
        // For example, below is what happens for a simple spec:
        //
        //  VARIABLE x
        //  Spec == x = 0 /\ [][x'=x+1]_x /\ WF_x(x'=x+1)     \* LNDisj(LNNeg(LNStateEnabled) \/ LNAction) in OSExprPem#AEAction
        //
        //  Prop1 == <>[][x' > x]_x                           \* LNNeg(LNAction) in OSExprPem#AEAction
        //  Prop2 == []<>(<<x' > x>>_x)                       \* LNNeg(LNAction) in OSExprPem#EAAction
        //  Prop3 == <>[](x \in Nat)                          \* LNNeg(LNState)  in OSExprPem#AEState
        //  Prop4 == <>(x \in Nat)                            \* LNAll(LNNeg(LNStateAST) in OSExprPem#tfs
        //

        // V:
        // Now, we will create our OrderOfSolutions. We lump together all
        // disjunctions that have the same tf. This will happen often in
        // cases such as (WF /\ SF) => (WF /\ SF /\ TF), since the WF and
        // SF will be broken up into many cases and the TF will remain the
        // same throughout. (Incidentally, we're checking equality on TFs
        // just syntactically. This is hopefully sufficient, because we
        // haven't done any real rearrangement of them, apart from munging
        // up \/ and /\ above them. tfbin contains the different tf's.
        // pembin is a vect of vect-of-pems collecting each tf's pems.

<HTML><ul></HTML> <HTML><li></HTML><HTML></HTML>Tfbin is an array of Tableau Particle. This is the doc:<HTML></HTML>

/**
 * See Section 5.5 "Particle Tableaux" in Temporal Verification of Reactive
 * Systems *Safety* by Zohar Manna and Amir Pnueli.
 * <p>
 * A {@link TBPar} means Tableau Particle. A particle is an incomplete atom
 * because it only adheres to a relaxed version of atoms. Due to its
 * incompleteness, it results in a more efficient tableau since its size is less
 * than that with complete atoms. However, it does not loose generality.
 * <p>
 * The formulas are in positive form, meaning negation
 * is only applied to state formulas. The state formulas are not keep in
 * {@link TBPar}, but in {@link TBGraphNode#statePreds} instead. There is also where the
 * successors of the particle are held.
 * <p>
 * TLA+ supports only future formulas and no past temporal operators (compare
 * with p. 43 fig. 0.15), thus it uses the PART-TAB algorithm (p. 456) for the
 * tableau construction.
 */

<HTML></li></HTML> <HTML><li></HTML><HTML></HTML>Then: VI: We then create an OrderOfSolution for each tf in tfbin.<HTML></HTML><HTML></li></HTML> <HTML><li></HTML><HTML></HTML>There is also an option to write the Tableau graph to disk:*// Uncomment to write the tableau in dot format to disk.*<HTML></HTML><HTML></li></HTML> <HTML><li></HTML><HTML></HTML>Then:<HTML></HTML>

// VII:
// We lump all the pems into a single checkState and checkAct,
// and oss[i].pems will simply be integer lookups into them.
//
// At this point, the temporal formulae are done and only the `[]<>A`, `<>[]A`, and `[]<>S`
// are added to the OOS.  The OOS holds the `[]<>S` and the union of `[]<>A` and `<>[]A`
// (OOS#checkState and OOS#checkAction). The PossibleErrorModel stores the indices into
// OOS#checkState and OOS#checkAction.
//
// The split into OrderOfSolution (OOS) and PossibleErrorModel (PEM) appears to
// be a code-level optimization to speed-up the check of the liveness/behavior-graph
// in LiveWorker.

<HTML></li></HTML><HTML></ul></HTML> <HTML></li></HTML> <HTML><li></HTML><HTML></HTML>Because this solution has no Tableau, a livechecker is created<HTML></HTML> <HTML></HTML>checker[soln] = new LiveChecker(solutions[soln], soln, bucketStatistics, writer);<HTML></HTML> <HTML><ul></HTML> <HTML><li></HTML>but this is an array, so depending on the OrderOfSolution, different formulas might need a TableauLiveChecker or a LiveChecker.<HTML></li></HTML><HTML></ul></HTML> <HTML></li></HTML> <HTML><li></HTML><HTML></li></HTML><HTML></ul></HTML> <HTML></li></HTML><HTML></ul></HTML> <HTML></li></HTML><HTML></ul></HTML> <HTML></li></HTML><HTML></ul></HTML>

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