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

Example 26 with ArithExpr

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

the class PropertyChecker method checkEqualLength.

/*
   * Computes whether a collection of source routers will always have
   * equal path length to destination port(s).
   */
public AnswerElement checkEqualLength(HeaderLocationQuestion q) {
    return checkProperty(q, (enc, srcRouters, destPorts) -> {
        PropertyAdder pa = new PropertyAdder(enc.getMainSlice());
        Map<String, ArithExpr> lenVars = pa.instrumentPathLength(destPorts);
        Map<String, BoolExpr> eqVars = new HashMap<>();
        List<Expr> lens = new ArrayList<>();
        for (String router : srcRouters) {
            lens.add(lenVars.get(router));
        }
        BoolExpr allEqual = PropertyAdder.allEqual(enc.getCtx(), lens);
        enc.add(enc.mkNot(allEqual));
        for (Entry<String, ArithExpr> entry : lenVars.entrySet()) {
            String name = entry.getKey();
            BoolExpr b = srcRouters.contains(name) ? allEqual : enc.mkTrue();
            eqVars.put(name, b);
        }
        return eqVars;
    }, (vp) -> new SmtOneAnswerElement(vp.getResult()));
}

Example 27 with ArithExpr

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

the class TransferSSA method compute.

/*
   * Convert a list of statements into a Z3 boolean expression for the transfer function.
   */
private TransferResult<BoolExpr, BoolExpr> compute(List<Statement> statements, TransferParam<SymbolicRoute> p, TransferResult<BoolExpr, BoolExpr> result) {
    boolean doesReturn = false;
    for (Statement stmt : statements) {
        if (stmt instanceof StaticStatement) {
            StaticStatement ss = (StaticStatement) stmt;
            switch(ss.getType()) {
                case ExitAccept:
                    doesReturn = true;
                    p.debug("ExitAccept");
                    result = returnValue(p, result, true);
                    break;
                case ReturnTrue:
                    doesReturn = true;
                    p.debug("ReturnTrue");
                    result = returnValue(p, result, true);
                    break;
                case ExitReject:
                    doesReturn = true;
                    p.debug("ExitReject");
                    result = returnValue(p, result, false);
                    break;
                case ReturnFalse:
                    doesReturn = true;
                    p.debug("ReturnFalse");
                    result = returnValue(p, result, false);
                    break;
                case SetDefaultActionAccept:
                    p.debug("SetDefaulActionAccept");
                    p = p.setDefaultAccept(true);
                    break;
                case SetDefaultActionReject:
                    p.debug("SetDefaultActionReject");
                    p = p.setDefaultAccept(false);
                    break;
                case SetLocalDefaultActionAccept:
                    p.debug("SetLocalDefaultActionAccept");
                    p = p.setDefaultAcceptLocal(true);
                    break;
                case SetLocalDefaultActionReject:
                    p.debug("SetLocalDefaultActionReject");
                    p = p.setDefaultAcceptLocal(false);
                    break;
                case ReturnLocalDefaultAction:
                    p.debug("ReturnLocalDefaultAction");
                    // TODO: need to set local default action in an environment
                    if (p.getDefaultAcceptLocal()) {
                        result = returnValue(p, result, true);
                    } else {
                        result = returnValue(p, result, false);
                    }
                    break;
                case FallThrough:
                    p.debug("Fallthrough");
                    result = fallthrough(p, result);
                    break;
                case Return:
                    // TODO: assumming this happens at the end of the function, so it is ignored for now.
                    p.debug("Return");
                    break;
                case RemovePrivateAs:
                    p.debug("RemovePrivateAs");
                    System.out.println("Warning: use of unimplemented feature RemovePrivateAs");
                    break;
                default:
                    throw new BatfishException("TODO: computeTransferFunction: " + ss.getType());
            }
        } else if (stmt instanceof If) {
            p.debug("If");
            If i = (If) stmt;
            TransferResult<BoolExpr, BoolExpr> r = compute(i.getGuard(), p);
            result = result.addChangedVariables(r);
            BoolExpr guard = (BoolExpr) r.getReturnValue().simplify();
            String str = guard.toString();
            // If there are updates in the guard, add them to the parameter p before entering branches
            for (Pair<String, Expr> changed : r.getChangedVariables()) {
                p.debug("CHANGED: " + changed.getFirst());
                updateSingleValue(p, changed.getFirst(), changed.getSecond());
            }
            p.debug("guard: " + str);
            // If we know the branch ahead of time, then specialize
            switch(str) {
                case "true":
                    p.debug("True Branch");
                    result = compute(i.getTrueStatements(), p.indent(), result);
                    break;
                case "false":
                    p.debug("False Branch");
                    compute(i.getFalseStatements(), p.indent(), result);
                    break;
                default:
                    p.debug("True Branch");
                    // clear changed variables before proceeding
                    TransferParam<SymbolicRoute> p1 = p.indent().setData(p.getData().copy());
                    TransferParam<SymbolicRoute> p2 = p.indent().setData(p.getData().copy());
                    TransferResult<BoolExpr, BoolExpr> trueBranch = compute(i.getTrueStatements(), p1, initialResult());
                    p.debug("False Branch");
                    TransferResult<BoolExpr, BoolExpr> falseBranch = compute(i.getFalseStatements(), p2, initialResult());
                    p.debug("JOIN");
                    PList<Pair<String, Pair<Expr, Expr>>> pairs = trueBranch.mergeChangedVariables(falseBranch);
                    // Extract and deal with the return value first so that other
                    // variables have this reflected in their value
                    int idx = pairs.find(pair -> pair.getFirst().equals("RETURN"));
                    if (idx >= 0) {
                        Pair<String, Pair<Expr, Expr>> ret = pairs.get(idx);
                        pairs = pairs.minus(idx);
                        pairs = pairs.plus(pairs.size(), ret);
                    }
                    for (Pair<String, Pair<Expr, Expr>> pair : pairs) {
                        String s = pair.getFirst();
                        p.debug("CHANGED: " + s);
                        Pair<Expr, Expr> x = joinPoint(p, result, guard, pair);
                        result = result.addChangedVariable(s, x.getFirst());
                        if (s.equals("RETURN")) {
                            result = result.setReturnValue((BoolExpr) x.getFirst()).setReturnAssignedValue((BoolExpr) x.getSecond());
                        }
                        if (s.equals("FALLTHROUGH")) {
                            result = result.setFallthroughValue((BoolExpr) x.getFirst()).setReturnAssignedValue((BoolExpr) x.getSecond());
                        }
                    }
                    break;
            }
        } else if (stmt instanceof SetDefaultPolicy) {
            p.debug("SetDefaultPolicy");
            p = p.setDefaultPolicy((SetDefaultPolicy) stmt);
        } else if (stmt instanceof SetMetric) {
            p.debug("SetMetric");
            // TODO: what is the semantics for BGP? Is this MED?
            if (!_current.getProto().isBgp()) {
                SetMetric sm = (SetMetric) stmt;
                LongExpr ie = sm.getMetric();
                ArithExpr newValue = applyLongExprModification(p.getData().getMetric(), ie);
                newValue = _enc.mkIf(result.getReturnAssignedValue(), p.getData().getMetric(), newValue);
                ArithExpr x = createArithVariableWith(p, "METRIC", newValue);
                p.getData().setMetric(x);
                result = result.addChangedVariable("METRIC", x);
            }
        } else if (stmt instanceof SetOspfMetricType) {
            p.debug("SetOspfMetricType");
            SetOspfMetricType somt = (SetOspfMetricType) stmt;
            OspfMetricType mt = somt.getMetricType();
            SymbolicOspfType t;
            if (mt == OspfMetricType.E1) {
                t = new SymbolicOspfType(_enc, OspfType.E1);
            } else {
                t = new SymbolicOspfType(_enc, OspfType.E2);
            }
            BitVecExpr newValue = t.getBitVec();
            newValue = _enc.mkIf(result.getReturnAssignedValue(), p.getData().getOspfType().getBitVec(), newValue);
            BitVecExpr x = createBitVecVariableWith(p, "OSPF-TYPE", 2, newValue);
            p.getData().getOspfType().setBitVec(x);
            result = result.addChangedVariable("OSPF-TYPE", x);
        } else if (stmt instanceof SetLocalPreference) {
            p.debug("SetLocalPreference");
            SetLocalPreference slp = (SetLocalPreference) stmt;
            IntExpr ie = slp.getLocalPreference();
            ArithExpr newValue = applyIntExprModification(p.getData().getLocalPref(), ie);
            newValue = _enc.mkIf(result.getReturnAssignedValue(), p.getData().getLocalPref(), newValue);
            ArithExpr x = createArithVariableWith(p, "LOCAL-PREF", newValue);
            p.getData().setLocalPref(x);
            result = result.addChangedVariable("LOCAL-PREF", x);
        } else if (stmt instanceof AddCommunity) {
            p.debug("AddCommunity");
            AddCommunity ac = (AddCommunity) stmt;
            Set<CommunityVar> comms = _enc.getGraph().findAllCommunities(_conf, ac.getExpr());
            for (CommunityVar cvar : comms) {
                BoolExpr newValue = _enc.mkIf(result.getReturnAssignedValue(), p.getData().getCommunities().get(cvar), _enc.mkTrue());
                BoolExpr x = createBoolVariableWith(p, cvar.getValue(), newValue);
                p.getData().getCommunities().put(cvar, x);
                result = result.addChangedVariable(cvar.getValue(), x);
            }
        } else if (stmt instanceof SetCommunity) {
            p.debug("SetCommunity");
            SetCommunity sc = (SetCommunity) stmt;
            Set<CommunityVar> comms = _enc.getGraph().findAllCommunities(_conf, sc.getExpr());
            for (CommunityVar cvar : comms) {
                BoolExpr newValue = _enc.mkIf(result.getReturnAssignedValue(), p.getData().getCommunities().get(cvar), _enc.mkTrue());
                BoolExpr x = createBoolVariableWith(p, cvar.getValue(), newValue);
                p.getData().getCommunities().put(cvar, x);
                result = result.addChangedVariable(cvar.getValue(), x);
            }
        } else if (stmt instanceof DeleteCommunity) {
            p.debug("DeleteCommunity");
            DeleteCommunity ac = (DeleteCommunity) stmt;
            Set<CommunityVar> comms = _enc.getGraph().findAllCommunities(_conf, ac.getExpr());
            Set<CommunityVar> toDelete = new HashSet<>();
            // Find comms to delete
            for (CommunityVar cvar : comms) {
                if (cvar.getType() == Type.REGEX) {
                    toDelete.addAll(_enc.getCommunityDependencies().get(cvar));
                } else {
                    toDelete.add(cvar);
                }
            }
            // Delete each community
            for (CommunityVar cvar : toDelete) {
                BoolExpr newValue = _enc.mkIf(result.getReturnAssignedValue(), p.getData().getCommunities().get(cvar), _enc.mkFalse());
                BoolExpr x = createBoolVariableWith(p, cvar.getValue(), newValue);
                p.getData().getCommunities().put(cvar, x);
                result = result.addChangedVariable(cvar.getValue(), x);
            }
        } else if (stmt instanceof RetainCommunity) {
            p.debug("RetainCommunity");
        // no op
        } else if (stmt instanceof PrependAsPath) {
            p.debug("PrependAsPath");
            PrependAsPath pap = (PrependAsPath) stmt;
            Integer prependCost = prependLength(pap.getExpr());
            ArithExpr newValue = _enc.mkSum(p.getData().getMetric(), _enc.mkInt(prependCost));
            newValue = _enc.mkIf(result.getReturnAssignedValue(), p.getData().getMetric(), newValue);
            ArithExpr x = createArithVariableWith(p, "METRIC", newValue);
            p.getData().setMetric(x);
            result = result.addChangedVariable("METRIC", x);
        } else if (stmt instanceof SetOrigin) {
            p.debug("SetOrigin");
            System.out.println("Warning: use of unimplemented feature SetOrigin");
        } else if (stmt instanceof SetNextHop) {
            p.debug("SetNextHop");
            System.out.println("Warning: use of unimplemented feature SetNextHop");
        } else {
            String s = (_isExport ? "export" : "import");
            String msg = String.format("Unimplemented feature %s for %s transfer function on interface %s", stmt.toString(), s, _graphEdge.toString());
            throw new BatfishException(msg);
        }
    }
    // If this is the outermost call, then we relate the variables
    if (p.getInitialCall()) {
        p.debug("InitialCall finalizing");
        // Apply the default action
        if (!doesReturn) {
            p.debug("Applying default action: " + p.getDefaultAccept());
            if (p.getDefaultAccept()) {
                result = returnValue(p, result, true);
            } else {
                result = returnValue(p, result, false);
            }
        }
        BoolExpr related = relateVariables(p, result);
        BoolExpr retValue = _enc.mkIf(result.getReturnValue(), related, _enc.mkNot(_current.getPermitted()));
        result = result.setReturnValue(retValue);
    }
    return result;
}

Example 28 with ArithExpr

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

the class TransferSSA method matchPrefixSet.

/*
   * Converts a prefix set to a boolean expression.
   */
private TransferResult<BoolExpr, BoolExpr> matchPrefixSet(Configuration conf, PrefixSetExpr e, SymbolicRoute other) {
    ArithExpr otherLen = other.getPrefixLength();
    TransferResult<BoolExpr, BoolExpr> result = new TransferResult<>();
    if (e instanceof ExplicitPrefixSet) {
        ExplicitPrefixSet x = (ExplicitPrefixSet) e;
        Set<PrefixRange> ranges = x.getPrefixSpace().getPrefixRanges();
        if (ranges.isEmpty()) {
            return result.setReturnValue(_enc.mkTrue());
        }
        // by checking for static/connected/OSPF routes specifically.
        if (ranges.size() == 1) {
            for (PrefixRange r : ranges) {
                int start = r.getLengthRange().getStart();
                int end = r.getLengthRange().getEnd();
                Prefix pfx = r.getPrefix();
                if (start == end && start == pfx.getPrefixLength()) {
                    String router = _conf.getName();
                    Set<Prefix> origin = _enc.getOriginatedNetworks().get(router, Protocol.BGP);
                    if (origin != null && origin.contains(pfx)) {
                        // Compute static and connected routes
                        Set<Prefix> ostatic = _enc.getOriginatedNetworks().get(router, Protocol.STATIC);
                        Set<Prefix> oconn = _enc.getOriginatedNetworks().get(router, Protocol.CONNECTED);
                        boolean hasStatic = ostatic != null && ostatic.contains(pfx);
                        boolean hasConnected = oconn != null && oconn.contains(pfx);
                        ArithExpr originLength = _enc.mkInt(pfx.getPrefixLength());
                        if (hasStatic || hasConnected) {
                            BoolExpr directRoute = _enc.isRelevantFor(originLength, r);
                            ArithExpr newLength = _enc.mkIf(directRoute, originLength, otherLen);
                            result = result.addChangedVariable("PREFIX-LEN", newLength);
                            return result.setReturnValue(directRoute);
                        } else {
                            // Also use network statement if OSPF has a route with the correct length
                            SymbolicRoute rec = _enc.getBestNeighborPerProtocol(router, Protocol.OSPF);
                            if (rec != null) {
                                BoolExpr ospfRelevant = _enc.isRelevantFor(rec.getPrefixLength(), r);
                                ArithExpr newLength = _enc.mkIf(ospfRelevant, originLength, otherLen);
                                result = result.addChangedVariable("PREFIX-LEN", newLength);
                                return result.setReturnValue(ospfRelevant);
                            }
                        }
                    }
                }
            }
        }
        // Compute if the other best route is relevant for this match statement
        BoolExpr acc = _enc.mkFalse();
        for (PrefixRange range : ranges) {
            acc = _enc.mkOr(acc, _enc.isRelevantFor(otherLen, range));
        }
        return result.setReturnValue(acc);
    } else if (e instanceof NamedPrefixSet) {
        NamedPrefixSet x = (NamedPrefixSet) e;
        String name = x.getName();
        RouteFilterList fl = conf.getRouteFilterLists().get(name);
        return result.setReturnValue(matchFilterList(fl, other));
    } else {
        throw new BatfishException("TODO: match prefix set: " + e);
    }
}

Example 29 with ArithExpr

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

the class TransferSSA method relateVariables.

/*
   * Relate the symbolic control plane route variables
   */
private BoolExpr relateVariables(TransferParam<SymbolicRoute> p, TransferResult<BoolExpr, BoolExpr> result) {
    ArithExpr defaultLen = _enc.mkInt(_enc.defaultLength());
    ArithExpr defaultAd = _enc.defaultAdminDistance(_conf, _proto, p.getData());
    ArithExpr defaultMed = _enc.mkInt(_enc.defaultMed(_proto));
    ArithExpr defaultLp = _enc.mkInt(_enc.defaultLocalPref());
    ArithExpr defaultId = _enc.mkInt(_enc.defaultId());
    ArithExpr defaultMet = _enc.mkInt(_enc.defaultMetric());
    // TODO: remove all isChanged calls with actual symbolic values that test for a change
    boolean isIbgp = _graphEdge.isAbstract() && _proto.isBgp();
    // Update prefix length when aggregation
    BoolExpr len = _enc.safeEq(_current.getPrefixLength(), getOrDefault(p.getData().getPrefixLength(), defaultLen));
    BoolExpr per = _enc.safeEq(_current.getPermitted(), p.getData().getPermitted());
    // Only update the router id for import edges
    BoolExpr id = _enc.mkTrue();
    if (!_isExport) {
        id = _enc.safeEq(_current.getRouterId(), getOrDefault(p.getData().getRouterId(), defaultId));
    }
    // Update OSPF area id
    BoolExpr area;
    if (p.getData().getOspfArea() == null || _iface.getOspfAreaName() == null) {
        area = _enc.mkTrue();
    } else {
        area = _enc.safeEqEnum(_current.getOspfArea(), _iface.getOspfAreaName());
    }
    // Set the IGP metric accordingly
    BoolExpr igpMet = _enc.mkTrue();
    boolean isNonClient = _graphEdge.isAbstract() && (_enc.getGraph().peerType(_graphEdge) != Graph.BgpSendType.TO_EBGP);
    boolean isClient = _graphEdge.isAbstract() && (_enc.getGraph().peerType(_graphEdge) == Graph.BgpSendType.TO_RR);
    if (_graphEdge.isAbstract() && _current.getIgpMetric() != null) {
        String router = _graphEdge.getRouter();
        String peer = _graphEdge.getPeer();
        // Case where it is a non client, we lookup the next-hop
        if (isNonClient) {
            EncoderSlice s = _enc.getEncoder().getSlice(peer);
            SymbolicRoute r = s.getSymbolicDecisions().getBestNeighbor().get(router);
            igpMet = _enc.mkEq(_current.getIgpMetric(), r.getMetric());
        }
        // Case where it is a client, next-hop depends on the clientId tag we added
        if (isClient) {
            BoolExpr acc = _enc.mkTrue();
            for (Map.Entry<String, Integer> entry : _enc.getGraph().getOriginatorId().entrySet()) {
                String r = entry.getKey();
                Integer clientId = entry.getValue();
                if (!r.equals(router)) {
                    EncoderSlice s = _enc.getEncoder().getSlice(r);
                    SymbolicRoute record = s.getSymbolicDecisions().getBestNeighbor().get(r);
                    BoolExpr eq = _enc.mkEq(_current.getIgpMetric(), record.getMetric());
                    acc = _enc.mkAnd(acc, _enc.mkImplies(p.getData().getClientId().checkIfValue(clientId), eq));
                }
            }
            igpMet = acc;
        }
    }
    // Set whether or not is iBGP or not on import
    BoolExpr isInternal = // TODO: and !isExport?
    _enc.safeEq(_current.getBgpInternal(), _enc.mkBool(isIbgp));
    // Update OSPF type
    BoolExpr type;
    if (result.isChanged("OSPF-TYPE")) {
        type = _enc.safeEqEnum(_current.getOspfType(), p.getData().getOspfType());
    } else {
        boolean hasAreaIface = _iface.getOspfAreaName() != null;
        boolean hasArea = p.getData().getOspfArea() != null;
        boolean hasType = p.getData().getOspfType() != null;
        boolean areaPossiblyChanged = hasType && hasArea && hasAreaIface;
        // Check if area changed
        if (areaPossiblyChanged) {
            BoolExpr internal = p.getData().getOspfType().isInternal();
            BoolExpr same = p.getData().getOspfArea().checkIfValue(_iface.getOspfAreaName());
            BoolExpr update = _enc.mkAnd(internal, _enc.mkNot(same));
            BoolExpr copyOld = _enc.safeEqEnum(_current.getOspfType(), p.getData().getOspfType());
            type = _enc.mkIf(update, _current.getOspfType().checkIfValue(OspfType.OIA), copyOld);
        } else {
            type = _enc.safeEqEnum(_current.getOspfType(), p.getData().getOspfType());
        }
    }
    BoolExpr comms = _enc.mkTrue();
    // update all community values
    for (Map.Entry<CommunityVar, BoolExpr> entry : _current.getCommunities().entrySet()) {
        CommunityVar cvar = entry.getKey();
        BoolExpr e = entry.getValue();
        BoolExpr eOther = p.getData().getCommunities().get(cvar);
        // Update the communities if they should be sent
        if (sendCommunity()) {
            if (cvar.getType() != CommunityVar.Type.REGEX) {
                comms = _enc.mkAnd(comms, _enc.mkEq(e, eOther));
            }
        } else {
            comms = _enc.mkAnd(comms, _enc.mkNot(e));
        }
    }
    ArithExpr otherAd = (p.getData().getAdminDist() == null ? defaultAd : p.getData().getAdminDist());
    ArithExpr otherMed = (p.getData().getMed() == null ? defaultMed : p.getData().getMed());
    ArithExpr otherLp = getOrDefault(p.getData().getLocalPref(), defaultLp);
    ArithExpr otherMet = getOrDefault(p.getData().getMetric(), defaultMet);
    // otherMet = applyMetricUpdate(otherMet);
    BoolExpr ad = _enc.safeEq(_current.getAdminDist(), otherAd);
    BoolExpr history = _enc.equalHistories(_current, p.getData());
    BoolExpr med = _enc.safeEq(_current.getMed(), otherMed);
    BoolExpr met = _enc.safeEq(_current.getMetric(), otherMet);
    BoolExpr lp = _enc.safeEq(_current.getLocalPref(), otherLp);
    // If this was an external route, then we need to add the correct next-hop tag
    boolean isEbgpEdge = _enc.getGraph().getEbgpNeighbors().get(_graphEdge) != null;
    BoolExpr cid = _enc.mkTrue();
    if (_isExport && _proto.isBgp() && p.getData().getClientId() != null) {
        if (isEbgpEdge) {
            cid = _current.getClientId().checkIfValue(0);
        } else {
            cid = _enc.safeEqEnum(_current.getClientId(), p.getData().getClientId());
        }
    }
    if (!_isExport && _proto.isBgp() && p.getData().getClientId() != null) {
        BoolExpr fromExternal = p.getData().getClientId().checkIfValue(0);
        BoolExpr edgeIsInternal = _enc.mkBool(!isClient && !isNonClient);
        BoolExpr copyOver = _enc.safeEqEnum(_current.getClientId(), p.getData().getClientId());
        Integer x = _enc.getGraph().getOriginatorId().get(_graphEdge.getRouter());
        SymbolicOriginatorId soid = _current.getClientId();
        BoolExpr setNewValue = (x == null ? soid.checkIfValue(0) : soid.checkIfValue(x));
        cid = _enc.mkIf(_enc.mkAnd(fromExternal, edgeIsInternal), setNewValue, copyOver);
    }
    BoolExpr updates = _enc.mkAnd(per, len, ad, med, lp, met, id, cid, type, area, comms, history, isInternal, igpMet);
    BoolExpr noOverflow = noOverflow(otherMet, _proto);
    return _enc.mkIf(noOverflow, updates, _enc.mkNot(_current.getPermitted()));
}