Examples with ArithExpr com.microsoft.z3.ArithExpr used on opensource projects

Example 16 with ArithExpr

use of com.microsoft.z3.ArithExpr in project batfish by batfish.

the class TransferSSA method joinPoint.

/*
   * The [phi] function from SSA that merges variables that may differ across
   * different branches of an mkIf statement.
   */
private Pair<Expr, Expr> joinPoint(TransferParam<SymbolicRoute> p, TransferResult<BoolExpr, BoolExpr> r, BoolExpr guard, Pair<String, Pair<Expr, Expr>> values) {
    String variableName = values.getFirst();
    Expr trueBranch = values.getSecond().getFirst();
    Expr falseBranch = values.getSecond().getSecond();
    if (variableName.equals("RETURN") || variableName.equals("FALLTHROUGH")) {
        Expr t = (trueBranch == null ? _enc.mkFalse() : // can use False because the value has not been assigned
        trueBranch);
        Expr f = (falseBranch == null ? _enc.mkFalse() : falseBranch);
        Expr tass = (trueBranch == null ? r.getReturnAssignedValue() : _enc.mkTrue());
        Expr fass = (falseBranch == null ? r.getReturnAssignedValue() : _enc.mkTrue());
        BoolExpr newAss = _enc.mkIf(guard, (BoolExpr) tass, (BoolExpr) fass);
        BoolExpr retAss = createBoolVariableWith(p, "ASSIGNED", newAss);
        BoolExpr variable = (variableName.equals("RETURN") ? r.getReturnValue() : r.getFallthroughValue());
        BoolExpr newValue = _enc.mkIf(r.getReturnAssignedValue(), variable, _enc.mkIf(guard, (BoolExpr) t, (BoolExpr) f));
        BoolExpr ret = createBoolVariableWith(p, variableName, newValue);
        return new Pair<>(ret, retAss);
    }
    if (variableName.equals("PREFIX-LEN")) {
        Expr t = (trueBranch == null ? p.getData().getPrefixLength() : trueBranch);
        Expr f = (falseBranch == null ? p.getData().getPrefixLength() : falseBranch);
        ArithExpr newValue = _enc.mkIf(guard, (ArithExpr) t, (ArithExpr) f);
        newValue = _enc.mkIf(r.getReturnAssignedValue(), p.getData().getPrefixLength(), newValue);
        ArithExpr ret = createArithVariableWith(p, "PREFIX-LEN", newValue);
        p.getData().setPrefixLength(ret);
        return new Pair<>(ret, null);
    }
    if (variableName.equals("ADMIN-DIST")) {
        Expr t = (trueBranch == null ? p.getData().getAdminDist() : trueBranch);
        Expr f = (falseBranch == null ? p.getData().getAdminDist() : falseBranch);
        ArithExpr newValue = _enc.mkIf(guard, (ArithExpr) t, (ArithExpr) f);
        newValue = _enc.mkIf(r.getReturnAssignedValue(), p.getData().getAdminDist(), newValue);
        ArithExpr ret = createArithVariableWith(p, "ADMIN-DIST", newValue);
        p.getData().setAdminDist(ret);
        return new Pair<>(ret, null);
    }
    if (variableName.equals("LOCAL-PREF")) {
        Expr t = (trueBranch == null ? p.getData().getLocalPref() : trueBranch);
        Expr f = (falseBranch == null ? p.getData().getLocalPref() : falseBranch);
        ArithExpr newValue = _enc.mkIf(guard, (ArithExpr) t, (ArithExpr) f);
        newValue = _enc.mkIf(r.getReturnAssignedValue(), p.getData().getLocalPref(), newValue);
        ArithExpr ret = createArithVariableWith(p, "LOCAL-PREF", newValue);
        p.getData().setLocalPref(ret);
        return new Pair<>(ret, null);
    }
    if (variableName.equals("METRIC")) {
        Expr t = (trueBranch == null ? p.getData().getMetric() : trueBranch);
        Expr f = (falseBranch == null ? p.getData().getMetric() : falseBranch);
        ArithExpr newValue = _enc.mkIf(guard, (ArithExpr) t, (ArithExpr) f);
        newValue = _enc.mkIf(r.getReturnAssignedValue(), p.getData().getMetric(), newValue);
        ArithExpr ret = createArithVariableWith(p, "METRIC", newValue);
        p.getData().setMetric(ret);
        return new Pair<>(ret, null);
    }
    if (variableName.equals("OSPF-TYPE")) {
        Expr t = (trueBranch == null ? p.getData().getOspfType().getBitVec() : trueBranch);
        Expr f = (falseBranch == null ? p.getData().getOspfType().getBitVec() : falseBranch);
        BitVecExpr newValue = _enc.mkIf(guard, (BitVecExpr) t, (BitVecExpr) f);
        newValue = _enc.mkIf(r.getReturnAssignedValue(), p.getData().getOspfType().getBitVec(), newValue);
        BitVecExpr ret = createBitVecVariableWith(p, "OSPF-TYPE", 2, newValue);
        p.getData().getOspfType().setBitVec(ret);
        return new Pair<>(ret, null);
    }
    for (Map.Entry<CommunityVar, BoolExpr> entry : p.getData().getCommunities().entrySet()) {
        CommunityVar cvar = entry.getKey();
        if (variableName.equals(cvar.getValue())) {
            Expr t = (trueBranch == null ? p.getData().getCommunities().get(cvar) : trueBranch);
            Expr f = (falseBranch == null ? p.getData().getCommunities().get(cvar) : falseBranch);
            BoolExpr newValue = _enc.mkIf(guard, (BoolExpr) t, (BoolExpr) f);
            newValue = _enc.mkIf(r.getReturnAssignedValue(), p.getData().getCommunities().get(cvar), newValue);
            BoolExpr ret = createBoolVariableWith(p, cvar.getValue(), newValue);
            p.getData().getCommunities().put(cvar, ret);
            return new Pair<>(ret, null);
        }
    }
    throw new BatfishException("[joinPoint]: unhandled case for " + variableName);
}

Example 17 with ArithExpr

use of com.microsoft.z3.ArithExpr in project batfish by batfish.

the class Encoder method initFailedLinkVariables.

/*
   * Initialize symbolic variables to represent link failures.
   */
private void initFailedLinkVariables() {
    for (List<GraphEdge> edges : _graph.getEdgeMap().values()) {
        for (GraphEdge ge : edges) {
            if (ge.getPeer() == null) {
                Interface i = ge.getStart();
                String name = getId() + "_FAILED-EDGE_" + ge.getRouter() + "_" + i.getName();
                ArithExpr var = getCtx().mkIntConst(name);
                _symbolicFailures.getFailedEdgeLinks().put(ge, var);
                _allVariables.put(var.toString(), var);
            }
        }
    }
    for (Entry<String, Set<String>> entry : _graph.getNeighbors().entrySet()) {
        String router = entry.getKey();
        Set<String> peers = entry.getValue();
        for (String peer : peers) {
            // sort names for unique
            String pair = (router.compareTo(peer) < 0 ? router + "_" + peer : peer + "_" + router);
            String name = getId() + "_FAILED-EDGE_" + pair;
            ArithExpr var = _ctx.mkIntConst(name);
            _symbolicFailures.getFailedInternalLinks().put(router, peer, var);
            _allVariables.put(var.toString(), var);
        }
    }
}

Example 18 with ArithExpr

use of com.microsoft.z3.ArithExpr in project batfish by batfish.

the class EncoderSlice method equal.

/*
   * Check for equality of a (best) symbolic record and another
   * symbolic record (vars). It checks pairwise that all fields
   * are equal, while filling in values missing due to optimizations
   * with default values based on the protocol.
   * If there is no corresponding edge e, then the value null can be used
   */
public BoolExpr equal(Configuration conf, Protocol proto, SymbolicRoute best, SymbolicRoute vars, @Nullable LogicalEdge e, boolean compareCommunities) {
    ArithExpr defaultLocal = mkInt(defaultLocalPref());
    ArithExpr defaultAdmin = defaultAdminDistance(conf, proto, vars);
    ArithExpr defaultMet = mkInt(defaultMetric());
    ArithExpr defaultMed = mkInt(defaultMed(proto));
    ArithExpr defaultLen = mkInt(defaultLength());
    ArithExpr defaultIgp = mkInt(defaultIgpMetric());
    BoolExpr equalLen;
    BoolExpr equalAd;
    BoolExpr equalLp;
    BoolExpr equalMet;
    BoolExpr equalMed;
    BoolExpr equalOspfArea;
    BoolExpr equalOspfType;
    BoolExpr equalId;
    BoolExpr equalHistory;
    BoolExpr equalBgpInternal;
    BoolExpr equalClientIds;
    BoolExpr equalIgpMet;
    BoolExpr equalCommunities;
    equalLen = equalHelper(best.getPrefixLength(), vars.getPrefixLength(), defaultLen);
    equalAd = equalHelper(best.getAdminDist(), vars.getAdminDist(), defaultAdmin);
    equalLp = equalHelper(best.getLocalPref(), vars.getLocalPref(), defaultLocal);
    equalMet = equalHelper(best.getMetric(), vars.getMetric(), defaultMet);
    equalMed = equalHelper(best.getMed(), vars.getMed(), defaultMed);
    equalIgpMet = equalHelper(best.getIgpMetric(), vars.getIgpMetric(), defaultIgp);
    equalOspfType = equalTypes(best, vars);
    equalOspfArea = equalAreas(best, vars, e);
    equalId = equalIds(best, vars, proto, e);
    equalHistory = equalHistories(best, vars);
    equalBgpInternal = equalBgpInternal(best, vars);
    equalClientIds = equalClientIds(conf.getName(), best, vars);
    equalCommunities = (compareCommunities ? equalCommunities(best, vars) : mkTrue());
    return mkAnd(equalLen, equalAd, equalLp, equalMet, equalMed, equalOspfArea, equalOspfType, equalId, equalHistory, equalBgpInternal, equalClientIds, equalIgpMet, equalCommunities);
}

Example 19 with ArithExpr

use of com.microsoft.z3.ArithExpr in project batfish by batfish.

the class EncoderSlice method isRelevantFor.

/*
   * Check if a prefix range match is applicable for the packet destination
   * Ip address, given the prefix length variable.
   */
BoolExpr isRelevantFor(ArithExpr prefixLen, PrefixRange range) {
    Prefix p = range.getPrefix();
    SubRange r = range.getLengthRange();
    long pfx = p.getStartIp().asLong();
    int len = p.getPrefixLength();
    int lower = r.getStart();
    int upper = r.getEnd();
    // well formed prefix
    assert (p.getPrefixLength() <= lower && lower <= upper);
    BoolExpr lowerBitsMatch = firstBitsEqual(_symbolicPacket.getDstIp(), pfx, len);
    if (lower == upper) {
        BoolExpr equalLen = mkEq(prefixLen, mkInt(lower));
        return mkAnd(equalLen, lowerBitsMatch);
    } else {
        BoolExpr lengthLowerBound = mkGe(prefixLen, mkInt(lower));
        BoolExpr lengthUpperBound = mkLe(prefixLen, mkInt(upper));
        return mkAnd(lengthLowerBound, lengthUpperBound, lowerBitsMatch);
    }
}

Example 20 with ArithExpr

use of com.microsoft.z3.ArithExpr in project batfish by batfish.

the class EncoderSlice method greaterOrEqual.

/*
   * Check if a (best) symbolic record is better than another
   * symbolic record (vars). This is done using a recursive lexicographic
   * encoding. The encoding is as follows:
   *
   * (best.length > vars.length) or
   * (best.length = vars.length) and (
   *    (best.adminDist < vars.adminDist) or
   *    (best.adminDist = vars.adminDist) and (
   *     ...
   *    )
   * )
   *
   * This recursive encoding introduces a new variable for each subexpressions,
   * which ends up being much more efficient than expanding out options.
   */
private BoolExpr greaterOrEqual(Configuration conf, Protocol proto, SymbolicRoute best, SymbolicRoute vars, @Nullable LogicalEdge e) {
    ArithExpr defaultLocal = mkInt(defaultLocalPref());
    ArithExpr defaultAdmin = defaultAdminDistance(conf, proto, vars);
    ArithExpr defaultMet = mkInt(defaultMetric());
    ArithExpr defaultMed = mkInt(defaultMed(proto));
    ArithExpr defaultLen = mkInt(defaultLength());
    ArithExpr defaultIgp = mkInt(defaultIgpMetric());
    ArithExpr defaultId = mkInt(0);
    BitVecExpr defaultOspfType = defaultOspfType();
    BoolExpr betterLen = geBetterHelper(best.getPrefixLength(), vars.getPrefixLength(), defaultLen, false);
    BoolExpr equalLen = geEqualHelper(best.getPrefixLength(), vars.getPrefixLength(), defaultLen);
    BoolExpr betterAd = geBetterHelper(best.getAdminDist(), vars.getAdminDist(), defaultAdmin, true);
    BoolExpr equalAd = geEqualHelper(best.getAdminDist(), vars.getAdminDist(), defaultAdmin);
    BoolExpr betterLp = geBetterHelper(best.getLocalPref(), vars.getLocalPref(), defaultLocal, false);
    BoolExpr equalLp = geEqualHelper(best.getLocalPref(), vars.getLocalPref(), defaultLocal);
    BoolExpr betterMet = geBetterHelper(best.getMetric(), vars.getMetric(), defaultMet, true);
    BoolExpr equalMet = geEqualHelper(best.getMetric(), vars.getMetric(), defaultMet);
    BoolExpr betterMed = geBetterHelper(best.getMed(), vars.getMed(), defaultMed, true);
    BoolExpr equalMed = geEqualHelper(best.getMed(), vars.getMed(), defaultMed);
    BitVecExpr bestType = (best.getOspfType() == null ? null : best.getOspfType().getBitVec());
    BitVecExpr varsType = (vars.getOspfType() == null ? null : vars.getOspfType().getBitVec());
    BoolExpr betterOspfType = geBetterHelper(bestType, varsType, defaultOspfType, true);
    BoolExpr equalOspfType = geEqualHelper(bestType, varsType, defaultOspfType);
    BoolExpr betterInternal = geBetterHelper(best.getBgpInternal(), vars.getBgpInternal(), mkFalse(), true);
    BoolExpr equalInternal = geEqualHelper(best.getBgpInternal(), vars.getBgpInternal(), mkFalse());
    BoolExpr betterIgpMet = geBetterHelper(best.getIgpMetric(), vars.getIgpMetric(), defaultIgp, true);
    BoolExpr equalIgpMet = geEqualHelper(best.getIgpMetric(), vars.getIgpMetric(), defaultIgp);
    BoolExpr tiebreak;
    if (vars.getRouterId() != null) {
        tiebreak = mkLe(best.getRouterId(), vars.getRouterId());
    } else if (best.getRouterId() != null) {
        if (e == null) {
            tiebreak = mkLe(best.getRouterId(), defaultId);
        } else {
            long peerId = getGraph().findRouterId(e.getEdge(), proto);
            tiebreak = mkLe(best.getRouterId(), mkInt(peerId));
        }
    } else {
        tiebreak = mkTrue();
    }
    BoolExpr b = mkAnd(equalOspfType, tiebreak);
    BoolExpr b1 = mkOr(betterOspfType, b);
    BoolExpr b2 = mkAnd(equalIgpMet, b1);
    BoolExpr b3 = mkOr(betterIgpMet, b2);
    BoolExpr b4 = mkAnd(equalInternal, b3);
    BoolExpr b5 = mkOr(betterInternal, b4);
    BoolExpr b6 = mkAnd(equalMed, b5);
    BoolExpr b7 = mkOr(betterMed, b6);
    BoolExpr b8 = mkAnd(equalMet, b7);
    BoolExpr b9 = mkOr(betterMet, b8);
    BoolExpr b10 = mkAnd(equalLp, b9);
    BoolExpr b11 = mkOr(betterLp, b10);
    BoolExpr b12 = mkAnd(equalAd, b11);
    BoolExpr b13 = mkOr(betterAd, b12);
    BoolExpr b14 = mkAnd(equalLen, b13);
    return mkOr(betterLen, b14);
}