7 files changed, 8062 insertions, 7954 deletions

diff --git a/Source/Houdini/AbstractHoudini.cs b/Source/Houdini/AbstractHoudini.cs
index de3d3779..e3625dcc 100644
--- a/Source/Houdini/AbstractHoudini.cs
+++ b/Source/Houdini/AbstractHoudini.cs
@@ -1,4609 +1,4714 @@
-using System;

-using System.Collections.Generic;

-using System.Linq;

-using System.Text;

-using Microsoft.Boogie;

-using Microsoft.Boogie.VCExprAST;

-using VC;

-using Outcome = VC.VCGen.Outcome;

-using Bpl = Microsoft.Boogie;

-using System.Diagnostics;

-using System.Diagnostics.Contracts;

-using Microsoft.Boogie.GraphUtil;

-

-namespace Microsoft.Boogie.Houdini {

-

-    public class AbsHoudini

-    {

-        Dictionary<string, Function> existentialFunctions;

-        Program program;

-        Dictionary<string, Implementation> name2Impl;

-        Dictionary<string, VCExpr> impl2VC;

-        Dictionary<string, List<Tuple<string, Function, NAryExpr>>> impl2FuncCalls;

-        // constant -> the naryexpr that it replaced

-        Dictionary<string, NAryExpr> constant2FuncCall;

-

-        // function -> its abstract value

-        Dictionary<string, IAbstractDomain> function2Value;

-

-        // impl -> functions assumed/asserted

-        Dictionary<string, HashSet<string>> impl2functionsAsserted, impl2functionsAssumed;

-

-        // funtions -> impls where assumed/asserted

-        Dictionary<string, HashSet<string>> function2implAssumed, function2implAsserted;

-

-        // impl -> handler, collector

-        Dictionary<string, Tuple<ProverInterface.ErrorHandler, AbsHoudiniCounterexampleCollector>> impl2ErrorHandler;

-

-        // Essentials: VCGen, Prover

-        VCGen vcgen;

-        ProverInterface prover;

-

-        // Stats

-        TimeSpan proverTime;

-        int numProverQueries;

-

-        public AbsHoudini(Program program, IAbstractDomain defaultElem)

-        {

-            this.program = program;

-            this.impl2VC = new Dictionary<string, VCExpr>();

-            this.impl2FuncCalls = new Dictionary<string, List<Tuple<string, Function, NAryExpr>>>();

-            this.existentialFunctions = new Dictionary<string, Function>();

-            this.name2Impl = new Dictionary<string, Implementation>();

-            this.impl2functionsAsserted = new Dictionary<string, HashSet<string>>();

-            this.impl2functionsAssumed = new Dictionary<string, HashSet<string>>();

-            this.function2implAsserted = new Dictionary<string, HashSet<string>>();

-            this.function2implAssumed = new Dictionary<string, HashSet<string>>();

-            this.impl2ErrorHandler = new Dictionary<string, Tuple<ProverInterface.ErrorHandler, AbsHoudiniCounterexampleCollector>>();

-            this.constant2FuncCall = new Dictionary<string, NAryExpr>();

-

-            // Find the existential functions

-            foreach (var func in program.Functions

-                .Where(f => QKeyValue.FindBoolAttribute(f.Attributes, "existential")))

-                existentialFunctions.Add(func.Name, func);

-

-            this.function2Value = new Dictionary<string, IAbstractDomain>();

-            foreach (var func in existentialFunctions.Values)

-            {

-                // Find if the function wishes to use a specific abstract domain

-                var domain = QKeyValue.FindStringAttribute(func.Attributes, "absdomain");

-                if (domain == null)

-                {

-                    function2Value[func.Name] = defaultElem.Bottom();

-                }

-                else

-                {

-                    function2Value[func.Name] = AbstractDomainFactory.GetInstance(domain);

-                }

-            }

-            existentialFunctions.Keys.Iter(f => function2implAssumed.Add(f, new HashSet<string>()));

-            existentialFunctions.Keys.Iter(f => function2implAsserted.Add(f, new HashSet<string>()));

-

-            // type check

-            existentialFunctions.Values.Iter(func =>

-                {

-                    if (func.OutParams.Count != 1 || !func.OutParams[0].TypedIdent.Type.IsBool)

-                        throw new AbsHoudiniInternalError(string.Format("Existential function {0} must return bool", func.Name));

-                    if(func.Body != null)

-                        throw new AbsHoudiniInternalError(string.Format("Existential function {0} should not have a body", func.Name));

-                    var args = new List<Type>();

-                    func.InParams.Iter(v => args.Add(v.TypedIdent.Type));

-                    string msg = "";

-                    if (!function2Value[func.Name].TypeCheck(args, out msg))

-                        throw new AbsHoudiniInternalError("TypeError: " + msg);

-                });

-

-            //if (CommandLineOptions.Clo.ProverKillTime > 0)

-            //    CommandLineOptions.Clo.ProverOptions.Add(string.Format("TIME_LIMIT={0}", CommandLineOptions.Clo.ProverKillTime));

-

-            Inline();

-

-            this.vcgen = new VCGen(program, CommandLineOptions.Clo.SimplifyLogFilePath, CommandLineOptions.Clo.SimplifyLogFileAppend, new List<Checker>());

-            this.prover = ProverInterface.CreateProver(program, CommandLineOptions.Clo.SimplifyLogFilePath, CommandLineOptions.Clo.SimplifyLogFileAppend, CommandLineOptions.Clo.ProverKillTime);

-

-            this.proverTime = TimeSpan.Zero;

-            this.numProverQueries = 0;

-

-            program.Implementations

-                .Where(impl => !impl.SkipVerification)

-                .Iter(impl => name2Impl.Add(impl.Name, impl));

-

-            // Let's do VC Gen (and also build dependencies)

-            name2Impl.Values.Iter(GenVC);

-        }

-

-        public VCGenOutcome ComputeSummaries()

-        {

-            var overallOutcome = new VCGenOutcome(ProverInterface.Outcome.Valid, new List<Counterexample>());

-

-            // Compute SCCs and determine a priority order for impls

-            var Succ = new Dictionary<string, HashSet<string>>();

-            var Pred = new Dictionary<string, HashSet<string>>();

-            name2Impl.Keys.Iter(s => Succ[s] = new HashSet<string>());

-            name2Impl.Keys.Iter(s => Pred[s] = new HashSet<string>());

-

-            foreach(var impl in name2Impl.Keys) {

-                Succ[impl] = new HashSet<string>();

-                impl2functionsAsserted[impl].Iter(f => 

-                    function2implAssumed[f].Iter(succ =>

-                        {

-                            Succ[impl].Add(succ);

-                            Pred[succ].Add(impl);

-                        }));

-            }

-

-            var sccs = new StronglyConnectedComponents<string>(name2Impl.Keys,

-                new Adjacency<string>(n => Pred[n]),

-                new Adjacency<string>(n => Succ[n]));

-            sccs.Compute();

-            

-            // impl -> priority

-            var impl2Priority = new Dictionary<string, int>();

-            int p = 0;

-            foreach (var scc in sccs)

-            {

-                foreach (var impl in scc)

-                {

-                    impl2Priority.Add(impl, p);

-                    p++;

-                }

-            }

-

-            var worklist = new SortedSet<Tuple<int, string>>();

-            name2Impl.Keys.Iter(k => worklist.Add(Tuple.Create(impl2Priority[k], k)));

-

-            while (worklist.Any())

-            {

-                var impl = worklist.First().Item2;

-                worklist.Remove(worklist.First());

-

-                var gen = prover.VCExprGen;

-                var terms = new List<Expr>();

-                foreach (var tup in impl2FuncCalls[impl])

-                {

-                    var controlVar = tup.Item2;

-                    var exprVars = tup.Item3;

-                    var varList = new List<Expr>();

-                    exprVars.Args.OfType<Expr>().Iter(v => varList.Add(v));

-                    

-                    var args = new List<Expr>();

-                    controlVar.InParams.Iter(v => args.Add(Expr.Ident(v)));

-                    Expr term = Expr.Eq(new NAryExpr(Token.NoToken, new FunctionCall(controlVar), args),

-                                 function2Value[tup.Item1].Gamma(varList));

-

-                    if (controlVar.InParams.Count != 0)

-                    {

-                        term = new ForallExpr(Token.NoToken, new List<Variable>(controlVar.InParams.ToArray()),

-                            new Trigger(Token.NoToken, true, new List<Expr> { new NAryExpr(Token.NoToken, new FunctionCall(controlVar), args) }),

-                            term);

-                    }

-                    terms.Add(term);

-                }

-                var env = Expr.BinaryTreeAnd(terms);

-

-                env.Typecheck(new TypecheckingContext((IErrorSink)null));

-                var envVC = prover.Context.BoogieExprTranslator.Translate(env);

-

-                var vc = gen.Implies(envVC, impl2VC[impl]);

-

-                if (CommandLineOptions.Clo.Trace)

-                {

-                    Console.WriteLine("Verifying {0}: ", impl);

-                    //Console.WriteLine("env: {0}", envVC);

-                    var envFuncs = new HashSet<string>();

-                    impl2FuncCalls[impl].Iter(tup => envFuncs.Add(tup.Item1));

-                    envFuncs.Iter(f => PrintFunction(existentialFunctions[f]));

-                }

-

-                var handler = impl2ErrorHandler[impl].Item1;

-                var collector = impl2ErrorHandler[impl].Item2;

-                collector.Reset(impl);

-

-                var start = DateTime.Now;

-

-                prover.Push();

-                prover.Assert(gen.Not(vc), true);

-                prover.FlushAxiomsToTheoremProver();

-                prover.Check();

-                ProverInterface.Outcome proverOutcome = prover.CheckOutcomeCore(handler);

-

-                //prover.BeginCheck(impl, vc, handler);

-                //ProverInterface.Outcome proverOutcome = prover.CheckOutcomeCore(handler);

-

-                var inc = (DateTime.Now - start);

-                proverTime += inc;

-                numProverQueries++;

-

-                if (CommandLineOptions.Clo.Trace)

-                    Console.WriteLine("Time taken = " + inc.TotalSeconds.ToString());

-

-                if (proverOutcome == ProverInterface.Outcome.TimeOut || proverOutcome == ProverInterface.Outcome.OutOfMemory)

-                {

-                    // pick some function; make it true and keep going

-                    bool changed = false;

-                    foreach (var f in impl2functionsAsserted[impl])

-                    {

-                        function2Value[f] = function2Value[f].MakeTop(out changed);

-                        if (changed) break;

-                    }

-                    if(!changed)

-                        return new VCGenOutcome(proverOutcome, new List<Counterexample>());

-                }

-

-                if (CommandLineOptions.Clo.Trace)

-                    Console.WriteLine(collector.numErrors > 0 ? "SAT" : "UNSAT");

-

-                if (collector.numErrors > 0)

-                {

-                    var funcsChanged = collector.funcsChanged;

-                    if (funcsChanged.Count == 0)

-                    {

-                        overallOutcome = new VCGenOutcome(ProverInterface.Outcome.Invalid, collector.errors);

-                        break;

-                    }

-

-                    // propagate dependent guys back into the worklist, including self

-                    var deps = new HashSet<string>();

-                    deps.Add(impl);

-                    funcsChanged.Iter(f => deps.UnionWith(function2implAssumed[f]));

-

-                    deps.Iter(s => worklist.Add(Tuple.Create(impl2Priority[s], s)));

-                }

-

-                prover.Pop();

-            }

-

-            if (CommandLineOptions.Clo.Trace)

-            {

-                Console.WriteLine("Prover time = {0}", proverTime.TotalSeconds.ToString("F2"));

-                Console.WriteLine("Number of prover queries = " + numProverQueries);

-            }

-

-            if (CommandLineOptions.Clo.PrintAssignment)

-            {

-                // Print the answer

-                existentialFunctions.Values.Iter(PrintFunction);

-            }

-

-            return overallOutcome;

-        }

-

-

-        public IEnumerable<Function> GetAssignment()

-        {

-            var ret = new List<Function>();

-            foreach (var func in existentialFunctions.Values)

-            {

-                var invars = new List<Expr>(func.InParams.OfType<Variable>().Select(v => Expr.Ident(v)));

-                func.Body = function2Value[func.Name].Gamma(invars);

-                ret.Add(func);

-            }

-            return ret;

-        }

-

-        private void PrintFunction(Function function)

-        {

-            var tt = new TokenTextWriter(Console.Out, /*pretty=*/ false);

-            var invars = new List<Expr>(function.InParams.OfType<Variable>().Select(v => Expr.Ident(v)));

-            function.Body = function2Value[function.Name].Gamma(invars);

-            function.Emit(tt, 0);

-            tt.Close();

-        }

-

-        public HashSet<string> HandleCounterExample(string impl, Counterexample error)

-        {

-            var funcsChanged = new HashSet<string>();

-            // Find the failing assert -- need to do a join there

-            // return the set of functions whose definition has changed

-            var cex = ExtractState(impl, error);

-            foreach (var tup in cex)

-            {

-                function2Value[tup.Item1] = function2Value[tup.Item1].Join(tup.Item2);

-                funcsChanged.Add(tup.Item1);

-            }

-            return funcsChanged;

-        }

-

-        private List<Tuple<string, List<Model.Element>>> ExtractState(string impl, Counterexample error)

-        {

-            var lastBlock = error.Trace.Last() as Block;

-            AssertCmd failingAssert = null;

-

-            CallCounterexample callCounterexample = error as CallCounterexample;

-            if (callCounterexample != null)

-            {

-                Procedure failingProcedure = callCounterexample.FailingCall.Proc;

-                Requires failingRequires = callCounterexample.FailingRequires;

-                failingAssert = lastBlock.Cmds.OfType<AssertRequiresCmd>().FirstOrDefault(ac => ac.Requires == failingRequires);

-            }

-            ReturnCounterexample returnCounterexample = error as ReturnCounterexample;

-            if (returnCounterexample != null)

-            {

-                Ensures failingEnsures = returnCounterexample.FailingEnsures;

-                failingAssert = lastBlock.Cmds.OfType<AssertEnsuresCmd>().FirstOrDefault(ac => ac.Ensures == failingEnsures);

-            }

-            AssertCounterexample assertCounterexample = error as AssertCounterexample;

-            if (assertCounterexample != null)

-            {

-                failingAssert = lastBlock.Cmds.OfType<AssertCmd>().FirstOrDefault(ac => ac == assertCounterexample.FailingAssert);

-            }

-

-            Debug.Assert(failingAssert != null);

-            return ExtractState(impl, failingAssert.Expr, error.Model);

-        }

-

-        private static int existentialConstCounter = 0;

-

-        private List<Tuple<string, List<Model.Element>>> ExtractState(string impl, Expr expr, Model model)

-        {

-            var funcsUsed = FunctionCollector.Collect(expr);

-

-            var ret = new List<Tuple<string, List<Model.Element>>>();

-

-            foreach (var tup in funcsUsed.Where(t => t.Item2 == null))

-            {

-                var constant = tup.Item1;

-                if (!constant2FuncCall.ContainsKey(constant.Name))

-                    continue;

-

-                var func = constant2FuncCall[constant.Name];

-                var funcName = (func.Fun as FunctionCall).FunctionName;

-                var vals = new List<Model.Element>();

-                prover.Context.BoogieExprTranslator.Translate(func.Args).Iter(ve => vals.Add(getValue(ve, model)));

-                ret.Add(Tuple.Create(funcName, vals));

-            }

-

-            foreach (var tup in funcsUsed.Where(t => t.Item2 != null))

-            {

-                var constant = tup.Item1;

-                var boundExpr = tup.Item2;

-

-                if (!constant2FuncCall.ContainsKey(constant.Name))

-                    continue;

-

-                // There are some bound variables (because the existential function was inside an \exists).

-                // We must find an assignment for bound varibles 

-

-                // First, peice apart the existential functions

-                var cd = new Duplicator();

-                var tup2 = ExistentialExprModelMassage.Massage(cd.VisitExpr(boundExpr.Body));

-                var be = tup2.Item1;

-                Expr env = Expr.True;

-                foreach (var ahFunc in tup2.Item2)

-                {

-                    var tup3 = impl2FuncCalls[impl].First(t => t.Item2.Name == ahFunc.Name);

-                    var varList = new List<Expr>();

-                    tup3.Item3.Args.OfType<Expr>().Iter(v => varList.Add(v));

-

-                    env = Expr.And(env, function2Value[tup3.Item1].Gamma(varList));

-                }

-                be = Expr.And(be, Expr.Not(env));

-

-                // map formals to constants

-                var formalToConstant = new Dictionary<string, Constant>();

-                foreach (var f in boundExpr.Dummies.OfType<Variable>())

-                    formalToConstant.Add(f.Name, new Constant(Token.NoToken, new TypedIdent(Token.NoToken, f.Name + "@subst@" + (existentialConstCounter++), f.TypedIdent.Type), false));

-                be = Substituter.Apply(new Substitution(v => formalToConstant.ContainsKey(v.Name) ? Expr.Ident(formalToConstant[v.Name]) : Expr.Ident(v)), be);

-                formalToConstant.Values.Iter(v => prover.Context.DeclareConstant(v, false, null));

-

-                var reporter = new AbstractHoudiniErrorReporter();

-                var ve = prover.Context.BoogieExprTranslator.Translate(be);

-                prover.Assert(ve, true);

-                prover.Check();

-                var proverOutcome = prover.CheckOutcomeCore(reporter);

-                if (proverOutcome != ProverInterface.Outcome.Invalid)

-                    continue;

-                model = reporter.model;

-

-                var func = constant2FuncCall[constant.Name];

-                var funcName = (func.Fun as FunctionCall).FunctionName;

-                var vals = new List<Model.Element>();

-                foreach (var funcArg in func.Args.OfType<Expr>())

-                {

-                    var arg = Substituter.Apply(new Substitution(v => formalToConstant.ContainsKey(v.Name) ? Expr.Ident(formalToConstant[v.Name]) : Expr.Ident(v)), funcArg);

-                    vals.Add(getValue(prover.Context.BoogieExprTranslator.Translate(arg), model));

-                }

-                ret.Add(Tuple.Create(funcName, vals));

-

-            }

-

-            return ret;

-        }

-

-        private Model.Element getValue(VCExpr arg, Model model)

-        {

-

-

-            if (arg is VCExprLiteral)

-            {

-                //return model.GetElement(arg.ToString());

-                return model.MkElement(arg.ToString());

-            }

-

-            else if (arg is VCExprVar)

-            {

-                var el = model.TryGetFunc(prover.Context.Lookup(arg as VCExprVar));

-                if (el != null)

-                {

-                    Debug.Assert(el.Arity == 0 && el.AppCount == 1);

-                    return el.Apps.First().Result;

-                }

-                else

-                {

-                    // Variable not defined; assign arbitrary value

-                    if (arg.Type.IsBool)

-                        return model.MkElement("false");

-                    else if (arg.Type.IsInt)

-                        return model.MkIntElement(0);

-                    else

-                        return null;

-                }

-            }

-            else if (arg is VCExprNAry && (arg as VCExprNAry).Op is VCExprBvOp)

-            {

-                // support for BV constants

-                var bvc = (arg as VCExprNAry)[0] as VCExprLiteral;

-                if (bvc != null)

-                {

-                    var ret = model.TryMkElement(bvc.ToString() + arg.Type.ToString());

-                    if (ret != null && (ret is Model.BitVector)) return ret;

-                }

-            }

-

-            var val = prover.Evaluate(arg);

-            if (val is int || val is bool || val is Microsoft.Basetypes.BigNum)

-            {

-                return model.MkElement(val.ToString());

-            }

-            else

-            {

-                Debug.Assert(false);

-            }

-            return null;

-        }

-

-        // Remove functions AbsHoudiniConstant from the expressions and substitute them with "true"

-        class ExistentialExprModelMassage : StandardVisitor

-        {

-            List<Function> ahFuncs;

-

-            public ExistentialExprModelMassage()

-            {

-                ahFuncs = new List<Function>();

-            }

-

-            public static Tuple<Expr, List<Function>> Massage(Expr expr)

-            {

-                var ee = new ExistentialExprModelMassage();

-                expr = ee.VisitExpr(expr);

-                return Tuple.Create(expr, ee.ahFuncs);

-            }

-

-            public override Expr VisitNAryExpr(NAryExpr node)

-            {

-                if (node.Fun is FunctionCall && (node.Fun as FunctionCall).FunctionName.StartsWith("AbsHoudiniConstant"))

-                {

-                    ahFuncs.Add((node.Fun as FunctionCall).Func);

-                    return Expr.True;

-                }

-

-                return base.VisitNAryExpr(node);

-            }

-        }

-

-        class FunctionCollector : ReadOnlyVisitor

-        {

-            public List<Tuple<Function, ExistsExpr>> functionsUsed;

-            ExistsExpr existentialExpr;

-

-            public FunctionCollector()

-            {

-                functionsUsed = new List<Tuple<Function, ExistsExpr>>();

-                existentialExpr = null;

-            }

-

-            public static List<Tuple<Function, ExistsExpr>> Collect(Expr expr)

-            {

-                var fv = new FunctionCollector();

-                fv.VisitExpr(expr);

-                return fv.functionsUsed;

-            }

-

-            public override QuantifierExpr VisitQuantifierExpr(QuantifierExpr node)

-            {

-                var oldE = existentialExpr;

-

-                if (node is ExistsExpr)

-                    existentialExpr = (node as ExistsExpr);

-

-                node = base.VisitQuantifierExpr(node);

-

-                existentialExpr = oldE;

-                return node;

-            }

-

-            public override Expr VisitNAryExpr(NAryExpr node)

-            {

-                if (node.Fun is FunctionCall)

-                {

-                    var collector = new VariableCollector();

-                    collector.Visit(node);

-

-                    if(existentialExpr != null && existentialExpr.Dummies.Intersect(collector.usedVars).Any())

-                        functionsUsed.Add(Tuple.Create((node.Fun as FunctionCall).Func, existentialExpr));

-                    else

-                        functionsUsed.Add(Tuple.Create<Function, ExistsExpr>((node.Fun as FunctionCall).Func, null));

-                }

-

-                return base.VisitNAryExpr(node);

-            }

-        }

-

-        class AbsHoudiniCounterexampleCollector : VerifierCallback

-        {

-            public HashSet<string> funcsChanged;

-            public string currImpl;

-            public int numErrors;

-            public List<Counterexample> errors;

-

-            AbsHoudini container;

-

-            public AbsHoudiniCounterexampleCollector(AbsHoudini container)

-            {

-                this.container = container;

-                Reset(null);

-            }

-

-            public void Reset(string impl)

-            {

-                funcsChanged = new HashSet<string>();

-                currImpl = impl;

-                numErrors = 0;

-                errors = new List<Counterexample>();

-            }

-

-            public override void OnCounterexample(Counterexample ce, string reason)

-            {

-                numErrors++;

-                errors.Add(ce);

-

-                funcsChanged.UnionWith(

-                    container.HandleCounterExample(currImpl, ce));

-            }

-        }

-

-        private void GenVC(Implementation impl)

-        {

-            ModelViewInfo mvInfo;

-            Dictionary<int, Absy> label2absy;

-            var collector = new AbsHoudiniCounterexampleCollector(this);

-            collector.OnProgress("HdnVCGen", 0, 0, 0.0);

-

-            if (CommandLineOptions.Clo.Trace)

-            {

-                Console.WriteLine("Generating VC of {0}", impl.Name);

-            }

-

-            vcgen.ConvertCFG2DAG(impl);

-            var gotoCmdOrigins = vcgen.PassifyImpl(impl, out mvInfo);

-

-            // Inline functions

-            (new InlineFunctionCalls()).VisitBlockList(impl.Blocks);

-

-            ExtractQuantifiedExprs(impl);

-            StripOutermostForall(impl);

-

-            //CommandLineOptions.Clo.PrintInstrumented = true;

-            //var tt = new TokenTextWriter(Console.Out);

-            //impl.Emit(tt, 0);

-            //tt.Close();

-

-            // Intercept the FunctionCalls of the existential functions, and replace them with Boolean constants

-            var existentialFunctionNames = new HashSet<string>(existentialFunctions.Keys);

-            var fv = new ReplaceFunctionCalls(existentialFunctionNames);

-            fv.VisitBlockList(impl.Blocks);

-

-            impl2functionsAsserted.Add(impl.Name, fv.functionsAsserted);

-            impl2functionsAssumed.Add(impl.Name, fv.functionsAssumed);

-

-            fv.functionsAssumed.Iter(f => function2implAssumed[f].Add(impl.Name));

-            fv.functionsAsserted.Iter(f => function2implAsserted[f].Add(impl.Name));

-

-            impl2FuncCalls.Add(impl.Name, fv.functionsUsed);

-            fv.functionsUsed.Iter(tup => constant2FuncCall.Add(tup.Item2.Name, tup.Item3));

-

-            var gen = prover.VCExprGen;

-            VCExpr controlFlowVariableExpr = CommandLineOptions.Clo.UseLabels ? null : gen.Integer(Microsoft.Basetypes.BigNum.ZERO);

-

-            var vcexpr = vcgen.GenerateVC(impl, controlFlowVariableExpr, out label2absy, prover.Context);

-            if (!CommandLineOptions.Clo.UseLabels)

-            {

-                VCExpr controlFlowFunctionAppl = gen.ControlFlowFunctionApplication(gen.Integer(Microsoft.Basetypes.BigNum.ZERO), gen.Integer(Microsoft.Basetypes.BigNum.ZERO));

-                VCExpr eqExpr = gen.Eq(controlFlowFunctionAppl, gen.Integer(Microsoft.Basetypes.BigNum.FromInt(impl.Blocks[0].UniqueId)));

-                vcexpr = gen.Implies(eqExpr, vcexpr);

-            }

-

-            ProverInterface.ErrorHandler handler = null;

-            if (CommandLineOptions.Clo.vcVariety == CommandLineOptions.VCVariety.Local)

-                handler = new VCGen.ErrorReporterLocal(gotoCmdOrigins, label2absy, impl.Blocks, vcgen.incarnationOriginMap, collector, mvInfo, prover.Context, program);

-            else

-                handler = new VCGen.ErrorReporter(gotoCmdOrigins, label2absy, impl.Blocks, vcgen.incarnationOriginMap, collector, mvInfo, prover.Context, program);

-

-            impl2ErrorHandler.Add(impl.Name, Tuple.Create(handler, collector));

-

-            //Console.WriteLine("VC of {0}: {1}", impl.Name, vcexpr);

-

-            // Create a macro so that the VC can sit with the theorem prover

-            Macro macro = new Macro(Token.NoToken, impl.Name + "Macro", new List<Variable>(), new Formal(Token.NoToken, new TypedIdent(Token.NoToken, "", Bpl.Type.Bool), false));

-            prover.DefineMacro(macro, vcexpr);

-

-            // Store VC

-            impl2VC.Add(impl.Name, gen.Function(macro));

-

-            // HACK: push the definitions of constants involved in function calls

-            // It is possible that some constants only appear in function calls. Thus, when

-            // they are replaced by Boolean constants, it is possible that (get-value) will 

-            // fail if the expression involves such constants. All we need to do is make sure

-            // these constants are declared, because otherwise, semantically we are doing

-            // the right thing.

-            foreach (var tup in fv.functionsUsed)

-            {

-                // Ignore ones with bound varibles

-                if (tup.Item2.InParams.Count > 0) continue;

-                var tt = prover.Context.BoogieExprTranslator.Translate(tup.Item3);

-                tt = prover.VCExprGen.Or(VCExpressionGenerator.True, tt);

-                prover.Assert(tt, true);

-            }

-        }

-

-        // convert "foo(... forall e ...) to:

-        //    (p iff forall e) ==> foo(... p ...) 

-        // where p is a fresh boolean variable and foo is an existential constant

-        private void ExtractQuantifiedExprs(Implementation impl)

-        {

-            var funcs = new HashSet<string>(existentialFunctions.Keys);

-            foreach (var blk in impl.Blocks)

-            {

-                foreach (var acmd in blk.Cmds.OfType<AssertCmd>())

-                {

-                    var ret = ExtractQuantifiers.Extract(acmd.Expr, funcs);

-                    acmd.Expr = ret.Item1;

-                    impl.LocVars.AddRange(ret.Item2);

-                }

-            }

-        }

-

-        // convert "assert e1 && forall x: e2" to

-        //    assert e1 && e2[x <- x@bound]

-        private void StripOutermostForall(Implementation impl)

-        {

-            var funcs = new HashSet<string>(existentialFunctions.Keys);

-            foreach (var blk in impl.Blocks)

-            {

-                foreach (var acmd in blk.Cmds.OfType<AssertCmd>())

-                {

-                    var ret = StripQuantifiers.Run(acmd.Expr, funcs);

-                    acmd.Expr = ret.Item1;

-                    impl.LocVars.AddRange(ret.Item2);

-                }

-            }

-        }

-

-        private void Inline()

-        {

-            if (CommandLineOptions.Clo.InlineDepth < 0)

-                return;

-

-            var callGraph = BuildCallGraph();

-

-            foreach (Implementation impl in callGraph.Nodes)

-            {

-                InlineEnsuresVisitor inlineEnsuresVisitor = new InlineEnsuresVisitor();

-                inlineEnsuresVisitor.Visit(impl);

-            }

-

-            foreach (Implementation impl in callGraph.Nodes)

-            {

-                impl.OriginalBlocks = impl.Blocks;

-                impl.OriginalLocVars = impl.LocVars;

-            }

-            foreach (Implementation impl in callGraph.Nodes)

-            {

-                CommandLineOptions.Inlining savedOption = CommandLineOptions.Clo.ProcedureInlining;

-                CommandLineOptions.Clo.ProcedureInlining = CommandLineOptions.Inlining.Spec;

-                Inliner.ProcessImplementationForHoudini(program, impl);

-                CommandLineOptions.Clo.ProcedureInlining = savedOption;

-            }

-            foreach (Implementation impl in callGraph.Nodes)

-            {

-                impl.OriginalBlocks = null;

-                impl.OriginalLocVars = null;

-            }

-

-            Graph<Implementation> oldCallGraph = callGraph;

-            callGraph = new Graph<Implementation>();

-            foreach (Implementation impl in oldCallGraph.Nodes)

-            {

-                callGraph.AddSource(impl);

-            }

-            foreach (Tuple<Implementation, Implementation> edge in oldCallGraph.Edges)

-            {

-                callGraph.AddEdge(edge.Item1, edge.Item2);

-            }

-            int count = CommandLineOptions.Clo.InlineDepth;

-            while (count > 0)

-            {

-                foreach (Implementation impl in oldCallGraph.Nodes)

-                {

-                    List<Implementation> newNodes = new List<Implementation>();

-                    foreach (Implementation succ in callGraph.Successors(impl))

-                    {

-                        newNodes.AddRange(oldCallGraph.Successors(succ));

-                    }

-                    foreach (Implementation newNode in newNodes)

-                    {

-                        callGraph.AddEdge(impl, newNode);

-                    }

-                }

-                count--;

-            }

-        }

-

-        private Graph<Implementation> BuildCallGraph()

-        {

-            Graph<Implementation> callGraph = new Graph<Implementation>();

-            Dictionary<Procedure, HashSet<Implementation>> procToImpls = new Dictionary<Procedure, HashSet<Implementation>>();

-            foreach (var proc in program.Procedures)

-            {

-                procToImpls[proc] = new HashSet<Implementation>();

-            }

-            foreach (var impl in program.Implementations)

-            {

-                if (impl.SkipVerification) continue;

-                callGraph.AddSource(impl);

-                procToImpls[impl.Proc].Add(impl);

-            }

-            foreach (var impl in program.Implementations)

-            {

-                if (impl.SkipVerification) continue;

-                foreach (Block b in impl.Blocks)

-                {

-                    foreach (Cmd c in b.Cmds)

-                    {

-                        CallCmd cc = c as CallCmd;

-                        if (cc == null) continue;

-                        foreach (Implementation callee in procToImpls[cc.Proc])

-                        {

-                            callGraph.AddEdge(impl, callee);

-                        }

-                    }

-                }

-            }

-            return callGraph;

-        }

-

-    }

-

-    class InlineFunctionCalls : StandardVisitor

-    {

-        public Stack<string> inlinedFunctionsStack;

-

-        public InlineFunctionCalls()

-        {

-            inlinedFunctionsStack = new Stack<string>();

-        }

-

-        public override Expr VisitNAryExpr(NAryExpr node)

-        {

-            var fc = node.Fun as FunctionCall;

-            if (fc != null && fc.Func.Body != null && QKeyValue.FindBoolAttribute(fc.Func.Attributes, "inline"))

-            {

-                if (inlinedFunctionsStack.Contains(fc.Func.Name))

-                {

-                    // recursion detected

-                    throw new AbsHoudiniInternalError("Recursion detected in function declarations");

-                }

-

-                // create a substitution

-                var subst = new Dictionary<Variable, Expr>();

-                for (int i = 0; i < node.Args.Count; i++)

-                {

-                    subst.Add(fc.Func.InParams[i], node.Args[i]);

-                }

-

-                var e =

-                    Substituter.Apply(new Substitution(v => subst.ContainsKey(v) ? subst[v] : Expr.Ident(v)), fc.Func.Body);

-

-                inlinedFunctionsStack.Push(fc.Func.Name);

-

-                e = base.VisitExpr(e);

-

-                inlinedFunctionsStack.Pop();

-

-                return e;

-            }

-            return base.VisitNAryExpr(node);

-        }

-    }

-

-    class ReplaceFunctionCalls : StandardVisitor

-    {

-        public List<Tuple<string, Function, NAryExpr>> functionsUsed;

-        public List<Function> boolConstants;

-

-        public HashSet<string> functionsAssumed;

-        public HashSet<string> functionsAsserted;

-        HashSet<string> functionsToReplace;

-

-        private bool inAssume;

-        private bool inAssert;

-        private bool inFunction;

-        private List<Dictionary<string, Variable>> boundVars;

-        private static int IdCounter = 0;

-

-        public ReplaceFunctionCalls(HashSet<string> functionsToReplace)

-        {

-            this.functionsUsed = new List<Tuple<string, Function, NAryExpr>>();

-            this.functionsToReplace = functionsToReplace;

-            this.functionsAsserted = new HashSet<string>();

-            this.functionsAssumed = new HashSet<string>();

-            this.boolConstants = new List<Function>();

-            this.boundVars = new List<Dictionary<string, Variable>>();

-

-            inAssume = false;

-            inAssert = false;

-            inFunction = false;

-        }

-

-        public override Cmd VisitAssertCmd(AssertCmd node)

-        {

-            inAssert = true;

-            var ret = base.VisitAssertCmd(node);

-            inAssert = false;

-            return ret;

-        }

-

-        public override Cmd VisitAssertEnsuresCmd(AssertEnsuresCmd node)

-        {

-            return this.VisitAssertCmd(node);

-        }

-

-        public override Cmd VisitAssertRequiresCmd(AssertRequiresCmd node)

-        {

-            return this.VisitAssertCmd(node);

-        }

-

-        public override Cmd VisitAssumeCmd(AssumeCmd node)

-        {

-            inAssume = true;

-            var ret = base.VisitAssumeCmd(node);

-            inAssume = false;

-            return ret;

-        }

-

-        public override QuantifierExpr VisitQuantifierExpr(QuantifierExpr node)

-        {

-            // gather the quantified variables

-            var dummies = new Dictionary<string, Variable>();

-            node.Dummies.Iter(v => dummies.Add(v.Name, v));

-

-            boundVars.Add(dummies);

-

-            node = base.VisitQuantifierExpr(node);

-

-            boundVars.RemoveAt(boundVars.Count - 1);

-

-            return node;

-        }

-

-        public override Expr VisitNAryExpr(NAryExpr node)

-        {

-            var inF = inFunction;

-

-            if (node.Fun is FunctionCall && functionsToReplace.Contains((node.Fun as FunctionCall).FunctionName))

-            {                

-                found((node.Fun as FunctionCall).FunctionName);

-                inFunction = true;

-

-                // collect all the variables used by this function

-                var collector = new VariableCollector();

-                collector.VisitExpr(node);

-

-                // Find the outermost bound variables

-                var bound = new List<Variable>();

-                if(boundVars.Count > 0) 

-                    bound.AddRange(collector.usedVars.Intersect(boundVars[0].Values));

-

-                // create boolean function to replace this guy

-                var constant = new Function(Token.NoToken, "AbsHoudiniConstant" + IdCounter, bound,

-                    new Formal(Token.NoToken, new TypedIdent(Token.NoToken, "r", Microsoft.Boogie.Type.Bool), false));

-                IdCounter++;

-                

-                functionsUsed.Add(Tuple.Create((node.Fun as FunctionCall).FunctionName, constant, node));

-                boolConstants.Add(constant);

-

-                var args = new List<Expr>();

-                bound.OfType<Variable>().Select(v => Expr.Ident(v)).Iter(v => args.Add(v));

-                return new NAryExpr(Token.NoToken, new FunctionCall(constant), args);

-            }

-            var ret = base.VisitNAryExpr(node);

-

-            inFunction = inF;

-

-            return ret;

-        }

-

-        public override Expr VisitIdentifierExpr(IdentifierExpr node)

-        {

-            if (inFunction)

-            {

-                // Inside functions we can only refer to the outermost bound variables

-                for (int i = boundVars.Count - 1; i >= 1; i--)

-                {

-                    if (boundVars[i].ContainsKey(node.Name))

-                        throw new AbsHoudiniInternalError("Existential functions can only refer to outermost bound variables in an expression");

-                }

-            }

-

-            return base.VisitIdentifierExpr(node);

-        }

-

-        private void found(string func)

-        {

-            if (inAssume) functionsAssumed.Add(func);

-            if (inAssert) functionsAsserted.Add(func);

-        }

-

-    }

-

-    // convert "foo(... forall e ...) to:

-    //    (p iff forall e) ==> foo(... p ...) 

-    // where p is a fresh boolean variable and foo is an existential constant

-    class ExtractQuantifiers : StandardVisitor

-    {

-        static int freshConstCounter = 0;

-        HashSet<string> existentialFunctions;

-        bool insideExistential;

-        Dictionary<Constant, Expr> newConstants;

-

-        private ExtractQuantifiers(HashSet<string> existentialFunctions)

-        {

-            this.existentialFunctions = existentialFunctions;

-            insideExistential = false;

-            newConstants = new Dictionary<Constant, Expr>();

-        }

-

-        public static Tuple<Expr, IEnumerable<Constant>> Extract(Expr expr, HashSet<string> existentialFunctions)

-        {

-            var eq = new ExtractQuantifiers(existentialFunctions);

-            expr = eq.VisitExpr(expr);

-            Expr ret = Expr.True;

-            foreach (var tup in eq.newConstants)

-            {

-                ret = Expr.And(ret, Expr.Eq(Expr.Ident(tup.Key), tup.Value));

-            }

-            ret = Expr.Imp(ret, expr);

-            return Tuple.Create(ret, eq.newConstants.Keys.AsEnumerable());

-        }

-

-        public override Expr VisitNAryExpr(NAryExpr node)

-        {

-            var oldIE = insideExistential;

-

-            if (node.Fun is FunctionCall && existentialFunctions.Contains((node.Fun as FunctionCall).FunctionName))

-                insideExistential = true;

-

-            var ret = base.VisitNAryExpr(node);

-

-            insideExistential = oldIE;

-            return ret;

-        }

-

-        public override Expr VisitExpr(Expr node)

-        {

-            if (node is QuantifierExpr)

-            {

-                return MyVisitQuantifierExpr(node as QuantifierExpr);

-            }

-            return base.VisitExpr(node);

-        }

-

-        public Expr MyVisitQuantifierExpr(QuantifierExpr node)

-        {

-            node = base.VisitQuantifierExpr(node);

-

-            if (insideExistential)

-            {

-                var constant = new Constant(Token.NoToken, new TypedIdent(Token.NoToken,

-                    "quant@const" + freshConstCounter, Microsoft.Boogie.Type.Bool), false);

-                freshConstCounter++;

-

-                newConstants.Add(constant, node);

-

-                return Expr.Ident(constant);                

-            }

-

-            return node;

-        }

-    }

-

-    // convert "assert e1 && forall x: e2" to

-    //    assert e1 && e2[x <- x@bound]

-    // only if e2 has an existential function

-    class StripQuantifiers : StandardVisitor

-    {

-        static int boundVarCounter = 0;

-        

-        // 0 -> None, 1 -> Forall, 2 -> Exists, 3 -> Nested

-        int insideQuantifier; 

-

-        bool searchExistentialFunction;

-        bool foundExistentialFunction;

-

-        HashSet<string> existentialFunctions;

-        Dictionary<string, LocalVariable> subst;

-        List<LocalVariable> LocalsToAdd;

-

-        private StripQuantifiers(HashSet<string> existentialFunctions)

-        {

-            this.existentialFunctions = existentialFunctions;

-            insideQuantifier = 0;

-            searchExistentialFunction = false;

-            foundExistentialFunction = false;

-            LocalsToAdd = new List<LocalVariable>();

-            subst = null;

-        }

-

-        public static Tuple<Expr,List<LocalVariable>> Run(Expr expr, HashSet<string> existentialFunctions)

-        {

-            // check for type errors first

-            var sq = new StripQuantifiers(existentialFunctions);

-            var ret = sq.VisitExpr(expr);

-

-            return Tuple.Create(ret, sq.LocalsToAdd);

-        }

-

-        public override Expr VisitExpr(Expr node)

-        {

-            if (node is QuantifierExpr)

-            {

-                return MyVisitQuantifierExpr(node as QuantifierExpr);

-            }

-

-            return base.VisitExpr(node);

-        }

-

-        private Expr MyVisitQuantifierExpr(QuantifierExpr node)

-        {

-            var oldIQ = insideQuantifier;

-            Expr ret = node;

-

-            // update "insideQuantifier"

-            if (insideQuantifier == 0)

-            {

-                if (node is ForallExpr) insideQuantifier = 1;

-                else insideQuantifier = 2;

-            }

-            else if (insideQuantifier > 0)

-            {

-                insideQuantifier = 3;

-            }

-

-            // Going inside Forall?

-            if (insideQuantifier == 1)

-            {

-                // see if there is any existential function inside

-                searchExistentialFunction = true;

-                foundExistentialFunction = false;

-                base.VisitQuantifierExpr(node);

-

-                if (foundExistentialFunction)

-                {

-                    // create substitution to apply

-                    subst = new Dictionary<string, LocalVariable>();

-                    foreach (var bv in node.Dummies.OfType<Variable>())

-                    {

-                        var lv = new LocalVariable(Token.NoToken, new TypedIdent(Token.NoToken,

-                            bv + "@bound" + boundVarCounter, bv.TypedIdent.Type));

-                        boundVarCounter++;

-                        subst.Add(bv.Name, lv);

-                        LocalsToAdd.Add(lv);

-                    }

-

-                    // apply the subst

-                    var body = base.VisitExpr(node.Body);

-                    ret = body;

-

-                    subst = null;

-                }

-                else

-                {

-                    ret = base.VisitQuantifierExpr(node);

-                }

-

-                searchExistentialFunction = false;

-                foundExistentialFunction = false;

-            }

-            else

-            {

-                ret = base.VisitQuantifierExpr(node);

-            }

-

-            insideQuantifier = oldIQ;

-            return ret;

-        }

-

-        public override Expr VisitNAryExpr(NAryExpr node)

-        {

-            if (node.Fun is FunctionCall && existentialFunctions.Contains((node.Fun as FunctionCall).FunctionName))

-            {

-                if (insideQuantifier == 3)

-                    throw new AbsHoudiniInternalError("Existential function found inside exists, or nested foralls");

-

-                if (searchExistentialFunction)

-                    foundExistentialFunction = true;

-

-            }

-

-            return base.VisitNAryExpr(node);

-        }

-

-        public override Expr VisitIdentifierExpr(IdentifierExpr node)

-        {

-            if (subst != null && subst.ContainsKey(node.Name))

-                return Expr.Ident(subst[node.Name]);

-            return base.VisitIdentifierExpr(node);

-        }

-

-    }

-

-    public class Intervals : IAbstractDomain

-    {

-        // [lower, upper]

-        int upper;

-        int lower;

-        // or: \bot

-        bool isBottom;

-        // number of times join has been performed

-        int nJoin;

-        // number of times before we widen

-        readonly static int maxJoin = 5;

-

-        public Intervals()

-        {

-            this.upper = 0;

-            this.lower = 0;

-            this.nJoin = 0;

-            this.isBottom = true;

-        }

-

-        private Intervals(int lower, int upper, int nJoin)

-        {

-            this.upper = upper;

-            this.lower = lower;

-            this.nJoin = nJoin;

-        }

-

-        public IAbstractDomain Bottom()

-        {

-            return new Intervals();

-        }

-

-        public IAbstractDomain MakeTop(out bool changed)

-        {

-            if (lower == Int32.MinValue && upper == Int32.MaxValue)

-            {

-                changed = false;

-                return this;

-            }

-            changed = true;

-            return new Intervals(Int32.MinValue, Int32.MaxValue, 0);

-        }

-

-        public IAbstractDomain Join(List<Model.Element> states)

-        {

-            Debug.Assert(states.Count == 1);

-            var state = states[0] as Model.Integer;

-            if (state == null)

-                throw new AbsHoudiniInternalError("Incorrect type, expected int");

-            var intval = state.AsInt();

-

-            if (isBottom)

-            {

-                return new Intervals(intval, intval, 1);

-            }

-

-            if(intval >= lower && intval <= upper)

-                return this;

-

-            if (nJoin > maxJoin)

-            {

-                // widen

-                if (intval > upper)

-                    return new Intervals(lower, Int32.MaxValue, 1);

-                if(intval < lower)

-                    return new Intervals(Int32.MinValue, upper, 1);

-

-                Debug.Assert(false);

-            }

-

-            if (intval > upper)

-                return new Intervals(lower, intval, nJoin + 1);

-            if (intval < lower)

-                return new Intervals(intval, upper, nJoin + 1);

-

-            Debug.Assert(false);

-            return null;

-        }

-

-        public Expr Gamma(List<Expr> vars)

-        {

-            Debug.Assert(vars.Count == 1);

-            var v = vars[0];

-            if (isBottom) return Expr.False;

-            Expr ret = Expr.True;

-            if (lower != Int32.MinValue)

-                ret = Expr.And(ret, Expr.Ge(v, Expr.Literal(lower)));

-            if (upper != Int32.MaxValue)

-                ret = Expr.And(ret, Expr.Le(v, Expr.Literal(upper)));

-            return ret;

-        }

-

-        public bool TypeCheck(List<Type> argTypes, out string msg)

-        {

-            msg = "";

-            if (argTypes.Count != 1)

-            {

-                msg = "Illegal number of arguments";

-                return false;

-            }

-            if (!argTypes[0].IsInt)

-            {

-                msg = "Illegal type, expecting int";

-                return false;

-            }

-            return true;

-        }

-    }

-

-    public class PredicateAbsElem : IAbstractDomain

-    {

-        public static class ExprExt

-        {

-            public static Expr AndSimp(Expr e1, Expr e2)

-            {

-                if (e1 == Expr.True) return e2;

-                if (e2 == Expr.True) return e1;

-                if (e1 == Expr.False || e2 == Expr.False) return Expr.False;

-                return Expr.And(e1, e2);

-            }

-

-            public static Expr OrSimp(Expr e1, Expr e2)

-            {

-                if (e1 == Expr.False) return e2;

-                if (e2 == Expr.False) return e1;

-                if (e1 == Expr.True || e2 == Expr.True) return Expr.True;

-                return Expr.Or(e1, e2); 

-            }

-        }

-

-        class Disjunct

-        {

-            public static int DisjunctBound = 3;

-            HashSet<int> pos;

-            HashSet<int> neg;

-            bool isTrue;

-

-            public Disjunct()

-            {

-                isTrue = true;

-                pos = new HashSet<int>();

-                neg = new HashSet<int>();

-            }

-

-            public Disjunct(IEnumerable<int> pos, IEnumerable<int> neg)

-            {

-                this.isTrue = false;

-                this.pos = new HashSet<int>(pos);

-                this.neg = new HashSet<int>(neg);

-                if (this.pos.Overlaps(this.neg))

-                {

-                    this.isTrue = true;

-                    this.pos = new HashSet<int>();

-                    this.neg = new HashSet<int>();

-                }

-                if (this.pos.Count + this.neg.Count > DisjunctBound)

-                {

-                    // Set to true

-                    this.isTrue = true;

-                    this.pos = new HashSet<int>();

-                    this.neg = new HashSet<int>();

-                }

-

-            }

-

-            public Disjunct OR(Disjunct that)

-            {

-                if (isTrue)

-                    return this;

-                if (that.isTrue)

-                    return that;

-

-                return new Disjunct(this.pos.Concat(that.pos), this.neg.Concat(that.neg));

-            }

-

-            public bool Implies(Disjunct that)

-            {

-                if (isTrue) return that.isTrue;

-                if (that.isTrue) return true;

-

-                return pos.IsSubsetOf(that.pos) && neg.IsSubsetOf(that.neg);

-            }

-

-            public Expr Gamma(List<Expr> vars)

-            {

-                if (isTrue) return Expr.True;

-                Expr ret = Expr.False;

-                pos.Iter(i => ret = ExprExt.OrSimp(ret, vars[i]));

-                neg.Iter(i => ret = ExprExt.OrSimp(ret, Expr.Not(vars[i])));

-                return ret;

-            }

-        }

-

-        // Conjunction of Disjuncts

-        List<Disjunct> conjuncts;

-        bool isFalse;

-

-        public PredicateAbsElem()

-        {

-            this.conjuncts = new List<Disjunct>();

-            this.isFalse = true;

-        }

-

-        public IAbstractDomain Bottom()

-        {

-            return new PredicateAbsElem();

-        }

-

-        public IAbstractDomain MakeTop(out bool changed)

-        {

-            if (conjuncts.Count == 0)

-            {

-                changed = false;

-                return this;

-            }

-            changed = true;

-            var ret = new PredicateAbsElem();

-            ret.isFalse = false;

-            return ret;

-        }

-

-        public IAbstractDomain Join(List<Model.Element> state)

-        {

-            if (state.Any(me => !(me is Model.Boolean)))

-                throw new AbsHoudiniInternalError("Predicate Abstraction requires that each argument be of type bool");

-

-            // quick return if this == true

-            if (!this.isFalse && conjuncts.Count == 0)

-                return this;

-

-            var ret = new PredicateAbsElem();

-            ret.isFalse = false;

-

-            for (int i = 0; i < state.Count; i++)

-            {

-                var b = (state[i] as Model.Boolean).Value;

-                Disjunct d = null;

-                if (b) d = new Disjunct(new int[] { i }, new int[] { });

-                else d = new Disjunct(new int[] { }, new int[] { i });

-

-                if (isFalse)

-                    ret.AddDisjunct(d);

-                else

-                {

-                    conjuncts.Iter(c => ret.AddDisjunct(c.OR(d)));

-                }

-            }

-

-            return ret;

-

-        }

-

-        public Expr Gamma(List<Expr> vars)

-        {

-            if (isFalse) return Expr.False;

-            Expr ret = Expr.True;

-

-            foreach (var c in conjuncts)

-            {

-                ret = ExprExt.AndSimp(ret, c.Gamma(vars));

-            }

-

-            return ret;

-        }

-

-        public bool TypeCheck(List<Type> argTypes, out string msg)

-        {

-            msg = "";

-            if (argTypes.Any(t => !t.IsBool))

-            {

-                msg = "Illegal type, expecting bool";

-                return false;

-            }

-            return true;

-        }

-

-        private void AddDisjunct(Disjunct d)

-        {

-            if (conjuncts.Any(c => c.Implies(d)))

-                return;

-

-            conjuncts.RemoveAll(c => d.Implies(c));

-            conjuncts.Add(d);

-        }

-    }

-

-    // [false -- (x == true) -- true]

-    public class HoudiniConst : IAbstractDomain

-    {

-        bool isBottom;

-        bool isTop;

-

-        private HoudiniConst(bool isTop, bool isBottom)

-        {

-            this.isBottom = isBottom;

-            this.isTop = isTop;

-            Debug.Assert(!(isTop && isBottom));

-        }

-

-        public static HoudiniConst GetExtObj()

-        {

-            return new HoudiniConst(false, false);

-        }

-

-        public static HoudiniConst GetTop()

-        {

-            return new HoudiniConst(true, false);

-        }

-

-        public static HoudiniConst GetBottom()

-        {

-            return new HoudiniConst(false, true);

-        }

-

-        public IAbstractDomain Bottom()

-        {

-            return GetBottom();

-        }

-

-        public IAbstractDomain MakeTop(out bool changed)

-        {

-            changed = false;

-            if (isTop) return this;

-            changed = true;

-            return GetTop();

-        }

-

-        public IAbstractDomain Join(List<Model.Element> states)

-        {

-            Debug.Assert(states.Count == 1);

-            var state = states[0];

-

-            if (isTop) return this;

-

-            if (state is Model.Boolean)

-            {

-                if ((state as Model.Boolean).Value)

-                    return GetExtObj();

-            }

-

-            return GetTop();

-        }

-

-        public Expr Gamma(List<Expr> vars)

-        {

-            Debug.Assert(vars.Count == 1);

-            var v = vars[0];

-            if (isBottom) return Expr.False;

-            if (isTop) return Expr.True;

-            return v;

-        }

-

-        public bool TypeCheck(List<Type> argTypes, out string msg)

-        {

-            msg = "";

-            if (argTypes.Count != 1)

-            {

-                msg = "Illegal number of arguments, expecting 1";

-                return false;

-            }

-            if (!argTypes[0].IsBool)

-            {

-                msg = "Illegal type, expecting bool";

-                return false;

-            }

-            return true;

-        }

-    }

-

-    // foo(x) = x < 2^j for some j <= 16

-    public class PowDomain : IAbstractDomain

-    {

-        enum Val { FALSE, NEITHER, TRUE };

-        Val tlevel;

-        bool isBottom { get { return tlevel == Val.FALSE; } }

-        bool isTop { get { return tlevel == Val.TRUE; } }

-

-        readonly int Max = 16;

-

-        int upper; // <= Max

-

-        private PowDomain(Val tlevel) :

-            this(tlevel, 0) { }

-

-        private PowDomain(Val tlevel, int upper)

-        {

-            this.tlevel = tlevel;

-            this.upper = upper;

-        }

-

-        public static IAbstractDomain GetBottom()

-        {

-            return new PowDomain(Val.FALSE) as IAbstractDomain;

-        }

-

-        public IAbstractDomain MakeTop(out bool changed)

-        {

-            if (isTop)

-            {

-                changed = false;

-                return this;

-            }

-            changed = true;

-            return new PowDomain(Val.TRUE);

-        }

-

-        IAbstractDomain IAbstractDomain.Bottom()

-        {

-            return GetBottom();

-        }

-

-        IAbstractDomain IAbstractDomain.Join(List<Model.Element> state)

-        {

-            if (isTop) return this;

-            

-            int v = 0;

-            if (state[0] is Model.BitVector)

-                v = (state[0] as Model.BitVector).AsInt();

-            else if (state[0] is Model.Integer)

-                v = (state[0] as Model.Integer).AsInt();

-            else Debug.Assert(false);

-

-            var nupper = upper;

-            while ((1 << nupper) < v) nupper++;

-            var ntlevel = Val.NEITHER;

-            if (nupper > Max) ntlevel = Val.TRUE;

-            return new PowDomain(ntlevel, nupper);

-        }

-

-        Expr IAbstractDomain.Gamma(List<Expr> vars)

-        {

-            if (isBottom) return Expr.False;

-            if (isTop) return Expr.True;

-            var v = vars[0];

-            if (v.Type.IsBv)

-            {

-                var bits = v.Type.BvBits;

-                if (!AbstractDomainFactory.bvslt.ContainsKey(bits))

-                    throw new AbsHoudiniInternalError("No builtin function found for bv" + bits.ToString());

-                var bvslt = AbstractDomainFactory.bvslt[bits];

-                return new NAryExpr(Token.NoToken, new FunctionCall(bvslt), new List<Expr> { v,

-                    new LiteralExpr(Token.NoToken, Basetypes.BigNum.FromInt(1 << (upper+1)), 32) });

-            }

-            else

-            {

-                return Expr.Lt(v, Expr.Literal(1 << (upper+1)));

-            }

-        }

-

-        bool IAbstractDomain.TypeCheck(List<Type> argTypes, out string msg)

-        {

-            msg = "";

-            if (argTypes.Count != 1)

-            {

-                msg = "Illegal number of arguments, expecting 1";

-                return false;

-            }

-            if (argTypes.Any(tt => !tt.IsInt && !tt.IsBv))

-            {

-                msg = "Illegal type, expecting int or bv";

-                return false;

-            }

-            return true;

-        }

-    }

-

-    // foo(x_i) = all equalities that hold

-    public class EqualitiesDomain : IAbstractDomain

-    {

-        bool isBottom;

-        List<HashSet<int>> equalities;

-

-        public EqualitiesDomain(bool isBottom, List<HashSet<int>> eq)

-        {

-            this.isBottom = isBottom;

-            this.equalities = eq;

-        }

-

-        public static IAbstractDomain GetBottom()

-        {

-            return new EqualitiesDomain(true, new List<HashSet<int>>());

-        }

-

-        IAbstractDomain IAbstractDomain.Bottom()

-        {

-            return GetBottom();

-        }

-

-        public IAbstractDomain MakeTop(out bool changed)

-        {

-            if (equalities.Count == 0)

-            {

-                changed = false;

-                return this;

-            }

-            changed = true;

-            return new EqualitiesDomain(false, new List<HashSet<int>>());

-        }

-

-        IAbstractDomain IAbstractDomain.Join(List<Model.Element> state)

-        {

-            // find the guys that are equal

-            var eq = new List<HashSet<int>>();

-            for (int i = 0; i < state.Count; i++)

-            {

-                var added = false;

-                foreach (var s in eq)

-                {

-                    var sv = s.First();

-                    if (state[i].ToString() == state[sv].ToString())

-                    {

-                        s.Add(i);

-                        added = true;

-                        break;

-                    }

-                }

-                if (!added) eq.Add(new HashSet<int>(new int[] { i }));

-            }

-            

-            if (isBottom)

-            {

-                return new EqualitiesDomain(false, eq);

-            }

-

-            // intersect two partitions equalities and eq

-            var m1 = GetMap(equalities, state.Count);

-            var m2 = GetMap(eq, state.Count);

-

-            for (int i = 0; i < state.Count; i++)

-                m2[i] = new HashSet<int>(m2[i].Intersect(m1[i]));

-

-

-            // map from representative to set

-            var repToSet = new Dictionary<int, HashSet<int>>();

-

-            for (int i = 0; i < state.Count; i++)

-            {

-                var rep = m2[i].Min();

-                if (!repToSet.ContainsKey(rep))

-                    repToSet[rep] = m2[i];

-            }

-

-            var ret = new List<HashSet<int>>();

-            repToSet.Values.Iter(s => ret.Add(s));

-

-            return new EqualitiesDomain(false, ret);

-        }

-

-        Expr IAbstractDomain.Gamma(List<Expr> vars)

-        {

-            if (isBottom) return Expr.False;

-            Expr ret = Expr.True;

-            foreach (var eq in equalities.Select(hs => hs.ToList()))

-            {

-                if (eq.Count == 1) continue;

-                var prev = eq[0];

-                for (int i = 1; i < eq.Count; i++)

-                {

-                    ret = Expr.And(ret, Expr.Eq(vars[prev], vars[eq[i]]));

-                    prev = eq[i];

-                }

-            }

-            return ret;

-        }

-

-        bool IAbstractDomain.TypeCheck(List<Type> argTypes, out string msg)

-        {

-            msg = "";

-            if (argTypes.Count == 0) return true;

-            var ot = argTypes[0];

-

-            if (argTypes.Any(tt => !tt.Equals(ot)))

-            {

-                msg = string.Format("Illegal type, expecting type {0}, got {1}", ot, argTypes.First(tt => !tt.Equals(ot)));

-                return false;

-            }

-            return true;

-        }

-

-        private HashSet<int>[] GetMap(List<HashSet<int>> eq, int n)

-        {

-            var ret = new HashSet<int>[n];

-            foreach (var s in eq)

-            {

-                foreach (var i in s)

-                    ret[i] = s;

-            }

-            return ret;

-        }

-    }

-

-    // foo(a,b) \in {false, \not a, a ==> b, true}

-    public class ImplicationDomain : IAbstractDomain

-    {

-        enum Val {FALSE, NOT_A, A_IMP_B, TRUE};

-        Val val;

-

-        private ImplicationDomain(Val val)

-        {

-            this.val = val;

-        }

-

-        public static ImplicationDomain GetBottom()

-        {

-            return new ImplicationDomain(Val.FALSE);

-        }

-

-        public IAbstractDomain Bottom()

-        {

-            return GetBottom();

-        }

-

-        public IAbstractDomain MakeTop(out bool changed)

-        {

-            if(val == Val.TRUE) {

-                changed = false;

-                return this;

-            }

-            changed = true;

-            return new ImplicationDomain(Val.TRUE);

-        }

-

-        public IAbstractDomain Join(List<Model.Element> states)

-        {

-            Debug.Assert(states.Count == 2);

-            var v1 = (states[0] as Model.Boolean).Value;

-            var v2 = (states[1] as Model.Boolean).Value;

-

-            if (val == Val.TRUE) return this;

-

-            var that = Val.TRUE;

-            if (!v1) that = Val.NOT_A;

-            else if (!v1 || v2) that = Val.A_IMP_B;

-

-            if (that == Val.TRUE || val == Val.FALSE)

-                return new ImplicationDomain(that);

-

-            // Now, neither this or that is FALSE or TRUE

-            if (val == that)

-                return this;

-

-            Debug.Assert(val == Val.A_IMP_B || that == Val.A_IMP_B);

-            return new ImplicationDomain(Val.A_IMP_B);

-        }

-

-        public Expr Gamma(List<Expr> vars)

-        {

-            Debug.Assert(vars.Count == 2);

-

-            var v1 = vars[0];

-            var v2 = vars[1];

-

-            if (val == Val.FALSE) return Expr.False;

-            if (val == Val.TRUE) return Expr.True;

-            if (val == Val.NOT_A) return Expr.Not(v1);

-            return Expr.Imp(v1, v2);

-        }

-

-        public bool TypeCheck(List<Type> argTypes, out string msg)

-        {

-            msg = "";

-            if (argTypes.Count != 2)

-            {

-                msg = "Illegal number of arguments, expecting 2";

-                return false;

-            }

-            if (argTypes.Any(tt => !tt.IsBool))

-            {

-                msg = "Illegal type, expecting bool";

-                return false;

-            }

-            return true;

-        }

-    }

-

-    public class ConstantProp : IAbstractDomain

-    {

-        object val;

-        bool isBottom;

-        bool isTop;

-

-        private ConstantProp(object val, bool isTop, bool isBottom)

-        {

-            this.val = val;

-            this.isBottom = isBottom;

-            this.isTop = isTop;

-            Debug.Assert(!(isTop && isBottom));

-            Debug.Assert(val == null || (val is int) || (val is bool));

-        }

-

-        public static ConstantProp GetExtObj(object val)

-        {

-            Debug.Assert(val != null);

-            return new ConstantProp(val, false, false);

-        }

-

-        public static ConstantProp GetTop()

-        {

-            return new ConstantProp(null, true, false);

-        }

-

-        public static ConstantProp GetBottom()

-        {

-            return new ConstantProp(null, false, true);

-        }

-

-        public IAbstractDomain MakeTop(out bool changed) {

-            if (isTop)

-            {

-                changed = false;

-                return this;

-            }

-            changed = true;

-            return GetTop();

-        }

-

-        private ConstantProp Join(ConstantProp that)

-        {

-            if (isBottom) return that;

-            if (isTop) return this;

-            if (that.isBottom) return this;

-            if (that.isTop) return that;

-

-            if ((val is int) && !(that.val is int))

-                throw new AbsHoudiniInternalError("Type mismatch in ExtObj");

-

-            if ((val is bool) && !(that.val is bool))

-                throw new AbsHoudiniInternalError("Type mismatch in ExtObj");

-

-            if (val is int)

-            {

-                var v1 = (int)val;

-                var v2 = (int)that.val;

-                if (v1 != v2) return GetTop();

-                return this;

-            }

-            else if (val is bool)

-            {

-                var v1 = (bool)val;

-                var v2 = (bool)that.val;

-                if (v1 != v2) return GetTop();

-                return this;

-            }

-            throw new AbsHoudiniInternalError("Illegal val type in ExtObj");

-        }

-

-        public IAbstractDomain Bottom()

-        {

-            return GetBottom();

-        }

-

-        public IAbstractDomain Join(List<Model.Element> states)

-        {

-            Debug.Assert(states.Count == 1);

-            var state = states[0];

-            ConstantProp that = null;

-

-            if (state is Model.Integer)

-            {

-                that = GetExtObj((state as Model.Integer).AsInt());

-            }

-            else if (state is Model.Boolean)

-            {

-                that = GetExtObj((state as Model.Boolean).Value);

-            }

-            else

-            {

-                throw new AbsHoudiniInternalError("Illegal type " + state.GetType().ToString());

-            }

-

-            return Join(that);

-        }

-

-        public Expr Gamma(List<Expr> vars)

-        {

-            Debug.Assert(vars.Count == 1);

-            var v = vars[0];

-            if (isBottom) return Expr.False;

-            if (isTop) return Expr.True;

-            if (val is int)

-                return Expr.Eq(v, Expr.Literal((int)val));

-            if (val is bool && (bool)val)

-                return v;

-            if (val is bool && !(bool)val)

-                return Expr.Not(v);

-

-            return null;

-        }

-

-        public bool TypeCheck(List<Type> argTypes, out string msg)

-        {

-            msg = "";

-            if (argTypes.Count != 1)

-            {

-                msg = "Illegal number of arguments, expecting 1";

-                return false;

-            }

-            if (!argTypes[0].IsInt && ! argTypes[0].IsBool)

-            {

-                msg = "Illegal type, expecting int or bool";

-                return false;

-            }

-            return true;

-        }

-    }

-

-

-    public class IndependentAttribute<T> : IAbstractDomain where T : class, IAbstractDomain

-    {

-        bool isBottom;

-        int numVars;

-        List<T> varVal;

-        T underlyingInstance;

-

-        public IndependentAttribute()

-        {

-            isBottom = true;

-            numVars = 0;

-            varVal = new List<T>();

-            underlyingInstance = null;

-        }

-

-        public IAbstractDomain Bottom()

-        {

-            return new IndependentAttribute<T>();

-        }

-

-        public IAbstractDomain MakeTop(out bool changed)

-        {

-            var mt = new Func<IAbstractDomain>(() =>

-                {

-                    var ret = new IndependentAttribute<T>();

-                    ret.isBottom = true;

-                    ret.numVars = numVars;

-                    ret.underlyingInstance = underlyingInstance;

-                    ret.varVal = new List<T>();

-                    bool tmp;

-                    for (int i = 0; i < varVal.Count; i++)

-                        ret.varVal.Add(varVal[i].MakeTop(out tmp) as T);

-                    return ret;

-                });

-

-            if (!isBottom)

-            {

-                foreach (var t in varVal)

-                {

-                    var top = t.MakeTop(out changed);

-                    if (changed)

-                    {

-                        return mt();

-                    }

-                }

-            }

-            else

-            {

-                changed = true;

-                return mt();

-            }

-

-            changed = false;

-            return this;

-        }

-        public IAbstractDomain Join(List<Model.Element> state)

-        {

-            SetUnderlyingInstance();

-

-            if (!isBottom && numVars != state.Count)

-            {

-                throw new AbsHoudiniInternalError(

-                    string.Format("Got illegal number of arguments ({0}), expected {1}", state.Count, numVars));

-            }

-

-            var ret = new IndependentAttribute<T>();

-            ret.isBottom = false;

-            ret.numVars = state.Count;

-            for(int i = 0; i < state.Count; i++)

-            {

-                var sl = new List<Model.Element>();

-                sl.Add(state[i]);

-                T prev = isBottom ? underlyingInstance.Bottom() as T : varVal[i];

-                ret.varVal.Add(prev.Join(sl) as T);

-            }

-

-            return ret;

-        }

-

-        public Expr Gamma(List<Expr> vars)

-        {

-            if (isBottom) return Expr.False;

-            if (numVars != vars.Count)

-                throw new AbsHoudiniInternalError(

-                    string.Format("Got illegal number of arguments ({0}), expected {1}", vars.Count, numVars));

-

-            Expr ret = Expr.True;

-            for (int i = 0; i < numVars; i++)

-            {

-                var sl = new List<Expr>(); sl.Add(vars[i]);

-                ret = Expr.And(ret, varVal[i].Gamma(sl));

-            }

-

-            return ret;

-        }

-

-        private void SetUnderlyingInstance()

-        {

-            if (underlyingInstance != null) return;

-            var tt = typeof(T);

-            underlyingInstance = AbstractDomainFactory.GetInstance(tt) as T;

-        }

-

-        public bool TypeCheck(List<Type> argTypes, out string msg)

-        {

-            SetUnderlyingInstance();

-

-            msg = "";

-            foreach(var t in argTypes) 

-            {

-                if(!underlyingInstance.TypeCheck(new List<Type>(new Type[] { t }), out msg))

-                    return false;

-            }

-            return true;

-        }

-    }

-

-    public class AbstractDomainFactory

-    {

-        // Type name -> Instance

-        private static Dictionary<string, IAbstractDomain> abstractDomainInstances = new Dictionary<string, IAbstractDomain>();

-        private static Dictionary<string, IAbstractDomain> abstractDomainInstancesFriendly = new Dictionary<string, IAbstractDomain>();

-        

-        // bitvector operations

-        public static Dictionary<int, Function> bvslt = new Dictionary<int, Function>();

-

-        public static void Register(string friendlyName, IAbstractDomain instance)

-        {

-            var Name = instance.GetType().FullName;

-            Debug.Assert(!abstractDomainInstances.ContainsKey(Name));

-            abstractDomainInstances.Add(Name, instance);

-            abstractDomainInstancesFriendly.Add(friendlyName, instance);

-        }

-

-        public static IAbstractDomain GetInstance(System.Type type)

-        {

-            var Name = type.FullName;

-            Debug.Assert(abstractDomainInstances.ContainsKey(Name));

-            return abstractDomainInstances[Name] as IAbstractDomain;

-        }

-

-        public static IAbstractDomain GetInstance(string friendlyName)

-        {

-            if (!abstractDomainInstancesFriendly.ContainsKey(friendlyName))

-            {

-                Console.WriteLine("Domain {0} not found", friendlyName);

-                Console.WriteLine("Supported domains are:");

-                abstractDomainInstancesFriendly.Keys.Iter(tup => Console.WriteLine("  {0}", tup));

-                throw new AbsHoudiniInternalError("Domain not found");

-            }

-            return abstractDomainInstancesFriendly[friendlyName] as IAbstractDomain;

-        }

-

-        public static void Initialize(Program program)

-        {

-            // Declare abstract domains

-            var domains = new List<System.Tuple<string, IAbstractDomain>>(new System.Tuple<string, IAbstractDomain>[] {

-                  System.Tuple.Create("HoudiniConst", HoudiniConst.GetBottom() as IAbstractDomain),

-                  System.Tuple.Create("Intervals", new Intervals() as IAbstractDomain),

-                  System.Tuple.Create("ConstantProp", ConstantProp.GetBottom() as IAbstractDomain),

-                  System.Tuple.Create("PredicateAbs", new PredicateAbsElem() as IAbstractDomain),

-                  System.Tuple.Create("ImplicationDomain", ImplicationDomain.GetBottom() as IAbstractDomain),

-                  System.Tuple.Create("PowDomain", PowDomain.GetBottom() as IAbstractDomain),

-                  System.Tuple.Create("EqualitiesDomain", EqualitiesDomain.GetBottom() as IAbstractDomain),

-                  System.Tuple.Create("IA[HoudiniConst]", new IndependentAttribute<HoudiniConst>()  as IAbstractDomain),

-                  System.Tuple.Create("IA[ConstantProp]", new IndependentAttribute<ConstantProp>()  as IAbstractDomain),

-                  System.Tuple.Create("IA[Intervals]", new IndependentAttribute<Intervals>()  as IAbstractDomain),

-                  System.Tuple.Create("IA[PowDomain]", new IndependentAttribute<PowDomain>() as IAbstractDomain),

-              });

-

-            domains.Iter(tup => AbstractDomainFactory.Register(tup.Item1, tup.Item2));

-            program.Functions.Iter(RegisterFunction);

-        }

-

-        private static void RegisterFunction(Function func)

-        {

-            var attr = QKeyValue.FindStringAttribute(func.Attributes, "bvbuiltin");

-            if (attr != null && attr == "bvslt" && func.InParams.Count == 2 && func.InParams[0].TypedIdent.Type.IsBv)

-                bvslt.Add(func.InParams[0].TypedIdent.Type.BvBits, func);

-        }

-    }

-

-    public interface IAbstractDomain

-    {

-        IAbstractDomain Bottom();

-        IAbstractDomain MakeTop(out bool changed);

-        IAbstractDomain Join(List<Model.Element> state);

-        Expr Gamma(List<Expr> vars);

-        bool TypeCheck(List<Type> argTypes, out string msg);

-    }

-

-    public class AbstractHoudini

-    {

-        // Input Program

-        Program program;

-        // Impl -> VC

-        Dictionary<string, VCExpr> impl2VC;

-        // Impl -> Vars at end of the impl

-        Dictionary<string, List<VCExpr>> impl2EndStateVars;

-        // Impl -> (callee,summary pred)

-        Dictionary<string, List<Tuple<string, bool, VCExprVar, VCExprNAry>>> impl2CalleeSummaries;

-        // pointer to summary class

-        ISummaryElement summaryClass;

-        // impl -> summary

-        Dictionary<string, ISummaryElement> impl2Summary;

-        // name -> impl

-        Dictionary<string, Implementation> name2Impl;

-        // Use Bilateral algorithm

-        public static bool UseBilateralAlgo = true;

-        public static int iterTimeLimit = -1; // ms

-

-        public static readonly string summaryPredSuffix = "SummaryPred";

-

-        // Essentials: VCGen, Prover, and reporter

-        VCGen vcgen;

-        ProverInterface prover;

-        AbstractHoudiniErrorReporter reporter;

-

-        // Stats

-        TimeSpan proverTime;

-        int numProverQueries;

-

-        // Produce witness for correctness: can be set programmatically

-        public static string WitnessFile = "absHoudiniWitness.bpl";

-

-        public AbstractHoudini(Program program)

-        {

-            this.program = program;

-            this.impl2VC = new Dictionary<string, VCExpr>();

-            this.impl2EndStateVars = new Dictionary<string, List<VCExpr>>();

-            this.impl2CalleeSummaries = new Dictionary<string, List<Tuple<string, bool, VCExprVar, VCExprNAry>>>();

-            this.impl2Summary = new Dictionary<string, ISummaryElement>();

-            this.name2Impl = SimpleUtil.nameImplMapping(program);

-

-            if (CommandLineOptions.Clo.ProverKillTime > 0)

-                CommandLineOptions.Clo.ProverOptions = CommandLineOptions.Clo.ProverOptions.Concat1(string.Format("TIME_LIMIT={0}", CommandLineOptions.Clo.ProverKillTime));

-

-            this.vcgen = new VCGen(program, CommandLineOptions.Clo.SimplifyLogFilePath, CommandLineOptions.Clo.SimplifyLogFileAppend, new List<Checker>());

-            this.prover = ProverInterface.CreateProver(program, CommandLineOptions.Clo.SimplifyLogFilePath, CommandLineOptions.Clo.SimplifyLogFileAppend, -1);

-

-            this.reporter = new AbstractHoudiniErrorReporter();

-

-            this.proverTime = TimeSpan.Zero;

-            this.numProverQueries = 0;

-

-            if (CommandLineOptions.Clo.AbstractHoudini == "0")

-                UseBilateralAlgo = false;

-        }

-

-        public void computeSummaries(ISummaryElement summaryClass)

-        {

-            // TODO: move this some place else

-            PredicateAbs.FindUnsatPairs(prover.VCExprGen, prover);

-

-            this.summaryClass = summaryClass;

-

-            name2Impl.Values.Iter(attachEnsures);

-

-            program.Implementations

-                .Iter(impl => impl2Summary.Add(impl.Name, summaryClass.GetFlaseSummary(program, impl)));

-

-            // Build call graph

-            var Succ = new Dictionary<Implementation, HashSet<Implementation>>();

-            var Pred = new Dictionary<Implementation, HashSet<Implementation>>();

-            name2Impl.Values.Iter(impl => Succ.Add(impl, new HashSet<Implementation>()));

-            name2Impl.Values.Iter(impl => Pred.Add(impl, new HashSet<Implementation>()));

-

-            foreach (var impl in program.Implementations)

-            {

-                foreach (var blk in impl.Blocks)

-                {

-                    foreach (var cmd in blk.Cmds.OfType<CallCmd>())

-                    {

-                        if (!name2Impl.ContainsKey(cmd.callee)) continue;

-                        Succ[impl].Add(name2Impl[cmd.callee]);

-                        Pred[name2Impl[cmd.callee]].Add(impl);

-                    }

-                }

-            }

-

-            // Build SCC

-            var sccs = new StronglyConnectedComponents<Implementation>(name2Impl.Values,

-                new Adjacency<Implementation>(n => Pred[n]),

-                new Adjacency<Implementation>(n => Succ[n]));

-            sccs.Compute();

-

-            // impl -> priority

-            var impl2Priority = new Dictionary<string, int>();

-            int p = 0;

-            foreach (var scc in sccs)

-            {

-                foreach (var impl in scc)

-                {

-                    impl2Priority.Add(impl.Name, p);

-                    p++;

-                }

-            }

-

-

-            Inline();

-

-            #region Witness generation setup

-            // Create a copy of the program

-            var copy = new Dictionary<string, Implementation>();

-            if (WitnessFile != null)

-            {

-                foreach (var impl in program.Implementations)

-                {

-                    var nimpl = new Implementation(Token.NoToken, impl.Name, impl.TypeParameters,

-                        impl.InParams, impl.OutParams, new List<Variable>(impl.LocVars), new List<Block>());

-                    foreach (var blk in impl.Blocks)

-                    {

-                        var cd = new CodeCopier();

-                        nimpl.Blocks.Add(new Block(Token.NoToken, blk.Label,

-                            cd.CopyCmdSeq(blk.Cmds), cd.CopyTransferCmd(blk.TransferCmd)));

-                    }

-

-                    copy.Add(impl.Name, nimpl);

-                }

-            }

-            #endregion

-

-            // Turn off subsumption. Why? Because then I see multiple occurences of the

-            // attached ensures in the VC

-            CommandLineOptions.Clo.UseSubsumption = CommandLineOptions.SubsumptionOption.Never;

-

-            // Create all VCs

-            name2Impl.Values

-                .Iter(GenVC);

-

-            // Start the iteration

-            var worklist = new SortedSet<Tuple<int, Implementation>>();

-            name2Impl.Values

-                .Iter(impl => worklist.Add(Tuple.Create(impl2Priority[impl.Name], impl)));

-

-            while (worklist.Any())

-            {

-                var impl = worklist.First().Item2;

-                worklist.Remove(worklist.First());

-

-                var changed = ProcessImpl(impl);

-

-                if (changed)

-                {

-                    Pred[impl].Where(pred => UseBilateralAlgo || pred != impl).Iter(pred => worklist.Add(Tuple.Create(impl2Priority[pred.Name], pred)));

-                }

-            }

-

-            var allImpls = new SortedSet<Tuple<int, string>>();

-            name2Impl.Values.Iter(impl => allImpls.Add(Tuple.Create(impl2Priority[impl.Name], impl.Name)));

-            if (CommandLineOptions.Clo.Trace)

-            {

-                foreach (var tup in allImpls)

-                {

-                    Console.WriteLine("Summary of {0}:", tup.Item2);

-                    Console.WriteLine("{0}", impl2Summary[tup.Item2]);

-                }

-                Console.WriteLine("Prover time = {0}", proverTime.TotalSeconds.ToString("F2"));

-                Console.WriteLine("Number of prover queries = " + numProverQueries);

-            }

-

-            ProduceWitness(copy);

-

-            prover.Close();

-            CommandLineOptions.Clo.TheProverFactory.Close();

-        }

-

-        public HashSet<string> GetPredicates()

-        {

-            var ret = new HashSet<string>();

-            prover = ProverInterface.CreateProver(program, CommandLineOptions.Clo.SimplifyLogFilePath, CommandLineOptions.Clo.SimplifyLogFileAppend, -1);

-

-            foreach (var tup in impl2Summary)

-            {

-                var s = tup.Value as PredicateAbs;

-                if (s == null) continue;

-                ret.UnionWith(s.GetPredicates(program, prover.VCExprGen, prover));

-                // debug output

-                //Console.WriteLine("Summary of {0}:", tup.Key);

-                //Console.WriteLine("{0}", tup.Value);

-            }

-

-            prover.Close();

-            CommandLineOptions.Clo.TheProverFactory.Close();

-            return ret;

-        }

-

-        // Obtain the summary expression for a procedure: used programmatically by clients

-        // of AbstractHoudini

-        public Expr GetSummary(Program program, Procedure proc)

-        {

-            if (!impl2Summary.ContainsKey(proc.Name))

-                return Expr.True;

-

-            var vars = new Dictionary<string, Expr>();

-            foreach (var g in program.GlobalVariables)

-                vars.Add(g.Name, Expr.Ident(g));

-            foreach (var v in proc.InParams.OfType<Variable>())

-                vars.Add(v.Name, Expr.Ident(v));

-            foreach (var v in proc.OutParams.OfType<Variable>())

-                vars.Add(v.Name, Expr.Ident(v));

-

-            return impl2Summary[proc.Name].GetSummaryExpr(

-                v => { if (vars.ContainsKey(v)) return vars[v]; else return null; },

-                v => { if (vars.ContainsKey(v)) return new OldExpr(Token.NoToken, vars[v]); else return null; });

-        }

-

-        public ISummaryElement GetSummaryLowLevel(Procedure proc)

-        {

-            if (!impl2Summary.ContainsKey(proc.Name)) return null;

-            return impl2Summary[proc.Name];

-        }

-

-        // Produce a witness that proves that the inferred annotations are correct

-        private void ProduceWitness(Dictionary<string, Implementation> copy)

-        {

-            if (WitnessFile == null)

-                return;

-

-            foreach (var proc in program.Procedures)

-            {

-                var nensures = new List<Ensures>();

-                proc.Ensures.OfType<Ensures>()

-                .Where(ens => !QKeyValue.FindBoolAttribute(ens.Attributes, "ah") &&

-                    !QKeyValue.FindBoolAttribute(ens.Attributes, "pre") &&

-                    !QKeyValue.FindBoolAttribute(ens.Attributes, "post") &&

-                    QKeyValue.FindStringAttribute(ens.Attributes, "pre") == null &&

-                    QKeyValue.FindStringAttribute(ens.Attributes, "post") == null)

-                .Iter(ens => nensures.Add(ens));

-                foreach (Ensures en in nensures)

-                    en.Attributes = removeAttr("InlineAssume", en.Attributes);

-

-                proc.Ensures = nensures;

-            }

-

-            var decls = new List<Declaration>(copy.Values);

-            decls.AddRange(program.TopLevelDeclarations.Where(decl => !(decl is Implementation)));

-            program.TopLevelDeclarations = decls;

-            var name2Proc = new Dictionary<string, Procedure>();

-            foreach (var proc in program.Procedures)

-            {

-                name2Proc.Add(proc.Name, proc);

-                if (impl2Summary.ContainsKey(proc.Name))

-                {

-                    var ens = new Ensures(false, 

-                        impl2Summary[proc.Name].GetSummaryExpr(

-                        new Func<string, Expr>(s => null), new Func<string, Expr>(s => null)));

-                    ens.Attributes = new QKeyValue(Token.NoToken, "inferred", new List<object>(), ens.Attributes);

-                    proc.Ensures.Add(ens);

-                }

-            }

-

-            using (var wt = new TokenTextWriter(WitnessFile, /*pretty=*/ false))

-            {

-                program.Emit(wt);

-            }

-

-            // Replace SummaryPreds with their definition

-            foreach (var impl in program.Implementations)

-            {

-                foreach (var blk in impl.Blocks)

-                {

-                    foreach (var cmd in blk.Cmds.OfType<AssumeCmd>())

-                    {

-                        var expr = cmd.Expr as NAryExpr;

-                        if (expr == null) continue;

-                        var op = expr.Fun as FunctionCall;

-                        if (op == null || !op.FunctionName.EndsWith(summaryPredSuffix)) continue;

-                        var calleeName = op.FunctionName.Substring(0, op.FunctionName.Length - summaryPredSuffix.Length);

-                        if (!impl2Summary.ContainsKey(calleeName)) continue;

-                        var callee = name2Impl[calleeName];

-

-                        // variable order: globals, ins, outs, modifies

-                        var forold = new Dictionary<string, Expr>();

-                        var always = new Dictionary<string, Expr>();

-                        int i = 0;

-                        foreach (var g in program.GlobalVariables)

-                        {

-                            forold.Add(g.Name, expr.Args[i]);

-                            always.Add(g.Name, expr.Args[i]);

-                            i++;

-                        }

-                        foreach (var v in callee.InParams.OfType<Variable>())

-                        {

-                            always.Add(v.Name, expr.Args[i]);

-                            i++;

-                        }

-                        foreach (var v in callee.OutParams.OfType<Variable>())

-                        {

-                            always.Add(v.Name, expr.Args[i]);

-                            i++;

-                        }

-                        foreach (var ie in name2Proc[calleeName].Modifies.OfType<IdentifierExpr>())

-                        {

-                            always[ie.Name] = expr.Args[i];

-                            i++;

-                        }

-

-                        cmd.Expr = impl2Summary[calleeName].GetSummaryExpr(

-                            v => { if (always.ContainsKey(v)) return always[v]; else return null; },

-                            v => { if (forold.ContainsKey(v)) return forold[v]; else return null; });

-                    }

-                }

-            }

-

-            using (var wt = new TokenTextWriter(WitnessFile, /*pretty=*/ false))

-            {

-                program.Emit(wt);

-            }

-            if (CommandLineOptions.Clo.Trace) Console.WriteLine("Witness written to {0}", WitnessFile);

-        }

-

-        private QKeyValue removeAttr(string key, QKeyValue attr)

-        {

-            if (attr == null) return attr;

-            if (attr.Key == key) return removeAttr(key, attr.Next);

-            attr.Next = removeAttr(key, attr.Next);

-            return attr;

-        }

-

-        private void Inline()

-        {

-            if (CommandLineOptions.Clo.InlineDepth < 0)

-                return;

-

-            var callGraph = BuildCallGraph();

-

-            foreach (Implementation impl in callGraph.Nodes)

-            {

-                InlineEnsuresVisitor inlineEnsuresVisitor = new InlineEnsuresVisitor();

-                inlineEnsuresVisitor.Visit(impl);

-            }

-

-            foreach (Implementation impl in callGraph.Nodes)

-            {

-                impl.OriginalBlocks = impl.Blocks;

-                impl.OriginalLocVars = impl.LocVars;

-            }

-            foreach (Implementation impl in callGraph.Nodes)

-            {

-                CommandLineOptions.Inlining savedOption = CommandLineOptions.Clo.ProcedureInlining;

-                CommandLineOptions.Clo.ProcedureInlining = CommandLineOptions.Inlining.Spec;

-                Inliner.ProcessImplementationForHoudini(program, impl);

-                CommandLineOptions.Clo.ProcedureInlining = savedOption;

-            }

-            foreach (Implementation impl in callGraph.Nodes)

-            {

-                impl.OriginalBlocks = null;

-                impl.OriginalLocVars = null;

-            }

-

-            Graph<Implementation> oldCallGraph = callGraph;

-            callGraph = new Graph<Implementation>();

-            foreach (Implementation impl in oldCallGraph.Nodes)

-            {

-                callGraph.AddSource(impl);

-            }

-            foreach (Tuple<Implementation, Implementation> edge in oldCallGraph.Edges)

-            {

-                callGraph.AddEdge(edge.Item1, edge.Item2);

-            }

-            int count = CommandLineOptions.Clo.InlineDepth;

-            while (count > 0)

-            {

-                foreach (Implementation impl in oldCallGraph.Nodes)

-                {

-                    List<Implementation> newNodes = new List<Implementation>();

-                    foreach (Implementation succ in callGraph.Successors(impl))

-                    {

-                        newNodes.AddRange(oldCallGraph.Successors(succ));

-                    }

-                    foreach (Implementation newNode in newNodes)

-                    {

-                        callGraph.AddEdge(impl, newNode);

-                    }

-                }

-                count--;

-            }

-        }

-

-        private Graph<Implementation> BuildCallGraph()

-        {

-            Graph<Implementation> callGraph = new Graph<Implementation>();

-            Dictionary<Procedure, HashSet<Implementation>> procToImpls = new Dictionary<Procedure, HashSet<Implementation>>();

-            foreach (var proc in program.Procedures)

-            {

-                procToImpls[proc] = new HashSet<Implementation>();

-            }

-            foreach (var impl in program.Implementations)

-            {

-                if (impl.SkipVerification) continue;

-                callGraph.AddSource(impl);

-                procToImpls[impl.Proc].Add(impl);

-            }

-            foreach (var impl in program.Implementations)

-            {

-                if (impl.SkipVerification) continue;

-                foreach (Block b in impl.Blocks)

-                {

-                    foreach (Cmd c in b.Cmds)

-                    {

-                        CallCmd cc = c as CallCmd;

-                        if (cc == null) continue;

-                        foreach (Implementation callee in procToImpls[cc.Proc])

-                        {

-                            callGraph.AddEdge(impl, callee);

-                        }

-                    }

-                }

-            }

-            return callGraph;

-        }

-

-

-        private bool ProcessImpl(Implementation impl)

-        {

-            var ret = false;

-            var gen = prover.VCExprGen;

-

-            // construct summaries

-            var env = VCExpressionGenerator.True;

-            foreach (var tup in impl2CalleeSummaries[impl.Name])

-            {

-                // Not Bilateral: then reject self predicates

-                if (UseBilateralAlgo == false && tup.Item1 == impl.Name)

-                    continue;

-

-                // Bilateral: only reject self summary

-                if (UseBilateralAlgo == true && tup.Item1 == impl.Name && tup.Item2)

-                    continue;

-

-                var calleeSummary = 

-                    impl2Summary[tup.Item1].GetSummaryExpr(

-                       GetVarMapping(name2Impl[tup.Item1], tup.Item4), prover.VCExprGen);

-                env = gen.AndSimp(env, gen.Eq(tup.Item3, calleeSummary));

-            }

-

-            var prev = impl2Summary[impl.Name].Copy();

-            var upper = impl2Summary[impl.Name].GetTrueSummary(program, impl);

-            var sw = new Stopwatch();

-            sw.Start();

-            var lowerTime = TimeSpan.Zero;

-

-            while(true)

-            {

-                var usedLower = true;

-                var query = impl2Summary[impl.Name];

-                sw.Restart();

-

-                // construct self summaries

-                var summaryExpr = VCExpressionGenerator.True;

-                foreach (var tup in impl2CalleeSummaries[impl.Name])

-                {

-                    if (UseBilateralAlgo == false && tup.Item1 != impl.Name)

-                        continue;

-                    if (UseBilateralAlgo == true && (tup.Item1 != impl.Name || !tup.Item2))

-                        continue;

-                    

-                    if (UseBilateralAlgo)

-                    {

-                        query = query.AbstractConsequence(upper);

-                        if (query == null) query = impl2Summary[tup.Item1];

-                        else usedLower = false;

-                    }

-

-                    var ts =

-                        query.GetSummaryExpr(

-                           GetVarMapping(name2Impl[tup.Item1], tup.Item4), prover.VCExprGen);

-                    summaryExpr = gen.AndSimp(summaryExpr, gen.Eq(tup.Item3, ts));

-                }

-                //Console.WriteLine("Trying summary for {0}: {1}", impl.Name, summaryExpr);

-

-                reporter.model = null;

-                var vc = gen.AndSimp(env, summaryExpr);

-                vc = gen.Implies(vc, impl2VC[impl.Name]);

-                

-                //Console.WriteLine("Checking: {0}", vc);

-                if (CommandLineOptions.Clo.Trace)

-                    Console.WriteLine("Verifying {0} ({1}): {2}", impl.Name, usedLower ? "lower" : "ac", query);

-

-                if (usedLower && lowerTime.TotalMilliseconds >= iterTimeLimit && iterTimeLimit >= 0)

-                {

-                    if (UseBilateralAlgo)

-                    {

-                        if (CommandLineOptions.Clo.Trace)

-                            Console.WriteLine("Timeout/Spaceout while verifying " + impl.Name);

-                        ret = prev.IsEqual(upper) ? false : true;

-                        impl2Summary[impl.Name] = upper;

-                        break;

-                    }

-                    else

-                    {

-                        if (CommandLineOptions.Clo.Trace)

-                            Console.WriteLine("Timeout/Spaceout while verifying " + impl.Name);

-                        var tt = impl2Summary[impl.Name].GetTrueSummary(program, impl);

-                        ret = prev.IsEqual(tt) ? false : true; ;

-                        impl2Summary[impl.Name] = tt;

-                        break;

-                    }

-                }

-

-                var start = DateTime.Now;

-

-                //prover.Push();

-                //prover.Assert(gen.Not(vc), true);

-                //prover.FlushAxiomsToTheoremProver();

-                //prover.Check();

-                //ProverInterface.Outcome proverOutcome = prover.CheckOutcome(reporter);

-                //prover.Pop();

-

-                prover.BeginCheck(impl.Name, vc, reporter);

-                ProverInterface.Outcome proverOutcome = prover.CheckOutcome(reporter);

-

-                var inc = (DateTime.Now - start);

-                proverTime += inc;

-                numProverQueries++;

-

-                sw.Stop();

-                if (usedLower) lowerTime += sw.Elapsed;

-

-                if(CommandLineOptions.Clo.Trace)

-                    Console.WriteLine("Time taken = " + inc.TotalSeconds.ToString()); 

-

-                if (UseBilateralAlgo)

-                {

-                    if (proverOutcome == ProverInterface.Outcome.TimeOut || proverOutcome == ProverInterface.Outcome.OutOfMemory)

-                    {

-                        if(CommandLineOptions.Clo.Trace)

-                            Console.WriteLine("Timeout/Spaceout while verifying " + impl.Name);

-                        ret = prev.IsEqual(upper) ? false : true;

-                        impl2Summary[impl.Name] = upper;

-                        break;

-                    }

-                    

-                    if (reporter.model == null && usedLower)

-                        break;

-

-                    if (reporter.model == null)

-                    {

-                        upper.Meet(query);

-                    }

-                    else

-                    {

-                        var state = CollectState(impl);

-                        impl2Summary[impl.Name].Join(state, reporter.model);

-                        ret = true;

-                    }

-                }

-                else

-                {

-                    if (proverOutcome == ProverInterface.Outcome.TimeOut || proverOutcome == ProverInterface.Outcome.OutOfMemory)

-                    {

-                        if (CommandLineOptions.Clo.Trace)

-                            Console.WriteLine("Timeout/Spaceout while verifying " + impl.Name);

-                        var tt = impl2Summary[impl.Name].GetTrueSummary(program, impl);

-                        ret = prev.IsEqual(tt) ? false : true; ;

-                        impl2Summary[impl.Name] = tt;

-                        break;

-                    }

-

-                    if (reporter.model == null)

-                        break;

-                    //reporter.model.Write(Console.Out);

-

-                    var state = CollectState(impl);

-                    impl2Summary[impl.Name].Join(state, reporter.model);

-                    ret = true;

-                }

-            }

-            return ret;

-        }

-

-        private Dictionary<string, VCExpr> GetVarMapping(Implementation impl, VCExprNAry summaryPred)

-        {

-            var ret = new Dictionary<string, VCExpr>();

-

-            var cnt = 0;

-            foreach (var g in program.GlobalVariables)

-            {

-                ret.Add(string.Format("old({0})", g.Name), summaryPred[cnt]);

-                cnt++;

-            }

-            foreach (var v in impl.InParams.OfType<Variable>().Concat(

-                impl.OutParams.OfType<Variable>().Concat(

-                impl.Proc.Modifies.OfType<IdentifierExpr>().Select(ie => ie.Decl))))

-            {

-                ret.Add(v.Name, summaryPred[cnt]);

-                cnt++;

-            }

-

-            // Fill up values of globals that are not modified

-            cnt = 0;

-            foreach (var g in program.GlobalVariables)

-            {

-                if (ret.ContainsKey(g.Name)) { cnt++; continue; }

-

-                ret.Add(string.Format("{0}", g.Name), summaryPred[cnt]);

-                cnt++;

-            }

-

-            // Constants

-            foreach (var c in program.Constants)

-            {

-                var value = prover.Context.BoogieExprTranslator.Translate(Expr.Ident(c));

-                ret.Add(string.Format("{0}", c.Name), value);

-                ret.Add(string.Format("old({0})", c.Name), value);

-            }

-

-            return ret;

-        }

-

-        private Dictionary<string, Model.Element> CollectState(Implementation impl)

-        {

-            var ret = new Dictionary<string, Model.Element>();

-

-            var model = reporter.model;

-            var implVars = impl2EndStateVars[impl.Name];

-

-            var cnt = 0;

-            foreach (var g in program.GlobalVariables)

-            {

-                ret.Add(string.Format("old({0})", g.Name), getValue(implVars[cnt], model));

-                cnt++;

-            }

-            foreach (var v in impl.InParams.OfType<Variable>().Concat(

-                impl.OutParams.OfType<Variable>().Concat(

-                impl.Proc.Modifies.OfType<IdentifierExpr>().Select(ie => ie.Decl))))

-            {

-                ret.Add(v.Name, getValue(implVars[cnt], model));

-                cnt++;

-            }

-

-            // Fill up values of globals that are not modified

-            cnt = 0;

-            foreach (var g in program.GlobalVariables)

-            {

-                if (ret.ContainsKey(g.Name)) { cnt++; continue; }

-

-                ret.Add(string.Format("{0}", g.Name), getValue(implVars[cnt], model));

-                cnt++;

-            }

-

-            // Constants

-            foreach (var c in program.Constants)

-            {

-                try

-                {

-                    var value = getValue(prover.Context.BoogieExprTranslator.Translate(Expr.Ident(c)), model);

-                    ret.Add(string.Format("{0}", c.Name), value);

-                    ret.Add(string.Format("old({0})", c.Name), value);

-                }

-                catch (Exception)

-                {

-                    // constant not assigned a value: add a default value

-                    Model.Element value = null;

-                    if (c.TypedIdent.Type.IsInt)

-                        value = model.MkIntElement(0);

-                    else if (c.TypedIdent.Type.IsBool)

-                        value = model.MkElement("false");

-

-                    ret.Add(string.Format("{0}", c.Name), value);

-                    ret.Add(string.Format("old({0})", c.Name), value);

-                }

-            }

-

-            return ret;

-        }

-

-        private Model.Element getValue(VCExpr arg, Model model)

-        {

-            if (arg is VCExprLiteral)

-            {

-                //return model.GetElement(arg.ToString());

-                return model.MkElement(arg.ToString());

-            }

-            else if (arg is VCExprVar)

-            {

-                var el = model.TryGetFunc(prover.Context.Lookup(arg as VCExprVar));

-                if (el != null)

-                {

-                    Debug.Assert(el.Arity == 0 && el.AppCount == 1);

-                    return el.Apps.First().Result;

-                }

-                else

-                {

-                    // Variable not defined; assign arbitrary value

-                    if (arg.Type.IsBool)

-                        return model.MkElement("false");

-                    else if (arg.Type.IsInt)

-                        return model.MkIntElement(0);

-                    else

-                        return null;

-                }

-            }

-            else

-            {

-                Debug.Assert(false);

-                return null;

-            }

-        }

-

-        private void attachEnsures(Implementation impl)

-        {

-            List<Variable> functionInterfaceVars = new List<Variable>();

-            foreach (Variable v in vcgen.program.GlobalVariables)

-            {

-                functionInterfaceVars.Add(new Formal(Token.NoToken, new TypedIdent(Token.NoToken, "", v.TypedIdent.Type), true));

-            }

-            foreach (Variable v in impl.InParams)

-            {

-                functionInterfaceVars.Add(new Formal(Token.NoToken, new TypedIdent(Token.NoToken, "", v.TypedIdent.Type), true));

-            }

-            foreach (Variable v in impl.OutParams)

-            {

-                functionInterfaceVars.Add(new Formal(Token.NoToken, new TypedIdent(Token.NoToken, "", v.TypedIdent.Type), true));

-            }

-            foreach (IdentifierExpr e in impl.Proc.Modifies)

-            {

-                if (e.Decl == null) continue;

-                functionInterfaceVars.Add(new Formal(Token.NoToken, new TypedIdent(Token.NoToken, "", e.Decl.TypedIdent.Type), true));

-            }

-            Formal returnVar = new Formal(Token.NoToken, new TypedIdent(Token.NoToken, "", Bpl.Type.Bool), false);

-            var function = new Function(Token.NoToken, impl.Name + summaryPredSuffix, functionInterfaceVars, returnVar);

-            prover.Context.DeclareFunction(function, "");

-

-            List<Expr> exprs = new List<Expr>();

-            foreach (Variable v in vcgen.program.GlobalVariables)

-            {

-                Contract.Assert(v != null);

-                exprs.Add(new OldExpr(Token.NoToken, new IdentifierExpr(Token.NoToken, v)));

-            }

-            foreach (Variable v in impl.Proc.InParams)

-            {

-                Contract.Assert(v != null);

-                exprs.Add(new IdentifierExpr(Token.NoToken, v));

-            }

-            foreach (Variable v in impl.Proc.OutParams)

-            {

-                Contract.Assert(v != null);

-                exprs.Add(new IdentifierExpr(Token.NoToken, v));

-            }

-            foreach (IdentifierExpr ie in impl.Proc.Modifies)

-            {

-                Contract.Assert(ie != null);

-                if (ie.Decl == null)

-                    continue;

-                exprs.Add(ie);

-            }

-            Expr postExpr = new NAryExpr(Token.NoToken, new FunctionCall(function), exprs);

-            impl.Proc.Ensures.Add(

-                new Ensures(Token.NoToken, false, postExpr, "", 

-                    new QKeyValue(Token.NoToken, "ah", new List<object>(), null)));

-        }

-

-        private void GenVC(Implementation impl)

-        {

-            ModelViewInfo mvInfo;

-            Dictionary<int, Absy> label2absy;

-

-            if (CommandLineOptions.Clo.Trace)

-            {

-                Console.WriteLine("Generating VC of {0}", impl.Name);

-            }

-

-            vcgen.ConvertCFG2DAG(impl);

-            vcgen.PassifyImpl(impl, out mvInfo);

-

-            var gen = prover.VCExprGen;

-            var vcexpr = vcgen.GenerateVC(impl, null, out label2absy, prover.Context);

-

-

-            // Find the assert

-            impl2EndStateVars.Add(impl.Name, new List<VCExpr>());

-            var found = false;

-            var assertId = -1;

-            foreach (var blk in impl.Blocks)

-            {

-                foreach (var cmd in blk.Cmds.OfType<AssertCmd>())

-                {

-                    if (SimpleUtil.isAssertTrue(cmd)) continue;

-                    var nary = cmd.Expr as NAryExpr;

-                    if (nary == null) continue;

-                    var pred = nary.Fun as FunctionCall;

-                    if (pred == null || pred.FunctionName != (impl.Name + (AbstractHoudini.summaryPredSuffix)))

-                        continue;

-

-                    Debug.Assert(!found);

-                    found = true;

-                    assertId = cmd.UniqueId;

-                    //Console.WriteLine("assert cmd id: {0}", cmd.UniqueId);

-                    nary.Args.OfType<Expr>()

-                        .Iter(expr => impl2EndStateVars[impl.Name].Add(prover.Context.BoogieExprTranslator.Translate(expr)));

-                }

-            }

-

-            // It is possible that no assert is found in the procedure. It happens when the

-            // procedure doesn't return.

-            //Debug.Assert(found);

-

-            // Grab summary predicates

-            var visitor = new FindSummaryPred(prover.VCExprGen, assertId);

-            vcexpr = visitor.Mutate(vcexpr, true);

-

-            // Create a macro so that the VC can sit with the theorem prover

-            Macro macro = new Macro(Token.NoToken, impl.Name + "Macro", new List<Variable>(), new Formal(Token.NoToken, new TypedIdent(Token.NoToken, "", Bpl.Type.Bool), false));

-            prover.DefineMacro(macro, vcexpr);

-

-            // Store VC

-            impl2VC.Add(impl.Name, gen.Function(macro));

-

-            //Console.WriteLine("VC of {0}: {1}", impl.Name, vcexpr);

-

-            // check sanity: only one predicate for self-summary

-            // (There may be none when the procedure doesn't return)

-            Debug.Assert(visitor.summaryPreds.Count(tup => tup.Item2) <= 1);

-

-            impl2CalleeSummaries.Add(impl.Name, new List<Tuple<string, bool, VCExprVar, VCExprNAry>>());

-            visitor.summaryPreds.Iter(tup => impl2CalleeSummaries[impl.Name].Add(tup));

-        }

-    }

-

-    public interface ISummaryElement

-    {

-        ISummaryElement Copy();

-        ISummaryElement GetFlaseSummary(Program program, Implementation impl);

-        void Join(Dictionary<string, Model.Element> state, Model model);

-        VCExpr GetSummaryExpr(Dictionary<string, VCExpr> incarnations, VCExpressionGenerator gen);

-        Expr GetSummaryExpr(Func<string, Expr> always, Func<string, Expr> forold);

-

-        // For Bilateral

-        ISummaryElement GetTrueSummary(Program program, Implementation impl);

-        void Meet(ISummaryElement other);

-        bool IsEqual(ISummaryElement other);

-        ISummaryElement AbstractConsequence(ISummaryElement upper);

-    }

-

-    public class ConstantVal : ISummaryElement

-    {

-        Program program;

-        Implementation impl;

-        // var -> const set

-        Dictionary<string, HashSet<int>> val;

-        // set of vars

-        HashSet<Variable> vars;

-

-        public static readonly int MAX = 3;

-

-        public ConstantVal()

-        {

-            // this is just a place holder

-            val = new Dictionary<string, HashSet<int>>();

-            vars = new HashSet<Variable>();

-        }

-

-        private ConstantVal(Program program, Implementation impl)

-        {

-            this.program = program;

-            this.impl = impl;

-            this.val = new Dictionary<string, HashSet<int>>();

-

-            vars = new HashSet<Variable>();

-            impl.Proc.Modifies

-                .OfType<IdentifierExpr>()

-                .Select(ie => ie.Decl)

-                .Where(v => v.TypedIdent.Type.IsInt)

-                .Iter(v => vars.Add(v));

-            impl.OutParams.OfType<Variable>()

-                .Where(v => v.TypedIdent.Type.IsInt)

-                .Iter(v => vars.Add(v));

-

-            vars.Iter(v => val.Add(v.Name, null));

-        }

-

-

-        public void Join(Dictionary<string, Model.Element> state, Model model)

-        {

-            foreach (var vv in vars)

-            {

-                var v = vv.Name;

-                var newv = state[v].AsInt();

-                var oldv = val[v];

-

-                if (oldv == null)

-                {

-                    val[v] = new HashSet<int>();

-                    val[v].Add(newv);

-                }

-                else if(oldv.Count > 0)

-                {

-                    val[v].Add(newv);

-                    if (val[v].Count > MAX)

-                        val[v] = new HashSet<int>();

-                } 

-

-            }

-        }

-

-        public VCExpr GetSummaryExpr(Dictionary<string, VCExpr> incarnations, VCExpressionGenerator gen)

-        {

-            VCExpr ret = VCExpressionGenerator.True;

-            if (val.Values.Any(v => v == null))

-                return VCExpressionGenerator.False;

-            

-            foreach (var v in vars)

-            {

-                var consts = val[v.Name];

-                Debug.Assert(consts != null);

-

-                if (consts.Count == 0)

-                    continue;

-

-                var vexpr = VCExpressionGenerator.False;

-                consts.Iter(c => vexpr = gen.OrSimp(vexpr, gen.Eq(incarnations[v.Name], gen.Integer(Microsoft.Basetypes.BigNum.FromInt(c)))));

-                ret = gen.AndSimp(ret, vexpr);

-            }

-

-            return ret;

-        }

-

-        public override string ToString()

-        {

-            var ret = "true";

-            if (val.Values.Any(v => v == null))

-                return "false";

-

-            foreach (var v in vars)

-            {

-                var consts = val[v.Name];

-                Debug.Assert(consts != null);

-

-                if (consts.Count == 0)

-                    continue;

-

-                var vexpr = "false";

-                consts.Iter(c => vexpr = 

-                    string.Format("{0} OR ({1} == {2})", vexpr, v.Name, c));

-

-                ret = string.Format("{0} AND ({1})", ret, vexpr);

-            }

-

-            return ret;

-        }

-

-

-        public ISummaryElement GetFlaseSummary(Program program, Implementation impl)

-        {

-            return new ConstantVal(program, impl);

-        }

-

-        #region ISummaryElement (Bilateral) Members

-

-

-        public ISummaryElement GetTrueSummary(Program program, Implementation impl)

-        {

-            throw new NotImplementedException();

-        }

-

-        public void Meet(ISummaryElement other)

-        {

-            throw new NotImplementedException();

-        }

-

-        public bool IsEqual(ISummaryElement other)

-        {

-            throw new NotImplementedException();

-        }

-

-        public ISummaryElement AbstractConsequence(ISummaryElement upper)

-        {

-            throw new NotImplementedException();

-        }

-

-        #endregion

-

-        #region ISummaryElement Members

-

-

-        public Expr GetSummaryExpr(Func<string, Expr> always, Func<string, Expr> forold)

-        {

-            throw new NotImplementedException();

-        }

-

-        #endregion

-

-        #region ISummaryElement Members

-

-        public ISummaryElement Copy()

-        {

-            throw new NotImplementedException();

-        }

-

-        #endregion

-    }

-

-    public class NamedExpr 

-    {

-        public string name;

-        public Expr expr;

-

-        public NamedExpr(string name, Expr expr)

-        {

-            this.name = name;

-            this.expr = expr;

-        }

-

-        public NamedExpr(Expr expr)

-        {

-            this.name = null;

-            this.expr = expr;

-        }

-

-        public override string ToString()

-        {

-            if (name != null)

-                return name;

-

-            return expr.ToString();

-        }

-    }

-

-    public class PredicateAbs : ISummaryElement

-    {

-        public static Dictionary<string, List<NamedExpr>> PrePreds { get; private set; }

-        public static Dictionary<string, HashSet<int>> PosPrePreds { get; private set; }

-        public static Dictionary<string, List<NamedExpr>> PostPreds { get; private set; }

-        public static Dictionary<Tuple<string, int>, List<PredicateAbsDisjunct>> UpperCandidates;

-        private static HashSet<string> boolConstants;

-        // {proc, pred-pair} -> polariry

-        public static HashSet<Tuple<string, int, int, bool, bool>> unsatPrePredPairs;

-        public static HashSet<Tuple<string, int, int, bool, bool>> unsatPostPredPairs;

-

-        // Temporary: used during eval

-        private static Model model = null;

-

-        string procName;

-        PredicateAbsDisjunct[] value;

-        bool isFalse;

-

-        public PredicateAbs(string procName)

-        {

-            this.procName = procName;

-            isFalse = true;

-            value = new PredicateAbsDisjunct[PostPreds[this.procName].Count];

-            for (int i = 0; i < PostPreds[this.procName].Count; i++) value[i] = null;

-        }

-

-        public static void Initialize(Program program)

-        {

-            PrePreds = new Dictionary<string, List<NamedExpr>>();

-            PostPreds = new Dictionary<string, List<NamedExpr>>();

-            PosPrePreds = new Dictionary<string, HashSet<int>>();

-

-            boolConstants = new HashSet<string>();

-            UpperCandidates = new Dictionary<Tuple<string, int>, List<PredicateAbsDisjunct>>();

-

-            program.Constants

-                .Where(c => c.TypedIdent.Type.IsBool)

-                .Iter(c => boolConstants.Add(c.Name));

-

-            // Add template pre-post to all procedures

-            var preT = new List<NamedExpr>();

-            var postT = new List<NamedExpr>();

-            var posPreT = new HashSet<int>();

-            var tempP = new HashSet<Procedure>();

-            foreach (var proc in

-                program.Procedures

-                .Where(proc => QKeyValue.FindBoolAttribute(proc.Attributes, "template")))

-            {

-                tempP.Add(proc);

-                foreach (var ens in proc.Ensures.OfType<Ensures>())

-                {

-                    var pos = QKeyValue.FindBoolAttribute(ens.Attributes, "positive");

-

-                    if (QKeyValue.FindBoolAttribute(ens.Attributes, "pre"))

-                    {

-                        preT.Add(new NamedExpr(null, ens.Condition));

-                        if (pos) posPreT.Add(preT.Count - 1);

-                    }

-

-                    if (QKeyValue.FindBoolAttribute(ens.Attributes, "post"))

-                        postT.Add(new NamedExpr(null, ens.Condition));

-

-                    var s = QKeyValue.FindStringAttribute(ens.Attributes, "pre");

-                    if (s != null)

-                    {

-                        preT.Add(new NamedExpr(s, ens.Condition));

-                        if (pos) posPreT.Add(preT.Count - 1);

-                    }

-

-                    s = QKeyValue.FindStringAttribute(ens.Attributes, "post");

-                    if (s != null)

-                        postT.Add(new NamedExpr(s, ens.Condition));

-                }

-            }

-

-            program.RemoveTopLevelDeclarations(decl => tempP.Contains(decl));

-            var upperPreds = new Dictionary<string, List<Expr>>();

-

-            foreach (var impl in program.Implementations)

-            {

-                PrePreds.Add(impl.Name, new List<NamedExpr>());

-                PostPreds.Add(impl.Name, new List<NamedExpr>());

-                PosPrePreds.Add(impl.Name, new HashSet<int>());

-

-                // Add "false" as the first post predicate

-                //PostPreds[impl.Name].Add(new NamedExpr(Expr.False));

-

-                preT.Iter(e => PrePreds[impl.Name].Add(e));

-                postT.Iter(e => PostPreds[impl.Name].Add(e));

-                PosPrePreds[impl.Name].UnionWith(posPreT);

-

-                // Pick up per-procedure pre-post

-                var nens = new List<Ensures>();

-                foreach (var ens in impl.Proc.Ensures.OfType<Ensures>())

-                {

-                    string s = null;

-                    var pos = QKeyValue.FindBoolAttribute(ens.Attributes, "positive");

-                    

-                    if (QKeyValue.FindBoolAttribute(ens.Attributes, "pre"))

-                    {

-                        PrePreds[impl.Name].Add(new NamedExpr(ens.Condition));

-                        PosPrePreds[impl.Name].Add(PrePreds[impl.Name].Count - 1);

-                    }

-                    else if (QKeyValue.FindBoolAttribute(ens.Attributes, "post"))

-                    {

-                        PostPreds[impl.Name].Add(new NamedExpr(ens.Condition));

-                    }

-                    else if ((s = QKeyValue.FindStringAttribute(ens.Attributes, "pre")) != null)

-                    {

-                        PrePreds[impl.Name].Add(new NamedExpr(s, ens.Condition));

-                        PosPrePreds[impl.Name].Add(PrePreds[impl.Name].Count - 1);

-                    }

-                    else if ((s = QKeyValue.FindStringAttribute(ens.Attributes, "post")) != null)

-                    {

-                        PostPreds[impl.Name].Add(new NamedExpr(s, ens.Condition));

-                    }

-                    else if (QKeyValue.FindBoolAttribute(ens.Attributes, "upper"))

-                    {

-                        var key = impl.Name;

-                        if (!upperPreds.ContainsKey(key))

-                            upperPreds.Add(key, new List<Expr>());

-                        upperPreds[key].Add(ens.Condition);

-                    }

-                    else

-                    {

-                        nens.Add(ens);

-                    }

-                }

-                impl.Proc.Ensures = nens;

-            }

-

-            foreach (var tup in upperPreds)

-            {

-                var procName = tup.Key;

-                var candidates = tup.Value;

-                if (!candidates.Any()) continue;

-

-                var strToPost = new Dictionary<string, int>();

-                for (int i = 0; i < PostPreds[procName].Count; i++)

-                {

-                    strToPost.Add(PostPreds[procName][i].expr.ToString(), i);

-                }

-

-                foreach (var expr in candidates)

-                {

-                    if (strToPost.ContainsKey(expr.ToString()))

-                    {

-                        var key = Tuple.Create(procName, strToPost[expr.ToString()]);

-                        if (!UpperCandidates.ContainsKey(key))

-                            UpperCandidates.Add(key, new List<PredicateAbsDisjunct>());

-                        UpperCandidates[key].Add(new PredicateAbsDisjunct(true, procName));

-                    }

-                    else

-                    {

-                        // Try parsing the expression as (pre-conjunct ==> post-pred)

-                        var parsed = ParseExpr(expr, procName);

-                        if (parsed != null && strToPost.ContainsKey(parsed.Item2.ToString()))

-                        {

-                            var key = Tuple.Create(procName, strToPost[parsed.Item2.ToString()]);

-                            if (!UpperCandidates.ContainsKey(key))

-                                UpperCandidates.Add(key, new List<PredicateAbsDisjunct>());

-                            UpperCandidates[key].Add(parsed.Item1);

-                        }

-                    }

-                }

-

-            }

-            //Console.WriteLine("Running Abstract Houdini");

-            //PostPreds.Iter(expr => Console.WriteLine("\tPost: {0}", expr));

-            //PrePreds.Iter(expr => Console.WriteLine("\tPre: {0}", expr));

-        }

-

-        // Try parsing the expression as (pre-conjunct ==> post-pred)

-        private static Tuple<PredicateAbsDisjunct, Expr> ParseExpr(Expr expr, string procName)

-        {

-            Expr postExpr = null;

-            Expr preExpr = null;

-

-            // Decompose outer Implies

-            var nexpr = expr as NAryExpr;

-            if (nexpr != null && (nexpr.Fun is BinaryOperator)

-                && (nexpr.Fun as BinaryOperator).Op == BinaryOperator.Opcode.Imp

-                && (nexpr.Args.Count == 2))

-            {

-                postExpr = nexpr.Args[1];

-                preExpr = nexpr.Args[0];

-            }

-            else

-            {

-                if(CommandLineOptions.Clo.Trace) Console.WriteLine("Failed to parse {0} (ignoring)", expr);

-                return null;

-            }

-

-

-            var atoms = DecomposeOuterAnd(preExpr);

-            var pos = new HashSet<int>();

-            var neg = new HashSet<int>();

-

-            foreach (var atom in atoms)

-            {

-                var index = PrePreds[procName].FindIndex(ne => ne.expr.ToString() == atom.ToString());

-                if (index == -1)

-                {

-                    index = PrePreds[procName].FindIndex(ne => Expr.Not(ne.expr).ToString() == atom.ToString());

-                    if (index == -1)

-                    {

-                        if(CommandLineOptions.Clo.Trace) Console.WriteLine("Failed to parse {0} (ignoring)", atom);

-                        return null;

-                    }

-                    else

-                    {

-                        neg.Add(index);

-                    }

-                }

-                else

-                {

-                    pos.Add(index);

-                }

-            }

-

-            var conj = new PredicateAbsConjunct(pos, neg, procName);

-            var conjls = new List<PredicateAbsConjunct>();

-            conjls.Add(conj);

-

-            return Tuple.Create(new PredicateAbsDisjunct(conjls, procName), postExpr);

-        }

-

-        // blah && blah ==> {blah, blah}

-        static IEnumerable<Expr> DecomposeOuterAnd(Expr expr)

-        {

-            var ret = new List<Expr>();

-

-            var nexpr = expr as NAryExpr;

-            if (nexpr == null

-                || !(nexpr.Fun is BinaryOperator)

-                || (nexpr.Fun as BinaryOperator).Op != BinaryOperator.Opcode.And)

-            {

-                    ret.Add(expr);

-            }

-            else

-            {

-                foreach (Expr a in nexpr.Args)

-                    ret.AddRange(DecomposeOuterAnd(a));

-            }

-

-            return ret;

-        }

-

-

-        private Model.Element Eval(Expr expr, Dictionary<string, Model.Element> state)

-        {

-            if (expr is LiteralExpr)

-            {

-                return ToElem((expr as LiteralExpr).Val);

-            }

-

-            if (expr is IdentifierExpr)

-            {

-                return LookupVariable((expr as IdentifierExpr).Name, state, false);

-            }

-

-            if (expr is OldExpr)

-            {

-                var ide = (expr as OldExpr).Expr as IdentifierExpr;

-                Debug.Assert(ide != null);

-

-                return LookupVariable(ide.Name, state, true);

-            }

-

-            if (expr is NAryExpr)

-            {

-                var nary = expr as NAryExpr;

-                if (nary.Fun is UnaryOperator)

-                {

-                    return ToElem((nary.Fun as UnaryOperator).Evaluate(ToValue(Eval(nary.Args[0], state))));

-                }

-                if (nary.Fun is BinaryOperator)

-                {

-                    return ToElem((nary.Fun as BinaryOperator).Evaluate(ToValue(Eval(nary.Args[0], state)), ToValue(Eval(nary.Args[1], state))));

-                }

-                if (nary.Fun is MapSelect && nary.Args.Count == 2)

-                {

-                    var index = Eval(nary.Args[1], state);

-                    var map = Eval(nary.Args[0], state) as Model.Array;

-                    Debug.Assert(map != null, "Variable of map type must have an Array-typed value");

-                    var ret = map.Value.TryEval(index as Model.Element);

-                    if (ret == null) ret = map.Value.Else;

-                    Debug.Assert(ret != null);

-                    return ret;

-                }

-                Debug.Assert(false, "No other op is handled");                

-            }

-            throw new NotImplementedException(string.Format("Expr of type {0} is not handled", expr.GetType().ToString()));

-        }

-

-        private Model.Element LookupVariable(string v, Dictionary<string, Model.Element> state, bool tryOld)

-        {

-            if (tryOld)

-            {

-                var oldv = string.Format("old({0})", v);

-                if (state.ContainsKey(oldv))

-                {

-                    return state[oldv];

-                }

-                throw new AbsHoudiniInternalError("Cannot handle this case");

-            }

-

-            if (state.ContainsKey(v))

-            {

-                return state[v];

-            }

-

-            /*

-            if (boolConstants.Contains(v))

-            {

-                // value of this constant is immaterial, return true

-                return model.MkElement("true");

-            }

-            */

-

-            throw new AbsHoudiniInternalError("Cannot handle this case");

-        }

-

-        private static VCExpr ToVcVar(string v, Dictionary<string, VCExpr> incarnations, bool tryOld)

-        {

-            if (tryOld)

-            {

-                var oldv = string.Format("old({0})", v);

-                if (incarnations.ContainsKey(oldv))

-                {

-                    return incarnations[oldv];

-                }

-                throw new AbsHoudiniInternalError("Cannot handle this case");

-            }

-

-            if (incarnations.ContainsKey(v))

-            {

-                return incarnations[v];

-            }

-

-            throw new AbsHoudiniInternalError("Cannot handle this case");

-        }

-

-        public static void FindUnsatPairs(VCExpressionGenerator gen, ProverInterface prover)

-        {

-            unsatPrePredPairs = new HashSet<Tuple<string, int, int, bool, bool>>();

-            unsatPostPredPairs = new HashSet<Tuple<string, int, int, bool, bool>>(); 

-

-            var cachePos = new HashSet<Tuple<string, string>>();

-            var cacheNeg = new HashSet<Tuple<string, string>>();

-            var record = new Action<object, string, int, int, bool, bool>(

-                (map, proc, e1, e2, p1, p2) => {

-                    var key = Tuple.Create(proc, e1, e2, p1, p2);

-                    if (map == PrePreds)

-                        unsatPrePredPairs.Add(key);

-                    else

-                        unsatPostPredPairs.Add(key);

-                }

-            );

-

-            var predMaps = new List<Dictionary<string, List<NamedExpr>>>();

-            predMaps.Add(PrePreds); predMaps.Add(PostPreds);

-

-            foreach (var map in predMaps)

-            {

-                foreach (var proc in map.Keys)

-                {

-                    for (int i = 0; i < 2 * map[proc].Count(); i++)

-                    {

-                        var p1 = (i % 2); // polarity

-                        var e1 = map[proc][i / 2].expr;

-                        if (p1 == 0) e1 = Expr.Not(e1);

-

-                        for (int j = 2 * ((i / 2) + 1); j < 2 * map[proc].Count(); j++)

-                        {

-                            var p2 = (j % 2); // polarity

-                            var e2 = map[proc][j / 2].expr;

-                            if (p2 == 0) e2 = Expr.Not(e2);

-

-                            var key = Tuple.Create(e1.ToString(), e2.ToString());

-                            if (cachePos.Contains(key))

-                            {

-                                record(map, proc, i / 2, j / 2, p1 == 1, p2 == 1);

-                                continue;

-                            }

-                            else if (cacheNeg.Contains(key))

-                            {

-                                continue;

-                            }

-

-                            if (!CheckIfUnsat(e1, e2, gen, prover))

-                            {

-                                cacheNeg.Add(key);

-                                continue;

-                            }

-                            cachePos.Add(key);

-                            record(map, proc, i / 2, j / 2, p1 == 1, p2 == 1);

-

-                            if (CommandLineOptions.Clo.Trace)

-                                Console.WriteLine("Proved UNSAT: {0}    {1}", e1, e2);

-                        }

-                    }

-                }

-            }

-        }

-

-        // Is a ^ b UNSAT?

-        private static bool CheckIfUnsat(Expr a, Expr b, VCExpressionGenerator gen, ProverInterface prover)

-        {

-            var gatherLitA = new GatherLiterals();

-            var gatherLitB = new GatherLiterals();

-

-            gatherLitA.Visit(a);

-            gatherLitB.Visit(b);

-

-            var seta = new HashSet<Variable>();

-            var setb = new HashSet<Variable>();

-            gatherLitA.literals.Iter(tup => seta.Add(tup.Item1));

-            gatherLitB.literals.Iter(tup => setb.Add(tup.Item1));

-            seta.IntersectWith(setb);

-            if (!seta.Any()) return false;

-            

-            // Create fresh variables

-            return CheckIfUnsat(Expr.And(a, b), gen, prover);

-        }

-

-        // Is a UNSAT?

-        private static bool CheckIfUnsat(Expr a, VCExpressionGenerator gen, ProverInterface prover)

-        {

-            var gatherLitA = new GatherLiterals();

-            gatherLitA.Visit(a);

-

-            // Create fresh variables

-            var counter = 0;

-            var incarnations = new Dictionary<string, VCExpr>();

-            foreach (var literal in gatherLitA.literals)

-            {

-                if (incarnations.ContainsKey(literal.Item2.ToString()))

-                    continue;

-

-                //if(!literal.Item1.TypedIdent.Type.IsInt && !literal.Item1.TypedIdent.Type.IsBool)

-                var v = gen.Variable("UNSATCheck" + counter, literal.Item1.TypedIdent.Type);

-                incarnations.Add(literal.Item2.ToString(), v);

-                counter++;

-            }

-

-            var vc1 = ToVcExpr(a, incarnations, gen);

-            var vc = gen.LabelPos("Temp", vc1);

-

-            // check

-            prover.AssertAxioms();

-            prover.Push();

-            prover.Assert(vc, true);

-            prover.Check();

-            var outcome = prover.CheckOutcomeCore(new AbstractHoudiniErrorReporter());

-            prover.Pop();

-

-            if (outcome == ProverInterface.Outcome.Valid)

-                return true;

-            return false;

-        }

-

-

-        class GatherLiterals : ReadOnlyVisitor

-        {

-            public List<Tuple<Variable, Expr>> literals;

-            bool inOld;

-

-            public GatherLiterals()

-            {

-                literals = new List<Tuple<Variable, Expr>>();

-                inOld = false;

-            }

-

-            public override Expr VisitOldExpr(OldExpr node)

-            {

-                var prev = inOld;

-                inOld = true;

-                var ret = base.VisitOldExpr(node);

-                inOld = prev;

-                return ret;

-            }

-

-            public override Expr VisitIdentifierExpr(IdentifierExpr node)

-            {

-                if (inOld)

-                    literals.Add(Tuple.Create(node.Decl, new OldExpr(Token.NoToken, node) as Expr));

-                else

-                    literals.Add(Tuple.Create(node.Decl, node as Expr));

-

-                return node;

-            }

-        }

-

-        private object ToValue(Model.Element elem)

-        {

-            if (elem is Model.Integer)

-            {

-                return Microsoft.Basetypes.BigNum.FromInt((elem as Model.Integer).AsInt());

-            }

-            if (elem is Model.Boolean)

-            {

-                return (elem as Model.Boolean).Value;

-            }

-            if (elem is Model.DatatypeValue && (elem as Model.DatatypeValue).Arguments.Length == 1 &&

-                (elem as Model.DatatypeValue).ConstructorName == "-" &&

-                (elem as Model.DatatypeValue).Arguments[0] is Model.Integer)

-            {

-                // negative number as "-" @ int

-                return Microsoft.Basetypes.BigNum.FromInt(-1 * ((elem as Model.DatatypeValue).Arguments[0] as Model.Integer).AsInt());

-            }

-            throw new NotImplementedException("Cannot yet handle this Model.Element type");

-        }

-

-        private Model.Element ToElem(object val)

-        {

-            if (val is bool || val is int || val is Basetypes.BigNum)

-                return model.MkElement(val.ToString());

-            throw new NotImplementedException("Cannot yet handle this value type");

-        }

-

-        // replace v by old(v)

-        private static Expr MakeOld(Expr expr)

-        {

-            var substalways = new Substitution(v => new OldExpr(Token.NoToken, Expr.Ident(v)));

-            var substold = new Substitution(v => Expr.Ident(v));

-

-            return Substituter.ApplyReplacingOldExprs(substalways, substold, expr);

-        }

-

-        private static Expr ToExpr(Expr expr, Func<string, Expr> always, Func<string, Expr> forold)

-        {

-            var substalways = new Substitution(v =>

-            {

-                var ret = always(v.Name);

-                if (ret != null) return ret;

-                else return Expr.Ident(v);

-            });

-            var substold = new Substitution(v =>

-            {

-                var ret = forold(v.Name);

-                if (ret != null) return ret;

-                else return new OldExpr(Token.NoToken, Expr.Ident(v));

-            });

-

-            return Substituter.ApplyReplacingOldExprs(substalways, substold, expr);

-        }

-

-        private static VCExpr ToVcExpr(Expr expr, Dictionary<string, VCExpr> incarnations, VCExpressionGenerator gen)

-        {

-            if (expr is LiteralExpr)

-            {

-                var val = (expr as LiteralExpr).Val;

-                if (val is bool)

-                {

-                    if ((bool)val)

-                    {

-                        return VCExpressionGenerator.True;

-                    }

-                    else

-                    {

-                        return VCExpressionGenerator.False;

-                    }

-                }

-                else if (val is Microsoft.Basetypes.BigNum)

-                {

-                    return gen.Integer((Microsoft.Basetypes.BigNum)val);

-                }

-

-                throw new NotImplementedException("Cannot handle literals of this type");

-            }

-

-            if (expr is IdentifierExpr)

-            {

-                return ToVcVar((expr as IdentifierExpr).Name, incarnations, false);

-            }

-

-            if (expr is OldExpr)

-            {

-                var ide = (expr as OldExpr).Expr as IdentifierExpr;

-                Debug.Assert(ide != null);

-

-                return ToVcVar(ide.Name, incarnations, true);

-            }

-

-            if (expr is NAryExpr)

-            {

-                var nary = expr as NAryExpr;

-                if (nary.Fun is UnaryOperator)

-                {

-                    if ((nary.Fun as UnaryOperator).Op == UnaryOperator.Opcode.Not)

-                        return gen.Not(ToVcExpr(nary.Args[0], incarnations, gen));

-                    else if ((nary.Fun as UnaryOperator).Op == UnaryOperator.Opcode.Neg)

-                        return gen.Function(VCExpressionGenerator.SubIOp, gen.Integer(Basetypes.BigNum.FromInt(0)), ToVcExpr(nary.Args[0], incarnations, gen));

-                    else

-                        Debug.Assert(false, "No other unary op is handled");

-                }

-                if (nary.Fun is BinaryOperator)

-                {

-                    return gen.Function(Translate(nary.Fun as BinaryOperator), ToVcExpr(nary.Args[0], incarnations, gen), ToVcExpr(nary.Args[1], incarnations, gen));

-                }

-                if (nary.Fun is MapSelect && nary.Args.Count == 2)

-                {

-                    return gen.Select(ToVcExpr(nary.Args[0], incarnations, gen), ToVcExpr(nary.Args[1], incarnations, gen));

-                }

-                Debug.Assert(false, "No other op is handled");

-            }

-            throw new NotImplementedException(string.Format("Expr of type {0} is not handled", expr.GetType().ToString()));

-        }

-

-        private static VCExprOp Translate(BinaryOperator op)

-        {

-            switch (op.Op)

-            {

-                case BinaryOperator.Opcode.Add:

-                    return VCExpressionGenerator.AddIOp;

-                case BinaryOperator.Opcode.Sub:

-                    return VCExpressionGenerator.SubIOp;

-                case BinaryOperator.Opcode.Mul:

-                    return VCExpressionGenerator.MulIOp;

-                case BinaryOperator.Opcode.Div:

-                    return VCExpressionGenerator.DivIOp;

-                case BinaryOperator.Opcode.Mod:

-                    return VCExpressionGenerator.ModOp;

-                case BinaryOperator.Opcode.Eq:

-                case BinaryOperator.Opcode.Iff:

-                    // we don't distinguish between equality and equivalence at this point

-                    return VCExpressionGenerator.EqOp;

-                case BinaryOperator.Opcode.Neq:

-                    return VCExpressionGenerator.NeqOp;

-                case BinaryOperator.Opcode.Lt:

-                    return VCExpressionGenerator.LtOp;

-                case BinaryOperator.Opcode.Le:

-                    return VCExpressionGenerator.LeOp;

-                case BinaryOperator.Opcode.Ge:

-                    return VCExpressionGenerator.GeOp;

-                case BinaryOperator.Opcode.Gt:

-                    return VCExpressionGenerator.GtOp;

-                case BinaryOperator.Opcode.Imp:

-                    return VCExpressionGenerator.ImpliesOp;

-                case BinaryOperator.Opcode.And:

-                    return VCExpressionGenerator.AndOp;

-                case BinaryOperator.Opcode.Or:

-                    return VCExpressionGenerator.OrOp;

-                case BinaryOperator.Opcode.Subtype:

-                    return VCExpressionGenerator.SubtypeOp;

-                default:

-                    Contract.Assert(false);

-                    throw new NotImplementedException();

-            }

-

-        }

-

-        // If "false" is a post-predicate, then remove its "pre" constraint from all others, whenever possible

-        public void Simplify()

-        {

-            // find "false"

-            var findex = PostPreds[procName].FindIndex(ne => (ne.expr is LiteralExpr) && (ne.expr as LiteralExpr).IsFalse);

-            if (findex < 0) return;

-            if (value[findex].isTrue)

-            {

-                // procedure doesn't return

-                for (int i = 0; i < value.Length; i++)

-                    if (i != findex) value[i] = new PredicateAbsDisjunct(false, procName);

-                return;

-            }

-            if (value[findex].isFalse)

-                return;

-

-            for (int i = 0; i < value.Length; i++)

-                if (i != findex) value[i].Subtract(value[findex]);

-        }

-

-        public HashSet<string> GetPredicates(Program program, VCExpressionGenerator gen, ProverInterface prover)

-        {

-            var ret = new HashSet<string>();

-            if (isFalse) return ret;

-            Simplify();

-

-            // Find the free expressions

-            var proc = program.Procedures.FirstOrDefault(p => p.Name == procName);

-            Contract.Assert(proc != null);

-            Expr freeSummary = Expr.True;

-            foreach (var req in proc.Requires.OfType<Requires>().Where(req => req.Free))

-            {

-                freeSummary = Expr.And(freeSummary, MakeOld(req.Condition));

-            }

-            foreach (var ens in proc.Ensures.OfType<Ensures>().Where(ens => ens.Free))

-            {

-                freeSummary = Expr.And(freeSummary, ens.Condition);

-            }

-            

-            for (int i = 0; i < PostPreds[procName].Count; i++)

-            {

-                if (value[i].isFalse) continue;

-                if (PostPreds[procName][i].expr is LiteralExpr && (PostPreds[procName][i].expr as LiteralExpr).IsFalse)

-                    continue;

-

-                if (value[i].isTrue)

-                    ret.Add(PostPreds[procName][i].expr.ToString());

-                else

-                {

-                    foreach (var c in value[i].GetConjuncts())

-                    {

-                        var s = Expr.Imp(c.ToExpr(j => PrePreds[procName][j].expr), PostPreds[procName][i].expr);

-                        if (CheckIfUnsat(Expr.And(freeSummary, Expr.Not(s)), gen, prover))

-                            continue;

-                        ret.Add(s.ToString());

-                    }

-                }

-            }

-            return ret;

-        }

-

-        public override string ToString()

-        {

-            var ret = "";

-            if (isFalse) return "false";

-            var first = true;

-

-            for(int i = 0; i < PostPreds[procName].Count; i++) 

-            {

-                if(value[i].isFalse) continue;

-                

-                if(value[i].isTrue)

-                    ret += string.Format("{0}{1}", first ? "" : " && ", PostPreds[procName][i]);

-                else

-                    ret += string.Format("{0}({1} ==> {2})", first ? "" : " && ", value[i], PostPreds[procName][i]);

-

-                first = false;

-            }

-            if (ret == "") ret = "true";

-            return ret;

-        }

-

-

-        #region ISummaryElement Members

-

-        public ISummaryElement Copy()

-        {

-            var ret = new PredicateAbs(procName);

-            ret.isFalse = isFalse;

-            ret.value = new PredicateAbsDisjunct[value.Length];

-            for (int i = 0; i < value.Length; i++)

-                ret.value[i] = value[i];

-            return ret;

-        }

-

-        public ISummaryElement GetFlaseSummary(Program program, Implementation impl)

-        {

-            return new PredicateAbs(impl.Name);

-        }

-

-        public ISummaryElement GetTrueSummary(Program program, Implementation impl)

-        {

-            var ret = new PredicateAbs(impl.Name);

-            ret.isFalse = false;

-            for (int i = 0; i < PostPreds[this.procName].Count; i++) ret.value[i] = new PredicateAbsDisjunct(false, impl.Name);

-

-            return ret;

-        }

-

-        public void Join(Dictionary<string, Model.Element> state, Model model)

-        {

-            PredicateAbs.model = model;

-

-            // Evaluate each predicate on the state

-            var prePredsVal = new bool[PrePreds[procName].Count];

-            var postPredsVal = new bool[PostPreds[procName].Count];

-

-            var indexSeq = new List<int>();

-            for (int i = 0; i < PrePreds[procName].Count; i++) indexSeq.Add(i);

-

-            for (int i = 0; i < PrePreds[procName].Count; i++)

-            {

-                var v = ToValue(Eval(PrePreds[procName][i].expr, state));

-                Debug.Assert(v is bool);

-                prePredsVal[i] = (bool)v;

-            }

-

-            for (int i = 0; i < PostPreds[procName].Count; i++)

-            {

-                var v = ToValue(Eval(PostPreds[procName][i].expr, state));

-                Debug.Assert(v is bool);

-                postPredsVal[i] = (bool)v;

-            }

-

-            for (int i = 0; i < PostPreds[procName].Count; i++)

-            {

-                // No hope for this post pred?

-                if (!isFalse && value[i].isFalse) continue;

-

-                var newDisj = new PredicateAbsDisjunct(true, procName);

-                if (!postPredsVal[i])

-                {

-                    newDisj = new PredicateAbsDisjunct(indexSeq.Where(j => !prePredsVal[j]), indexSeq.Where(j => prePredsVal[j] && !PosPrePreds[procName].Contains(j)), procName);

-                }

-

-                if (isFalse)

-                    value[i] = newDisj;

-                else

-                    value[i] = PredicateAbsDisjunct.And(value[i], newDisj);

-            }

-

-            /*

-            // do beta(model)

-            var that = new PredicateAbsDisjunct[PostPreds[procName].Count];

-            for (int i = 0; i < PostPreds[procName].Count; i++)

-            {

-                if (postPredsVal[i])

-                    that[i] = new PredicateAbsDisjunct(true, procName);

-                else if (i == 0)

-                {

-                    Debug.Assert(PostPreds[procName][0].ToString() == "false");

-                    var newDisj = new PredicateAbsDisjunct(true, procName);

-                    newDisj = new PredicateAbsDisjunct(indexSeq.Where(j => !prePredsVal[j]), indexSeq.Where(j => prePredsVal[j]), procName);

-                    that[i] = newDisj;

-                }

-                else

-                {

-                    // false

-                    that[i] = new PredicateAbsDisjunct(false, procName);

-                }

-            }

-

-            // Do join

-            for (int i = 0; i < PostPreds[procName].Count; i++)

-            {

-                if (isFalse)

-                    value[i] = that[i];

-                else

-                {

-                    if (i == 0)

-                        value[i] = PredicateAbsDisjunct.And(value[i], that[i]);

-                    else

-                    {

-                        var c1 = PredicateAbsDisjunct.And(value[i], that[i]);

-                        var c2 = PredicateAbsDisjunct.And(value[i], that[0]);

-                        var c3 = PredicateAbsDisjunct.And(value[0], that[i]);

-                        value[i] = PredicateAbsDisjunct.Or(c1, c2);

-                        value[i] = PredicateAbsDisjunct.Or(value[i], c3);

-                    }

-                }

-            }

-            */

-            isFalse = false;

-

-            //Console.WriteLine("Result of Join: {0}", this.ToString());

-        }

-

-        // Precondition: the upper guys are just {true/false/upper-candidate} ==> post-pred

-        public void Meet(ISummaryElement iother)

-        {

-            var other = iother as PredicateAbs;

-            if (isFalse) return;

-            if (other.isFalse)

-            {

-                isFalse = true;

-                for (int i = 0; i < PostPreds[this.procName].Count; i++) value[i] = null;

-                return;

-            }

-            Debug.Assert(this.procName == other.procName);

-

-            for (int i = 0; i < PostPreds[this.procName].Count; i++)

-            {

-                value[i] = PredicateAbsDisjunct.Or(value[i], other.value[i]);

-            }

-        }

-

-        public bool IsEqual(ISummaryElement other)

-        {

-            var that = other as PredicateAbs;

-            if (isFalse && that.isFalse) return true;

-            if (isFalse || that.isFalse) return false;

-            for (int i = 0; i < PostPreds[procName].Count; i++)

-            {

-                if (!PredicateAbsDisjunct.syntacticLessThan(value[i], that.value[i]) ||

-                    !PredicateAbsDisjunct.syntacticLessThan(that.value[i], value[i]))

-                    return false;

-            }

-            return true;

-        }

-

-        // Precondition: the upper guys are just {true/false/upper-candidate} ==> post-pred

-        // Postcondition: the returned value is also of this form (for just one post-pred)

-        public ISummaryElement AbstractConsequence(ISummaryElement iupper)

-        {

-            var upper = iupper as PredicateAbs;

-

-            for (int i = 0; i < PostPreds[this.procName].Count; i++)

-            {

-                if (upper.value[i].isTrue) continue;

-                if (!UpperCandidates.ContainsKey(Tuple.Create(procName, i))) continue;

-

-                foreach (var candidate in UpperCandidates[Tuple.Create(procName, i)])

-                {

-                    if (PredicateAbsDisjunct.syntacticLessThan(candidate, upper.value[i]))

-                        continue;

-                    if (!this.isFalse && !PredicateAbsDisjunct.syntacticLessThan(candidate, this.value[i]))

-                        continue;

-

-                    var ret = new PredicateAbs(this.procName);

-                    ret.isFalse = false;

-                    for (int j = 0; j < PostPreds[this.procName].Count; j++)

-                        ret.value[j] = new PredicateAbsDisjunct(false, this.procName);

-

-                    ret.value[i] = candidate;

-

-                    return ret;

-                }

-            }

-

-            // Giveup: the abstract consequence is too difficult to compute

-            return null;

-        }

-

-        public VCExpr GetSummaryExpr(Dictionary<string, VCExpr> incarnations, VCExpressionGenerator gen)

-        {

-            if (isFalse)

-                return VCExpressionGenerator.False;

-

-            var ret = VCExpressionGenerator.True;

-

-            for(int i = 0; i < PostPreds[procName].Count; i++)

-            {

-                ret = gen.AndSimp(ret, gen.ImpliesSimp(value[i].ToVcExpr(j => ToVcExpr(PrePreds[procName][j].expr, incarnations, gen), gen), ToVcExpr(PostPreds[procName][i].expr, incarnations, gen)));

-            }

-

-            return ret;

-        }

-

-        public Expr GetSummaryExpr(Func<string, Expr> always, Func<string, Expr> forold)

-        {

-            if (isFalse)

-                return Expr.False;

-

-            Expr ret = Expr.True;

-

-            for (int i = 0; i < PostPreds[procName].Count; i++)

-            {

-                ret = Expr.And(ret, Expr.Imp(value[i].ToExpr(j => ToExpr(PrePreds[procName][j].expr, always, forold)), ToExpr(PostPreds[procName][i].expr, always, forold)));

-            }

-

-            return ret;

-        }

-

-        #endregion

-    }

-

-    public class PredicateAbsDisjunct

-    {

-        List<PredicateAbsConjunct> conjuncts;

-        string ProcName;

-        public bool isTrue {get; private set;}

-        public bool isFalse

-        {

-            get

-            {

-                if (isTrue) return false;

-                return conjuncts.Count == 0;

-            }

-        }

-

-        public PredicateAbsDisjunct(bool isTrue, string ProcName)

-        {

-            this.isTrue = isTrue;

-            this.ProcName = ProcName;

-            conjuncts = new List<PredicateAbsConjunct>();

-        }

-

-        public PredicateAbsDisjunct(List<PredicateAbsConjunct> conjuncts, string ProcName)

-        {

-            isTrue = false;

-            this.conjuncts = conjuncts;

-            this.ProcName = ProcName;

-        }

-

-        // Disjunct of singleton conjuncts

-        public PredicateAbsDisjunct(IEnumerable<int> pos, IEnumerable<int> neg, string ProcName)

-        {

-            this.ProcName = ProcName;

-            conjuncts = new List<PredicateAbsConjunct>();

-            isTrue = false;

-            pos.Iter(p => conjuncts.Add(PredicateAbsConjunct.Singleton(p, true, ProcName)));

-            neg.Iter(p => conjuncts.Add(PredicateAbsConjunct.Singleton(p, false, ProcName)));

-        }

-

-        // Does d1 describe a smaller set of states than d2? This is true when every conjunct of d1

-        // is smaller than some conjunct of d2

-        public static bool syntacticLessThan(PredicateAbsDisjunct d1, PredicateAbsDisjunct d2)

-        {

-            if (d2.isTrue) return true;

-            if (d1.isTrue) return false;

-            if (d1.isFalse) return true;

-            if (d2.isFalse) return false;

-

-            foreach (var c1 in d1.conjuncts)

-            {

-                if (d2.conjuncts.Any(c2 => PredicateAbsConjunct.syntacticLessThan(c1, c2)))

-                    continue;

-                else

-                    return false;

-            }

-            return true;

-        }

-

-        public static PredicateAbsDisjunct And(PredicateAbsDisjunct v1, PredicateAbsDisjunct v2)

-        {

-            if (v1.isTrue) return v2;

-            if (v2.isTrue) return v1;

-

-            var result = new List<PredicateAbsConjunct>();

-

-            foreach (var c1 in v1.conjuncts)

-            {

-                foreach (var c2 in v2.conjuncts)

-                {

-                    var c = PredicateAbsConjunct.And(c1, c2);

-                    if (c.isFalse) continue;

-                    if (result.Any(cprime => c.implies(cprime))) continue;

-                    var tmp = new List<PredicateAbsConjunct>();

-                    tmp.Add(c);

-                    result.Where(cprime => !cprime.implies(c)).Iter(cprime => tmp.Add(cprime));

-                    result = tmp;

-                }

-            }

-

-            return new PredicateAbsDisjunct(result, v1.ProcName);

-        }

-

-        public static PredicateAbsDisjunct Or(PredicateAbsDisjunct v1, PredicateAbsDisjunct v2)

-        {

-            if (v1.isTrue) return v1;

-            if (v2.isTrue) return v2;

-            if (v1.isFalse) return v2;

-            if (v2.isFalse) return v1;

-

-            var result = new List<PredicateAbsConjunct>();

-            v1.conjuncts.Iter(c => result.Add(c));

-

-            foreach (var c in v2.conjuncts)

-            {

-                if (result.Any(cprime => c.implies(cprime))) continue;

-                var tmp = new List<PredicateAbsConjunct>();

-                tmp.Add(c);

-                result.Where(cprime => !cprime.implies(c)).Iter(cprime => tmp.Add(cprime));

-                result = tmp;

-            }

-

-            return new PredicateAbsDisjunct(result, v1.ProcName);

-        }

-

-        public VCExpr ToVcExpr(Func<int, VCExpr> predToExpr, VCExpressionGenerator gen)

-        {

-            if (isTrue) return VCExpressionGenerator.True;

-            var ret = VCExpressionGenerator.False;

-            conjuncts.Iter(c => ret = gen.OrSimp(ret, c.ToVcExpr(predToExpr, gen)));

-            return ret;

-        }

-

-        public Expr ToExpr(Func<int, Expr> predToExpr)

-        {

-            if (isTrue) return Expr.True;

-            Expr ret = Expr.False;

-            conjuncts.Iter(c => ret = Expr.Or(ret, c.ToExpr(predToExpr)));

-            return ret;

-        }

-

-        public override string ToString()

-        {

-            if(isTrue) 

-                return "true";

-            var ret = "";

-            var first = true;

-            foreach (var c in conjuncts)

-            {

-                if (c.isFalse) continue;

-                ret += string.Format("{0}{1}", first ? "" : " || ", c);

-                first = false;

-            }

-            return ret;

-        }

-

-        public void Subtract(PredicateAbsDisjunct that)

-        {

-            var ncon = new List<PredicateAbsConjunct>();

-            foreach (var c1 in conjuncts)

-            {

-                if (that.conjuncts.Any(c2 => c1.implies(c2)))

-                    continue;

-                ncon.Add(c1);

-            }

-            conjuncts = ncon;

-        }

-

-        public IEnumerable<PredicateAbsConjunct> GetConjuncts()

-        {

-            return conjuncts;

-        }

-

-    }

-

-    public class PredicateAbsConjunct

-    {

-        static int ConjunctBound = 3;

-

-        public bool isFalse { get; private set; }

-        HashSet<int> posPreds;

-        HashSet<int> negPreds;

-        string ProcName;

-

-        public static void Initialize(int bound)

-        {

-            ConjunctBound = bound;

-        }

-

-        private void Normalize()

-        {

-            if (posPreds.Intersect(negPreds).Any() || negPreds.Intersect(posPreds).Any() || (posPreds.Count + negPreds.Count > ConjunctBound))

-            {

-                isFalse = true;

-                posPreds = new HashSet<int>();

-                negPreds = new HashSet<int>();

-            }

-        }

-

-        // Do this step only once in a while?

-        private void StrongNormalize()

-        {

-            if (isFalse) return;

-

-            var candidates = new List<Tuple<int, bool>>();

-            posPreds.Iter(p => candidates.Add(Tuple.Create(p, true)));

-            negPreds.Iter(p => candidates.Add(Tuple.Create(p, false)));

-            var drop = new HashSet<int>();

-            for (int i = 0; i < candidates.Count; i++)

-            {

-                for (int j = 0; j < candidates.Count; j++)

-                {

-                    if (i == j) continue;

-

-                    var key = Tuple.Create(ProcName, candidates[i].Item1, candidates[j].Item1,

-                        candidates[i].Item2, candidates[j].Item2);

-                    if (PredicateAbs.unsatPrePredPairs.Contains(key))

-                    {

-                        isFalse = true;

-                        posPreds = new HashSet<int>();

-                        negPreds = new HashSet<int>();

-                        return;

-                    }

-

-                    key = Tuple.Create(ProcName, candidates[i].Item1, candidates[j].Item1,

-                        candidates[i].Item2, !candidates[j].Item2);

-

-                    if (PredicateAbs.unsatPrePredPairs.Contains(key))

-                        drop.Add(candidates[j].Item1);

-                }

-            }

-

-            posPreds.ExceptWith(drop);

-            negPreds.ExceptWith(drop);

-        }

-

-        public PredicateAbsConjunct(bool isFalse, string ProcName)

-        {

-            posPreds = new HashSet<int>();

-            negPreds = new HashSet<int>();

-            this.isFalse = isFalse;

-            this.ProcName = ProcName;

-        }

-

-        // do we know that c1 is surely less than or equal to c2? That is, c1 describes a smaller

-        // concretization. We check that c2 is a sub-conjunct of c1

-        public static bool syntacticLessThan(PredicateAbsConjunct c1, PredicateAbsConjunct c2)

-        {

-            if (c1.isFalse) return true;

-            if (c2.isFalse) return false;

-            return (c2.posPreds.IsSubsetOf(c1.posPreds) && c2.negPreds.IsSubsetOf(c1.negPreds));

-        }

-

-        public static PredicateAbsConjunct Singleton(int v, bool isPositive, string ProcName)

-        {

-            if (isPositive)

-                return new PredicateAbsConjunct(new int[] { v }, new HashSet<int>(), ProcName);

-            else

-                return new PredicateAbsConjunct(new HashSet<int>(), new int[] { v }, ProcName);

-        }

-

-        public PredicateAbsConjunct(IEnumerable<int> pos, IEnumerable<int> neg, string ProcName)

-        {

-            isFalse = false;

-            posPreds = new HashSet<int>(pos);

-            negPreds = new HashSet<int>(neg);

-            this.ProcName = ProcName;

-            Normalize();

-        }

-

-        public static PredicateAbsConjunct And(PredicateAbsConjunct v1, PredicateAbsConjunct v2)

-        {

-            if (v1.isFalse || v2.isFalse) return new PredicateAbsConjunct(true, v1.ProcName);

-            var ret =  new PredicateAbsConjunct(v1.posPreds.Union(v2.posPreds), v1.negPreds.Union(v2.negPreds), v1.ProcName);

-            ret.StrongNormalize();

-            return ret;

-        }

-

-        public bool implies(PredicateAbsConjunct v)

-        {

-            if (isFalse) return true;

-            if (v.isFalse) return false;

-            return (posPreds.IsSupersetOf(v.posPreds) && negPreds.IsSupersetOf(v.negPreds));

-        }

-

-        public VCExpr ToVcExpr(Func<int, VCExpr> predToExpr, VCExpressionGenerator gen)

-        {

-            if (isFalse) return VCExpressionGenerator.False;

-            var ret = VCExpressionGenerator.True;

-            posPreds.Iter(p => ret = gen.AndSimp(ret, predToExpr(p)));

-            negPreds.Iter(p => ret = gen.AndSimp(ret, gen.Not(predToExpr(p))));

-            return ret;

-        }

-

-        public Expr ToExpr(Func<int, Expr> predToExpr)

-        {

-            if (isFalse) return Expr.False;

-            Expr ret = Expr.True;

-            var pp = posPreds.ToList(); pp.Sort();

-            var np = negPreds.ToList(); np.Sort();

-            pp.Iter(p => ret = Expr.And(ret, predToExpr(p)));

-            np.Iter(p => ret = Expr.And(ret, Expr.Not(predToExpr(p)))); 

-            return ret;

-        }

-

-        public override string ToString()

-        {

-            if (isFalse)

-                return "false";

-

-            var ret = "";

-            var first = true;

-            foreach (var p in posPreds)

-            {

-                ret += string.Format("{0}{1}", first ? "" : " && ", PredicateAbs.PrePreds[ProcName][p]);

-                first = false;

-            }

-            foreach (var p in negPreds)

-            {

-                ret += string.Format("{0}!{1}", first ? "" : " && ", PredicateAbs.PrePreds[ProcName][p]);

-                first = false;

-            }

-            return ret;

-        }

-    }

-

-    class FindSummaryPred : MutatingVCExprVisitor<bool>

-    {

-        public List<Tuple<string, bool, VCExprVar, VCExprNAry>> summaryPreds;

-        int assertId;

-        private static int CounterId = 0;

-

-        public FindSummaryPred(VCExpressionGenerator gen, int assertId)

-            : base(gen)

-        {

-            summaryPreds = new List<Tuple<string, bool, VCExprVar, VCExprNAry>>();

-            this.assertId = assertId;

-        }

-

-        protected override VCExpr/*!*/ UpdateModifiedNode(VCExprNAry/*!*/ originalNode,

-                                              List<VCExpr/*!*/>/*!*/ newSubExprs,

-            // has any of the subexpressions changed?

-                                              bool changed,

-                                              bool arg)

-        {

-            Contract.Ensures(Contract.Result<VCExpr>() != null);

-

-            VCExpr ret;

-            if (changed)

-                ret = Gen.Function(originalNode.Op,

-                                   newSubExprs, originalNode.TypeArguments);

-            else

-                ret = originalNode;

-

-            VCExprNAry retnary = ret as VCExprNAry;

-            if (retnary == null) return ret;

-            var op = retnary.Op as VCExprBoogieFunctionOp;

-

-            if (op == null)

-            {

-                var lop = retnary.Op as VCExprLabelOp;

-                if (lop == null) return ret;

-                if (lop.pos) return ret;

-                if (!lop.label.Equals("@" + assertId.ToString())) return ret;

-                

-                //var subexpr = retnary[0] as VCExprNAry;

-                //if (subexpr == null) return ret;

-                //op = subexpr.Op as VCExprBoogieFunctionOp;

-                //if (op == null) return ret;

-

-                var subexpr = retnary[0] as VCExprVar;

-                if (subexpr == null) return ret;

-                if (!subexpr.Name.StartsWith("AbstractHoudiniControl")) return ret;

-

-                for (int i = 0; i < summaryPreds.Count; i++)

-                {

-                    if (summaryPreds[i].Item3 == subexpr)

-                        summaryPreds[i] = Tuple.Create(summaryPreds[i].Item1, true, summaryPreds[i].Item3, summaryPreds[i].Item4);

-                }

-                return ret;

-            }

-

-            string calleeName = op.Func.Name;

-

-            if (!calleeName.EndsWith(AbstractHoudini.summaryPredSuffix))

-                return ret;

-

-            var controlConst = Gen.Variable("AbstractHoudiniControl" + CounterId, Microsoft.Boogie.Type.Bool);

-            CounterId++;

-

-            summaryPreds.Add(Tuple.Create(calleeName.Substring(0, calleeName.Length - AbstractHoudini.summaryPredSuffix.Length), false, controlConst, retnary));

-

-            return controlConst;

-            //return ret;

-        }

-

-    }

-

-    class FindExistentialFunctions : MutatingVCExprVisitor<bool>

-    {

-        public List<Tuple<string, VCExprVar, VCExprNAry>> funcCalls;

-        private HashSet<string> existentialFunctions;

-        private static int CounterId = 0;

-

-        public FindExistentialFunctions(VCExpressionGenerator gen, HashSet<string> existentialFunctions)

-            : base(gen)

-        {

-            funcCalls = new List<Tuple<string, VCExprVar, VCExprNAry>>();

-            this.existentialFunctions = existentialFunctions;

-        }

-

-        protected override VCExpr/*!*/ UpdateModifiedNode(VCExprNAry/*!*/ originalNode,

-                                              List<VCExpr/*!*/>/*!*/ newSubExprs,

-            // has any of the subexpressions changed?

-                                              bool changed,

-                                              bool arg)

-        {

-            Contract.Ensures(Contract.Result<VCExpr>() != null);

-

-            VCExpr ret;

-            if (changed)

-                ret = Gen.Function(originalNode.Op,

-                                   newSubExprs, originalNode.TypeArguments);

-            else

-                ret = originalNode;

-

-            VCExprNAry retnary = ret as VCExprNAry;

-            if (retnary == null) return ret;

-            var op = retnary.Op as VCExprBoogieFunctionOp;

-            if (op == null) return ret;

-

-            string calleeName = op.Func.Name;

-

-            if (!existentialFunctions.Contains(calleeName))

-                return ret;

-

-            var controlConst = Gen.Variable("AbsHoudiniControl" + CounterId, Microsoft.Boogie.Type.Bool);

-            CounterId++;

-

-            funcCalls.Add(Tuple.Create(calleeName, controlConst, retnary));

-

-            return controlConst;

-        }

-

-    }

-

-    class AbstractHoudiniErrorReporter : ProverInterface.ErrorHandler

-    {

-        public Model model;

-

-        public AbstractHoudiniErrorReporter()

-        {

-            model = null;

-        }

-

-        public override void OnModel(IList<string> labels, Model model, ProverInterface.Outcome proverOutcome)

-        {

-            Debug.Assert(model != null);

-            if(CommandLineOptions.Clo.PrintErrorModel >= 1) model.Write(Console.Out);

-            this.model = model;

-        }

-    }

-

-    public class AbsHoudiniInternalError : System.ApplicationException

-    {

-        public AbsHoudiniInternalError(string msg) : base(msg) { }

-

-    };

-

-    public class SimpleUtil

-    {

-        // Constructs a mapping from procedure names to the implementation

-        public static Dictionary<string, Implementation> nameImplMapping(Program p)

-        {

-            var m = new Dictionary<string, Implementation>();

-            foreach (var impl in p.Implementations)

-            {

-                m.Add(impl.Name, impl);

-            }

-

-            return m;

-        }

-

-        // is "assert true"?

-        public static bool isAssertTrue(Cmd cmd)

-        {

-            var acmd = cmd as AssertCmd;

-            if (acmd == null) return false;

-            var le = acmd.Expr as LiteralExpr;

-            if (le == null) return false;

-            if (le.IsTrue) return true;

-            return false;

-        }

-    }

-

-}

+using System;
+using System.Collections.Generic;
+using System.Linq;
+using System.Text;
+using Microsoft.Boogie;
+using Microsoft.Boogie.VCExprAST;
+using VC;
+using Outcome = VC.VCGen.Outcome;
+using Bpl = Microsoft.Boogie;
+using System.Diagnostics;
+using System.Diagnostics.Contracts;
+using Microsoft.Boogie.GraphUtil;
+
+namespace Microsoft.Boogie.Houdini {
+
+    public class AbsHoudini
+    {
+        Dictionary<string, Function> existentialFunctions;
+        Program program;
+        Dictionary<string, Implementation> name2Impl;
+        Dictionary<string, VCExpr> impl2VC;
+        Dictionary<string, List<Tuple<string, Function, NAryExpr>>> impl2FuncCalls;
+        // constant -> the naryexpr that it replaced
+        Dictionary<string, NAryExpr> constant2FuncCall;
+
+        // function -> its abstract value
+        Dictionary<string, IAbstractDomain> function2Value;
+
+        // impl -> functions assumed/asserted
+        Dictionary<string, HashSet<string>> impl2functionsAsserted, impl2functionsAssumed;
+
+        // funtions -> impls where assumed/asserted
+        Dictionary<string, HashSet<string>> function2implAssumed, function2implAsserted;
+
+        // impl -> handler, collector
+        Dictionary<string, Tuple<ProverInterface.ErrorHandler, AbsHoudiniCounterexampleCollector>> impl2ErrorHandler;
+
+        // Essentials: VCGen, Prover
+        VCGen vcgen;
+        ProverInterface prover;
+
+        // Stats
+        TimeSpan proverTime;
+        int numProverQueries;
+
+        public AbsHoudini(Program program, IAbstractDomain defaultElem)
+        {
+            this.program = program;
+            this.impl2VC = new Dictionary<string, VCExpr>();
+            this.impl2FuncCalls = new Dictionary<string, List<Tuple<string, Function, NAryExpr>>>();
+            this.existentialFunctions = new Dictionary<string, Function>();
+            this.name2Impl = new Dictionary<string, Implementation>();
+            this.impl2functionsAsserted = new Dictionary<string, HashSet<string>>();
+            this.impl2functionsAssumed = new Dictionary<string, HashSet<string>>();
+            this.function2implAsserted = new Dictionary<string, HashSet<string>>();
+            this.function2implAssumed = new Dictionary<string, HashSet<string>>();
+            this.impl2ErrorHandler = new Dictionary<string, Tuple<ProverInterface.ErrorHandler, AbsHoudiniCounterexampleCollector>>();
+            this.constant2FuncCall = new Dictionary<string, NAryExpr>();
+
+            // Find the existential functions
+            foreach (var func in program.Functions
+                .Where(f => QKeyValue.FindBoolAttribute(f.Attributes, "existential")))
+                existentialFunctions.Add(func.Name, func);
+
+            this.function2Value = new Dictionary<string, IAbstractDomain>();
+            foreach (var func in existentialFunctions.Values)
+            {
+                // Find if the function wishes to use a specific abstract domain
+                var domain = QKeyValue.FindStringAttribute(func.Attributes, "absdomain");
+                if (domain == null)
+                {
+                    function2Value[func.Name] = defaultElem.Bottom();
+                }
+                else
+                {
+                    function2Value[func.Name] = AbstractDomainFactory.GetInstance(domain);
+                }
+            }
+            existentialFunctions.Keys.Iter(f => function2implAssumed.Add(f, new HashSet<string>()));
+            existentialFunctions.Keys.Iter(f => function2implAsserted.Add(f, new HashSet<string>()));
+
+            // type check
+            existentialFunctions.Values.Iter(func =>
+                {
+                    if (func.OutParams.Count != 1 || !func.OutParams[0].TypedIdent.Type.IsBool)
+                        throw new AbsHoudiniInternalError(string.Format("Existential function {0} must return bool", func.Name));
+                    if(func.Body != null)
+                        throw new AbsHoudiniInternalError(string.Format("Existential function {0} should not have a body", func.Name));
+                    var args = new List<Type>();
+                    func.InParams.Iter(v => args.Add(v.TypedIdent.Type));
+                    string msg = "";
+                    if (!function2Value[func.Name].TypeCheck(args, out msg))
+                        throw new AbsHoudiniInternalError("TypeError: " + msg);
+                });
+
+            //if (CommandLineOptions.Clo.ProverKillTime > 0)
+            //    CommandLineOptions.Clo.ProverOptions.Add(string.Format("TIME_LIMIT={0}", CommandLineOptions.Clo.ProverKillTime));
+
+            Inline();
+
+            this.vcgen = new VCGen(program, CommandLineOptions.Clo.SimplifyLogFilePath, CommandLineOptions.Clo.SimplifyLogFileAppend, new List<Checker>());
+            this.prover = ProverInterface.CreateProver(program, CommandLineOptions.Clo.SimplifyLogFilePath, CommandLineOptions.Clo.SimplifyLogFileAppend, CommandLineOptions.Clo.ProverKillTime);
+
+            this.proverTime = TimeSpan.Zero;
+            this.numProverQueries = 0;
+
+            program.Implementations
+                .Where(impl => !impl.SkipVerification)
+                .Iter(impl => name2Impl.Add(impl.Name, impl));
+
+            // Let's do VC Gen (and also build dependencies)
+            name2Impl.Values.Iter(GenVC);
+        }
+
+        public VCGenOutcome ComputeSummaries()
+        {
+            var overallOutcome = new VCGenOutcome(ProverInterface.Outcome.Valid, new List<Counterexample>());
+
+            // Compute SCCs and determine a priority order for impls
+            var Succ = new Dictionary<string, HashSet<string>>();
+            var Pred = new Dictionary<string, HashSet<string>>();
+            name2Impl.Keys.Iter(s => Succ[s] = new HashSet<string>());
+            name2Impl.Keys.Iter(s => Pred[s] = new HashSet<string>());
+
+            foreach(var impl in name2Impl.Keys) {
+                Succ[impl] = new HashSet<string>();
+                impl2functionsAsserted[impl].Iter(f => 
+                    function2implAssumed[f].Iter(succ =>
+                        {
+                            Succ[impl].Add(succ);
+                            Pred[succ].Add(impl);
+                        }));
+            }
+
+            var sccs = new StronglyConnectedComponents<string>(name2Impl.Keys,
+                new Adjacency<string>(n => Pred[n]),
+                new Adjacency<string>(n => Succ[n]));
+            sccs.Compute();
+            
+            // impl -> priority
+            var impl2Priority = new Dictionary<string, int>();
+            int p = 0;
+            foreach (var scc in sccs)
+            {
+                foreach (var impl in scc)
+                {
+                    impl2Priority.Add(impl, p);
+                    p++;
+                }
+            }
+
+            var worklist = new SortedSet<Tuple<int, string>>();
+            name2Impl.Keys.Iter(k => worklist.Add(Tuple.Create(impl2Priority[k], k)));
+
+            while (worklist.Any())
+            {
+                var impl = worklist.First().Item2;
+                worklist.Remove(worklist.First());
+
+                var gen = prover.VCExprGen;
+                var terms = new List<Expr>();
+                foreach (var tup in impl2FuncCalls[impl])
+                {
+                    var controlVar = tup.Item2;
+                    var exprVars = tup.Item3;
+                    var varList = new List<Expr>();
+                    exprVars.Args.OfType<Expr>().Iter(v => varList.Add(v));
+                    
+                    var args = new List<Expr>();
+                    controlVar.InParams.Iter(v => args.Add(Expr.Ident(v)));
+                    Expr term = Expr.Eq(new NAryExpr(Token.NoToken, new FunctionCall(controlVar), args),
+                                 function2Value[tup.Item1].Gamma(varList));
+
+                    if (controlVar.InParams.Count != 0)
+                    {
+                        term = new ForallExpr(Token.NoToken, new List<Variable>(controlVar.InParams.ToArray()),
+                            new Trigger(Token.NoToken, true, new List<Expr> { new NAryExpr(Token.NoToken, new FunctionCall(controlVar), args) }),
+                            term);
+                    }
+                    terms.Add(term);
+                }
+                var env = Expr.BinaryTreeAnd(terms);
+
+                env.Typecheck(new TypecheckingContext((IErrorSink)null));
+                var envVC = prover.Context.BoogieExprTranslator.Translate(env);
+
+                var vc = gen.Implies(envVC, impl2VC[impl]);
+
+                if (CommandLineOptions.Clo.Trace)
+                {
+                    Console.WriteLine("Verifying {0}: ", impl);
+                    //Console.WriteLine("env: {0}", envVC);
+                    var envFuncs = new HashSet<string>();
+                    impl2FuncCalls[impl].Iter(tup => envFuncs.Add(tup.Item1));
+                    envFuncs.Iter(f => PrintFunction(existentialFunctions[f]));
+                }
+
+                var handler = impl2ErrorHandler[impl].Item1;
+                var collector = impl2ErrorHandler[impl].Item2;
+                collector.Reset(impl);
+
+                var start = DateTime.Now;
+
+                prover.Push();
+                prover.Assert(gen.Not(vc), true);
+                prover.FlushAxiomsToTheoremProver();
+                prover.Check();
+                ProverInterface.Outcome proverOutcome = prover.CheckOutcomeCore(handler);
+
+                //prover.BeginCheck(impl, vc, handler);
+                //ProverInterface.Outcome proverOutcome = prover.CheckOutcomeCore(handler);
+
+                var inc = (DateTime.Now - start);
+                proverTime += inc;
+                numProverQueries++;
+
+                if (CommandLineOptions.Clo.Trace)
+                    Console.WriteLine("Time taken = " + inc.TotalSeconds.ToString());
+
+                if (proverOutcome == ProverInterface.Outcome.TimeOut || proverOutcome == ProverInterface.Outcome.OutOfMemory)
+                {
+                    // pick some function; make it true and keep going
+                    bool changed = false;
+                    foreach (var f in impl2functionsAsserted[impl])
+                    {
+                        function2Value[f] = function2Value[f].MakeTop(out changed);
+                        if (changed) break;
+                    }
+                    if(!changed)
+                        return new VCGenOutcome(proverOutcome, new List<Counterexample>());
+                }
+
+                if (CommandLineOptions.Clo.Trace)
+                    Console.WriteLine(collector.numErrors > 0 ? "SAT" : "UNSAT");
+
+                if (collector.numErrors > 0)
+                {
+                    var funcsChanged = collector.funcsChanged;
+                    if (funcsChanged.Count == 0)
+                    {
+                        overallOutcome = new VCGenOutcome(ProverInterface.Outcome.Invalid, collector.errors);
+                        break;
+                    }
+
+                    // propagate dependent guys back into the worklist, including self
+                    var deps = new HashSet<string>();
+                    deps.Add(impl);
+                    funcsChanged.Iter(f => deps.UnionWith(function2implAssumed[f]));
+
+                    deps.Iter(s => worklist.Add(Tuple.Create(impl2Priority[s], s)));
+                }
+
+                prover.Pop();
+            }
+
+            if (CommandLineOptions.Clo.Trace)
+            {
+                Console.WriteLine("Prover time = {0}", proverTime.TotalSeconds.ToString("F2"));
+                Console.WriteLine("Number of prover queries = " + numProverQueries);
+            }
+
+            if (CommandLineOptions.Clo.PrintAssignment)
+            {
+                // Print the answer
+                existentialFunctions.Values.Iter(PrintFunction);
+            }
+
+            return overallOutcome;
+        }
+
+
+        public IEnumerable<Function> GetAssignment()
+        {
+            var ret = new List<Function>();
+            foreach (var func in existentialFunctions.Values)
+            {
+                var invars = new List<Expr>(func.InParams.OfType<Variable>().Select(v => Expr.Ident(v)));
+                func.Body = function2Value[func.Name].Gamma(invars);
+                ret.Add(func);
+            }
+            return ret;
+        }
+
+        private void PrintFunction(Function function)
+        {
+            var tt = new TokenTextWriter(Console.Out, /*pretty=*/ false);
+            var invars = new List<Expr>(function.InParams.OfType<Variable>().Select(v => Expr.Ident(v)));
+            function.Body = function2Value[function.Name].Gamma(invars);
+            function.Emit(tt, 0);
+            tt.Close();
+        }
+
+        public HashSet<string> HandleCounterExample(string impl, Counterexample error)
+        {
+            var funcsChanged = new HashSet<string>();
+            // Find the failing assert -- need to do a join there
+            // return the set of functions whose definition has changed
+            var cex = ExtractState(impl, error);
+            foreach (var tup in cex)
+            {
+                function2Value[tup.Item1] = function2Value[tup.Item1].Join(tup.Item2);
+                funcsChanged.Add(tup.Item1);
+            }
+            return funcsChanged;
+        }
+
+        private List<Tuple<string, List<Model.Element>>> ExtractState(string impl, Counterexample error)
+        {
+            var lastBlock = error.Trace.Last() as Block;
+            AssertCmd failingAssert = null;
+
+            CallCounterexample callCounterexample = error as CallCounterexample;
+            if (callCounterexample != null)
+            {
+                Procedure failingProcedure = callCounterexample.FailingCall.Proc;
+                Requires failingRequires = callCounterexample.FailingRequires;
+                failingAssert = lastBlock.Cmds.OfType<AssertRequiresCmd>().FirstOrDefault(ac => ac.Requires == failingRequires);
+            }
+            ReturnCounterexample returnCounterexample = error as ReturnCounterexample;
+            if (returnCounterexample != null)
+            {
+                Ensures failingEnsures = returnCounterexample.FailingEnsures;
+                failingAssert = lastBlock.Cmds.OfType<AssertEnsuresCmd>().FirstOrDefault(ac => ac.Ensures == failingEnsures);
+            }
+            AssertCounterexample assertCounterexample = error as AssertCounterexample;
+            if (assertCounterexample != null)
+            {
+                failingAssert = lastBlock.Cmds.OfType<AssertCmd>().FirstOrDefault(ac => ac == assertCounterexample.FailingAssert);
+            }
+
+            Debug.Assert(failingAssert != null);
+            return ExtractState(impl, failingAssert.Expr, error.Model);
+        }
+
+        private static int existentialConstCounter = 0;
+
+        private List<Tuple<string, List<Model.Element>>> ExtractState(string impl, Expr expr, Model model)
+        {
+            var funcsUsed = FunctionCollector.Collect(expr);
+
+            var ret = new List<Tuple<string, List<Model.Element>>>();
+
+            foreach (var tup in funcsUsed.Where(t => t.Item2 == null))
+            {
+                var constant = tup.Item1;
+                if (!constant2FuncCall.ContainsKey(constant.Name))
+                    continue;
+
+                var func = constant2FuncCall[constant.Name];
+                var funcName = (func.Fun as FunctionCall).FunctionName;
+                var vals = new List<Model.Element>();
+                prover.Context.BoogieExprTranslator.Translate(func.Args).Iter(ve => vals.Add(getValue(ve, model)));
+                ret.Add(Tuple.Create(funcName, vals));
+            }
+
+            foreach (var tup in funcsUsed.Where(t => t.Item2 != null))
+            {
+                var constant = tup.Item1;
+                var boundExpr = tup.Item2;
+
+                if (!constant2FuncCall.ContainsKey(constant.Name))
+                    continue;
+
+                // There are some bound variables (because the existential function was inside an \exists).
+                // We must find an assignment for bound varibles 
+
+                // First, peice apart the existential functions
+                var cd = new Duplicator();
+                var tup2 = ExistentialExprModelMassage.Massage(cd.VisitExpr(boundExpr.Body));
+                var be = tup2.Item1;
+                Expr env = Expr.True;
+                foreach (var ahFunc in tup2.Item2)
+                {
+                    var tup3 = impl2FuncCalls[impl].First(t => t.Item2.Name == ahFunc.Name);
+                    var varList = new List<Expr>();
+                    tup3.Item3.Args.OfType<Expr>().Iter(v => varList.Add(v));
+
+                    env = Expr.And(env, function2Value[tup3.Item1].Gamma(varList));
+                }
+                be = Expr.And(be, Expr.Not(env));
+
+                // map formals to constants
+                var formalToConstant = new Dictionary<string, Constant>();
+                foreach (var f in boundExpr.Dummies.OfType<Variable>())
+                    formalToConstant.Add(f.Name, new Constant(Token.NoToken, new TypedIdent(Token.NoToken, f.Name + "@subst@" + (existentialConstCounter++), f.TypedIdent.Type), false));
+                be = Substituter.Apply(new Substitution(v => formalToConstant.ContainsKey(v.Name) ? Expr.Ident(formalToConstant[v.Name]) : Expr.Ident(v)), be);
+                formalToConstant.Values.Iter(v => prover.Context.DeclareConstant(v, false, null));
+
+                var reporter = new AbstractHoudiniErrorReporter();
+                var ve = prover.Context.BoogieExprTranslator.Translate(be);
+                prover.Assert(ve, true);
+                prover.Check();
+                var proverOutcome = prover.CheckOutcomeCore(reporter);
+                if (proverOutcome != ProverInterface.Outcome.Invalid)
+                    continue;
+                model = reporter.model;
+
+                var func = constant2FuncCall[constant.Name];
+                var funcName = (func.Fun as FunctionCall).FunctionName;
+                var vals = new List<Model.Element>();
+                foreach (var funcArg in func.Args.OfType<Expr>())
+                {
+                    var arg = Substituter.Apply(new Substitution(v => formalToConstant.ContainsKey(v.Name) ? Expr.Ident(formalToConstant[v.Name]) : Expr.Ident(v)), funcArg);
+                    vals.Add(getValue(prover.Context.BoogieExprTranslator.Translate(arg), model));
+                }
+                ret.Add(Tuple.Create(funcName, vals));
+
+            }
+
+            return ret;
+        }
+
+        private Model.Element getValue(VCExpr arg, Model model)
+        {
+
+
+            if (arg is VCExprLiteral)
+            {
+                //return model.GetElement(arg.ToString());
+                return model.MkElement(arg.ToString());
+            }
+
+            else if (arg is VCExprVar)
+            {
+                var el = model.TryGetFunc(prover.Context.Lookup(arg as VCExprVar));
+                if (el != null)
+                {
+                    Debug.Assert(el.Arity == 0 && el.AppCount == 1);
+                    return el.Apps.First().Result;
+                }
+                else
+                {
+                    // Variable not defined; assign arbitrary value
+                    if (arg.Type.IsBool)
+                        return model.MkElement("false");
+                    else if (arg.Type.IsInt)
+                        return model.MkIntElement(0);
+                    else
+                        return null;
+                }
+            }
+            else if (arg is VCExprNAry && (arg as VCExprNAry).Op is VCExprBvOp)
+            {
+                // support for BV constants
+                var bvc = (arg as VCExprNAry)[0] as VCExprLiteral;
+                if (bvc != null)
+                {
+                    var ret = model.TryMkElement(bvc.ToString() + arg.Type.ToString());
+                    if (ret != null && (ret is Model.BitVector)) return ret;
+                }
+            }
+
+            object val;
+
+            try
+            {
+                val = prover.Evaluate(arg);
+            }
+            catch (ProverInterface.VCExprEvaluationException)
+            {
+                Console.WriteLine("AbsHoudni: Error evaluating expression {0}", arg);
+                throw;
+            }
+
+            if (val is int || val is bool || val is Microsoft.Basetypes.BigNum)
+            {
+                return model.MkElement(val.ToString());
+            }
+            else
+            {
+                Debug.Assert(false);
+            }
+            return null;
+        }
+
+        // Remove functions AbsHoudiniConstant from the expressions and substitute them with "true"
+        class ExistentialExprModelMassage : StandardVisitor
+        {
+            List<Function> ahFuncs;
+
+            public ExistentialExprModelMassage()
+            {
+                ahFuncs = new List<Function>();
+            }
+
+            public static Tuple<Expr, List<Function>> Massage(Expr expr)
+            {
+                var ee = new ExistentialExprModelMassage();
+                expr = ee.VisitExpr(expr);
+                return Tuple.Create(expr, ee.ahFuncs);
+            }
+
+            public override Expr VisitNAryExpr(NAryExpr node)
+            {
+                if (node.Fun is FunctionCall && (node.Fun as FunctionCall).FunctionName.StartsWith("AbsHoudiniConstant"))
+                {
+                    ahFuncs.Add((node.Fun as FunctionCall).Func);
+                    return Expr.True;
+                }
+
+                return base.VisitNAryExpr(node);
+            }
+        }
+
+        class FunctionCollector : ReadOnlyVisitor
+        {
+            public List<Tuple<Function, ExistsExpr>> functionsUsed;
+            ExistsExpr existentialExpr;
+
+            public FunctionCollector()
+            {
+                functionsUsed = new List<Tuple<Function, ExistsExpr>>();
+                existentialExpr = null;
+            }
+
+            public static List<Tuple<Function, ExistsExpr>> Collect(Expr expr)
+            {
+                var fv = new FunctionCollector();
+                fv.VisitExpr(expr);
+                return fv.functionsUsed;
+            }
+
+            public override QuantifierExpr VisitQuantifierExpr(QuantifierExpr node)
+            {
+                var oldE = existentialExpr;
+
+                if (node is ExistsExpr)
+                    existentialExpr = (node as ExistsExpr);
+
+                node = base.VisitQuantifierExpr(node);
+
+                existentialExpr = oldE;
+                return node;
+            }
+
+            public override Expr VisitNAryExpr(NAryExpr node)
+            {
+                if (node.Fun is FunctionCall)
+                {
+                    var collector = new VariableCollector();
+                    collector.Visit(node);
+
+                    if(existentialExpr != null && existentialExpr.Dummies.Intersect(collector.usedVars).Any())
+                        functionsUsed.Add(Tuple.Create((node.Fun as FunctionCall).Func, existentialExpr));
+                    else
+                        functionsUsed.Add(Tuple.Create<Function, ExistsExpr>((node.Fun as FunctionCall).Func, null));
+                }
+
+                return base.VisitNAryExpr(node);
+            }
+        }
+
+        class AbsHoudiniCounterexampleCollector : VerifierCallback
+        {
+            public HashSet<string> funcsChanged;
+            public string currImpl;
+            public int numErrors;
+            public List<Counterexample> errors;
+
+            AbsHoudini container;
+
+            public AbsHoudiniCounterexampleCollector(AbsHoudini container)
+            {
+                this.container = container;
+                Reset(null);
+            }
+
+            public void Reset(string impl)
+            {
+                funcsChanged = new HashSet<string>();
+                currImpl = impl;
+                numErrors = 0;
+                errors = new List<Counterexample>();
+            }
+
+            public override void OnCounterexample(Counterexample ce, string reason)
+            {
+                numErrors++;
+                errors.Add(ce);
+
+                funcsChanged.UnionWith(
+                    container.HandleCounterExample(currImpl, ce));
+            }
+        }
+
+        private void GenVC(Implementation impl)
+        {
+            ModelViewInfo mvInfo;
+            Dictionary<int, Absy> label2absy;
+            var collector = new AbsHoudiniCounterexampleCollector(this);
+            collector.OnProgress("HdnVCGen", 0, 0, 0.0);
+
+            if (CommandLineOptions.Clo.Trace)
+            {
+                Console.WriteLine("Generating VC of {0}", impl.Name);
+            }
+
+            vcgen.ConvertCFG2DAG(impl);
+            var gotoCmdOrigins = vcgen.PassifyImpl(impl, out mvInfo);
+
+            // Inline functions
+            (new InlineFunctionCalls()).VisitBlockList(impl.Blocks);
+
+            
+            StripOutermostForall(impl);
+            //ExtractQuantifiedExprs(impl);
+            ExtractBoolExprs(impl);
+
+            //CommandLineOptions.Clo.PrintInstrumented = true;
+            //using (var tt = new TokenTextWriter(Console.Out))
+            //    impl.Emit(tt, 0);
+
+            // Intercept the FunctionCalls of the existential functions, and replace them with Boolean constants
+            var existentialFunctionNames = new HashSet<string>(existentialFunctions.Keys);
+            var fv = new ReplaceFunctionCalls(existentialFunctionNames);
+            fv.VisitBlockList(impl.Blocks);
+
+            //using (var tt = new TokenTextWriter(Console.Out))
+            //    impl.Emit(tt, 0);
+
+
+            impl2functionsAsserted.Add(impl.Name, fv.functionsAsserted);
+            impl2functionsAssumed.Add(impl.Name, fv.functionsAssumed);
+
+            fv.functionsAssumed.Iter(f => function2implAssumed[f].Add(impl.Name));
+            fv.functionsAsserted.Iter(f => function2implAsserted[f].Add(impl.Name));
+
+            impl2FuncCalls.Add(impl.Name, fv.functionsUsed);
+            fv.functionsUsed.Iter(tup => constant2FuncCall.Add(tup.Item2.Name, tup.Item3));
+
+            var gen = prover.VCExprGen;
+            VCExpr controlFlowVariableExpr = CommandLineOptions.Clo.UseLabels ? null : gen.Integer(Microsoft.Basetypes.BigNum.ZERO);
+
+            var vcexpr = vcgen.GenerateVC(impl, controlFlowVariableExpr, out label2absy, prover.Context);
+            if (!CommandLineOptions.Clo.UseLabels)
+            {
+                VCExpr controlFlowFunctionAppl = gen.ControlFlowFunctionApplication(gen.Integer(Microsoft.Basetypes.BigNum.ZERO), gen.Integer(Microsoft.Basetypes.BigNum.ZERO));
+                VCExpr eqExpr = gen.Eq(controlFlowFunctionAppl, gen.Integer(Microsoft.Basetypes.BigNum.FromInt(impl.Blocks[0].UniqueId)));
+                vcexpr = gen.Implies(eqExpr, vcexpr);
+            }
+
+            ProverInterface.ErrorHandler handler = null;
+            if (CommandLineOptions.Clo.vcVariety == CommandLineOptions.VCVariety.Local)
+                handler = new VCGen.ErrorReporterLocal(gotoCmdOrigins, label2absy, impl.Blocks, vcgen.incarnationOriginMap, collector, mvInfo, prover.Context, program);
+            else
+                handler = new VCGen.ErrorReporter(gotoCmdOrigins, label2absy, impl.Blocks, vcgen.incarnationOriginMap, collector, mvInfo, prover.Context, program);
+
+            impl2ErrorHandler.Add(impl.Name, Tuple.Create(handler, collector));
+
+            //Console.WriteLine("VC of {0}: {1}", impl.Name, vcexpr);
+
+            // Create a macro so that the VC can sit with the theorem prover
+            Macro macro = new Macro(Token.NoToken, impl.Name + "Macro", new List<Variable>(), new Formal(Token.NoToken, new TypedIdent(Token.NoToken, "", Bpl.Type.Bool), false));
+            prover.DefineMacro(macro, vcexpr);
+
+            // Store VC
+            impl2VC.Add(impl.Name, gen.Function(macro));
+
+            // HACK: push the definitions of constants involved in function calls
+            // It is possible that some constants only appear in function calls. Thus, when
+            // they are replaced by Boolean constants, it is possible that (get-value) will 
+            // fail if the expression involves such constants. All we need to do is make sure
+            // these constants are declared, because otherwise, semantically we are doing
+            // the right thing.
+            foreach (var tup in fv.functionsUsed)
+            {
+                // Ignore ones with bound varibles
+                if (tup.Item2.InParams.Count > 0) continue;
+                var tt = prover.Context.BoogieExprTranslator.Translate(tup.Item3);
+                tt = prover.VCExprGen.Or(VCExpressionGenerator.True, tt);
+                prover.Assert(tt, true);
+            }
+        }
+
+        // convert "foo(... forall e ...) to:
+        //    (p iff forall e) ==> foo(... p ...) 
+        // where p is a fresh boolean variable and foo is an existential constant
+        private void ExtractQuantifiedExprs(Implementation impl)
+        {
+            var funcs = new HashSet<string>(existentialFunctions.Keys);
+            foreach (var blk in impl.Blocks)
+            {
+                foreach (var acmd in blk.Cmds.OfType<AssertCmd>())
+                {
+                    var ret = ExtractQuantifiers.Extract(acmd.Expr, funcs);
+                    acmd.Expr = ret.Item1;
+                    impl.LocVars.AddRange(ret.Item2);
+                }
+            }
+        }
+
+        // convert "foo(... e ...) to:
+        //    (p iff e) ==> foo(... p ...) 
+        // where p is a fresh boolean variable, foo is an existential constant
+        // and e is a Boolean-typed argument of foo
+        private void ExtractBoolExprs(Implementation impl)
+        {
+            var funcs = new HashSet<string>(existentialFunctions.Keys);
+            foreach (var blk in impl.Blocks)
+            {
+                foreach (var acmd in blk.Cmds.OfType<AssertCmd>())
+                {
+                    var ret = ExtractBoolArgs.Extract(acmd.Expr, funcs);
+                    acmd.Expr = ret.Item1;
+                    impl.LocVars.AddRange(ret.Item2);
+                }
+            }
+        }
+
+        // convert "assert e1 && forall x: e2" to
+        //    assert e1 && e2[x <- x@bound]
+        private void StripOutermostForall(Implementation impl)
+        {
+            var funcs = new HashSet<string>(existentialFunctions.Keys);
+            foreach (var blk in impl.Blocks)
+            {
+                foreach (var acmd in blk.Cmds.OfType<AssertCmd>())
+                {
+                    var ret = StripQuantifiers.Run(acmd.Expr, funcs);
+                    acmd.Expr = ret.Item1;
+                    impl.LocVars.AddRange(ret.Item2);
+                }
+            }
+        }
+
+        private void Inline()
+        {
+            if (CommandLineOptions.Clo.InlineDepth < 0)
+                return;
+
+            var callGraph = BuildCallGraph();
+
+            foreach (Implementation impl in callGraph.Nodes)
+            {
+                InlineEnsuresVisitor inlineEnsuresVisitor = new InlineEnsuresVisitor();
+                inlineEnsuresVisitor.Visit(impl);
+            }
+
+            foreach (Implementation impl in callGraph.Nodes)
+            {
+                impl.OriginalBlocks = impl.Blocks;
+                impl.OriginalLocVars = impl.LocVars;
+            }
+            foreach (Implementation impl in callGraph.Nodes)
+            {
+                CommandLineOptions.Inlining savedOption = CommandLineOptions.Clo.ProcedureInlining;
+                CommandLineOptions.Clo.ProcedureInlining = CommandLineOptions.Inlining.Spec;
+                Inliner.ProcessImplementationForHoudini(program, impl);
+                CommandLineOptions.Clo.ProcedureInlining = savedOption;
+            }
+            foreach (Implementation impl in callGraph.Nodes)
+            {
+                impl.OriginalBlocks = null;
+                impl.OriginalLocVars = null;
+            }
+
+            Graph<Implementation> oldCallGraph = callGraph;
+            callGraph = new Graph<Implementation>();
+            foreach (Implementation impl in oldCallGraph.Nodes)
+            {
+                callGraph.AddSource(impl);
+            }
+            foreach (Tuple<Implementation, Implementation> edge in oldCallGraph.Edges)
+            {
+                callGraph.AddEdge(edge.Item1, edge.Item2);
+            }
+            int count = CommandLineOptions.Clo.InlineDepth;
+            while (count > 0)
+            {
+                foreach (Implementation impl in oldCallGraph.Nodes)
+                {
+                    List<Implementation> newNodes = new List<Implementation>();
+                    foreach (Implementation succ in callGraph.Successors(impl))
+                    {
+                        newNodes.AddRange(oldCallGraph.Successors(succ));
+                    }
+                    foreach (Implementation newNode in newNodes)
+                    {
+                        callGraph.AddEdge(impl, newNode);
+                    }
+                }
+                count--;
+            }
+        }
+
+        private Graph<Implementation> BuildCallGraph()
+        {
+            Graph<Implementation> callGraph = new Graph<Implementation>();
+            Dictionary<Procedure, HashSet<Implementation>> procToImpls = new Dictionary<Procedure, HashSet<Implementation>>();
+            foreach (var proc in program.Procedures)
+            {
+                procToImpls[proc] = new HashSet<Implementation>();
+            }
+            foreach (var impl in program.Implementations)
+            {
+                if (impl.SkipVerification) continue;
+                callGraph.AddSource(impl);
+                procToImpls[impl.Proc].Add(impl);
+            }
+            foreach (var impl in program.Implementations)
+            {
+                if (impl.SkipVerification) continue;
+                foreach (Block b in impl.Blocks)
+                {
+                    foreach (Cmd c in b.Cmds)
+                    {
+                        CallCmd cc = c as CallCmd;
+                        if (cc == null) continue;
+                        foreach (Implementation callee in procToImpls[cc.Proc])
+                        {
+                            callGraph.AddEdge(impl, callee);
+                        }
+                    }
+                }
+            }
+            return callGraph;
+        }
+
+    }
+
+    class InlineFunctionCalls : StandardVisitor
+    {
+        public Stack<string> inlinedFunctionsStack;
+
+        public InlineFunctionCalls()
+        {
+            inlinedFunctionsStack = new Stack<string>();
+        }
+
+        public override Expr VisitNAryExpr(NAryExpr node)
+        {
+            var fc = node.Fun as FunctionCall;
+            if (fc != null && fc.Func.Body != null && QKeyValue.FindBoolAttribute(fc.Func.Attributes, "inline"))
+            {
+                if (inlinedFunctionsStack.Contains(fc.Func.Name))
+                {
+                    // recursion detected
+                    throw new AbsHoudiniInternalError("Recursion detected in function declarations");
+                }
+
+                // create a substitution
+                var subst = new Dictionary<Variable, Expr>();
+                for (int i = 0; i < node.Args.Count; i++)
+                {
+                    subst.Add(fc.Func.InParams[i], node.Args[i]);
+                }
+
+                var e =
+                    Substituter.Apply(new Substitution(v => subst.ContainsKey(v) ? subst[v] : Expr.Ident(v)), fc.Func.Body);
+
+                inlinedFunctionsStack.Push(fc.Func.Name);
+
+                e = base.VisitExpr(e);
+
+                inlinedFunctionsStack.Pop();
+
+                return e;
+            }
+            return base.VisitNAryExpr(node);
+        }
+    }
+
+    class ReplaceFunctionCalls : StandardVisitor
+    {
+        public List<Tuple<string, Function, NAryExpr>> functionsUsed;
+        public List<Function> boolConstants;
+
+        public HashSet<string> functionsAssumed;
+        public HashSet<string> functionsAsserted;
+        HashSet<string> functionsToReplace;
+
+        private bool inAssume;
+        private bool inAssert;
+        private bool inFunction;
+        private List<Dictionary<string, Variable>> boundVars;
+        private static int IdCounter = 0;
+
+        public ReplaceFunctionCalls(HashSet<string> functionsToReplace)
+        {
+            this.functionsUsed = new List<Tuple<string, Function, NAryExpr>>();
+            this.functionsToReplace = functionsToReplace;
+            this.functionsAsserted = new HashSet<string>();
+            this.functionsAssumed = new HashSet<string>();
+            this.boolConstants = new List<Function>();
+            this.boundVars = new List<Dictionary<string, Variable>>();
+
+            inAssume = false;
+            inAssert = false;
+            inFunction = false;
+        }
+
+        public override Cmd VisitAssertCmd(AssertCmd node)
+        {
+            inAssert = true;
+            var ret = base.VisitAssertCmd(node);
+            inAssert = false;
+            return ret;
+        }
+
+        public override Cmd VisitAssertEnsuresCmd(AssertEnsuresCmd node)
+        {
+            return this.VisitAssertCmd(node);
+        }
+
+        public override Cmd VisitAssertRequiresCmd(AssertRequiresCmd node)
+        {
+            return this.VisitAssertCmd(node);
+        }
+
+        public override Cmd VisitAssumeCmd(AssumeCmd node)
+        {
+            inAssume = true;
+            var ret = base.VisitAssumeCmd(node);
+            inAssume = false;
+            return ret;
+        }
+
+        public override QuantifierExpr VisitQuantifierExpr(QuantifierExpr node)
+        {
+            // gather the quantified variables
+            var dummies = new Dictionary<string, Variable>();
+            node.Dummies.Iter(v => dummies.Add(v.Name, v));
+
+            boundVars.Add(dummies);
+
+            node = base.VisitQuantifierExpr(node);
+
+            boundVars.RemoveAt(boundVars.Count - 1);
+
+            return node;
+        }
+
+        public override Expr VisitNAryExpr(NAryExpr node)
+        {
+            var inF = inFunction;
+
+            if (node.Fun is FunctionCall && functionsToReplace.Contains((node.Fun as FunctionCall).FunctionName))
+            {                
+                found((node.Fun as FunctionCall).FunctionName);
+                inFunction = true;
+
+                // collect all the variables used by this function
+                var collector = new VariableCollector();
+                collector.VisitExpr(node);
+
+                // Find the outermost bound variables
+                var bound = new List<Variable>();
+                if(boundVars.Count > 0) 
+                    bound.AddRange(collector.usedVars.Intersect(boundVars[0].Values));
+
+                // create boolean function to replace this guy
+                var constant = new Function(Token.NoToken, "AbsHoudiniConstant" + IdCounter, bound,
+                    new Formal(Token.NoToken, new TypedIdent(Token.NoToken, "r", Microsoft.Boogie.Type.Bool), false));
+                IdCounter++;
+                
+                functionsUsed.Add(Tuple.Create((node.Fun as FunctionCall).FunctionName, constant, node));
+                boolConstants.Add(constant);
+
+                var args = new List<Expr>();
+                bound.OfType<Variable>().Select(v => Expr.Ident(v)).Iter(v => args.Add(v));
+                return new NAryExpr(Token.NoToken, new FunctionCall(constant), args);
+            }
+            var ret = base.VisitNAryExpr(node);
+
+            inFunction = inF;
+
+            return ret;
+        }
+
+        public override Expr VisitIdentifierExpr(IdentifierExpr node)
+        {
+            if (inFunction)
+            {
+                // Inside functions we can only refer to the outermost bound variables
+                for (int i = boundVars.Count - 1; i >= 1; i--)
+                {
+                    if (boundVars[i].ContainsKey(node.Name))
+                        throw new AbsHoudiniInternalError("Existential functions can only refer to outermost bound variables in an expression");
+                }
+            }
+
+            return base.VisitIdentifierExpr(node);
+        }
+
+        private void found(string func)
+        {
+            if (inAssume) functionsAssumed.Add(func);
+            if (inAssert) functionsAsserted.Add(func);
+        }
+
+    }
+
+    // convert "foo(... e ...) to:
+    //    (p iff e) ==> foo(... p ...) 
+    // where p is a fresh boolean variable, foo is an existential constant
+    // and e is a Boolean-typed argument of foo
+    class ExtractBoolArgs : StandardVisitor
+    {
+        static int freshConstCounter = 0;
+        HashSet<string> existentialFunctions;
+        HashSet<Constant> newConstants;
+
+        private ExtractBoolArgs(HashSet<string> existentialFunctions)
+        {
+            this.existentialFunctions = existentialFunctions;
+            this.newConstants = new HashSet<Constant>();
+        }
+
+        public static Tuple<Expr, IEnumerable<Constant>> Extract(Expr expr, HashSet<string> existentialFunctions)
+        {
+            var eq = new ExtractBoolArgs(existentialFunctions);
+            expr = eq.VisitExpr(expr);
+            return Tuple.Create(expr, eq.newConstants.AsEnumerable());
+        }
+
+        public override Expr VisitNAryExpr(NAryExpr node)
+        {
+            if (node.Fun is FunctionCall && existentialFunctions.Contains((node.Fun as FunctionCall).FunctionName))
+            {
+                var constants = new Dictionary<Constant, Expr>();
+                for (int i = 0; i < node.Args.Count; i++)
+                {
+                    if (node.Args[i].Type == Type.Bool)
+                    {
+                        var constant = new Constant(Token.NoToken, new TypedIdent(Token.NoToken,
+                            "boolArg@const" + freshConstCounter, Microsoft.Boogie.Type.Bool), false);
+                        freshConstCounter++;
+                        constants.Add(constant, node.Args[i]);
+                        node.Args[i] = Expr.Ident(constant);
+                    }
+                }
+
+                newConstants.UnionWith(constants.Keys);
+
+                Expr ret = Expr.True;
+                foreach (var tup in constants)
+                {
+                    ret = Expr.And(ret, Expr.Eq(Expr.Ident(tup.Key), tup.Value));
+                }
+                return Expr.Imp(ret, node);
+            } 
+
+            return base.VisitNAryExpr(node);
+        }
+    }
+
+
+    // convert "foo(... forall e ...) to:
+    //    (p iff forall e) ==> foo(... p ...) 
+    // where p is a fresh boolean variable and foo is an existential constant
+    class ExtractQuantifiers : StandardVisitor
+    {
+        static int freshConstCounter = 0;
+        HashSet<string> existentialFunctions;
+        bool insideExistential;
+        Dictionary<Constant, Expr> newConstants;
+
+        private ExtractQuantifiers(HashSet<string> existentialFunctions)
+        {
+            this.existentialFunctions = existentialFunctions;
+            insideExistential = false;
+            newConstants = new Dictionary<Constant, Expr>();
+        }
+
+        public static Tuple<Expr, IEnumerable<Constant>> Extract(Expr expr, HashSet<string> existentialFunctions)
+        {
+            var eq = new ExtractQuantifiers(existentialFunctions);
+            expr = eq.VisitExpr(expr);
+            Expr ret = Expr.True;
+            foreach (var tup in eq.newConstants)
+            {
+                ret = Expr.And(ret, Expr.Eq(Expr.Ident(tup.Key), tup.Value));
+            }
+            ret = Expr.Imp(ret, expr);
+            return Tuple.Create(ret, eq.newConstants.Keys.AsEnumerable());
+        }
+
+        public override Expr VisitNAryExpr(NAryExpr node)
+        {
+            var oldIE = insideExistential;
+
+            if (node.Fun is FunctionCall && existentialFunctions.Contains((node.Fun as FunctionCall).FunctionName))
+                insideExistential = true;
+
+            var ret = base.VisitNAryExpr(node);
+
+            insideExistential = oldIE;
+            return ret;
+        }
+
+        public override Expr VisitExpr(Expr node)
+        {
+            if (node is QuantifierExpr)
+            {
+                return MyVisitQuantifierExpr(node as QuantifierExpr);
+            }
+            return base.VisitExpr(node);
+        }
+
+        public Expr MyVisitQuantifierExpr(QuantifierExpr node)
+        {
+            node = base.VisitQuantifierExpr(node);
+
+            if (insideExistential)
+            {
+                var constant = new Constant(Token.NoToken, new TypedIdent(Token.NoToken,
+                    "quant@const" + freshConstCounter, Microsoft.Boogie.Type.Bool), false);
+                freshConstCounter++;
+
+                newConstants.Add(constant, node);
+
+                return Expr.Ident(constant);                
+            }
+
+            return node;
+        }
+    }
+
+    // convert "assert e1 && forall x: e2" to
+    //    assert e1 && e2[x <- x@bound]
+    // only if e2 has an existential function
+    class StripQuantifiers : StandardVisitor
+    {
+        static int boundVarCounter = 0;
+        
+        // 0 -> None, 1 -> Forall, 2 -> Exists, 3 -> Nested
+        int insideQuantifier; 
+
+        bool searchExistentialFunction;
+        bool foundExistentialFunction;
+
+        HashSet<string> existentialFunctions;
+        Dictionary<string, LocalVariable> subst;
+        List<LocalVariable> LocalsToAdd;
+
+        private StripQuantifiers(HashSet<string> existentialFunctions)
+        {
+            this.existentialFunctions = existentialFunctions;
+            insideQuantifier = 0;
+            searchExistentialFunction = false;
+            foundExistentialFunction = false;
+            LocalsToAdd = new List<LocalVariable>();
+            subst = null;
+        }
+
+        public static Tuple<Expr,List<LocalVariable>> Run(Expr expr, HashSet<string> existentialFunctions)
+        {
+            // check for type errors first
+            var sq = new StripQuantifiers(existentialFunctions);
+            var ret = sq.VisitExpr(expr);
+
+            return Tuple.Create(ret, sq.LocalsToAdd);
+        }
+
+        public override Expr VisitExpr(Expr node)
+        {
+            if (node is QuantifierExpr)
+            {
+                return MyVisitQuantifierExpr(node as QuantifierExpr);
+            }
+
+            return base.VisitExpr(node);
+        }
+
+        private Expr MyVisitQuantifierExpr(QuantifierExpr node)
+        {
+            var oldIQ = insideQuantifier;
+            Expr ret = node;
+
+            // update "insideQuantifier"
+            if (insideQuantifier == 0)
+            {
+                if (node is ForallExpr) insideQuantifier = 1;
+                else insideQuantifier = 2;
+            }
+            else if (insideQuantifier > 0)
+            {
+                insideQuantifier = 3;
+            }
+
+            // Going inside Forall?
+            if (insideQuantifier == 1)
+            {
+                // see if there is any existential function inside
+                searchExistentialFunction = true;
+                foundExistentialFunction = false;
+                base.VisitQuantifierExpr(node);
+
+                if (foundExistentialFunction)
+                {
+                    // create substitution to apply
+                    subst = new Dictionary<string, LocalVariable>();
+                    foreach (var bv in node.Dummies.OfType<Variable>())
+                    {
+                        var lv = new LocalVariable(Token.NoToken, new TypedIdent(Token.NoToken,
+                            bv + "@bound" + boundVarCounter, bv.TypedIdent.Type));
+                        boundVarCounter++;
+                        subst.Add(bv.Name, lv);
+                        LocalsToAdd.Add(lv);
+                    }
+
+                    // apply the subst
+                    var body = base.VisitExpr(node.Body);
+                    ret = body;
+
+                    subst = null;
+                }
+                else
+                {
+                    ret = base.VisitQuantifierExpr(node);
+                }
+
+                searchExistentialFunction = false;
+                foundExistentialFunction = false;
+            }
+            else
+            {
+                ret = base.VisitQuantifierExpr(node);
+            }
+
+            insideQuantifier = oldIQ;
+            return ret;
+        }
+
+        public override Expr VisitNAryExpr(NAryExpr node)
+        {
+            if (node.Fun is FunctionCall && existentialFunctions.Contains((node.Fun as FunctionCall).FunctionName))
+            {
+                if (insideQuantifier == 3)
+                    throw new AbsHoudiniInternalError("Existential function found inside exists, or nested foralls");
+
+                if (searchExistentialFunction)
+                    foundExistentialFunction = true;
+
+            }
+
+            return base.VisitNAryExpr(node);
+        }
+
+        public override Expr VisitIdentifierExpr(IdentifierExpr node)
+        {
+            if (subst != null && subst.ContainsKey(node.Name))
+                return Expr.Ident(subst[node.Name]);
+            return base.VisitIdentifierExpr(node);
+        }
+
+    }
+
+    public class Intervals : IAbstractDomain
+    {
+        // [lower, upper]
+        int upper;
+        int lower;
+        // or: \bot
+        bool isBottom;
+        // number of times join has been performed
+        int nJoin;
+        // number of times before we widen
+        readonly static int maxJoin = 5;
+
+        public Intervals()
+        {
+            this.upper = 0;
+            this.lower = 0;
+            this.nJoin = 0;
+            this.isBottom = true;
+        }
+
+        private Intervals(int lower, int upper, int nJoin)
+        {
+            this.upper = upper;
+            this.lower = lower;
+            this.nJoin = nJoin;
+        }
+
+        public IAbstractDomain Bottom()
+        {
+            return new Intervals();
+        }
+
+        public IAbstractDomain MakeTop(out bool changed)
+        {
+            if (lower == Int32.MinValue && upper == Int32.MaxValue)
+            {
+                changed = false;
+                return this;
+            }
+            changed = true;
+            return new Intervals(Int32.MinValue, Int32.MaxValue, 0);
+        }
+
+        public IAbstractDomain Join(List<Model.Element> states)
+        {
+            Debug.Assert(states.Count == 1);
+            var state = states[0] as Model.Integer;
+            if (state == null)
+                throw new AbsHoudiniInternalError("Incorrect type, expected int");
+            var intval = state.AsInt();
+
+            if (isBottom)
+            {
+                return new Intervals(intval, intval, 1);
+            }
+
+            if(intval >= lower && intval <= upper)
+                return this;
+
+            if (nJoin > maxJoin)
+            {
+                // widen
+                if (intval > upper)
+                    return new Intervals(lower, Int32.MaxValue, 1);
+                if(intval < lower)
+                    return new Intervals(Int32.MinValue, upper, 1);
+
+                Debug.Assert(false);
+            }
+
+            if (intval > upper)
+                return new Intervals(lower, intval, nJoin + 1);
+            if (intval < lower)
+                return new Intervals(intval, upper, nJoin + 1);
+
+            Debug.Assert(false);
+            return null;
+        }
+
+        public Expr Gamma(List<Expr> vars)
+        {
+            Debug.Assert(vars.Count == 1);
+            var v = vars[0];
+            if (isBottom) return Expr.False;
+            Expr ret = Expr.True;
+            if (lower != Int32.MinValue)
+                ret = Expr.And(ret, Expr.Ge(v, Expr.Literal(lower)));
+            if (upper != Int32.MaxValue)
+                ret = Expr.And(ret, Expr.Le(v, Expr.Literal(upper)));
+            return ret;
+        }
+
+        public bool TypeCheck(List<Type> argTypes, out string msg)
+        {
+            msg = "";
+            if (argTypes.Count != 1)
+            {
+                msg = "Illegal number of arguments";
+                return false;
+            }
+            if (!argTypes[0].IsInt)
+            {
+                msg = "Illegal type, expecting int";
+                return false;
+            }
+            return true;
+        }
+    }
+
+    public class PredicateAbsFullElem : PredicateAbsElem
+    {
+        public PredicateAbsFullElem()
+            : base(1000)
+        { }
+    }
+
+    public class PredicateAbsElem : IAbstractDomain
+    {
+        public static class ExprExt
+        {
+            public static Expr AndSimp(Expr e1, Expr e2)
+            {
+                if (e1 == Expr.True) return e2;
+                if (e2 == Expr.True) return e1;
+                if (e1 == Expr.False || e2 == Expr.False) return Expr.False;
+                return Expr.And(e1, e2);
+            }
+
+            public static Expr OrSimp(Expr e1, Expr e2)
+            {
+                if (e1 == Expr.False) return e2;
+                if (e2 == Expr.False) return e1;
+                if (e1 == Expr.True || e2 == Expr.True) return Expr.True;
+                return Expr.Or(e1, e2); 
+            }
+        }
+
+        class Disjunct
+        {
+            HashSet<int> pos;
+            HashSet<int> neg;
+            bool isTrue;
+
+            public Disjunct()
+            {
+                isTrue = true;
+                pos = new HashSet<int>();
+                neg = new HashSet<int>();
+            }
+
+            public Disjunct(IEnumerable<int> pos, IEnumerable<int> neg, int bound)
+            {
+                this.isTrue = false;
+                this.pos = new HashSet<int>(pos);
+                this.neg = new HashSet<int>(neg);
+                if (this.pos.Overlaps(this.neg))
+                {
+                    this.isTrue = true;
+                    this.pos = new HashSet<int>();
+                    this.neg = new HashSet<int>();
+                }
+                if (this.pos.Count + this.neg.Count > bound)
+                {
+                    // Set to true
+                    this.isTrue = true;
+                    this.pos = new HashSet<int>();
+                    this.neg = new HashSet<int>();
+                }
+
+            }
+
+            public Disjunct OR(Disjunct that, int bound)
+            {
+                if (isTrue)
+                    return this;
+                if (that.isTrue)
+                    return that;
+
+                return new Disjunct(this.pos.Concat(that.pos), this.neg.Concat(that.neg), bound);
+            }
+
+            public bool Implies(Disjunct that)
+            {
+                if (isTrue) return that.isTrue;
+                if (that.isTrue) return true;
+
+                return pos.IsSubsetOf(that.pos) && neg.IsSubsetOf(that.neg);
+            }
+
+            public Expr Gamma(List<Expr> vars)
+            {
+                if (isTrue) return Expr.True;
+                Expr ret = Expr.False;
+                pos.Iter(i => ret = ExprExt.OrSimp(ret, vars[i]));
+                neg.Iter(i => ret = ExprExt.OrSimp(ret, Expr.Not(vars[i])));
+                return ret;
+            }
+        }
+
+        // Conjunction of Disjuncts
+        List<Disjunct> conjuncts;
+        int DisjunctBound;
+        bool isFalse;
+
+        public PredicateAbsElem()
+        {
+            this.conjuncts = new List<Disjunct>();
+            this.isFalse = true;
+            this.DisjunctBound = 3;
+        }
+
+        public PredicateAbsElem(int bound)
+        {
+            this.conjuncts = new List<Disjunct>();
+            this.isFalse = true;
+            this.DisjunctBound = bound;
+        }
+
+        public IAbstractDomain Bottom()
+        {
+            return new PredicateAbsElem(DisjunctBound);
+        }
+
+        public IAbstractDomain MakeTop(out bool changed)
+        {
+            if (conjuncts.Count == 0)
+            {
+                changed = false;
+                return this;
+            }
+            changed = true;
+            var ret = new PredicateAbsElem(DisjunctBound);
+            ret.isFalse = false;
+            return ret;
+        }
+
+        public IAbstractDomain Join(List<Model.Element> state)
+        {
+            if (state.Any(me => !(me is Model.Boolean)))
+                throw new AbsHoudiniInternalError("Predicate Abstraction requires that each argument be of type bool");
+
+            // quick return if this == true
+            if (!this.isFalse && conjuncts.Count == 0)
+                return this;
+
+            var ret = new PredicateAbsElem(DisjunctBound);
+            ret.isFalse = false;
+
+            for (int i = 0; i < state.Count; i++)
+            {
+                var b = (state[i] as Model.Boolean).Value;
+                Disjunct d = null;
+                if (b) d = new Disjunct(new int[] { i }, new int[] { }, DisjunctBound);
+                else d = new Disjunct(new int[] { }, new int[] { i }, DisjunctBound);
+
+                if (isFalse)
+                    ret.AddDisjunct(d);
+                else
+                {
+                    conjuncts.Iter(c => ret.AddDisjunct(c.OR(d, DisjunctBound)));
+                }
+            }
+
+            return ret;
+
+        }
+
+        public Expr Gamma(List<Expr> vars)
+        {
+            if (isFalse) return Expr.False;
+            Expr ret = Expr.True;
+
+            foreach (var c in conjuncts)
+            {
+                ret = ExprExt.AndSimp(ret, c.Gamma(vars));
+            }
+
+            return ret;
+        }
+
+        public bool TypeCheck(List<Type> argTypes, out string msg)
+        {
+            msg = "";
+            if (argTypes.Any(t => !t.IsBool))
+            {
+                msg = "Illegal type, expecting bool";
+                return false;
+            }
+            return true;
+        }
+
+        private void AddDisjunct(Disjunct d)
+        {
+            if (conjuncts.Any(c => c.Implies(d)))
+                return;
+
+            conjuncts.RemoveAll(c => d.Implies(c));
+            conjuncts.Add(d);
+        }
+    }
+
+    // [false -- (x == true) -- true]
+    public class HoudiniConst : IAbstractDomain
+    {
+        bool isBottom;
+        bool isTop;
+
+        private HoudiniConst(bool isTop, bool isBottom)
+        {
+            this.isBottom = isBottom;
+            this.isTop = isTop;
+            Debug.Assert(!(isTop && isBottom));
+        }
+
+        public static HoudiniConst GetExtObj()
+        {
+            return new HoudiniConst(false, false);
+        }
+
+        public static HoudiniConst GetTop()
+        {
+            return new HoudiniConst(true, false);
+        }
+
+        public static HoudiniConst GetBottom()
+        {
+            return new HoudiniConst(false, true);
+        }
+
+        public IAbstractDomain Bottom()
+        {
+            return GetBottom();
+        }
+
+        public IAbstractDomain MakeTop(out bool changed)
+        {
+            changed = false;
+            if (isTop) return this;
+            changed = true;
+            return GetTop();
+        }
+
+        public IAbstractDomain Join(List<Model.Element> states)
+        {
+            Debug.Assert(states.Count == 1);
+            var state = states[0];
+
+            if (isTop) return this;
+
+            if (state is Model.Boolean)
+            {
+                if ((state as Model.Boolean).Value)
+                    return GetExtObj();
+            }
+
+            return GetTop();
+        }
+
+        public Expr Gamma(List<Expr> vars)
+        {
+            Debug.Assert(vars.Count == 1);
+            var v = vars[0];
+            if (isBottom) return Expr.False;
+            if (isTop) return Expr.True;
+            return v;
+        }
+
+        public bool TypeCheck(List<Type> argTypes, out string msg)
+        {
+            msg = "";
+            if (argTypes.Count != 1)
+            {
+                msg = "Illegal number of arguments, expecting 1";
+                return false;
+            }
+            if (!argTypes[0].IsBool)
+            {
+                msg = "Illegal type, expecting bool";
+                return false;
+            }
+            return true;
+        }
+    }
+
+    // foo(x) = x < 2^j for some j <= 16
+    public class PowDomain : IAbstractDomain
+    {
+        enum Val { FALSE, NEITHER, TRUE };
+        Val tlevel;
+        bool isBottom { get { return tlevel == Val.FALSE; } }
+        bool isTop { get { return tlevel == Val.TRUE; } }
+
+        readonly int Max = 16;
+
+        int upper; // <= Max
+
+        private PowDomain(Val tlevel) :
+            this(tlevel, 0) { }
+
+        private PowDomain(Val tlevel, int upper)
+        {
+            this.tlevel = tlevel;
+            this.upper = upper;
+        }
+
+        public static IAbstractDomain GetBottom()
+        {
+            return new PowDomain(Val.FALSE) as IAbstractDomain;
+        }
+
+        public IAbstractDomain MakeTop(out bool changed)
+        {
+            if (isTop)
+            {
+                changed = false;
+                return this;
+            }
+            changed = true;
+            return new PowDomain(Val.TRUE);
+        }
+
+        IAbstractDomain IAbstractDomain.Bottom()
+        {
+            return GetBottom();
+        }
+
+        IAbstractDomain IAbstractDomain.Join(List<Model.Element> state)
+        {
+            if (isTop) return this;
+            
+            int v = 0;
+            if (state[0] is Model.BitVector)
+                v = (state[0] as Model.BitVector).AsInt();
+            else if (state[0] is Model.Integer)
+                v = (state[0] as Model.Integer).AsInt();
+            else Debug.Assert(false);
+
+            var nupper = upper;
+            while ((1 << nupper) < v) nupper++;
+            var ntlevel = Val.NEITHER;
+            if (nupper > Max) ntlevel = Val.TRUE;
+            return new PowDomain(ntlevel, nupper);
+        }
+
+        Expr IAbstractDomain.Gamma(List<Expr> vars)
+        {
+            if (isBottom) return Expr.False;
+            if (isTop) return Expr.True;
+            var v = vars[0];
+            if (v.Type.IsBv)
+            {
+                var bits = v.Type.BvBits;
+                if (!AbstractDomainFactory.bvslt.ContainsKey(bits))
+                    throw new AbsHoudiniInternalError("No builtin function found for bv" + bits.ToString());
+                var bvslt = AbstractDomainFactory.bvslt[bits];
+                return new NAryExpr(Token.NoToken, new FunctionCall(bvslt), new List<Expr> { v,
+                    new LiteralExpr(Token.NoToken, Basetypes.BigNum.FromInt(1 << (upper+1)), 32) });
+            }
+            else
+            {
+                return Expr.Lt(v, Expr.Literal(1 << (upper+1)));
+            }
+        }
+
+        bool IAbstractDomain.TypeCheck(List<Type> argTypes, out string msg)
+        {
+            msg = "";
+            if (argTypes.Count != 1)
+            {
+                msg = "Illegal number of arguments, expecting 1";
+                return false;
+            }
+            if (argTypes.Any(tt => !tt.IsInt && !tt.IsBv))
+            {
+                msg = "Illegal type, expecting int or bv";
+                return false;
+            }
+            return true;
+        }
+    }
+
+    // foo(x_i) = all equalities that hold
+    public class EqualitiesDomain : IAbstractDomain
+    {
+        bool isBottom;
+        List<HashSet<int>> equalities;
+
+        public EqualitiesDomain(bool isBottom, List<HashSet<int>> eq)
+        {
+            this.isBottom = isBottom;
+            this.equalities = eq;
+        }
+
+        public static IAbstractDomain GetBottom()
+        {
+            return new EqualitiesDomain(true, new List<HashSet<int>>());
+        }
+
+        IAbstractDomain IAbstractDomain.Bottom()
+        {
+            return GetBottom();
+        }
+
+        public IAbstractDomain MakeTop(out bool changed)
+        {
+            if (equalities.Count == 0)
+            {
+                changed = false;
+                return this;
+            }
+            changed = true;
+            return new EqualitiesDomain(false, new List<HashSet<int>>());
+        }
+
+        IAbstractDomain IAbstractDomain.Join(List<Model.Element> state)
+        {
+            // find the guys that are equal
+            var eq = new List<HashSet<int>>();
+            for (int i = 0; i < state.Count; i++)
+            {
+                var added = false;
+                foreach (var s in eq)
+                {
+                    var sv = s.First();
+                    if (state[i].ToString() == state[sv].ToString())
+                    {
+                        s.Add(i);
+                        added = true;
+                        break;
+                    }
+                }
+                if (!added) eq.Add(new HashSet<int>(new int[] { i }));
+            }
+            
+            if (isBottom)
+            {
+                return new EqualitiesDomain(false, eq);
+            }
+
+            // intersect two partitions equalities and eq
+            var m1 = GetMap(equalities, state.Count);
+            var m2 = GetMap(eq, state.Count);
+
+            for (int i = 0; i < state.Count; i++)
+                m2[i] = new HashSet<int>(m2[i].Intersect(m1[i]));
+
+
+            // map from representative to set
+            var repToSet = new Dictionary<int, HashSet<int>>();
+
+            for (int i = 0; i < state.Count; i++)
+            {
+                var rep = m2[i].Min();
+                if (!repToSet.ContainsKey(rep))
+                    repToSet[rep] = m2[i];
+            }
+
+            var ret = new List<HashSet<int>>();
+            repToSet.Values.Iter(s => ret.Add(s));
+
+            return new EqualitiesDomain(false, ret);
+        }
+
+        Expr IAbstractDomain.Gamma(List<Expr> vars)
+        {
+            if (isBottom) return Expr.False;
+            Expr ret = Expr.True;
+            foreach (var eq in equalities.Select(hs => hs.ToList()))
+            {
+                if (eq.Count == 1) continue;
+                var prev = eq[0];
+                for (int i = 1; i < eq.Count; i++)
+                {
+                    ret = Expr.And(ret, Expr.Eq(vars[prev], vars[eq[i]]));
+                    prev = eq[i];
+                }
+            }
+            return ret;
+        }
+
+        bool IAbstractDomain.TypeCheck(List<Type> argTypes, out string msg)
+        {
+            msg = "";
+            if (argTypes.Count == 0) return true;
+            var ot = argTypes[0];
+
+            if (argTypes.Any(tt => !tt.Equals(ot)))
+            {
+                msg = string.Format("Illegal type, expecting type {0}, got {1}", ot, argTypes.First(tt => !tt.Equals(ot)));
+                return false;
+            }
+            return true;
+        }
+
+        private HashSet<int>[] GetMap(List<HashSet<int>> eq, int n)
+        {
+            var ret = new HashSet<int>[n];
+            foreach (var s in eq)
+            {
+                foreach (var i in s)
+                    ret[i] = s;
+            }
+            return ret;
+        }
+    }
+
+    // foo(a,b) \in {false, \not a, a ==> b, true}
+    public class ImplicationDomain : IAbstractDomain
+    {
+        enum Val {FALSE, NOT_A, A_IMP_B, TRUE};
+        Val val;
+
+        private ImplicationDomain(Val val)
+        {
+            this.val = val;
+        }
+
+        public static ImplicationDomain GetBottom()
+        {
+            return new ImplicationDomain(Val.FALSE);
+        }
+
+        public IAbstractDomain Bottom()
+        {
+            return GetBottom();
+        }
+
+        public IAbstractDomain MakeTop(out bool changed)
+        {
+            if(val == Val.TRUE) {
+                changed = false;
+                return this;
+            }
+            changed = true;
+            return new ImplicationDomain(Val.TRUE);
+        }
+
+        public IAbstractDomain Join(List<Model.Element> states)
+        {
+            Debug.Assert(states.Count == 2);
+            var v1 = (states[0] as Model.Boolean).Value;
+            var v2 = (states[1] as Model.Boolean).Value;
+
+            if (val == Val.TRUE) return this;
+
+            var that = Val.TRUE;
+            if (!v1) that = Val.NOT_A;
+            else if (!v1 || v2) that = Val.A_IMP_B;
+
+            if (that == Val.TRUE || val == Val.FALSE)
+                return new ImplicationDomain(that);
+
+            // Now, neither this or that is FALSE or TRUE
+            if (val == that)
+                return this;
+
+            Debug.Assert(val == Val.A_IMP_B || that == Val.A_IMP_B);
+            return new ImplicationDomain(Val.A_IMP_B);
+        }
+
+        public Expr Gamma(List<Expr> vars)
+        {
+            Debug.Assert(vars.Count == 2);
+
+            var v1 = vars[0];
+            var v2 = vars[1];
+
+            if (val == Val.FALSE) return Expr.False;
+            if (val == Val.TRUE) return Expr.True;
+            if (val == Val.NOT_A) return Expr.Not(v1);
+            return Expr.Imp(v1, v2);
+        }
+
+        public bool TypeCheck(List<Type> argTypes, out string msg)
+        {
+            msg = "";
+            if (argTypes.Count != 2)
+            {
+                msg = "Illegal number of arguments, expecting 2";
+                return false;
+            }
+            if (argTypes.Any(tt => !tt.IsBool))
+            {
+                msg = "Illegal type, expecting bool";
+                return false;
+            }
+            return true;
+        }
+    }
+
+    public class ConstantProp : IAbstractDomain
+    {
+        object val;
+        bool isBottom;
+        bool isTop;
+
+        private ConstantProp(object val, bool isTop, bool isBottom)
+        {
+            this.val = val;
+            this.isBottom = isBottom;
+            this.isTop = isTop;
+            Debug.Assert(!(isTop && isBottom));
+            Debug.Assert(val == null || (val is int) || (val is bool));
+        }
+
+        public static ConstantProp GetExtObj(object val)
+        {
+            Debug.Assert(val != null);
+            return new ConstantProp(val, false, false);
+        }
+
+        public static ConstantProp GetTop()
+        {
+            return new ConstantProp(null, true, false);
+        }
+
+        public static ConstantProp GetBottom()
+        {
+            return new ConstantProp(null, false, true);
+        }
+
+        public IAbstractDomain MakeTop(out bool changed) {
+            if (isTop)
+            {
+                changed = false;
+                return this;
+            }
+            changed = true;
+            return GetTop();
+        }
+
+        private ConstantProp Join(ConstantProp that)
+        {
+            if (isBottom) return that;
+            if (isTop) return this;
+            if (that.isBottom) return this;
+            if (that.isTop) return that;
+
+            if ((val is int) && !(that.val is int))
+                throw new AbsHoudiniInternalError("Type mismatch in ExtObj");
+
+            if ((val is bool) && !(that.val is bool))
+                throw new AbsHoudiniInternalError("Type mismatch in ExtObj");
+
+            if (val is int)
+            {
+                var v1 = (int)val;
+                var v2 = (int)that.val;
+                if (v1 != v2) return GetTop();
+                return this;
+            }
+            else if (val is bool)
+            {
+                var v1 = (bool)val;
+                var v2 = (bool)that.val;
+                if (v1 != v2) return GetTop();
+                return this;
+            }
+            throw new AbsHoudiniInternalError("Illegal val type in ExtObj");
+        }
+
+        public IAbstractDomain Bottom()
+        {
+            return GetBottom();
+        }
+
+        public IAbstractDomain Join(List<Model.Element> states)
+        {
+            Debug.Assert(states.Count == 1);
+            var state = states[0];
+            ConstantProp that = null;
+
+            if (state is Model.Integer)
+            {
+                that = GetExtObj((state as Model.Integer).AsInt());
+            }
+            else if (state is Model.Boolean)
+            {
+                that = GetExtObj((state as Model.Boolean).Value);
+            }
+            else
+            {
+                throw new AbsHoudiniInternalError("Illegal type " + state.GetType().ToString());
+            }
+
+            return Join(that);
+        }
+
+        public Expr Gamma(List<Expr> vars)
+        {
+            Debug.Assert(vars.Count == 1);
+            var v = vars[0];
+            if (isBottom) return Expr.False;
+            if (isTop) return Expr.True;
+            if (val is int)
+                return Expr.Eq(v, Expr.Literal((int)val));
+            if (val is bool && (bool)val)
+                return v;
+            if (val is bool && !(bool)val)
+                return Expr.Not(v);
+
+            return null;
+        }
+
+        public bool TypeCheck(List<Type> argTypes, out string msg)
+        {
+            msg = "";
+            if (argTypes.Count != 1)
+            {
+                msg = "Illegal number of arguments, expecting 1";
+                return false;
+            }
+            if (!argTypes[0].IsInt && ! argTypes[0].IsBool)
+            {
+                msg = "Illegal type, expecting int or bool";
+                return false;
+            }
+            return true;
+        }
+    }
+
+
+    public class IndependentAttribute<T> : IAbstractDomain where T : class, IAbstractDomain
+    {
+        bool isBottom;
+        int numVars;
+        List<T> varVal;
+        T underlyingInstance;
+
+        public IndependentAttribute()
+        {
+            isBottom = true;
+            numVars = 0;
+            varVal = new List<T>();
+            underlyingInstance = null;
+        }
+
+        public IAbstractDomain Bottom()
+        {
+            return new IndependentAttribute<T>();
+        }
+
+        public IAbstractDomain MakeTop(out bool changed)
+        {
+            var mt = new Func<IAbstractDomain>(() =>
+                {
+                    var ret = new IndependentAttribute<T>();
+                    ret.isBottom = true;
+                    ret.numVars = numVars;
+                    ret.underlyingInstance = underlyingInstance;
+                    ret.varVal = new List<T>();
+                    bool tmp;
+                    for (int i = 0; i < varVal.Count; i++)
+                        ret.varVal.Add(varVal[i].MakeTop(out tmp) as T);
+                    return ret;
+                });
+
+            if (!isBottom)
+            {
+                foreach (var t in varVal)
+                {
+                    var top = t.MakeTop(out changed);
+                    if (changed)
+                    {
+                        return mt();
+                    }
+                }
+            }
+            else
+            {
+                changed = true;
+                return mt();
+            }
+
+            changed = false;
+            return this;
+        }
+        public IAbstractDomain Join(List<Model.Element> state)
+        {
+            SetUnderlyingInstance();
+
+            if (!isBottom && numVars != state.Count)
+            {
+                throw new AbsHoudiniInternalError(
+                    string.Format("Got illegal number of arguments ({0}), expected {1}", state.Count, numVars));
+            }
+
+            var ret = new IndependentAttribute<T>();
+            ret.isBottom = false;
+            ret.numVars = state.Count;
+            for(int i = 0; i < state.Count; i++)
+            {
+                var sl = new List<Model.Element>();
+                sl.Add(state[i]);
+                T prev = isBottom ? underlyingInstance.Bottom() as T : varVal[i];
+                ret.varVal.Add(prev.Join(sl) as T);
+            }
+
+            return ret;
+        }
+
+        public Expr Gamma(List<Expr> vars)
+        {
+            if (isBottom) return Expr.False;
+            if (numVars != vars.Count)
+                throw new AbsHoudiniInternalError(
+                    string.Format("Got illegal number of arguments ({0}), expected {1}", vars.Count, numVars));
+
+            Expr ret = Expr.True;
+            for (int i = 0; i < numVars; i++)
+            {
+                var sl = new List<Expr>(); sl.Add(vars[i]);
+                ret = Expr.And(ret, varVal[i].Gamma(sl));
+            }
+
+            return ret;
+        }
+
+        private void SetUnderlyingInstance()
+        {
+            if (underlyingInstance != null) return;
+            var tt = typeof(T);
+            underlyingInstance = AbstractDomainFactory.GetInstance(tt) as T;
+        }
+
+        public bool TypeCheck(List<Type> argTypes, out string msg)
+        {
+            SetUnderlyingInstance();
+
+            msg = "";
+            foreach(var t in argTypes) 
+            {
+                if(!underlyingInstance.TypeCheck(new List<Type>(new Type[] { t }), out msg))
+                    return false;
+            }
+            return true;
+        }
+    }
+
+    public class AbstractDomainFactory
+    {
+        // Type name -> Instance
+        private static Dictionary<string, IAbstractDomain> abstractDomainInstances = new Dictionary<string, IAbstractDomain>();
+        private static Dictionary<string, IAbstractDomain> abstractDomainInstancesFriendly = new Dictionary<string, IAbstractDomain>();
+        
+        // bitvector operations
+        public static Dictionary<int, Function> bvslt = new Dictionary<int, Function>();
+
+        public static void Register(string friendlyName, IAbstractDomain instance)
+        {
+            var Name = instance.GetType().FullName;
+            Debug.Assert(!abstractDomainInstances.ContainsKey(Name));
+            abstractDomainInstances.Add(Name, instance);
+            abstractDomainInstancesFriendly.Add(friendlyName, instance);
+        }
+
+        public static IAbstractDomain GetInstance(System.Type type)
+        {
+            var Name = type.FullName;
+            Debug.Assert(abstractDomainInstances.ContainsKey(Name));
+            return abstractDomainInstances[Name] as IAbstractDomain;
+        }
+
+        public static IAbstractDomain GetInstance(string friendlyName)
+        {
+            if (!abstractDomainInstancesFriendly.ContainsKey(friendlyName))
+            {
+                Console.WriteLine("Domain {0} not found", friendlyName);
+                Console.WriteLine("Supported domains are:");
+                abstractDomainInstancesFriendly.Keys.Iter(tup => Console.WriteLine("  {0}", tup));
+                throw new AbsHoudiniInternalError("Domain not found");
+            }
+            return abstractDomainInstancesFriendly[friendlyName] as IAbstractDomain;
+        }
+
+        public static void Initialize(Program program)
+        {
+            // Declare abstract domains
+            var domains = new List<System.Tuple<string, IAbstractDomain>>(new System.Tuple<string, IAbstractDomain>[] {
+                  System.Tuple.Create("HoudiniConst", HoudiniConst.GetBottom() as IAbstractDomain),
+                  System.Tuple.Create("Intervals", new Intervals() as IAbstractDomain),
+                  System.Tuple.Create("ConstantProp", ConstantProp.GetBottom() as IAbstractDomain),
+                  System.Tuple.Create("PredicateAbs", new PredicateAbsElem() as IAbstractDomain),
+                  System.Tuple.Create("PredicateAbsFull", new PredicateAbsFullElem() as IAbstractDomain),
+                  System.Tuple.Create("ImplicationDomain", ImplicationDomain.GetBottom() as IAbstractDomain),
+                  System.Tuple.Create("PowDomain", PowDomain.GetBottom() as IAbstractDomain),
+                  System.Tuple.Create("EqualitiesDomain", EqualitiesDomain.GetBottom() as IAbstractDomain),
+                  System.Tuple.Create("IA[HoudiniConst]", new IndependentAttribute<HoudiniConst>()  as IAbstractDomain),
+                  System.Tuple.Create("IA[ConstantProp]", new IndependentAttribute<ConstantProp>()  as IAbstractDomain),
+                  System.Tuple.Create("IA[Intervals]", new IndependentAttribute<Intervals>()  as IAbstractDomain),
+                  System.Tuple.Create("IA[PowDomain]", new IndependentAttribute<PowDomain>() as IAbstractDomain),
+              });
+
+            domains.Iter(tup => AbstractDomainFactory.Register(tup.Item1, tup.Item2));
+            program.Functions.Iter(RegisterFunction);
+        }
+
+        private static void RegisterFunction(Function func)
+        {
+            var attr = QKeyValue.FindStringAttribute(func.Attributes, "bvbuiltin");
+            if (attr != null && attr == "bvslt" && func.InParams.Count == 2 && func.InParams[0].TypedIdent.Type.IsBv)
+                bvslt.Add(func.InParams[0].TypedIdent.Type.BvBits, func);
+        }
+    }
+
+    public interface IAbstractDomain
+    {
+        IAbstractDomain Bottom();
+        IAbstractDomain MakeTop(out bool changed);
+        IAbstractDomain Join(List<Model.Element> state);
+        Expr Gamma(List<Expr> vars);
+        bool TypeCheck(List<Type> argTypes, out string msg);
+    }
+
+    public class AbstractHoudini
+    {
+        // Input Program
+        Program program;
+        // Impl -> VC
+        Dictionary<string, VCExpr> impl2VC;
+        // Impl -> Vars at end of the impl
+        Dictionary<string, List<VCExpr>> impl2EndStateVars;
+        // Impl -> (callee,summary pred)
+        Dictionary<string, List<Tuple<string, bool, VCExprVar, VCExprNAry>>> impl2CalleeSummaries;
+        // pointer to summary class
+        ISummaryElement summaryClass;
+        // impl -> summary
+        Dictionary<string, ISummaryElement> impl2Summary;
+        // name -> impl
+        Dictionary<string, Implementation> name2Impl;
+        // Use Bilateral algorithm
+        public static bool UseBilateralAlgo = true;
+        public static int iterTimeLimit = -1; // ms
+
+        public static readonly string summaryPredSuffix = "SummaryPred";
+
+        // Essentials: VCGen, Prover, and reporter
+        VCGen vcgen;
+        ProverInterface prover;
+        AbstractHoudiniErrorReporter reporter;
+
+        // Stats
+        TimeSpan proverTime;
+        int numProverQueries;
+
+        // Produce witness for correctness: can be set programmatically
+        public static string WitnessFile = "absHoudiniWitness.bpl";
+
+        public AbstractHoudini(Program program)
+        {
+            this.program = program;
+            this.impl2VC = new Dictionary<string, VCExpr>();
+            this.impl2EndStateVars = new Dictionary<string, List<VCExpr>>();
+            this.impl2CalleeSummaries = new Dictionary<string, List<Tuple<string, bool, VCExprVar, VCExprNAry>>>();
+            this.impl2Summary = new Dictionary<string, ISummaryElement>();
+            this.name2Impl = SimpleUtil.nameImplMapping(program);
+
+            if (CommandLineOptions.Clo.ProverKillTime > 0)
+                CommandLineOptions.Clo.ProverOptions = CommandLineOptions.Clo.ProverOptions.Concat1(string.Format("TIME_LIMIT={0}", CommandLineOptions.Clo.ProverKillTime));
+
+            this.vcgen = new VCGen(program, CommandLineOptions.Clo.SimplifyLogFilePath, CommandLineOptions.Clo.SimplifyLogFileAppend, new List<Checker>());
+            this.prover = ProverInterface.CreateProver(program, CommandLineOptions.Clo.SimplifyLogFilePath, CommandLineOptions.Clo.SimplifyLogFileAppend, -1);
+
+            this.reporter = new AbstractHoudiniErrorReporter();
+
+            this.proverTime = TimeSpan.Zero;
+            this.numProverQueries = 0;
+
+            if (CommandLineOptions.Clo.AbstractHoudini == "0")
+                UseBilateralAlgo = false;
+        }
+
+        public void computeSummaries(ISummaryElement summaryClass)
+        {
+            // TODO: move this some place else
+            PredicateAbs.FindUnsatPairs(prover.VCExprGen, prover);
+
+            this.summaryClass = summaryClass;
+
+            name2Impl.Values.Iter(attachEnsures);
+
+            program.Implementations
+                .Iter(impl => impl2Summary.Add(impl.Name, summaryClass.GetFlaseSummary(program, impl)));
+
+            // Build call graph
+            var Succ = new Dictionary<Implementation, HashSet<Implementation>>();
+            var Pred = new Dictionary<Implementation, HashSet<Implementation>>();
+            name2Impl.Values.Iter(impl => Succ.Add(impl, new HashSet<Implementation>()));
+            name2Impl.Values.Iter(impl => Pred.Add(impl, new HashSet<Implementation>()));
+
+            foreach (var impl in program.Implementations)
+            {
+                foreach (var blk in impl.Blocks)
+                {
+                    foreach (var cmd in blk.Cmds.OfType<CallCmd>())
+                    {
+                        if (!name2Impl.ContainsKey(cmd.callee)) continue;
+                        Succ[impl].Add(name2Impl[cmd.callee]);
+                        Pred[name2Impl[cmd.callee]].Add(impl);
+                    }
+                }
+            }
+
+            // Build SCC
+            var sccs = new StronglyConnectedComponents<Implementation>(name2Impl.Values,
+                new Adjacency<Implementation>(n => Pred[n]),
+                new Adjacency<Implementation>(n => Succ[n]));
+            sccs.Compute();
+
+            // impl -> priority
+            var impl2Priority = new Dictionary<string, int>();
+            int p = 0;
+            foreach (var scc in sccs)
+            {
+                foreach (var impl in scc)
+                {
+                    impl2Priority.Add(impl.Name, p);
+                    p++;
+                }
+            }
+
+
+            Inline();
+
+            #region Witness generation setup
+            // Create a copy of the program
+            var copy = new Dictionary<string, Implementation>();
+            if (WitnessFile != null)
+            {
+                foreach (var impl in program.Implementations)
+                {
+                    var nimpl = new Implementation(Token.NoToken, impl.Name, impl.TypeParameters,
+                        impl.InParams, impl.OutParams, new List<Variable>(impl.LocVars), new List<Block>());
+                    foreach (var blk in impl.Blocks)
+                    {
+                        var cd = new CodeCopier();
+                        nimpl.Blocks.Add(new Block(Token.NoToken, blk.Label,
+                            cd.CopyCmdSeq(blk.Cmds), cd.CopyTransferCmd(blk.TransferCmd)));
+                    }
+
+                    copy.Add(impl.Name, nimpl);
+                }
+            }
+            #endregion
+
+            // Turn off subsumption. Why? Because then I see multiple occurences of the
+            // attached ensures in the VC
+            CommandLineOptions.Clo.UseSubsumption = CommandLineOptions.SubsumptionOption.Never;
+
+            // Create all VCs
+            name2Impl.Values
+                .Iter(GenVC);
+
+            // Start the iteration
+            var worklist = new SortedSet<Tuple<int, Implementation>>();
+            name2Impl.Values
+                .Iter(impl => worklist.Add(Tuple.Create(impl2Priority[impl.Name], impl)));
+
+            while (worklist.Any())
+            {
+                var impl = worklist.First().Item2;
+                worklist.Remove(worklist.First());
+
+                var changed = ProcessImpl(impl);
+
+                if (changed)
+                {
+                    Pred[impl].Where(pred => UseBilateralAlgo || pred != impl).Iter(pred => worklist.Add(Tuple.Create(impl2Priority[pred.Name], pred)));
+                }
+            }
+
+            var allImpls = new SortedSet<Tuple<int, string>>();
+            name2Impl.Values.Iter(impl => allImpls.Add(Tuple.Create(impl2Priority[impl.Name], impl.Name)));
+            if (CommandLineOptions.Clo.Trace)
+            {
+                foreach (var tup in allImpls)
+                {
+                    Console.WriteLine("Summary of {0}:", tup.Item2);
+                    Console.WriteLine("{0}", impl2Summary[tup.Item2]);
+                }
+                Console.WriteLine("Prover time = {0}", proverTime.TotalSeconds.ToString("F2"));
+                Console.WriteLine("Number of prover queries = " + numProverQueries);
+            }
+
+            ProduceWitness(copy);
+
+            prover.Close();
+            CommandLineOptions.Clo.TheProverFactory.Close();
+        }
+
+        public HashSet<string> GetPredicates()
+        {
+            var ret = new HashSet<string>();
+            prover = ProverInterface.CreateProver(program, CommandLineOptions.Clo.SimplifyLogFilePath, CommandLineOptions.Clo.SimplifyLogFileAppend, -1);
+
+            foreach (var tup in impl2Summary)
+            {
+                var s = tup.Value as PredicateAbs;
+                if (s == null) continue;
+                ret.UnionWith(s.GetPredicates(program, prover.VCExprGen, prover));
+                // debug output
+                //Console.WriteLine("Summary of {0}:", tup.Key);
+                //Console.WriteLine("{0}", tup.Value);
+            }
+
+            prover.Close();
+            CommandLineOptions.Clo.TheProverFactory.Close();
+            return ret;
+        }
+
+        // Obtain the summary expression for a procedure: used programmatically by clients
+        // of AbstractHoudini
+        public Expr GetSummary(Program program, Procedure proc)
+        {
+            if (!impl2Summary.ContainsKey(proc.Name))
+                return Expr.True;
+
+            var vars = new Dictionary<string, Expr>();
+            foreach (var g in program.GlobalVariables)
+                vars.Add(g.Name, Expr.Ident(g));
+            foreach (var v in proc.InParams.OfType<Variable>())
+                vars.Add(v.Name, Expr.Ident(v));
+            foreach (var v in proc.OutParams.OfType<Variable>())
+                vars.Add(v.Name, Expr.Ident(v));
+
+            return impl2Summary[proc.Name].GetSummaryExpr(
+                v => { if (vars.ContainsKey(v)) return vars[v]; else return null; },
+                v => { if (vars.ContainsKey(v)) return new OldExpr(Token.NoToken, vars[v]); else return null; });
+        }
+
+        public ISummaryElement GetSummaryLowLevel(Procedure proc)
+        {
+            if (!impl2Summary.ContainsKey(proc.Name)) return null;
+            return impl2Summary[proc.Name];
+        }
+
+        // Produce a witness that proves that the inferred annotations are correct
+        private void ProduceWitness(Dictionary<string, Implementation> copy)
+        {
+            if (WitnessFile == null)
+                return;
+
+            foreach (var proc in program.Procedures)
+            {
+                var nensures = new List<Ensures>();
+                proc.Ensures.OfType<Ensures>()
+                .Where(ens => !QKeyValue.FindBoolAttribute(ens.Attributes, "ah") &&
+                    !QKeyValue.FindBoolAttribute(ens.Attributes, "pre") &&
+                    !QKeyValue.FindBoolAttribute(ens.Attributes, "post") &&
+                    QKeyValue.FindStringAttribute(ens.Attributes, "pre") == null &&
+                    QKeyValue.FindStringAttribute(ens.Attributes, "post") == null)
+                .Iter(ens => nensures.Add(ens));
+                foreach (Ensures en in nensures)
+                    en.Attributes = removeAttr("InlineAssume", en.Attributes);
+
+                proc.Ensures = nensures;
+            }
+
+            var decls = new List<Declaration>(copy.Values);
+            decls.AddRange(program.TopLevelDeclarations.Where(decl => !(decl is Implementation)));
+            program.TopLevelDeclarations = decls;
+            var name2Proc = new Dictionary<string, Procedure>();
+            foreach (var proc in program.Procedures)
+            {
+                name2Proc.Add(proc.Name, proc);
+                if (impl2Summary.ContainsKey(proc.Name))
+                {
+                    var ens = new Ensures(false, 
+                        impl2Summary[proc.Name].GetSummaryExpr(
+                        new Func<string, Expr>(s => null), new Func<string, Expr>(s => null)));
+                    ens.Attributes = new QKeyValue(Token.NoToken, "inferred", new List<object>(), ens.Attributes);
+                    proc.Ensures.Add(ens);
+                }
+            }
+
+            using (var wt = new TokenTextWriter(WitnessFile, /*pretty=*/ false))
+            {
+                program.Emit(wt);
+            }
+
+            // Replace SummaryPreds with their definition
+            foreach (var impl in program.Implementations)
+            {
+                foreach (var blk in impl.Blocks)
+                {
+                    foreach (var cmd in blk.Cmds.OfType<AssumeCmd>())
+                    {
+                        var expr = cmd.Expr as NAryExpr;
+                        if (expr == null) continue;
+                        var op = expr.Fun as FunctionCall;
+                        if (op == null || !op.FunctionName.EndsWith(summaryPredSuffix)) continue;
+                        var calleeName = op.FunctionName.Substring(0, op.FunctionName.Length - summaryPredSuffix.Length);
+                        if (!impl2Summary.ContainsKey(calleeName)) continue;
+                        var callee = name2Impl[calleeName];
+
+                        // variable order: globals, ins, outs, modifies
+                        var forold = new Dictionary<string, Expr>();
+                        var always = new Dictionary<string, Expr>();
+                        int i = 0;
+                        foreach (var g in program.GlobalVariables)
+                        {
+                            forold.Add(g.Name, expr.Args[i]);
+                            always.Add(g.Name, expr.Args[i]);
+                            i++;
+                        }
+                        foreach (var v in callee.InParams.OfType<Variable>())
+                        {
+                            always.Add(v.Name, expr.Args[i]);
+                            i++;
+                        }
+                        foreach (var v in callee.OutParams.OfType<Variable>())
+                        {
+                            always.Add(v.Name, expr.Args[i]);
+                            i++;
+                        }
+                        foreach (var ie in name2Proc[calleeName].Modifies.OfType<IdentifierExpr>())
+                        {
+                            always[ie.Name] = expr.Args[i];
+                            i++;
+                        }
+
+                        cmd.Expr = impl2Summary[calleeName].GetSummaryExpr(
+                            v => { if (always.ContainsKey(v)) return always[v]; else return null; },
+                            v => { if (forold.ContainsKey(v)) return forold[v]; else return null; });
+                    }
+                }
+            }
+
+            using (var wt = new TokenTextWriter(WitnessFile, /*pretty=*/ false))
+            {
+                program.Emit(wt);
+            }
+            if (CommandLineOptions.Clo.Trace) Console.WriteLine("Witness written to {0}", WitnessFile);
+        }
+
+        private QKeyValue removeAttr(string key, QKeyValue attr)
+        {
+            if (attr == null) return attr;
+            if (attr.Key == key) return removeAttr(key, attr.Next);
+            attr.Next = removeAttr(key, attr.Next);
+            return attr;
+        }
+
+        private void Inline()
+        {
+            if (CommandLineOptions.Clo.InlineDepth < 0)
+                return;
+
+            var callGraph = BuildCallGraph();
+
+            foreach (Implementation impl in callGraph.Nodes)
+            {
+                InlineEnsuresVisitor inlineEnsuresVisitor = new InlineEnsuresVisitor();
+                inlineEnsuresVisitor.Visit(impl);
+            }
+
+            foreach (Implementation impl in callGraph.Nodes)
+            {
+                impl.OriginalBlocks = impl.Blocks;
+                impl.OriginalLocVars = impl.LocVars;
+            }
+            foreach (Implementation impl in callGraph.Nodes)
+            {
+                CommandLineOptions.Inlining savedOption = CommandLineOptions.Clo.ProcedureInlining;
+                CommandLineOptions.Clo.ProcedureInlining = CommandLineOptions.Inlining.Spec;
+                Inliner.ProcessImplementationForHoudini(program, impl);
+                CommandLineOptions.Clo.ProcedureInlining = savedOption;
+            }
+            foreach (Implementation impl in callGraph.Nodes)
+            {
+                impl.OriginalBlocks = null;
+                impl.OriginalLocVars = null;
+            }
+
+            Graph<Implementation> oldCallGraph = callGraph;
+            callGraph = new Graph<Implementation>();
+            foreach (Implementation impl in oldCallGraph.Nodes)
+            {
+                callGraph.AddSource(impl);
+            }
+            foreach (Tuple<Implementation, Implementation> edge in oldCallGraph.Edges)
+            {
+                callGraph.AddEdge(edge.Item1, edge.Item2);
+            }
+            int count = CommandLineOptions.Clo.InlineDepth;
+            while (count > 0)
+            {
+                foreach (Implementation impl in oldCallGraph.Nodes)
+                {
+                    List<Implementation> newNodes = new List<Implementation>();
+                    foreach (Implementation succ in callGraph.Successors(impl))
+                    {
+                        newNodes.AddRange(oldCallGraph.Successors(succ));
+                    }
+                    foreach (Implementation newNode in newNodes)
+                    {
+                        callGraph.AddEdge(impl, newNode);
+                    }
+                }
+                count--;
+            }
+        }
+
+        private Graph<Implementation> BuildCallGraph()
+        {
+            Graph<Implementation> callGraph = new Graph<Implementation>();
+            Dictionary<Procedure, HashSet<Implementation>> procToImpls = new Dictionary<Procedure, HashSet<Implementation>>();
+            foreach (var proc in program.Procedures)
+            {
+                procToImpls[proc] = new HashSet<Implementation>();
+            }
+            foreach (var impl in program.Implementations)
+            {
+                if (impl.SkipVerification) continue;
+                callGraph.AddSource(impl);
+                procToImpls[impl.Proc].Add(impl);
+            }
+            foreach (var impl in program.Implementations)
+            {
+                if (impl.SkipVerification) continue;
+                foreach (Block b in impl.Blocks)
+                {
+                    foreach (Cmd c in b.Cmds)
+                    {
+                        CallCmd cc = c as CallCmd;
+                        if (cc == null) continue;
+                        foreach (Implementation callee in procToImpls[cc.Proc])
+                        {
+                            callGraph.AddEdge(impl, callee);
+                        }
+                    }
+                }
+            }
+            return callGraph;
+        }
+
+
+        private bool ProcessImpl(Implementation impl)
+        {
+            var ret = false;
+            var gen = prover.VCExprGen;
+
+            // construct summaries
+            var env = VCExpressionGenerator.True;
+            foreach (var tup in impl2CalleeSummaries[impl.Name])
+            {
+                // Not Bilateral: then reject self predicates
+                if (UseBilateralAlgo == false && tup.Item1 == impl.Name)
+                    continue;
+
+                // Bilateral: only reject self summary
+                if (UseBilateralAlgo == true && tup.Item1 == impl.Name && tup.Item2)
+                    continue;
+
+                var calleeSummary = 
+                    impl2Summary[tup.Item1].GetSummaryExpr(
+                       GetVarMapping(name2Impl[tup.Item1], tup.Item4), prover.VCExprGen);
+                env = gen.AndSimp(env, gen.Eq(tup.Item3, calleeSummary));
+            }
+
+            var prev = impl2Summary[impl.Name].Copy();
+            var upper = impl2Summary[impl.Name].GetTrueSummary(program, impl);
+            var sw = new Stopwatch();
+            sw.Start();
+            var lowerTime = TimeSpan.Zero;
+
+            while(true)
+            {
+                var usedLower = true;
+                var query = impl2Summary[impl.Name];
+                sw.Restart();
+
+                // construct self summaries
+                var summaryExpr = VCExpressionGenerator.True;
+                foreach (var tup in impl2CalleeSummaries[impl.Name])
+                {
+                    if (UseBilateralAlgo == false && tup.Item1 != impl.Name)
+                        continue;
+                    if (UseBilateralAlgo == true && (tup.Item1 != impl.Name || !tup.Item2))
+                        continue;
+                    
+                    if (UseBilateralAlgo)
+                    {
+                        query = query.AbstractConsequence(upper);
+                        if (query == null) query = impl2Summary[tup.Item1];
+                        else usedLower = false;
+                    }
+
+                    var ts =
+                        query.GetSummaryExpr(
+                           GetVarMapping(name2Impl[tup.Item1], tup.Item4), prover.VCExprGen);
+                    summaryExpr = gen.AndSimp(summaryExpr, gen.Eq(tup.Item3, ts));
+                }
+                //Console.WriteLine("Trying summary for {0}: {1}", impl.Name, summaryExpr);
+
+                reporter.model = null;
+                var vc = gen.AndSimp(env, summaryExpr);
+                vc = gen.Implies(vc, impl2VC[impl.Name]);
+                
+                //Console.WriteLine("Checking: {0}", vc);
+                if (CommandLineOptions.Clo.Trace)
+                    Console.WriteLine("Verifying {0} ({1}): {2}", impl.Name, usedLower ? "lower" : "ac", query);
+
+                if (usedLower && lowerTime.TotalMilliseconds >= iterTimeLimit && iterTimeLimit >= 0)
+                {
+                    if (UseBilateralAlgo)
+                    {
+                        if (CommandLineOptions.Clo.Trace)
+                            Console.WriteLine("Timeout/Spaceout while verifying " + impl.Name);
+                        ret = prev.IsEqual(upper) ? false : true;
+                        impl2Summary[impl.Name] = upper;
+                        break;
+                    }
+                    else
+                    {
+                        if (CommandLineOptions.Clo.Trace)
+                            Console.WriteLine("Timeout/Spaceout while verifying " + impl.Name);
+                        var tt = impl2Summary[impl.Name].GetTrueSummary(program, impl);
+                        ret = prev.IsEqual(tt) ? false : true; ;
+                        impl2Summary[impl.Name] = tt;
+                        break;
+                    }
+                }
+
+                var start = DateTime.Now;
+
+                //prover.Push();
+                //prover.Assert(gen.Not(vc), true);
+                //prover.FlushAxiomsToTheoremProver();
+                //prover.Check();
+                //ProverInterface.Outcome proverOutcome = prover.CheckOutcome(reporter);
+                //prover.Pop();
+
+                prover.BeginCheck(impl.Name, vc, reporter);
+                ProverInterface.Outcome proverOutcome = prover.CheckOutcome(reporter);
+
+                var inc = (DateTime.Now - start);
+                proverTime += inc;
+                numProverQueries++;
+
+                sw.Stop();
+                if (usedLower) lowerTime += sw.Elapsed;
+
+                if(CommandLineOptions.Clo.Trace)
+                    Console.WriteLine("Time taken = " + inc.TotalSeconds.ToString()); 
+
+                if (UseBilateralAlgo)
+                {
+                    if (proverOutcome == ProverInterface.Outcome.TimeOut || proverOutcome == ProverInterface.Outcome.OutOfMemory)
+                    {
+                        if(CommandLineOptions.Clo.Trace)
+                            Console.WriteLine("Timeout/Spaceout while verifying " + impl.Name);
+                        ret = prev.IsEqual(upper) ? false : true;
+                        impl2Summary[impl.Name] = upper;
+                        break;
+                    }
+                    
+                    if (reporter.model == null && usedLower)
+                        break;
+
+                    if (reporter.model == null)
+                    {
+                        upper.Meet(query);
+                    }
+                    else
+                    {
+                        var state = CollectState(impl);
+                        impl2Summary[impl.Name].Join(state, reporter.model);
+                        ret = true;
+                    }
+                }
+                else
+                {
+                    if (proverOutcome == ProverInterface.Outcome.TimeOut || proverOutcome == ProverInterface.Outcome.OutOfMemory)
+                    {
+                        if (CommandLineOptions.Clo.Trace)
+                            Console.WriteLine("Timeout/Spaceout while verifying " + impl.Name);
+                        var tt = impl2Summary[impl.Name].GetTrueSummary(program, impl);
+                        ret = prev.IsEqual(tt) ? false : true; ;
+                        impl2Summary[impl.Name] = tt;
+                        break;
+                    }
+
+                    if (reporter.model == null)
+                        break;
+                    //reporter.model.Write(Console.Out);
+
+                    var state = CollectState(impl);
+                    impl2Summary[impl.Name].Join(state, reporter.model);
+                    ret = true;
+                }
+            }
+            return ret;
+        }
+
+        private Dictionary<string, VCExpr> GetVarMapping(Implementation impl, VCExprNAry summaryPred)
+        {
+            var ret = new Dictionary<string, VCExpr>();
+
+            var cnt = 0;
+            foreach (var g in program.GlobalVariables)
+            {
+                ret.Add(string.Format("old({0})", g.Name), summaryPred[cnt]);
+                cnt++;
+            }
+            foreach (var v in impl.InParams.OfType<Variable>().Concat(
+                impl.OutParams.OfType<Variable>().Concat(
+                impl.Proc.Modifies.OfType<IdentifierExpr>().Select(ie => ie.Decl))))
+            {
+                ret.Add(v.Name, summaryPred[cnt]);
+                cnt++;
+            }
+
+            // Fill up values of globals that are not modified
+            cnt = 0;
+            foreach (var g in program.GlobalVariables)
+            {
+                if (ret.ContainsKey(g.Name)) { cnt++; continue; }
+
+                ret.Add(string.Format("{0}", g.Name), summaryPred[cnt]);
+                cnt++;
+            }
+
+            // Constants
+            foreach (var c in program.Constants)
+            {
+                var value = prover.Context.BoogieExprTranslator.Translate(Expr.Ident(c));
+                ret.Add(string.Format("{0}", c.Name), value);
+                ret.Add(string.Format("old({0})", c.Name), value);
+            }
+
+            return ret;
+        }
+
+        private Dictionary<string, Model.Element> CollectState(Implementation impl)
+        {
+            var ret = new Dictionary<string, Model.Element>();
+
+            var model = reporter.model;
+            var implVars = impl2EndStateVars[impl.Name];
+
+            var cnt = 0;
+            foreach (var g in program.GlobalVariables)
+            {
+                ret.Add(string.Format("old({0})", g.Name), getValue(implVars[cnt], model));
+                cnt++;
+            }
+            foreach (var v in impl.InParams.OfType<Variable>().Concat(
+                impl.OutParams.OfType<Variable>().Concat(
+                impl.Proc.Modifies.OfType<IdentifierExpr>().Select(ie => ie.Decl))))
+            {
+                ret.Add(v.Name, getValue(implVars[cnt], model));
+                cnt++;
+            }
+
+            // Fill up values of globals that are not modified
+            cnt = 0;
+            foreach (var g in program.GlobalVariables)
+            {
+                if (ret.ContainsKey(g.Name)) { cnt++; continue; }
+
+                ret.Add(string.Format("{0}", g.Name), getValue(implVars[cnt], model));
+                cnt++;
+            }
+
+            // Constants
+            foreach (var c in program.Constants)
+            {
+                try
+                {
+                    var value = getValue(prover.Context.BoogieExprTranslator.Translate(Expr.Ident(c)), model);
+                    ret.Add(string.Format("{0}", c.Name), value);
+                    ret.Add(string.Format("old({0})", c.Name), value);
+                }
+                catch (Exception)
+                {
+                    // constant not assigned a value: add a default value
+                    Model.Element value = null;
+                    if (c.TypedIdent.Type.IsInt)
+                        value = model.MkIntElement(0);
+                    else if (c.TypedIdent.Type.IsBool)
+                        value = model.MkElement("false");
+
+                    ret.Add(string.Format("{0}", c.Name), value);
+                    ret.Add(string.Format("old({0})", c.Name), value);
+                }
+            }
+
+            return ret;
+        }
+
+        private Model.Element getValue(VCExpr arg, Model model)
+        {
+            if (arg is VCExprLiteral)
+            {
+                //return model.GetElement(arg.ToString());
+                return model.MkElement(arg.ToString());
+            }
+            else if (arg is VCExprVar)
+            {
+                var el = model.TryGetFunc(prover.Context.Lookup(arg as VCExprVar));
+                if (el != null)
+                {
+                    Debug.Assert(el.Arity == 0 && el.AppCount == 1);
+                    return el.Apps.First().Result;
+                }
+                else
+                {
+                    // Variable not defined; assign arbitrary value
+                    if (arg.Type.IsBool)
+                        return model.MkElement("false");
+                    else if (arg.Type.IsInt)
+                        return model.MkIntElement(0);
+                    else
+                        return null;
+                }
+            }
+            else
+            {
+                Debug.Assert(false);
+                return null;
+            }
+        }
+
+        private void attachEnsures(Implementation impl)
+        {
+            List<Variable> functionInterfaceVars = new List<Variable>();
+            foreach (Variable v in vcgen.program.GlobalVariables)
+            {
+                functionInterfaceVars.Add(new Formal(Token.NoToken, new TypedIdent(Token.NoToken, "", v.TypedIdent.Type), true));
+            }
+            foreach (Variable v in impl.InParams)
+            {
+                functionInterfaceVars.Add(new Formal(Token.NoToken, new TypedIdent(Token.NoToken, "", v.TypedIdent.Type), true));
+            }
+            foreach (Variable v in impl.OutParams)
+            {
+                functionInterfaceVars.Add(new Formal(Token.NoToken, new TypedIdent(Token.NoToken, "", v.TypedIdent.Type), true));
+            }
+            foreach (IdentifierExpr e in impl.Proc.Modifies)
+            {
+                if (e.Decl == null) continue;
+                functionInterfaceVars.Add(new Formal(Token.NoToken, new TypedIdent(Token.NoToken, "", e.Decl.TypedIdent.Type), true));
+            }
+            Formal returnVar = new Formal(Token.NoToken, new TypedIdent(Token.NoToken, "", Bpl.Type.Bool), false);
+            var function = new Function(Token.NoToken, impl.Name + summaryPredSuffix, functionInterfaceVars, returnVar);
+            prover.Context.DeclareFunction(function, "");
+
+            List<Expr> exprs = new List<Expr>();
+            foreach (Variable v in vcgen.program.GlobalVariables)
+            {
+                Contract.Assert(v != null);
+                exprs.Add(new OldExpr(Token.NoToken, new IdentifierExpr(Token.NoToken, v)));
+            }
+            foreach (Variable v in impl.Proc.InParams)
+            {
+                Contract.Assert(v != null);
+                exprs.Add(new IdentifierExpr(Token.NoToken, v));
+            }
+            foreach (Variable v in impl.Proc.OutParams)
+            {
+                Contract.Assert(v != null);
+                exprs.Add(new IdentifierExpr(Token.NoToken, v));
+            }
+            foreach (IdentifierExpr ie in impl.Proc.Modifies)
+            {
+                Contract.Assert(ie != null);
+                if (ie.Decl == null)
+                    continue;
+                exprs.Add(ie);
+            }
+            Expr postExpr = new NAryExpr(Token.NoToken, new FunctionCall(function), exprs);
+            impl.Proc.Ensures.Add(
+                new Ensures(Token.NoToken, false, postExpr, "", 
+                    new QKeyValue(Token.NoToken, "ah", new List<object>(), null)));
+        }
+
+        private void GenVC(Implementation impl)
+        {
+            ModelViewInfo mvInfo;
+            Dictionary<int, Absy> label2absy;
+
+            if (CommandLineOptions.Clo.Trace)
+            {
+                Console.WriteLine("Generating VC of {0}", impl.Name);
+            }
+
+            vcgen.ConvertCFG2DAG(impl);
+            vcgen.PassifyImpl(impl, out mvInfo);
+
+            var gen = prover.VCExprGen;
+            var vcexpr = vcgen.GenerateVC(impl, null, out label2absy, prover.Context);
+
+
+            // Find the assert
+            impl2EndStateVars.Add(impl.Name, new List<VCExpr>());
+            var found = false;
+            var assertId = -1;
+            foreach (var blk in impl.Blocks)
+            {
+                foreach (var cmd in blk.Cmds.OfType<AssertCmd>())
+                {
+                    if (SimpleUtil.isAssertTrue(cmd)) continue;
+                    var nary = cmd.Expr as NAryExpr;
+                    if (nary == null) continue;
+                    var pred = nary.Fun as FunctionCall;
+                    if (pred == null || pred.FunctionName != (impl.Name + (AbstractHoudini.summaryPredSuffix)))
+                        continue;
+
+                    Debug.Assert(!found);
+                    found = true;
+                    assertId = cmd.UniqueId;
+                    //Console.WriteLine("assert cmd id: {0}", cmd.UniqueId);
+                    nary.Args.OfType<Expr>()
+                        .Iter(expr => impl2EndStateVars[impl.Name].Add(prover.Context.BoogieExprTranslator.Translate(expr)));
+                }
+            }
+
+            // It is possible that no assert is found in the procedure. It happens when the
+            // procedure doesn't return.
+            //Debug.Assert(found);
+
+            // Grab summary predicates
+            var visitor = new FindSummaryPred(prover.VCExprGen, assertId);
+            vcexpr = visitor.Mutate(vcexpr, true);
+
+            // Create a macro so that the VC can sit with the theorem prover
+            Macro macro = new Macro(Token.NoToken, impl.Name + "Macro", new List<Variable>(), new Formal(Token.NoToken, new TypedIdent(Token.NoToken, "", Bpl.Type.Bool), false));
+            prover.DefineMacro(macro, vcexpr);
+
+            // Store VC
+            impl2VC.Add(impl.Name, gen.Function(macro));
+
+            //Console.WriteLine("VC of {0}: {1}", impl.Name, vcexpr);
+
+            // check sanity: only one predicate for self-summary
+            // (There may be none when the procedure doesn't return)
+            Debug.Assert(visitor.summaryPreds.Count(tup => tup.Item2) <= 1);
+
+            impl2CalleeSummaries.Add(impl.Name, new List<Tuple<string, bool, VCExprVar, VCExprNAry>>());
+            visitor.summaryPreds.Iter(tup => impl2CalleeSummaries[impl.Name].Add(tup));
+        }
+    }
+
+    public interface ISummaryElement
+    {
+        ISummaryElement Copy();
+        ISummaryElement GetFlaseSummary(Program program, Implementation impl);
+        void Join(Dictionary<string, Model.Element> state, Model model);
+        VCExpr GetSummaryExpr(Dictionary<string, VCExpr> incarnations, VCExpressionGenerator gen);
+        Expr GetSummaryExpr(Func<string, Expr> always, Func<string, Expr> forold);
+
+        // For Bilateral
+        ISummaryElement GetTrueSummary(Program program, Implementation impl);
+        void Meet(ISummaryElement other);
+        bool IsEqual(ISummaryElement other);
+        ISummaryElement AbstractConsequence(ISummaryElement upper);
+    }
+
+    public class ConstantVal : ISummaryElement
+    {
+        Program program;
+        Implementation impl;
+        // var -> const set
+        Dictionary<string, HashSet<int>> val;
+        // set of vars
+        HashSet<Variable> vars;
+
+        public static readonly int MAX = 3;
+
+        public ConstantVal()
+        {
+            // this is just a place holder
+            val = new Dictionary<string, HashSet<int>>();
+            vars = new HashSet<Variable>();
+        }
+
+        private ConstantVal(Program program, Implementation impl)
+        {
+            this.program = program;
+            this.impl = impl;
+            this.val = new Dictionary<string, HashSet<int>>();
+
+            vars = new HashSet<Variable>();
+            impl.Proc.Modifies
+                .OfType<IdentifierExpr>()
+                .Select(ie => ie.Decl)
+                .Where(v => v.TypedIdent.Type.IsInt)
+                .Iter(v => vars.Add(v));
+            impl.OutParams.OfType<Variable>()
+                .Where(v => v.TypedIdent.Type.IsInt)
+                .Iter(v => vars.Add(v));
+
+            vars.Iter(v => val.Add(v.Name, null));
+        }
+
+
+        public void Join(Dictionary<string, Model.Element> state, Model model)
+        {
+            foreach (var vv in vars)
+            {
+                var v = vv.Name;
+                var newv = state[v].AsInt();
+                var oldv = val[v];
+
+                if (oldv == null)
+                {
+                    val[v] = new HashSet<int>();
+                    val[v].Add(newv);
+                }
+                else if(oldv.Count > 0)
+                {
+                    val[v].Add(newv);
+                    if (val[v].Count > MAX)
+                        val[v] = new HashSet<int>();
+                } 
+
+            }
+        }
+
+        public VCExpr GetSummaryExpr(Dictionary<string, VCExpr> incarnations, VCExpressionGenerator gen)
+        {
+            VCExpr ret = VCExpressionGenerator.True;
+            if (val.Values.Any(v => v == null))
+                return VCExpressionGenerator.False;
+            
+            foreach (var v in vars)
+            {
+                var consts = val[v.Name];
+                Debug.Assert(consts != null);
+
+                if (consts.Count == 0)
+                    continue;
+
+                var vexpr = VCExpressionGenerator.False;
+                consts.Iter(c => vexpr = gen.OrSimp(vexpr, gen.Eq(incarnations[v.Name], gen.Integer(Microsoft.Basetypes.BigNum.FromInt(c)))));
+                ret = gen.AndSimp(ret, vexpr);
+            }
+
+            return ret;
+        }
+
+        public override string ToString()
+        {
+            var ret = "true";
+            if (val.Values.Any(v => v == null))
+                return "false";
+
+            foreach (var v in vars)
+            {
+                var consts = val[v.Name];
+                Debug.Assert(consts != null);
+
+                if (consts.Count == 0)
+                    continue;
+
+                var vexpr = "false";
+                consts.Iter(c => vexpr = 
+                    string.Format("{0} OR ({1} == {2})", vexpr, v.Name, c));
+
+                ret = string.Format("{0} AND ({1})", ret, vexpr);
+            }
+
+            return ret;
+        }
+
+
+        public ISummaryElement GetFlaseSummary(Program program, Implementation impl)
+        {
+            return new ConstantVal(program, impl);
+        }
+
+        #region ISummaryElement (Bilateral) Members
+
+
+        public ISummaryElement GetTrueSummary(Program program, Implementation impl)
+        {
+            throw new NotImplementedException();
+        }
+
+        public void Meet(ISummaryElement other)
+        {
+            throw new NotImplementedException();
+        }
+
+        public bool IsEqual(ISummaryElement other)
+        {
+            throw new NotImplementedException();
+        }
+
+        public ISummaryElement AbstractConsequence(ISummaryElement upper)
+        {
+            throw new NotImplementedException();
+        }
+
+        #endregion
+
+        #region ISummaryElement Members
+
+
+        public Expr GetSummaryExpr(Func<string, Expr> always, Func<string, Expr> forold)
+        {
+            throw new NotImplementedException();
+        }
+
+        #endregion
+
+        #region ISummaryElement Members
+
+        public ISummaryElement Copy()
+        {
+            throw new NotImplementedException();
+        }
+
+        #endregion
+    }
+
+    public class NamedExpr 
+    {
+        public string name;
+        public Expr expr;
+
+        public NamedExpr(string name, Expr expr)
+        {
+            this.name = name;
+            this.expr = expr;
+        }
+
+        public NamedExpr(Expr expr)
+        {
+            this.name = null;
+            this.expr = expr;
+        }
+
+        public override string ToString()
+        {
+            if (name != null)
+                return name;
+
+            return expr.ToString();
+        }
+    }
+
+    public class PredicateAbs : ISummaryElement
+    {
+        public static Dictionary<string, List<NamedExpr>> PrePreds { get; private set; }
+        public static Dictionary<string, HashSet<int>> PosPrePreds { get; private set; }
+        public static Dictionary<string, List<NamedExpr>> PostPreds { get; private set; }
+        public static Dictionary<Tuple<string, int>, List<PredicateAbsDisjunct>> UpperCandidates;
+        private static HashSet<string> boolConstants;
+        // {proc, pred-pair} -> polariry
+        public static HashSet<Tuple<string, int, int, bool, bool>> unsatPrePredPairs;
+        public static HashSet<Tuple<string, int, int, bool, bool>> unsatPostPredPairs;
+
+        // Temporary: used during eval
+        private static Model model = null;
+
+        string procName;
+        PredicateAbsDisjunct[] value;
+        bool isFalse;
+
+        public PredicateAbs(string procName)
+        {
+            this.procName = procName;
+            isFalse = true;
+            value = new PredicateAbsDisjunct[PostPreds[this.procName].Count];
+            for (int i = 0; i < PostPreds[this.procName].Count; i++) value[i] = null;
+        }
+
+        public static void Initialize(Program program)
+        {
+            PrePreds = new Dictionary<string, List<NamedExpr>>();
+            PostPreds = new Dictionary<string, List<NamedExpr>>();
+            PosPrePreds = new Dictionary<string, HashSet<int>>();
+
+            boolConstants = new HashSet<string>();
+            UpperCandidates = new Dictionary<Tuple<string, int>, List<PredicateAbsDisjunct>>();
+
+            program.Constants
+                .Where(c => c.TypedIdent.Type.IsBool)
+                .Iter(c => boolConstants.Add(c.Name));
+
+            // Add template pre-post to all procedures
+            var preT = new List<NamedExpr>();
+            var postT = new List<NamedExpr>();
+            var posPreT = new HashSet<int>();
+            var tempP = new HashSet<Procedure>();
+            foreach (var proc in
+                program.Procedures
+                .Where(proc => QKeyValue.FindBoolAttribute(proc.Attributes, "template")))
+            {
+                tempP.Add(proc);
+                foreach (var ens in proc.Ensures.OfType<Ensures>())
+                {
+                    var pos = QKeyValue.FindBoolAttribute(ens.Attributes, "positive");
+
+                    if (QKeyValue.FindBoolAttribute(ens.Attributes, "pre"))
+                    {
+                        preT.Add(new NamedExpr(null, ens.Condition));
+                        if (pos) posPreT.Add(preT.Count - 1);
+                    }
+
+                    if (QKeyValue.FindBoolAttribute(ens.Attributes, "post"))
+                        postT.Add(new NamedExpr(null, ens.Condition));
+
+                    var s = QKeyValue.FindStringAttribute(ens.Attributes, "pre");
+                    if (s != null)
+                    {
+                        preT.Add(new NamedExpr(s, ens.Condition));
+                        if (pos) posPreT.Add(preT.Count - 1);
+                    }
+
+                    s = QKeyValue.FindStringAttribute(ens.Attributes, "post");
+                    if (s != null)
+                        postT.Add(new NamedExpr(s, ens.Condition));
+                }
+            }
+
+            program.RemoveTopLevelDeclarations(decl => tempP.Contains(decl));
+            var upperPreds = new Dictionary<string, List<Expr>>();
+
+            foreach (var impl in program.Implementations)
+            {
+                PrePreds.Add(impl.Name, new List<NamedExpr>());
+                PostPreds.Add(impl.Name, new List<NamedExpr>());
+                PosPrePreds.Add(impl.Name, new HashSet<int>());
+
+                // Add "false" as the first post predicate
+                //PostPreds[impl.Name].Add(new NamedExpr(Expr.False));
+
+                preT.Iter(e => PrePreds[impl.Name].Add(e));
+                postT.Iter(e => PostPreds[impl.Name].Add(e));
+                PosPrePreds[impl.Name].UnionWith(posPreT);
+
+                // Pick up per-procedure pre-post
+                var nens = new List<Ensures>();
+                foreach (var ens in impl.Proc.Ensures.OfType<Ensures>())
+                {
+                    string s = null;
+                    var pos = QKeyValue.FindBoolAttribute(ens.Attributes, "positive");
+                    
+                    if (QKeyValue.FindBoolAttribute(ens.Attributes, "pre"))
+                    {
+                        PrePreds[impl.Name].Add(new NamedExpr(ens.Condition));
+                        PosPrePreds[impl.Name].Add(PrePreds[impl.Name].Count - 1);
+                    }
+                    else if (QKeyValue.FindBoolAttribute(ens.Attributes, "post"))
+                    {
+                        PostPreds[impl.Name].Add(new NamedExpr(ens.Condition));
+                    }
+                    else if ((s = QKeyValue.FindStringAttribute(ens.Attributes, "pre")) != null)
+                    {
+                        PrePreds[impl.Name].Add(new NamedExpr(s, ens.Condition));
+                        PosPrePreds[impl.Name].Add(PrePreds[impl.Name].Count - 1);
+                    }
+                    else if ((s = QKeyValue.FindStringAttribute(ens.Attributes, "post")) != null)
+                    {
+                        PostPreds[impl.Name].Add(new NamedExpr(s, ens.Condition));
+                    }
+                    else if (QKeyValue.FindBoolAttribute(ens.Attributes, "upper"))
+                    {
+                        var key = impl.Name;
+                        if (!upperPreds.ContainsKey(key))
+                            upperPreds.Add(key, new List<Expr>());
+                        upperPreds[key].Add(ens.Condition);
+                    }
+                    else
+                    {
+                        nens.Add(ens);
+                    }
+                }
+                impl.Proc.Ensures = nens;
+            }
+
+            foreach (var tup in upperPreds)
+            {
+                var procName = tup.Key;
+                var candidates = tup.Value;
+                if (!candidates.Any()) continue;
+
+                var strToPost = new Dictionary<string, int>();
+                for (int i = 0; i < PostPreds[procName].Count; i++)
+                {
+                    strToPost.Add(PostPreds[procName][i].expr.ToString(), i);
+                }
+
+                foreach (var expr in candidates)
+                {
+                    if (strToPost.ContainsKey(expr.ToString()))
+                    {
+                        var key = Tuple.Create(procName, strToPost[expr.ToString()]);
+                        if (!UpperCandidates.ContainsKey(key))
+                            UpperCandidates.Add(key, new List<PredicateAbsDisjunct>());
+                        UpperCandidates[key].Add(new PredicateAbsDisjunct(true, procName));
+                    }
+                    else
+                    {
+                        // Try parsing the expression as (pre-conjunct ==> post-pred)
+                        var parsed = ParseExpr(expr, procName);
+                        if (parsed != null && strToPost.ContainsKey(parsed.Item2.ToString()))
+                        {
+                            var key = Tuple.Create(procName, strToPost[parsed.Item2.ToString()]);
+                            if (!UpperCandidates.ContainsKey(key))
+                                UpperCandidates.Add(key, new List<PredicateAbsDisjunct>());
+                            UpperCandidates[key].Add(parsed.Item1);
+                        }
+                    }
+                }
+
+            }
+            //Console.WriteLine("Running Abstract Houdini");
+            //PostPreds.Iter(expr => Console.WriteLine("\tPost: {0}", expr));
+            //PrePreds.Iter(expr => Console.WriteLine("\tPre: {0}", expr));
+        }
+
+        // Try parsing the expression as (pre-conjunct ==> post-pred)
+        private static Tuple<PredicateAbsDisjunct, Expr> ParseExpr(Expr expr, string procName)
+        {
+            Expr postExpr = null;
+            Expr preExpr = null;
+
+            // Decompose outer Implies
+            var nexpr = expr as NAryExpr;
+            if (nexpr != null && (nexpr.Fun is BinaryOperator)
+                && (nexpr.Fun as BinaryOperator).Op == BinaryOperator.Opcode.Imp
+                && (nexpr.Args.Count == 2))
+            {
+                postExpr = nexpr.Args[1];
+                preExpr = nexpr.Args[0];
+            }
+            else
+            {
+                if(CommandLineOptions.Clo.Trace) Console.WriteLine("Failed to parse {0} (ignoring)", expr);
+                return null;
+            }
+
+
+            var atoms = DecomposeOuterAnd(preExpr);
+            var pos = new HashSet<int>();
+            var neg = new HashSet<int>();
+
+            foreach (var atom in atoms)
+            {
+                var index = PrePreds[procName].FindIndex(ne => ne.expr.ToString() == atom.ToString());
+                if (index == -1)
+                {
+                    index = PrePreds[procName].FindIndex(ne => Expr.Not(ne.expr).ToString() == atom.ToString());
+                    if (index == -1)
+                    {
+                        if(CommandLineOptions.Clo.Trace) Console.WriteLine("Failed to parse {0} (ignoring)", atom);
+                        return null;
+                    }
+                    else
+                    {
+                        neg.Add(index);
+                    }
+                }
+                else
+                {
+                    pos.Add(index);
+                }
+            }
+
+            var conj = new PredicateAbsConjunct(pos, neg, procName);
+            var conjls = new List<PredicateAbsConjunct>();
+            conjls.Add(conj);
+
+            return Tuple.Create(new PredicateAbsDisjunct(conjls, procName), postExpr);
+        }
+
+        // blah && blah ==> {blah, blah}
+        static IEnumerable<Expr> DecomposeOuterAnd(Expr expr)
+        {
+            var ret = new List<Expr>();
+
+            var nexpr = expr as NAryExpr;
+            if (nexpr == null
+                || !(nexpr.Fun is BinaryOperator)
+                || (nexpr.Fun as BinaryOperator).Op != BinaryOperator.Opcode.And)
+            {
+                    ret.Add(expr);
+            }
+            else
+            {
+                foreach (Expr a in nexpr.Args)
+                    ret.AddRange(DecomposeOuterAnd(a));
+            }
+
+            return ret;
+        }
+
+
+        private Model.Element Eval(Expr expr, Dictionary<string, Model.Element> state)
+        {
+            if (expr is LiteralExpr)
+            {
+                return ToElem((expr as LiteralExpr).Val);
+            }
+
+            if (expr is IdentifierExpr)
+            {
+                return LookupVariable((expr as IdentifierExpr).Name, state, false);
+            }
+
+            if (expr is OldExpr)
+            {
+                var ide = (expr as OldExpr).Expr as IdentifierExpr;
+                Debug.Assert(ide != null);
+
+                return LookupVariable(ide.Name, state, true);
+            }
+
+            if (expr is NAryExpr)
+            {
+                var nary = expr as NAryExpr;
+                if (nary.Fun is UnaryOperator)
+                {
+                    return ToElem((nary.Fun as UnaryOperator).Evaluate(ToValue(Eval(nary.Args[0], state))));
+                }
+                if (nary.Fun is BinaryOperator)
+                {
+                    return ToElem((nary.Fun as BinaryOperator).Evaluate(ToValue(Eval(nary.Args[0], state)), ToValue(Eval(nary.Args[1], state))));
+                }
+                if (nary.Fun is MapSelect && nary.Args.Count == 2)
+                {
+                    var index = Eval(nary.Args[1], state);
+                    var map = Eval(nary.Args[0], state) as Model.Array;
+                    Debug.Assert(map != null, "Variable of map type must have an Array-typed value");
+                    var ret = map.Value.TryEval(index as Model.Element);
+                    if (ret == null) ret = map.Value.Else;
+                    Debug.Assert(ret != null);
+                    return ret;
+                }
+                Debug.Assert(false, "No other op is handled");                
+            }
+            throw new NotImplementedException(string.Format("Expr of type {0} is not handled", expr.GetType().ToString()));
+        }
+
+        private Model.Element LookupVariable(string v, Dictionary<string, Model.Element> state, bool tryOld)
+        {
+            if (tryOld)
+            {
+                var oldv = string.Format("old({0})", v);
+                if (state.ContainsKey(oldv))
+                {
+                    return state[oldv];
+                }
+                throw new AbsHoudiniInternalError("Cannot handle this case");
+            }
+
+            if (state.ContainsKey(v))
+            {
+                return state[v];
+            }
+
+            /*
+            if (boolConstants.Contains(v))
+            {
+                // value of this constant is immaterial, return true
+                return model.MkElement("true");
+            }
+            */
+
+            throw new AbsHoudiniInternalError("Cannot handle this case");
+        }
+
+        private static VCExpr ToVcVar(string v, Dictionary<string, VCExpr> incarnations, bool tryOld)
+        {
+            if (tryOld)
+            {
+                var oldv = string.Format("old({0})", v);
+                if (incarnations.ContainsKey(oldv))
+                {
+                    return incarnations[oldv];
+                }
+                throw new AbsHoudiniInternalError("Cannot handle this case");
+            }
+
+            if (incarnations.ContainsKey(v))
+            {
+                return incarnations[v];
+            }
+
+            throw new AbsHoudiniInternalError("Cannot handle this case");
+        }
+
+        public static void FindUnsatPairs(VCExpressionGenerator gen, ProverInterface prover)
+        {
+            unsatPrePredPairs = new HashSet<Tuple<string, int, int, bool, bool>>();
+            unsatPostPredPairs = new HashSet<Tuple<string, int, int, bool, bool>>(); 
+
+            var cachePos = new HashSet<Tuple<string, string>>();
+            var cacheNeg = new HashSet<Tuple<string, string>>();
+            var record = new Action<object, string, int, int, bool, bool>(
+                (map, proc, e1, e2, p1, p2) => {
+                    var key = Tuple.Create(proc, e1, e2, p1, p2);
+                    if (map == PrePreds)
+                        unsatPrePredPairs.Add(key);
+                    else
+                        unsatPostPredPairs.Add(key);
+                }
+            );
+
+            var predMaps = new List<Dictionary<string, List<NamedExpr>>>();
+            predMaps.Add(PrePreds); predMaps.Add(PostPreds);
+
+            foreach (var map in predMaps)
+            {
+                foreach (var proc in map.Keys)
+                {
+                    for (int i = 0; i < 2 * map[proc].Count(); i++)
+                    {
+                        var p1 = (i % 2); // polarity
+                        var e1 = map[proc][i / 2].expr;
+                        if (p1 == 0) e1 = Expr.Not(e1);
+
+                        for (int j = 2 * ((i / 2) + 1); j < 2 * map[proc].Count(); j++)
+                        {
+                            var p2 = (j % 2); // polarity
+                            var e2 = map[proc][j / 2].expr;
+                            if (p2 == 0) e2 = Expr.Not(e2);
+
+                            var key = Tuple.Create(e1.ToString(), e2.ToString());
+                            if (cachePos.Contains(key))
+                            {
+                                record(map, proc, i / 2, j / 2, p1 == 1, p2 == 1);
+                                continue;
+                            }
+                            else if (cacheNeg.Contains(key))
+                            {
+                                continue;
+                            }
+
+                            if (!CheckIfUnsat(e1, e2, gen, prover))
+                            {
+                                cacheNeg.Add(key);
+                                continue;
+                            }
+                            cachePos.Add(key);
+                            record(map, proc, i / 2, j / 2, p1 == 1, p2 == 1);
+
+                            if (CommandLineOptions.Clo.Trace)
+                                Console.WriteLine("Proved UNSAT: {0}    {1}", e1, e2);
+                        }
+                    }
+                }
+            }
+        }
+
+        // Is a ^ b UNSAT?
+        private static bool CheckIfUnsat(Expr a, Expr b, VCExpressionGenerator gen, ProverInterface prover)
+        {
+            var gatherLitA = new GatherLiterals();
+            var gatherLitB = new GatherLiterals();
+
+            gatherLitA.Visit(a);
+            gatherLitB.Visit(b);
+
+            var seta = new HashSet<Variable>();
+            var setb = new HashSet<Variable>();
+            gatherLitA.literals.Iter(tup => seta.Add(tup.Item1));
+            gatherLitB.literals.Iter(tup => setb.Add(tup.Item1));
+            seta.IntersectWith(setb);
+            if (!seta.Any()) return false;
+            
+            // Create fresh variables
+            return CheckIfUnsat(Expr.And(a, b), gen, prover);
+        }
+
+        // Is a UNSAT?
+        private static bool CheckIfUnsat(Expr a, VCExpressionGenerator gen, ProverInterface prover)
+        {
+            var gatherLitA = new GatherLiterals();
+            gatherLitA.Visit(a);
+
+            // Create fresh variables
+            var counter = 0;
+            var incarnations = new Dictionary<string, VCExpr>();
+            foreach (var literal in gatherLitA.literals)
+            {
+                if (incarnations.ContainsKey(literal.Item2.ToString()))
+                    continue;
+
+                //if(!literal.Item1.TypedIdent.Type.IsInt && !literal.Item1.TypedIdent.Type.IsBool)
+                var v = gen.Variable("UNSATCheck" + counter, literal.Item1.TypedIdent.Type);
+                incarnations.Add(literal.Item2.ToString(), v);
+                counter++;
+            }
+
+            var vc1 = ToVcExpr(a, incarnations, gen);
+            var vc = gen.LabelPos("Temp", vc1);
+
+            // check
+            prover.AssertAxioms();
+            prover.Push();
+            prover.Assert(vc, true);
+            prover.Check();
+            var outcome = prover.CheckOutcomeCore(new AbstractHoudiniErrorReporter());
+            prover.Pop();
+
+            if (outcome == ProverInterface.Outcome.Valid)
+                return true;
+            return false;
+        }
+
+
+        class GatherLiterals : ReadOnlyVisitor
+        {
+            public List<Tuple<Variable, Expr>> literals;
+            bool inOld;
+
+            public GatherLiterals()
+            {
+                literals = new List<Tuple<Variable, Expr>>();
+                inOld = false;
+            }
+
+            public override Expr VisitOldExpr(OldExpr node)
+            {
+                var prev = inOld;
+                inOld = true;
+                var ret = base.VisitOldExpr(node);
+                inOld = prev;
+                return ret;
+            }
+
+            public override Expr VisitIdentifierExpr(IdentifierExpr node)
+            {
+                if (inOld)
+                    literals.Add(Tuple.Create(node.Decl, new OldExpr(Token.NoToken, node) as Expr));
+                else
+                    literals.Add(Tuple.Create(node.Decl, node as Expr));
+
+                return node;
+            }
+        }
+
+        private object ToValue(Model.Element elem)
+        {
+            if (elem is Model.Integer)
+            {
+                return Microsoft.Basetypes.BigNum.FromInt((elem as Model.Integer).AsInt());
+            }
+            if (elem is Model.Boolean)
+            {
+                return (elem as Model.Boolean).Value;
+            }
+            if (elem is Model.DatatypeValue && (elem as Model.DatatypeValue).Arguments.Length == 1 &&
+                (elem as Model.DatatypeValue).ConstructorName == "-" &&
+                (elem as Model.DatatypeValue).Arguments[0] is Model.Integer)
+            {
+                // negative number as "-" @ int
+                return Microsoft.Basetypes.BigNum.FromInt(-1 * ((elem as Model.DatatypeValue).Arguments[0] as Model.Integer).AsInt());
+            }
+            throw new NotImplementedException("Cannot yet handle this Model.Element type");
+        }
+
+        private Model.Element ToElem(object val)
+        {
+            if (val is bool || val is int || val is Basetypes.BigNum)
+                return model.MkElement(val.ToString());
+            throw new NotImplementedException("Cannot yet handle this value type");
+        }
+
+        // replace v by old(v)
+        private static Expr MakeOld(Expr expr)
+        {
+            var substalways = new Substitution(v => new OldExpr(Token.NoToken, Expr.Ident(v)));
+            var substold = new Substitution(v => Expr.Ident(v));
+
+            return Substituter.ApplyReplacingOldExprs(substalways, substold, expr);
+        }
+
+        private static Expr ToExpr(Expr expr, Func<string, Expr> always, Func<string, Expr> forold)
+        {
+            var substalways = new Substitution(v =>
+            {
+                var ret = always(v.Name);
+                if (ret != null) return ret;
+                else return Expr.Ident(v);
+            });
+            var substold = new Substitution(v =>
+            {
+                var ret = forold(v.Name);
+                if (ret != null) return ret;
+                else return new OldExpr(Token.NoToken, Expr.Ident(v));
+            });
+
+            return Substituter.ApplyReplacingOldExprs(substalways, substold, expr);
+        }
+
+        private static VCExpr ToVcExpr(Expr expr, Dictionary<string, VCExpr> incarnations, VCExpressionGenerator gen)
+        {
+            if (expr is LiteralExpr)
+            {
+                var val = (expr as LiteralExpr).Val;
+                if (val is bool)
+                {
+                    if ((bool)val)
+                    {
+                        return VCExpressionGenerator.True;
+                    }
+                    else
+                    {
+                        return VCExpressionGenerator.False;
+                    }
+                }
+                else if (val is Microsoft.Basetypes.BigNum)
+                {
+                    return gen.Integer((Microsoft.Basetypes.BigNum)val);
+                }
+
+                throw new NotImplementedException("Cannot handle literals of this type");
+            }
+
+            if (expr is IdentifierExpr)
+            {
+                return ToVcVar((expr as IdentifierExpr).Name, incarnations, false);
+            }
+
+            if (expr is OldExpr)
+            {
+                var ide = (expr as OldExpr).Expr as IdentifierExpr;
+                Debug.Assert(ide != null);
+
+                return ToVcVar(ide.Name, incarnations, true);
+            }
+
+            if (expr is NAryExpr)
+            {
+                var nary = expr as NAryExpr;
+                if (nary.Fun is UnaryOperator)
+                {
+                    if ((nary.Fun as UnaryOperator).Op == UnaryOperator.Opcode.Not)
+                        return gen.Not(ToVcExpr(nary.Args[0], incarnations, gen));
+                    else if ((nary.Fun as UnaryOperator).Op == UnaryOperator.Opcode.Neg)
+                        return gen.Function(VCExpressionGenerator.SubIOp, gen.Integer(Basetypes.BigNum.FromInt(0)), ToVcExpr(nary.Args[0], incarnations, gen));
+                    else
+                        Debug.Assert(false, "No other unary op is handled");
+                }
+                if (nary.Fun is BinaryOperator)
+                {
+                    return gen.Function(Translate(nary.Fun as BinaryOperator), ToVcExpr(nary.Args[0], incarnations, gen), ToVcExpr(nary.Args[1], incarnations, gen));
+                }
+                if (nary.Fun is MapSelect && nary.Args.Count == 2)
+                {
+                    return gen.Select(ToVcExpr(nary.Args[0], incarnations, gen), ToVcExpr(nary.Args[1], incarnations, gen));
+                }
+                Debug.Assert(false, "No other op is handled");
+            }
+            throw new NotImplementedException(string.Format("Expr of type {0} is not handled", expr.GetType().ToString()));
+        }
+
+        private static VCExprOp Translate(BinaryOperator op)
+        {
+            switch (op.Op)
+            {
+                case BinaryOperator.Opcode.Add:
+                    return VCExpressionGenerator.AddIOp;
+                case BinaryOperator.Opcode.Sub:
+                    return VCExpressionGenerator.SubIOp;
+                case BinaryOperator.Opcode.Mul:
+                    return VCExpressionGenerator.MulIOp;
+                case BinaryOperator.Opcode.Div:
+                    return VCExpressionGenerator.DivIOp;
+                case BinaryOperator.Opcode.Mod:
+                    return VCExpressionGenerator.ModOp;
+                case BinaryOperator.Opcode.Eq:
+                case BinaryOperator.Opcode.Iff:
+                    // we don't distinguish between equality and equivalence at this point
+                    return VCExpressionGenerator.EqOp;
+                case BinaryOperator.Opcode.Neq:
+                    return VCExpressionGenerator.NeqOp;
+                case BinaryOperator.Opcode.Lt:
+                    return VCExpressionGenerator.LtOp;
+                case BinaryOperator.Opcode.Le:
+                    return VCExpressionGenerator.LeOp;
+                case BinaryOperator.Opcode.Ge:
+                    return VCExpressionGenerator.GeOp;
+                case BinaryOperator.Opcode.Gt:
+                    return VCExpressionGenerator.GtOp;
+                case BinaryOperator.Opcode.Imp:
+                    return VCExpressionGenerator.ImpliesOp;
+                case BinaryOperator.Opcode.And:
+                    return VCExpressionGenerator.AndOp;
+                case BinaryOperator.Opcode.Or:
+                    return VCExpressionGenerator.OrOp;
+                case BinaryOperator.Opcode.Subtype:
+                    return VCExpressionGenerator.SubtypeOp;
+                default:
+                    Contract.Assert(false);
+                    throw new NotImplementedException();
+            }
+
+        }
+
+        // If "false" is a post-predicate, then remove its "pre" constraint from all others, whenever possible
+        public void Simplify()
+        {
+            // find "false"
+            var findex = PostPreds[procName].FindIndex(ne => (ne.expr is LiteralExpr) && (ne.expr as LiteralExpr).IsFalse);
+            if (findex < 0) return;
+            if (value[findex].isTrue)
+            {
+                // procedure doesn't return
+                for (int i = 0; i < value.Length; i++)
+                    if (i != findex) value[i] = new PredicateAbsDisjunct(false, procName);
+                return;
+            }
+            if (value[findex].isFalse)
+                return;
+
+            for (int i = 0; i < value.Length; i++)
+                if (i != findex) value[i].Subtract(value[findex]);
+        }
+
+        public HashSet<string> GetPredicates(Program program, VCExpressionGenerator gen, ProverInterface prover)
+        {
+            var ret = new HashSet<string>();
+            if (isFalse) return ret;
+            Simplify();
+
+            // Find the free expressions
+            var proc = program.Procedures.FirstOrDefault(p => p.Name == procName);
+            Contract.Assert(proc != null);
+            Expr freeSummary = Expr.True;
+            foreach (var req in proc.Requires.OfType<Requires>().Where(req => req.Free))
+            {
+                freeSummary = Expr.And(freeSummary, MakeOld(req.Condition));
+            }
+            foreach (var ens in proc.Ensures.OfType<Ensures>().Where(ens => ens.Free))
+            {
+                freeSummary = Expr.And(freeSummary, ens.Condition);
+            }
+            
+            for (int i = 0; i < PostPreds[procName].Count; i++)
+            {
+                if (value[i].isFalse) continue;
+                if (PostPreds[procName][i].expr is LiteralExpr && (PostPreds[procName][i].expr as LiteralExpr).IsFalse)
+                    continue;
+
+                if (value[i].isTrue)
+                    ret.Add(PostPreds[procName][i].expr.ToString());
+                else
+                {
+                    foreach (var c in value[i].GetConjuncts())
+                    {
+                        var s = Expr.Imp(c.ToExpr(j => PrePreds[procName][j].expr), PostPreds[procName][i].expr);
+                        if (CheckIfUnsat(Expr.And(freeSummary, Expr.Not(s)), gen, prover))
+                            continue;
+                        ret.Add(s.ToString());
+                    }
+                }
+            }
+            return ret;
+        }
+
+        public override string ToString()
+        {
+            var ret = "";
+            if (isFalse) return "false";
+            var first = true;
+
+            for(int i = 0; i < PostPreds[procName].Count; i++) 
+            {
+                if(value[i].isFalse) continue;
+                
+                if(value[i].isTrue)
+                    ret += string.Format("{0}{1}", first ? "" : " && ", PostPreds[procName][i]);
+                else
+                    ret += string.Format("{0}({1} ==> {2})", first ? "" : " && ", value[i], PostPreds[procName][i]);
+
+                first = false;
+            }
+            if (ret == "") ret = "true";
+            return ret;
+        }
+
+
+        #region ISummaryElement Members
+
+        public ISummaryElement Copy()
+        {
+            var ret = new PredicateAbs(procName);
+            ret.isFalse = isFalse;
+            ret.value = new PredicateAbsDisjunct[value.Length];
+            for (int i = 0; i < value.Length; i++)
+                ret.value[i] = value[i];
+            return ret;
+        }
+
+        public ISummaryElement GetFlaseSummary(Program program, Implementation impl)
+        {
+            return new PredicateAbs(impl.Name);
+        }
+
+        public ISummaryElement GetTrueSummary(Program program, Implementation impl)
+        {
+            var ret = new PredicateAbs(impl.Name);
+            ret.isFalse = false;
+            for (int i = 0; i < PostPreds[this.procName].Count; i++) ret.value[i] = new PredicateAbsDisjunct(false, impl.Name);
+
+            return ret;
+        }
+
+        public void Join(Dictionary<string, Model.Element> state, Model model)
+        {
+            PredicateAbs.model = model;
+
+            // Evaluate each predicate on the state
+            var prePredsVal = new bool[PrePreds[procName].Count];
+            var postPredsVal = new bool[PostPreds[procName].Count];
+
+            var indexSeq = new List<int>();
+            for (int i = 0; i < PrePreds[procName].Count; i++) indexSeq.Add(i);
+
+            for (int i = 0; i < PrePreds[procName].Count; i++)
+            {
+                var v = ToValue(Eval(PrePreds[procName][i].expr, state));
+                Debug.Assert(v is bool);
+                prePredsVal[i] = (bool)v;
+            }
+
+            for (int i = 0; i < PostPreds[procName].Count; i++)
+            {
+                var v = ToValue(Eval(PostPreds[procName][i].expr, state));
+                Debug.Assert(v is bool);
+                postPredsVal[i] = (bool)v;
+            }
+
+            for (int i = 0; i < PostPreds[procName].Count; i++)
+            {
+                // No hope for this post pred?
+                if (!isFalse && value[i].isFalse) continue;
+
+                var newDisj = new PredicateAbsDisjunct(true, procName);
+                if (!postPredsVal[i])
+                {
+                    newDisj = new PredicateAbsDisjunct(indexSeq.Where(j => !prePredsVal[j]), indexSeq.Where(j => prePredsVal[j] && !PosPrePreds[procName].Contains(j)), procName);
+                }
+
+                if (isFalse)
+                    value[i] = newDisj;
+                else
+                    value[i] = PredicateAbsDisjunct.And(value[i], newDisj);
+            }
+
+            /*
+            // do beta(model)
+            var that = new PredicateAbsDisjunct[PostPreds[procName].Count];
+            for (int i = 0; i < PostPreds[procName].Count; i++)
+            {
+                if (postPredsVal[i])
+                    that[i] = new PredicateAbsDisjunct(true, procName);
+                else if (i == 0)
+                {
+                    Debug.Assert(PostPreds[procName][0].ToString() == "false");
+                    var newDisj = new PredicateAbsDisjunct(true, procName);
+                    newDisj = new PredicateAbsDisjunct(indexSeq.Where(j => !prePredsVal[j]), indexSeq.Where(j => prePredsVal[j]), procName);
+                    that[i] = newDisj;
+                }
+                else
+                {
+                    // false
+                    that[i] = new PredicateAbsDisjunct(false, procName);
+                }
+            }
+
+            // Do join
+            for (int i = 0; i < PostPreds[procName].Count; i++)
+            {
+                if (isFalse)
+                    value[i] = that[i];
+                else
+                {
+                    if (i == 0)
+                        value[i] = PredicateAbsDisjunct.And(value[i], that[i]);
+                    else
+                    {
+                        var c1 = PredicateAbsDisjunct.And(value[i], that[i]);
+                        var c2 = PredicateAbsDisjunct.And(value[i], that[0]);
+                        var c3 = PredicateAbsDisjunct.And(value[0], that[i]);
+                        value[i] = PredicateAbsDisjunct.Or(c1, c2);
+                        value[i] = PredicateAbsDisjunct.Or(value[i], c3);
+                    }
+                }
+            }
+            */
+            isFalse = false;
+
+            //Console.WriteLine("Result of Join: {0}", this.ToString());
+        }
+
+        // Precondition: the upper guys are just {true/false/upper-candidate} ==> post-pred
+        public void Meet(ISummaryElement iother)
+        {
+            var other = iother as PredicateAbs;
+            if (isFalse) return;
+            if (other.isFalse)
+            {
+                isFalse = true;
+                for (int i = 0; i < PostPreds[this.procName].Count; i++) value[i] = null;
+                return;
+            }
+            Debug.Assert(this.procName == other.procName);
+
+            for (int i = 0; i < PostPreds[this.procName].Count; i++)
+            {
+                value[i] = PredicateAbsDisjunct.Or(value[i], other.value[i]);
+            }
+        }
+
+        public bool IsEqual(ISummaryElement other)
+        {
+            var that = other as PredicateAbs;
+            if (isFalse && that.isFalse) return true;
+            if (isFalse || that.isFalse) return false;
+            for (int i = 0; i < PostPreds[procName].Count; i++)
+            {
+                if (!PredicateAbsDisjunct.syntacticLessThan(value[i], that.value[i]) ||
+                    !PredicateAbsDisjunct.syntacticLessThan(that.value[i], value[i]))
+                    return false;
+            }
+            return true;
+        }
+
+        // Precondition: the upper guys are just {true/false/upper-candidate} ==> post-pred
+        // Postcondition: the returned value is also of this form (for just one post-pred)
+        public ISummaryElement AbstractConsequence(ISummaryElement iupper)
+        {
+            var upper = iupper as PredicateAbs;
+
+            for (int i = 0; i < PostPreds[this.procName].Count; i++)
+            {
+                if (upper.value[i].isTrue) continue;
+                if (!UpperCandidates.ContainsKey(Tuple.Create(procName, i))) continue;
+
+                foreach (var candidate in UpperCandidates[Tuple.Create(procName, i)])
+                {
+                    if (PredicateAbsDisjunct.syntacticLessThan(candidate, upper.value[i]))
+                        continue;
+                    if (!this.isFalse && !PredicateAbsDisjunct.syntacticLessThan(candidate, this.value[i]))
+                        continue;
+
+                    var ret = new PredicateAbs(this.procName);
+                    ret.isFalse = false;
+                    for (int j = 0; j < PostPreds[this.procName].Count; j++)
+                        ret.value[j] = new PredicateAbsDisjunct(false, this.procName);
+
+                    ret.value[i] = candidate;
+
+                    return ret;
+                }
+            }
+
+            // Giveup: the abstract consequence is too difficult to compute
+            return null;
+        }
+
+        public VCExpr GetSummaryExpr(Dictionary<string, VCExpr> incarnations, VCExpressionGenerator gen)
+        {
+            if (isFalse)
+                return VCExpressionGenerator.False;
+
+            var ret = VCExpressionGenerator.True;
+
+            for(int i = 0; i < PostPreds[procName].Count; i++)
+            {
+                ret = gen.AndSimp(ret, gen.ImpliesSimp(value[i].ToVcExpr(j => ToVcExpr(PrePreds[procName][j].expr, incarnations, gen), gen), ToVcExpr(PostPreds[procName][i].expr, incarnations, gen)));
+            }
+
+            return ret;
+        }
+
+        public Expr GetSummaryExpr(Func<string, Expr> always, Func<string, Expr> forold)
+        {
+            if (isFalse)
+                return Expr.False;
+
+            Expr ret = Expr.True;
+
+            for (int i = 0; i < PostPreds[procName].Count; i++)
+            {
+                ret = Expr.And(ret, Expr.Imp(value[i].ToExpr(j => ToExpr(PrePreds[procName][j].expr, always, forold)), ToExpr(PostPreds[procName][i].expr, always, forold)));
+            }
+
+            return ret;
+        }
+
+        #endregion
+    }
+
+    public class PredicateAbsDisjunct
+    {
+        List<PredicateAbsConjunct> conjuncts;
+        string ProcName;
+        public bool isTrue {get; private set;}
+        public bool isFalse
+        {
+            get
+            {
+                if (isTrue) return false;
+                return conjuncts.Count == 0;
+            }
+        }
+
+        public PredicateAbsDisjunct(bool isTrue, string ProcName)
+        {
+            this.isTrue = isTrue;
+            this.ProcName = ProcName;
+            conjuncts = new List<PredicateAbsConjunct>();
+        }
+
+        public PredicateAbsDisjunct(List<PredicateAbsConjunct> conjuncts, string ProcName)
+        {
+            isTrue = false;
+            this.conjuncts = conjuncts;
+            this.ProcName = ProcName;
+        }
+
+        // Disjunct of singleton conjuncts
+        public PredicateAbsDisjunct(IEnumerable<int> pos, IEnumerable<int> neg, string ProcName)
+        {
+            this.ProcName = ProcName;
+            conjuncts = new List<PredicateAbsConjunct>();
+            isTrue = false;
+            pos.Iter(p => conjuncts.Add(PredicateAbsConjunct.Singleton(p, true, ProcName)));
+            neg.Iter(p => conjuncts.Add(PredicateAbsConjunct.Singleton(p, false, ProcName)));
+        }
+
+        // Does d1 describe a smaller set of states than d2? This is true when every conjunct of d1
+        // is smaller than some conjunct of d2
+        public static bool syntacticLessThan(PredicateAbsDisjunct d1, PredicateAbsDisjunct d2)
+        {
+            if (d2.isTrue) return true;
+            if (d1.isTrue) return false;
+            if (d1.isFalse) return true;
+            if (d2.isFalse) return false;
+
+            foreach (var c1 in d1.conjuncts)
+            {
+                if (d2.conjuncts.Any(c2 => PredicateAbsConjunct.syntacticLessThan(c1, c2)))
+                    continue;
+                else
+                    return false;
+            }
+            return true;
+        }
+
+        public static PredicateAbsDisjunct And(PredicateAbsDisjunct v1, PredicateAbsDisjunct v2)
+        {
+            if (v1.isTrue) return v2;
+            if (v2.isTrue) return v1;
+
+            var result = new List<PredicateAbsConjunct>();
+
+            foreach (var c1 in v1.conjuncts)
+            {
+                foreach (var c2 in v2.conjuncts)
+                {
+                    var c = PredicateAbsConjunct.And(c1, c2);
+                    if (c.isFalse) continue;
+                    if (result.Any(cprime => c.implies(cprime))) continue;
+                    var tmp = new List<PredicateAbsConjunct>();
+                    tmp.Add(c);
+                    result.Where(cprime => !cprime.implies(c)).Iter(cprime => tmp.Add(cprime));
+                    result = tmp;
+                }
+            }
+
+            return new PredicateAbsDisjunct(result, v1.ProcName);
+        }
+
+        public static PredicateAbsDisjunct Or(PredicateAbsDisjunct v1, PredicateAbsDisjunct v2)
+        {
+            if (v1.isTrue) return v1;
+            if (v2.isTrue) return v2;
+            if (v1.isFalse) return v2;
+            if (v2.isFalse) return v1;
+
+            var result = new List<PredicateAbsConjunct>();
+            v1.conjuncts.Iter(c => result.Add(c));
+
+            foreach (var c in v2.conjuncts)
+            {
+                if (result.Any(cprime => c.implies(cprime))) continue;
+                var tmp = new List<PredicateAbsConjunct>();
+                tmp.Add(c);
+                result.Where(cprime => !cprime.implies(c)).Iter(cprime => tmp.Add(cprime));
+                result = tmp;
+            }
+
+            return new PredicateAbsDisjunct(result, v1.ProcName);
+        }
+
+        public VCExpr ToVcExpr(Func<int, VCExpr> predToExpr, VCExpressionGenerator gen)
+        {
+            if (isTrue) return VCExpressionGenerator.True;
+            var ret = VCExpressionGenerator.False;
+            conjuncts.Iter(c => ret = gen.OrSimp(ret, c.ToVcExpr(predToExpr, gen)));
+            return ret;
+        }
+
+        public Expr ToExpr(Func<int, Expr> predToExpr)
+        {
+            if (isTrue) return Expr.True;
+            Expr ret = Expr.False;
+            conjuncts.Iter(c => ret = Expr.Or(ret, c.ToExpr(predToExpr)));
+            return ret;
+        }
+
+        public override string ToString()
+        {
+            if(isTrue) 
+                return "true";
+            var ret = "";
+            var first = true;
+            foreach (var c in conjuncts)
+            {
+                if (c.isFalse) continue;
+                ret += string.Format("{0}{1}", first ? "" : " || ", c);
+                first = false;
+            }
+            return ret;
+        }
+
+        public void Subtract(PredicateAbsDisjunct that)
+        {
+            var ncon = new List<PredicateAbsConjunct>();
+            foreach (var c1 in conjuncts)
+            {
+                if (that.conjuncts.Any(c2 => c1.implies(c2)))
+                    continue;
+                ncon.Add(c1);
+            }
+            conjuncts = ncon;
+        }
+
+        public IEnumerable<PredicateAbsConjunct> GetConjuncts()
+        {
+            return conjuncts;
+        }
+
+    }
+
+    public class PredicateAbsConjunct
+    {
+        static int ConjunctBound = 3;
+
+        public bool isFalse { get; private set; }
+        HashSet<int> posPreds;
+        HashSet<int> negPreds;
+        string ProcName;
+
+        public static void Initialize(int bound)
+        {
+            ConjunctBound = bound;
+        }
+
+        private void Normalize()
+        {
+            if (posPreds.Intersect(negPreds).Any() || negPreds.Intersect(posPreds).Any() || (posPreds.Count + negPreds.Count > ConjunctBound))
+            {
+                isFalse = true;
+                posPreds = new HashSet<int>();
+                negPreds = new HashSet<int>();
+            }
+        }
+
+        // Do this step only once in a while?
+        private void StrongNormalize()
+        {
+            if (isFalse) return;
+
+            var candidates = new List<Tuple<int, bool>>();
+            posPreds.Iter(p => candidates.Add(Tuple.Create(p, true)));
+            negPreds.Iter(p => candidates.Add(Tuple.Create(p, false)));
+            var drop = new HashSet<int>();
+            for (int i = 0; i < candidates.Count; i++)
+            {
+                for (int j = 0; j < candidates.Count; j++)
+                {
+                    if (i == j) continue;
+
+                    var key = Tuple.Create(ProcName, candidates[i].Item1, candidates[j].Item1,
+                        candidates[i].Item2, candidates[j].Item2);
+                    if (PredicateAbs.unsatPrePredPairs.Contains(key))
+                    {
+                        isFalse = true;
+                        posPreds = new HashSet<int>();
+                        negPreds = new HashSet<int>();
+                        return;
+                    }
+
+                    key = Tuple.Create(ProcName, candidates[i].Item1, candidates[j].Item1,
+                        candidates[i].Item2, !candidates[j].Item2);
+
+                    if (PredicateAbs.unsatPrePredPairs.Contains(key))
+                        drop.Add(candidates[j].Item1);
+                }
+            }
+
+            posPreds.ExceptWith(drop);
+            negPreds.ExceptWith(drop);
+        }
+
+        public PredicateAbsConjunct(bool isFalse, string ProcName)
+        {
+            posPreds = new HashSet<int>();
+            negPreds = new HashSet<int>();
+            this.isFalse = isFalse;
+            this.ProcName = ProcName;
+        }
+
+        // do we know that c1 is surely less than or equal to c2? That is, c1 describes a smaller
+        // concretization. We check that c2 is a sub-conjunct of c1
+        public static bool syntacticLessThan(PredicateAbsConjunct c1, PredicateAbsConjunct c2)
+        {
+            if (c1.isFalse) return true;
+            if (c2.isFalse) return false;
+            return (c2.posPreds.IsSubsetOf(c1.posPreds) && c2.negPreds.IsSubsetOf(c1.negPreds));
+        }
+
+        public static PredicateAbsConjunct Singleton(int v, bool isPositive, string ProcName)
+        {
+            if (isPositive)
+                return new PredicateAbsConjunct(new int[] { v }, new HashSet<int>(), ProcName);
+            else
+                return new PredicateAbsConjunct(new HashSet<int>(), new int[] { v }, ProcName);
+        }
+
+        public PredicateAbsConjunct(IEnumerable<int> pos, IEnumerable<int> neg, string ProcName)
+        {
+            isFalse = false;
+            posPreds = new HashSet<int>(pos);
+            negPreds = new HashSet<int>(neg);
+            this.ProcName = ProcName;
+            Normalize();
+        }
+
+        public static PredicateAbsConjunct And(PredicateAbsConjunct v1, PredicateAbsConjunct v2)
+        {
+            if (v1.isFalse || v2.isFalse) return new PredicateAbsConjunct(true, v1.ProcName);
+            var ret =  new PredicateAbsConjunct(v1.posPreds.Union(v2.posPreds), v1.negPreds.Union(v2.negPreds), v1.ProcName);
+            ret.StrongNormalize();
+            return ret;
+        }
+
+        public bool implies(PredicateAbsConjunct v)
+        {
+            if (isFalse) return true;
+            if (v.isFalse) return false;
+            return (posPreds.IsSupersetOf(v.posPreds) && negPreds.IsSupersetOf(v.negPreds));
+        }
+
+        public VCExpr ToVcExpr(Func<int, VCExpr> predToExpr, VCExpressionGenerator gen)
+        {
+            if (isFalse) return VCExpressionGenerator.False;
+            var ret = VCExpressionGenerator.True;
+            posPreds.Iter(p => ret = gen.AndSimp(ret, predToExpr(p)));
+            negPreds.Iter(p => ret = gen.AndSimp(ret, gen.Not(predToExpr(p))));
+            return ret;
+        }
+
+        public Expr ToExpr(Func<int, Expr> predToExpr)
+        {
+            if (isFalse) return Expr.False;
+            Expr ret = Expr.True;
+            var pp = posPreds.ToList(); pp.Sort();
+            var np = negPreds.ToList(); np.Sort();
+            pp.Iter(p => ret = Expr.And(ret, predToExpr(p)));
+            np.Iter(p => ret = Expr.And(ret, Expr.Not(predToExpr(p)))); 
+            return ret;
+        }
+
+        public override string ToString()
+        {
+            if (isFalse)
+                return "false";
+
+            var ret = "";
+            var first = true;
+            foreach (var p in posPreds)
+            {
+                ret += string.Format("{0}{1}", first ? "" : " && ", PredicateAbs.PrePreds[ProcName][p]);
+                first = false;
+            }
+            foreach (var p in negPreds)
+            {
+                ret += string.Format("{0}!{1}", first ? "" : " && ", PredicateAbs.PrePreds[ProcName][p]);
+                first = false;
+            }
+            return ret;
+        }
+    }
+
+    class FindSummaryPred : MutatingVCExprVisitor<bool>
+    {
+        public List<Tuple<string, bool, VCExprVar, VCExprNAry>> summaryPreds;
+        int assertId;
+        private static int CounterId = 0;
+
+        public FindSummaryPred(VCExpressionGenerator gen, int assertId)
+            : base(gen)
+        {
+            summaryPreds = new List<Tuple<string, bool, VCExprVar, VCExprNAry>>();
+            this.assertId = assertId;
+        }
+
+        protected override VCExpr/*!*/ UpdateModifiedNode(VCExprNAry/*!*/ originalNode,
+                                              List<VCExpr/*!*/>/*!*/ newSubExprs,
+            // has any of the subexpressions changed?
+                                              bool changed,
+                                              bool arg)
+        {
+            Contract.Ensures(Contract.Result<VCExpr>() != null);
+
+            VCExpr ret;
+            if (changed)
+                ret = Gen.Function(originalNode.Op,
+                                   newSubExprs, originalNode.TypeArguments);
+            else
+                ret = originalNode;
+
+            VCExprNAry retnary = ret as VCExprNAry;
+            if (retnary == null) return ret;
+            var op = retnary.Op as VCExprBoogieFunctionOp;
+
+            if (op == null)
+            {
+                var lop = retnary.Op as VCExprLabelOp;
+                if (lop == null) return ret;
+                if (lop.pos) return ret;
+                if (!lop.label.Equals("@" + assertId.ToString())) return ret;
+                
+                //var subexpr = retnary[0] as VCExprNAry;
+                //if (subexpr == null) return ret;
+                //op = subexpr.Op as VCExprBoogieFunctionOp;
+                //if (op == null) return ret;
+
+                var subexpr = retnary[0] as VCExprVar;
+                if (subexpr == null) return ret;
+                if (!subexpr.Name.StartsWith("AbstractHoudiniControl")) return ret;
+
+                for (int i = 0; i < summaryPreds.Count; i++)
+                {
+                    if (summaryPreds[i].Item3 == subexpr)
+                        summaryPreds[i] = Tuple.Create(summaryPreds[i].Item1, true, summaryPreds[i].Item3, summaryPreds[i].Item4);
+                }
+                return ret;
+            }
+
+            string calleeName = op.Func.Name;
+
+            if (!calleeName.EndsWith(AbstractHoudini.summaryPredSuffix))
+                return ret;
+
+            var controlConst = Gen.Variable("AbstractHoudiniControl" + CounterId, Microsoft.Boogie.Type.Bool);
+            CounterId++;
+
+            summaryPreds.Add(Tuple.Create(calleeName.Substring(0, calleeName.Length - AbstractHoudini.summaryPredSuffix.Length), false, controlConst, retnary));
+
+            return controlConst;
+            //return ret;
+        }
+
+    }
+
+    class FindExistentialFunctions : MutatingVCExprVisitor<bool>
+    {
+        public List<Tuple<string, VCExprVar, VCExprNAry>> funcCalls;
+        private HashSet<string> existentialFunctions;
+        private static int CounterId = 0;
+
+        public FindExistentialFunctions(VCExpressionGenerator gen, HashSet<string> existentialFunctions)
+            : base(gen)
+        {
+            funcCalls = new List<Tuple<string, VCExprVar, VCExprNAry>>();
+            this.existentialFunctions = existentialFunctions;
+        }
+
+        protected override VCExpr/*!*/ UpdateModifiedNode(VCExprNAry/*!*/ originalNode,
+                                              List<VCExpr/*!*/>/*!*/ newSubExprs,
+            // has any of the subexpressions changed?
+                                              bool changed,
+                                              bool arg)
+        {
+            Contract.Ensures(Contract.Result<VCExpr>() != null);
+
+            VCExpr ret;
+            if (changed)
+                ret = Gen.Function(originalNode.Op,
+                                   newSubExprs, originalNode.TypeArguments);
+            else
+                ret = originalNode;
+
+            VCExprNAry retnary = ret as VCExprNAry;
+            if (retnary == null) return ret;
+            var op = retnary.Op as VCExprBoogieFunctionOp;
+            if (op == null) return ret;
+
+            string calleeName = op.Func.Name;
+
+            if (!existentialFunctions.Contains(calleeName))
+                return ret;
+
+            var controlConst = Gen.Variable("AbsHoudiniControl" + CounterId, Microsoft.Boogie.Type.Bool);
+            CounterId++;
+
+            funcCalls.Add(Tuple.Create(calleeName, controlConst, retnary));
+
+            return controlConst;
+        }
+
+    }
+
+    class AbstractHoudiniErrorReporter : ProverInterface.ErrorHandler
+    {
+        public Model model;
+
+        public AbstractHoudiniErrorReporter()
+        {
+            model = null;
+        }
+
+        public override void OnModel(IList<string> labels, Model model, ProverInterface.Outcome proverOutcome)
+        {
+            Debug.Assert(model != null);
+            if(CommandLineOptions.Clo.PrintErrorModel >= 1) model.Write(Console.Out);
+            this.model = model;
+        }
+    }
+
+    public class AbsHoudiniInternalError : System.ApplicationException
+    {
+        public AbsHoudiniInternalError(string msg) : base(msg) { }
+
+    };
+
+    public class SimpleUtil
+    {
+        // Constructs a mapping from procedure names to the implementation
+        public static Dictionary<string, Implementation> nameImplMapping(Program p)
+        {
+            var m = new Dictionary<string, Implementation>();
+            foreach (var impl in p.Implementations)
+            {
+                m.Add(impl.Name, impl);
+            }
+
+            return m;
+        }
+
+        // is "assert true"?
+        public static bool isAssertTrue(Cmd cmd)
+        {
+            var acmd = cmd as AssertCmd;
+            if (acmd == null) return false;
+            var le = acmd.Expr as LiteralExpr;
+            if (le == null) return false;
+            if (le.IsTrue) return true;
+            return false;
+        }
+    }
+
+}
diff --git a/Source/Houdini/AnnotationDependenceAnalyser.cs b/Source/Houdini/AnnotationDependenceAnalyser.cs
index e925d413..dacac233 100644
--- a/Source/Houdini/AnnotationDependenceAnalyser.cs
+++ b/Source/Houdini/AnnotationDependenceAnalyser.cs
@@ -1,878 +1,878 @@
-using System;

-using System.Collections.Generic;

-using System.Linq;

-using System.Text;

-using Microsoft.Boogie.GraphUtil;

-using Microsoft.Basetypes;

-using System.Diagnostics;

-

-namespace Microsoft.Boogie.Houdini {

-

-  public class AnnotationDependenceAnalyser {

-

-    private const string COARSE_STAGES = "COARSE";

-    private const string FINE_STAGES = "FINE";

-    private const string BALANCED_STAGES = "BALANCED";

-

-    private Program prog;

-    private IVariableDependenceAnalyser varDepAnalyser;

-    private IEnumerable<string> CandidateIdentifiers; // Candidate Boolean names

-    private IEnumerable<string> NonCandidateIdentifiers; // Additional names introduced for non-candidate annotations

-    private Dictionary<string, HashSet<VariableDescriptor>> annotationDependsOn;

-    private Dictionary<VariableDescriptor, HashSet<string>> variableDirectlyReferredToByAnnotations;

-    private Graph<string> AnnotationDependences;

-    private StronglyConnectedComponents<string> SCCs;

-    private Graph<SCC<string>> StagesDAG;

-    private StagedHoudiniPlan Plan;

-

-    public AnnotationDependenceAnalyser(Program prog) {

-      this.prog = prog;

-      this.varDepAnalyser = new VariableDependenceAnalyser(prog);

-      varDepAnalyser.Analyse();

-    }

-

-    public void Analyse() {

-      if (CommandLineOptions.Clo.Trace) {

-        Console.WriteLine("Annotation dependence analysis: Getting annotations");

-      }

-

-      CandidateIdentifiers = GetCandidates();

-      NonCandidateIdentifiers = GetNonCandidateAnnotations();

-

-      DetermineAnnotationVariableDependences();

-

-      ConstructAnnotationDependenceGraph();

-

-      ConstructStagesDAG();

-

-    }

-

-    private IEnumerable<string> AllAnnotationIdentifiers() {

-      HashSet<string> Result = new HashSet<string>();

-      foreach (var c in CandidateIdentifiers) {

-        Result.Add(c);

-      }

-      foreach (var a in NonCandidateIdentifiers) {

-        Result.Add(a);

-      }

-      return Result;

-    }

-

-    private void ConstructStagesDAG()

-    {

-      if (CommandLineOptions.Clo.Trace)

-      {

-        Console.WriteLine("Annotation dependence analysis: Computing SCCs");

-      }

-

-      Adjacency<string> next = new Adjacency<string>(AnnotationDependences.Successors);

-      Adjacency<string> prev = new Adjacency<string>(AnnotationDependences.Predecessors);

-      SCCs = new StronglyConnectedComponents<string>(

-        AnnotationDependences.Nodes, next, prev);

-      SCCs.Compute();

-

-      if (CommandLineOptions.Clo.Trace)

-      {

-        Console.WriteLine("Annotation dependence analysis: Building stages DAG");

-      }

-

-      Dictionary<string, SCC<string>> rep = new Dictionary<string, SCC<string>>();

-      foreach (var scc in SCCs)

-      {

-        foreach (var s in scc)

-        {

-          rep[s] = scc;

-        }

-      }

-

-      StagesDAG = new Graph<SCC<string>>();

-

-      foreach (var edge in AnnotationDependences.Edges)

-      {

-        if (rep[edge.Item1] != rep[edge.Item2])

-        {

-          StagesDAG.AddEdge(rep[edge.Item1], rep[edge.Item2]);

-        }

-      }

-

-      SCC<string> dummy = new SCC<string>();

-      foreach (var scc in SCCs)

-      {

-        StagesDAG.AddEdge(scc, dummy);

-      }

-    }

-

-    private void ConstructAnnotationDependenceGraph()

-    {

-      if (CommandLineOptions.Clo.Trace)

-      {

-        Console.WriteLine("Annotation dependence analysis: Building dependence graph");

-      }

-

-      IAnnotationReachabilityChecker reachabilityChecker;

-      

-      if(CommandLineOptions.Clo.StagedHoudiniReachabilityAnalysis) {

-        reachabilityChecker = new AnnotationReachabilityChecker(prog, AllAnnotationIdentifiers());

-      } else {

-        reachabilityChecker = new DummyAnnotationReachabilityChecker();

-      }

-

-      AnnotationDependences = new Graph<string>();

-      foreach (var c in AllAnnotationIdentifiers())

-      {

-        AnnotationDependences.AddEdge(c, c);

-        foreach (var vd in annotationDependsOn[c])

-        {

-          if (variableDirectlyReferredToByAnnotations.ContainsKey(vd))

-          {

-            foreach (var d in variableDirectlyReferredToByAnnotations[vd])

-            {

-              if(reachabilityChecker.MayReach(d, c))

-              {

-                AnnotationDependences.AddEdge(c, d);

-              }

-            }

-          }

-        }

-      }

-

-      if(CommandLineOptions.Clo.StagedHoudiniMergeIgnoredAnnotations) {

-        MergeIgnoredAnnotations();

-      }

-

-    }

-

-    private void MergeIgnoredAnnotations()

-    {

-      var IgnoredAnnotationsToVariables = new Dictionary<string, HashSet<Variable>>();

-      foreach(var c in AllAnnotationIdentifiers()) {

-        IgnoredAnnotationsToVariables[c] = new HashSet<Variable>();

-      }

-      foreach(var ci in AnnotationInstances()) {

-        if(!IgnoredAnnotationsToVariables.ContainsKey(ci.AnnotationIdentifier)) {

-          continue;

-        }

-        VariableCollector vc = new VariableCollector();

-        vc.Visit(ci.Expr);

-        if(vc.usedVars.Select(Item => varDepAnalyser.VariableRelevantToAnalysis(Item, ci.Proc)).Count() != 0) {

-          continue;

-        }

-        foreach(var v in vc.usedVars) {

-          if(varDepAnalyser.Ignoring(v, ci.Proc)) {

-            IgnoredAnnotationsToVariables[ci.AnnotationIdentifier].Add(v);

-          }

-        }

-      }

-      foreach(var c in IgnoredAnnotationsToVariables.Keys) {

-        foreach(var d in IgnoredAnnotationsToVariables.Keys) {

-          if(c == d) {

-            continue;

-          }

-          if(IgnoredAnnotationsToVariables[c].Equals(IgnoredAnnotationsToVariables[d])) {

-            AnnotationDependences.AddEdge(c, d);

-          }

-        }

-      }

-    }

-

-

-

-    private void DetermineAnnotationVariableDependences()

-    {

-      if (CommandLineOptions.Clo.Trace)

-      {

-        Console.WriteLine("Annotation dependence analysis: Working out what annotations depend on");

-      }

-      annotationDependsOn = new Dictionary<string, HashSet<VariableDescriptor>>();

-      variableDirectlyReferredToByAnnotations = new Dictionary<VariableDescriptor, HashSet<string>>();

-      foreach (var c in AllAnnotationIdentifiers())

-      {

-        annotationDependsOn[c] = new HashSet<VariableDescriptor>();

-      }

-

-      foreach(var annotationInstance in AnnotationInstances()) {

-        AddDependences(annotationInstance);

-      }

-

-    }

-

-    private IEnumerable<AnnotationInstance> AnnotationInstances()

-    {

-      foreach (var impl in prog.Implementations)

-      {

-        foreach (PredicateCmd p in impl.Blocks.SelectMany(Item => Item.Cmds).OfType<PredicateCmd>())

-        {

-          string c;

-          if(Houdini.MatchCandidate(p.Expr, CandidateIdentifiers, out c)) {

-            yield return new AnnotationInstance(c, impl.Name, p.Expr);

-          } else if((p is AssertCmd) && QKeyValue.FindBoolAttribute(p.Attributes, "originated_from_invariant")) {

-            var tag = GetTagFromNonCandidateAttributes(p.Attributes);

-            if (tag != null) {

-              yield return new AnnotationInstance(tag, impl.Name, p.Expr);

-            }

-          }

-        }

-      }

-

-      foreach (var proc in prog.NonInlinedProcedures())

-      {

-        foreach (Requires r in proc.Requires)

-        {

-          string c;

-          if(Houdini.MatchCandidate(r.Condition, CandidateIdentifiers, out c)) {

-            yield return new AnnotationInstance(c, proc.Name, r.Condition);

-          } else {

-            var tag = GetTagFromNonCandidateAttributes(r.Attributes);

-            if (tag != null) {

-              yield return new AnnotationInstance(tag, proc.Name, r.Condition);

-            }

-          }

-        }

-        foreach (Ensures e in proc.Ensures)

-        {

-          string c;

-          if(Houdini.MatchCandidate(e.Condition, CandidateIdentifiers, out c)) {

-            yield return new AnnotationInstance(c, proc.Name, e.Condition);

-          } else {

-            var tag = GetTagFromNonCandidateAttributes(e.Attributes);

-            if (tag != null) {

-              yield return new AnnotationInstance(tag, proc.Name, e.Condition);

-            }

-          }

-        }

-      }

-    }

-

-    internal static string GetTagFromNonCandidateAttributes(QKeyValue Attributes)

-    {

-      string tag = QKeyValue.FindStringAttribute(Attributes, "staged_houdini_tag");

-      return tag;

-    }

-

-    private bool FindInDAG(Graph<SCC<string>> DAG, SCC<string> toFind, SCC<string> start) {

-      if (toFind == start) {

-        return true;

-      }

-      foreach (var n in DAG.Successors(start)) {

-        if (FindInDAG(DAG, toFind, n)) {

-          return true;

-        }

-      }

-      return false;

-    }

-

-    private void AddDependences(AnnotationInstance ci) {

-      VariableCollector vc = new VariableCollector();

-      vc.VisitExpr(ci.Expr);

-

-      foreach (var v in vc.usedVars.Where(Item => varDepAnalyser.VariableRelevantToAnalysis(Item, ci.Proc))) {

-        VariableDescriptor vd =

-          varDepAnalyser.MakeDescriptor(ci.Proc, v);

-        if (!variableDirectlyReferredToByAnnotations.ContainsKey(vd)) {

-          variableDirectlyReferredToByAnnotations[vd] = new HashSet<string>();

-        }

-        variableDirectlyReferredToByAnnotations[vd].Add(ci.AnnotationIdentifier);

-

-        foreach (var w in varDepAnalyser.DependsOn(vd)) {

-          annotationDependsOn[ci.AnnotationIdentifier].Add(w);

-        }

-      }

-    }

-

-    private bool IsStageDependence(SCC<string> Src, SCC<string> Dst) {

-      foreach (var c in Src) {

-        foreach (var d in AnnotationDependences.Successors(c)) {

-          if (Dst.Contains(d)) {

-            return true;

-          }

-        }

-      }

-      return false;

-    }

-

-

-    public void dump() {

-

-      if(CommandLineOptions.Clo.DebugStagedHoudini) {

-        varDepAnalyser.dump();

-

-        Console.WriteLine("Annotations and the variables they depend on");

-        Console.WriteLine("============================================");

-        foreach (var entry in annotationDependsOn) {

-          Console.WriteLine(entry.Key + " <- ");

-          foreach (var vd in entry.Value) {

-            Console.WriteLine("  " + vd + ", ");

-          }

-        }

-

-        Console.WriteLine("");

-

-        Console.WriteLine("Variables and the annotations that directly refer to them");

-        Console.WriteLine("========================================================");

-        foreach (var entry in variableDirectlyReferredToByAnnotations) {

-          Console.WriteLine(entry.Key + " <- ");

-          foreach (var annotation in entry.Value) {

-            Console.WriteLine("  " + annotation + ", ");

-          }

-        }

-

-        Console.WriteLine("");

-

-        Console.WriteLine("Annotation dependence graph");

-        Console.WriteLine("==========================");

-        foreach (var c in AnnotationDependences.Nodes) {

-          Console.WriteLine(c + " <- ");

-          foreach (var d in AnnotationDependences.Successors(c)) {

-            Console.WriteLine("  " + d);

-          }

-        }

-      }

-

-      Console.WriteLine("");

-

-      Console.WriteLine("Strongly connected components");

-      Console.WriteLine("=============================");

-

-      List<SCC<string>> Components = StagesDAG.TopologicalSort().ToList();

-

-      for (int i = 0; i < Components.Count(); i++) {

-        Console.Write(i + ": ");

-        DumpSCC(Components[i]);

-        Console.WriteLine(); Console.WriteLine();

-      }

-

-      Console.WriteLine("Stages DAG");

-      Console.WriteLine("==========");

-      for (int i = 0; i < Components.Count(); i++) {

-        Console.Write(i + " -> { ");

-        bool first = true;

-        foreach (var d in StagesDAG.Successors(Components[i])) {

-          if (first) {

-            first = false;

-          }

-          else {

-            Console.Write(", ");

-          }

-          Console.Write(Components.IndexOf(d));

-        }

-        Console.WriteLine(" }");

-      }

-    

-    }

-

-    private static void DumpSCC(SCC<string> component) {

-      var sortedComponent = component.ToList();

-      sortedComponent.Sort();

-      Console.Write("{ ");

-      bool first = true;

-      foreach (var s in sortedComponent) {

-        if (first) {

-          first = false;

-        }

-        else {

-          Console.Write(", ");

-        }

-        Console.Write(s);

-      }

-      Console.Write(" }");

-    }

-

-    private bool OnlyRefersToConstants(Expr e) {

-      VariableCollector vc = new VariableCollector();

-      vc.Visit(e);

-      return vc.usedVars.OfType<Constant>().Count() == vc.usedVars.Count();

-    }

-

-    private IEnumerable<string> GetNonCandidateAnnotations() {

-      var Result = new HashSet<string>();

-      int Counter = 0;

-      foreach(var Assertion in prog.Blocks().SelectMany(Item => Item.Cmds).

-        OfType<AssertCmd>()) {

-

-        string unused;

-        if (Houdini.MatchCandidate(Assertion.Expr, CandidateIdentifiers, out unused)) {

-          continue;

-        }

-

-        if (!QKeyValue.FindBoolAttribute(Assertion.Attributes, "originated_from_invariant")) {

-          continue;

-        }

-

-        if (OnlyRefersToConstants(Assertion.Expr)) {

-          continue;

-        }

-

-        string Tag = "staged_houdini_tag_" + Counter;

-        Result.Add(Tag);

-        Assertion.Attributes = new QKeyValue(Token.NoToken, "staged_houdini_tag", 

-          new List<object> { Tag }, Assertion.Attributes);

-        Counter++;

-      }

-      

-      foreach(var Req in prog.NonInlinedProcedures().SelectMany(Item => Item.Requires)) {

-

-        string unused;

-        if (Houdini.MatchCandidate(Req.Condition, CandidateIdentifiers, out unused)) {

-          continue;

-        }

-

-        if (OnlyRefersToConstants(Req.Condition)) {

-          continue;

-        }

-

-        string Tag = "staged_houdini_tag_" + Counter;

-        Result.Add(Tag);

-        Req.Attributes = new QKeyValue(Token.NoToken, "staged_houdini_tag", 

-          new List<object> { Tag }, Req.Attributes);

-        Counter++;

-

-      }

-

-      foreach(var Ens in prog.NonInlinedProcedures().SelectMany(Item => Item.Ensures)) {

-

-        string unused;

-        if (Houdini.MatchCandidate(Ens.Condition, CandidateIdentifiers, out unused)) {

-          continue;

-        }

-

-        if (OnlyRefersToConstants(Ens.Condition)) {

-          continue;

-        }

-

-        string Tag = "staged_houdini_tag_" + Counter;

-        Result.Add(Tag);

-        Ens.Attributes = new QKeyValue(Token.NoToken, "staged_houdini_tag", 

-          new List<object> { Tag }, Ens.Attributes);

-        Counter++;

-

-      }

-

-      return Result;

-    }

-

-    private IEnumerable<string> GetCandidates() {

-      return prog.Variables.Where(Item =>

-        QKeyValue.FindBoolAttribute(Item.Attributes, "existential")).Select(Item => Item.Name);

-    }

-

-

-    public StagedHoudiniPlan ApplyStages() {

-

-        if (NoStages())

-        {

-          Debug.Assert(false);

-          var TrivialGraph = new Graph<ScheduledStage>();

-          TrivialGraph.AddSource(new ScheduledStage(0, new HashSet<string>()));

-          return new StagedHoudiniPlan(TrivialGraph);

-        }

-

-        #region Assign annotations to stages at a given level of granularity

-      

-        switch(CommandLineOptions.Clo.StagedHoudini) {

-          case COARSE_STAGES:

-            Plan = ComputeCoarseStages();

-            break;

-          case FINE_STAGES:

-            Plan = ComputeFineStages();

-            break;

-          case BALANCED_STAGES:

-            Plan = ComputeBalancedStages();

-            break;

-          default:

-            Debug.Assert(false);

-            Plan = null;

-            break;

-        }

-

-        foreach(var c in AllAnnotationIdentifiers()) {

-          Debug.Assert(Plan.StageForAnnotation(c) != null);

-        }

-        #endregion

-

-        #region Generate boolean variables to control stages

-        var stageToActiveBoolean = new Dictionary<int, Constant>();

-        var stageToCompleteBoolean = new Dictionary<int, Constant>();

-

-        foreach (var stage in Plan)

-        {

-            var stageActive = new Constant(Token.NoToken,

-                new TypedIdent(Token.NoToken, "_stage_" + stage.GetId() + "_active", Type.Bool),

-                false);

-            stageActive.AddAttribute("stage_active", new object[] { new LiteralExpr(Token.NoToken, BigNum.FromInt(stage.GetId())) });

-            prog.AddTopLevelDeclaration(stageActive);

-            stageToActiveBoolean[stage.GetId()] = stageActive;

-

-            var stageComplete = new Constant(Token.NoToken, 

-                new TypedIdent(Token.NoToken, "_stage_" + stage.GetId() + "_complete", Type.Bool),

-                false);

-            stageComplete.AddAttribute("stage_complete", new object[] { new LiteralExpr(Token.NoToken, BigNum.FromInt(stage.GetId())) });

-            prog.AddTopLevelDeclaration(stageComplete);

-            stageToCompleteBoolean[stage.GetId()] = stageComplete;

-        }

-        #endregion

-

-        #region Adapt annotation assertions to take account of stages

-        foreach (var b in prog.Implementations.Select(Item => Item.Blocks).SelectMany(Item => Item))

-        {

-            List<Cmd> newCmds = new List<Cmd>();

-            foreach (var cmd in b.Cmds)

-            {

-                var a = cmd as AssertCmd;

-                string c;

-                if (a != null) {

-                    if (Houdini.MatchCandidate(a.Expr, CandidateIdentifiers, out c))

-                    {

-                        newCmds.Add(new AssertCmd(a.tok, Houdini.AddConditionToCandidate(a.Expr,

-                            Expr.Ident(stageToActiveBoolean[Plan.StageForAnnotation(c).GetId()]), c), a.Attributes));

-                        newCmds.Add(new AssumeCmd(a.tok, Houdini.AddConditionToCandidate(a.Expr,

-                            Expr.Ident(stageToCompleteBoolean[Plan.StageForAnnotation(c).GetId()]), c), a.Attributes));

-                    } else if (QKeyValue.FindBoolAttribute(a.Attributes, "originated_from_invariant")) {

-                        string tag = GetTagFromNonCandidateAttributes(a.Attributes);

-                        if (tag == null) {

-                          newCmds.Add(a);

-                        } else {

-                          newCmds.Add(new AssertCmd(a.tok, Expr.Imp(

-                              Expr.Ident(stageToActiveBoolean[Plan.StageForAnnotation(tag).GetId()]), a.Expr),

-                              a.Attributes));

-                          newCmds.Add(new AssumeCmd(a.tok, Expr.Imp(

-                              Expr.Ident(stageToCompleteBoolean[Plan.StageForAnnotation(tag).GetId()]), a.Expr),

-                              a.Attributes));

-                        }

-                    }

-                }

-                else

-                {

-                    newCmds.Add(cmd);

-                }

-            }

-            b.Cmds = newCmds;

-        }

-        #endregion

-

-        #region Adapt pre/postconditions to take account of stages

-        foreach (var p in prog.NonInlinedProcedures())

-        {

-

-          #region Handle the preconditions

-          {

-            List<Requires> newRequires = new List<Requires>();

-            foreach(Requires r in p.Requires) {

-              string c;

-              if (Houdini.MatchCandidate(r.Condition, CandidateIdentifiers, out c)) {

-                newRequires.Add(new Requires(r.tok, false, 

-                  Houdini.AddConditionToCandidate(r.Condition,

-                  Expr.Ident(stageToActiveBoolean[Plan.StageForAnnotation(c).GetId()]), c),

-                  r.Comment, r.Attributes));

-                newRequires.Add(new Requires(r.tok, true, 

-                  Houdini.AddConditionToCandidate(r.Condition,

-                  Expr.Ident(stageToCompleteBoolean[Plan.StageForAnnotation(c).GetId()]), c),

-                  r.Comment, r.Attributes));

-              } else {

-                string tag = GetTagFromNonCandidateAttributes(r.Attributes);

-                if (tag == null) {

-                  newRequires.Add(r);

-                } else {

-                  newRequires.Add(new Requires(r.tok, false, 

-                    Expr.Imp(Expr.Ident(stageToActiveBoolean[Plan.StageForAnnotation(tag).GetId()]), r.Condition),

-                    r.Comment, r.Attributes));

-                  newRequires.Add(new Requires(r.tok, true, 

-                    Expr.Imp(Expr.Ident(stageToCompleteBoolean[Plan.StageForAnnotation(tag).GetId()]), r.Condition),

-                    r.Comment, r.Attributes));

-                }

-              }

-            }

-            p.Requires = newRequires;

-          }

-          #endregion

-

-          #region Handle the postconditions

-          {

-            List<Ensures> newEnsures = new List<Ensures>();

-            foreach(Ensures e in p.Ensures) {

-              string c;

-              if (Houdini.MatchCandidate(e.Condition, CandidateIdentifiers, out c)) {

-                int stage = Plan.StageForAnnotation(c).GetId();

-                newEnsures.Add(new Ensures(e.tok, false, 

-                  Houdini.AddConditionToCandidate(e.Condition,

-                  Expr.Ident(stageToActiveBoolean[stage]), c),

-                  e.Comment, e.Attributes));

-                newEnsures.Add(new Ensures(e.tok, true, 

-                  Houdini.AddConditionToCandidate(e.Condition,

-                  Expr.Ident(stageToCompleteBoolean[stage]), c),

-                  e.Comment, e.Attributes));

-              } else {

-                string tag = GetTagFromNonCandidateAttributes(e.Attributes);

-                if (tag == null) {

-                  newEnsures.Add(e);

-                } else {

-                  newEnsures.Add(new Ensures(e.tok, false, 

-                    Expr.Imp(Expr.Ident(stageToActiveBoolean[Plan.StageForAnnotation(tag).GetId()]), e.Condition),

-                    e.Comment, e.Attributes));

-                  newEnsures.Add(new Ensures(e.tok, true, 

-                    Expr.Imp(Expr.Ident(stageToCompleteBoolean[Plan.StageForAnnotation(tag).GetId()]), e.Condition),

-                    e.Comment, e.Attributes));

-                }

-              }

-            }

-            p.Ensures = newEnsures;

-          }

-          #endregion

-

-        }

-        #endregion

-

-        return Plan;

-

-    }

-

-    private int FindLargestStage() {

-      return StagesDAG.Nodes.Select(Item => Item.Count()).Max();

-    }

-

-

-    private StagedHoudiniPlan ComputeCoarseStages()

-    {

-        foreach(var n in StagesDAG.Nodes) {

-          Debug.Assert(!StagesDAG.Successors(n).Contains(n));

-        }

-

-        Graph<ScheduledStage> Dependences = new Graph<ScheduledStage>();

-

-        var done = new Dictionary<SCC<string>, ScheduledStage>();

-        done[GetStartNodeOfStagesDAG()] = new ScheduledStage(0, new HashSet<string>());

-

-        for(int stageId = 1; done.Count() != StagesDAG.Nodes.Count(); stageId++)

-        {

-            var Stage = new ScheduledStage(stageId, new HashSet<string>());

-            HashSet<SCC<string>> AssignedToThisStage = new HashSet<SCC<string>>();

-

-            foreach (var n in StagesDAG.Nodes.Where(Item => !done.ContainsKey(Item)))

-            {

-              if(StagesDAG.Successors(n).Where(Item => !done.ContainsKey(Item)).Count() == 0) {

-                foreach(var s in StagesDAG.Successors(n)) {

-                  Debug.Assert(s != n);

-                  Debug.Assert(Stage != done[s]);

-                  Dependences.AddEdge(Stage, done[s]);

-                }

-                foreach (var a in n)

-                {

-                  Stage.AddAnnotation(a);

-                }

-                AssignedToThisStage.Add(n);

-              }

-            }

-

-            foreach(var n in AssignedToThisStage) {

-              done[n] = Stage;

-            }

-        }

-        return new StagedHoudiniPlan(Dependences);

-    }

-

-    private StagedHoudiniPlan ComputeBalancedStages()

-    {

-      Graph<ScheduledStage> Dependences = new Graph<ScheduledStage>();

-      var done = new Dictionary<SCC<string>, ScheduledStage>();

-      done[GetStartNodeOfStagesDAG()] = new ScheduledStage(0, new HashSet<string>());

-

-      int maxStageSize = 200;

-

-      for(int stageId = 1; done.Count() != StagesDAG.Nodes.Count(); stageId++)

-      {

-        int stageSize = 0;

-        ScheduledStage Stage = new ScheduledStage(stageId, new HashSet<string>());

-        HashSet<SCC<string>> AddedToThisStage = new HashSet<SCC<string>>();

-

-        foreach (var n in StagesDAG.Nodes.Where(Item => !done.ContainsKey(Item)))

-        {

-          if(stageSize + n.Count() > maxStageSize) {

-            continue;

-          }

-          if(StagesDAG.Successors(n).Where(Item => !done.ContainsKey(Item)).Count() == 0) {

-            foreach (var c in n)

-            {

-              Stage.AddAnnotation(c);

-              stageSize++;

-            }

-            foreach(var s in StagesDAG.Successors(n)) {

-              Dependences.AddEdge(Stage, done[s]);

-            }

-            AddedToThisStage.Add(n);

-          }

-        }

-        foreach(var n in AddedToThisStage) {

-          done[n] = Stage;

-        }

-        if(stageSize == 0) {

-          maxStageSize *= 2;

-        }

-      }

-      return new StagedHoudiniPlan(Dependences);

-    }

-

-    private StagedHoudiniPlan ComputeFineStages()

-    {

-      Graph<ScheduledStage> Dependences = new Graph<ScheduledStage>();

-      var done = new Dictionary<SCC<string>, ScheduledStage>();

-

-      List<SCC<string>> components = StagesDAG.TopologicalSort().ToList();

-      components.Reverse();

-

-      for (int i = 0; i < components.Count(); i++)

-      {

-        ScheduledStage Stage = new ScheduledStage(i, new HashSet<string>());

-        done[components[i]] = Stage;

-        foreach (var c in components[i])

-        {

-          Stage.AddAnnotation(c);

-        }

-        foreach(var s in StagesDAG.Successors(components[i])) {

-          Dependences.AddEdge(Stage, done[s]);

-        }

-      }

-      return new StagedHoudiniPlan(Dependences);

-    }

-

-    private SCC<string> GetStartNodeOfStagesDAG()

-    {

-      return StagesDAG.Nodes.Where(Item => StagesDAG.Successors(Item).Count() == 0).

-        ToList()[0];

-    }

-

-    private bool NoStages()

-    {

-        return AllAnnotationIdentifiers().Count() == 0 || StagesDAG.Nodes.Count() == 0;

-    }

-  }

-

-  interface IAnnotationReachabilityChecker {

-    bool MayReach(string c, string d);

-  }

-

-  class DummyAnnotationReachabilityChecker : IAnnotationReachabilityChecker {

-    public bool MayReach(string c, string d) {

-      return true;

-    }

-  }

-

-  class AnnotationReachabilityChecker : IAnnotationReachabilityChecker {

-

-    private enum PrePost {

-      PRE, POST

-    }

-

-    private Program prog;

-    private IEnumerable<string> AnnotationIdentifiers;

-    private IInterproceduralReachabilityGraph reachabilityGraph;

-    private Dictionary<string, HashSet<object>> annotationToOccurences;

-

-    internal AnnotationReachabilityChecker(Program prog, IEnumerable<string> AnnotationIdentifiers) {

-      this.prog = prog;

-      this.AnnotationIdentifiers = AnnotationIdentifiers;

-      this.reachabilityGraph = new InterproceduralReachabilityGraph(prog);

-      this.annotationToOccurences = new Dictionary<string,HashSet<object>>();

-

-      // Add all annotation occurrences in blocks

-      foreach(Block b in prog.Blocks()) {

-        foreach(var assertCmd in b.Cmds.OfType<AssertCmd>()) {

-          string c;

-          if(Houdini.MatchCandidate(assertCmd.Expr, AnnotationIdentifiers, out c)) {

-            AddAnnotationOccurrence(c, b);

-          } else {

-            var tag = AnnotationDependenceAnalyser.GetTagFromNonCandidateAttributes(assertCmd.Attributes);

-            if (tag != null) {

-              AddAnnotationOccurrence(tag, b);

-            }

-          }

-        }

-      }

-

-      // Add all annotation occurrences in pre and post conditions

-      foreach(var proc in prog.NonInlinedProcedures()) {

-        foreach(Requires r in proc.Requires) {

-          string c;

-          if(Houdini.MatchCandidate(r.Condition, AnnotationIdentifiers, out c)) {

-            AddAnnotationOccurrence(c, new Tuple<string, PrePost>(proc.Name, PrePost.PRE));

-          } else {

-            string tag = AnnotationDependenceAnalyser.GetTagFromNonCandidateAttributes(r.Attributes);

-            if(tag != null) {

-              AddAnnotationOccurrence(tag, new Tuple<string, PrePost>(proc.Name, PrePost.PRE));

-            }

-          }

-        }

-        foreach(Ensures e in proc.Ensures) {

-          string c;

-          if(Houdini.MatchCandidate(e.Condition, AnnotationIdentifiers, out c)) {

-            AddAnnotationOccurrence(c, new Tuple<string, PrePost>(proc.Name, PrePost.POST));

-          } else {

-            string tag = AnnotationDependenceAnalyser.GetTagFromNonCandidateAttributes(e.Attributes);

-            if(tag != null) {

-              AddAnnotationOccurrence(tag, new Tuple<string, PrePost>(proc.Name, PrePost.PRE));

-            }

-          }

-        }

-      }

-      

-    }

-

-    private void AddAnnotationOccurrence(string c, object o) {

-      Debug.Assert(o is Block || o is Tuple<string, PrePost>);

-      if(!annotationToOccurences.ContainsKey(c)) {

-        annotationToOccurences[c] = new HashSet<object>();

-      }

-      annotationToOccurences[c].Add(o);

-    }

-

-    public bool MayReach(string c, string d) {

-      foreach(object cOccurrence in annotationToOccurences[c]) {

-        foreach(object dOccurrence in annotationToOccurences[d]) {

-          if(OccurrencesMayReach(cOccurrence, dOccurrence)) {

-            return true;

-          }

-        }

-      }

-      return false;

-    }

-

-    private bool OccurrencesMayReach(object cOccurrence, object dOccurrence) {

-      Debug.Assert(cOccurrence is Block || cOccurrence is Tuple<string, PrePost>);

-      Debug.Assert(dOccurrence is Block || dOccurrence is Tuple<string, PrePost>);

-

-      Block cInterproceduralBlock = GetInterproceduralBlock(cOccurrence);

-      Block dInterproceduralBlock = GetInterproceduralBlock(dOccurrence);

-

-      return reachabilityGraph.MayReach(cInterproceduralBlock, dInterproceduralBlock);

-

-    }

-

-    private Block GetInterproceduralBlock(object cOccurrence)

-    {

-      Debug.Assert(cOccurrence is Block || cOccurrence is Tuple<string, PrePost>);

-

-      var stringPrePostPair = cOccurrence as Tuple<string, PrePost>;

-      if(stringPrePostPair != null) {

-        if(stringPrePostPair.Item2 == PrePost.PRE) {

-          return reachabilityGraph.GetNewEntryBlock(stringPrePostPair.Item1);

-        } else {

-          return reachabilityGraph.GetNewExitBlock(stringPrePostPair.Item1);

-        }

-      }

-

-      return reachabilityGraph.GetNewBlock((Block)cOccurrence);

-

-    }

-  }

-

-  class AnnotationInstance {

-    public string AnnotationIdentifier;

-    public string Proc;

-    public Expr Expr;

-

-    internal AnnotationInstance(string AnnotationIdentifier, string Proc, Expr Expr) {

-      this.AnnotationIdentifier = AnnotationIdentifier;

-      this.Proc = Proc;

-      this.Expr = Expr;

-    }

-  }

-

-}

+using System;
+using System.Collections.Generic;
+using System.Linq;
+using System.Text;
+using Microsoft.Boogie.GraphUtil;
+using Microsoft.Basetypes;
+using System.Diagnostics;
+
+namespace Microsoft.Boogie.Houdini {
+
+  public class AnnotationDependenceAnalyser {
+
+    private const string COARSE_STAGES = "COARSE";
+    private const string FINE_STAGES = "FINE";
+    private const string BALANCED_STAGES = "BALANCED";
+
+    private Program prog;
+    private IVariableDependenceAnalyser varDepAnalyser;
+    private IEnumerable<string> CandidateIdentifiers; // Candidate Boolean names
+    private IEnumerable<string> NonCandidateIdentifiers; // Additional names introduced for non-candidate annotations
+    private Dictionary<string, HashSet<VariableDescriptor>> annotationDependsOn;
+    private Dictionary<VariableDescriptor, HashSet<string>> variableDirectlyReferredToByAnnotations;
+    private Graph<string> AnnotationDependences;
+    private StronglyConnectedComponents<string> SCCs;
+    private Graph<SCC<string>> StagesDAG;
+    private StagedHoudiniPlan Plan;
+
+    public AnnotationDependenceAnalyser(Program prog) {
+      this.prog = prog;
+      this.varDepAnalyser = new VariableDependenceAnalyser(prog);
+      varDepAnalyser.Analyse();
+    }
+
+    public void Analyse() {
+      if (CommandLineOptions.Clo.Trace) {
+        Console.WriteLine("Annotation dependence analysis: Getting annotations");
+      }
+
+      CandidateIdentifiers = GetCandidates();
+      NonCandidateIdentifiers = GetNonCandidateAnnotations();
+
+      DetermineAnnotationVariableDependences();
+
+      ConstructAnnotationDependenceGraph();
+
+      ConstructStagesDAG();
+
+    }
+
+    private IEnumerable<string> AllAnnotationIdentifiers() {
+      HashSet<string> Result = new HashSet<string>();
+      foreach (var c in CandidateIdentifiers) {
+        Result.Add(c);
+      }
+      foreach (var a in NonCandidateIdentifiers) {
+        Result.Add(a);
+      }
+      return Result;
+    }
+
+    private void ConstructStagesDAG()
+    {
+      if (CommandLineOptions.Clo.Trace)
+      {
+        Console.WriteLine("Annotation dependence analysis: Computing SCCs");
+      }
+
+      Adjacency<string> next = new Adjacency<string>(AnnotationDependences.Successors);
+      Adjacency<string> prev = new Adjacency<string>(AnnotationDependences.Predecessors);
+      SCCs = new StronglyConnectedComponents<string>(
+        AnnotationDependences.Nodes, next, prev);
+      SCCs.Compute();
+
+      if (CommandLineOptions.Clo.Trace)
+      {
+        Console.WriteLine("Annotation dependence analysis: Building stages DAG");
+      }
+
+      Dictionary<string, SCC<string>> rep = new Dictionary<string, SCC<string>>();
+      foreach (var scc in SCCs)
+      {
+        foreach (var s in scc)
+        {
+          rep[s] = scc;
+        }
+      }
+
+      StagesDAG = new Graph<SCC<string>>();
+
+      foreach (var edge in AnnotationDependences.Edges)
+      {
+        if (rep[edge.Item1] != rep[edge.Item2])
+        {
+          StagesDAG.AddEdge(rep[edge.Item1], rep[edge.Item2]);
+        }
+      }
+
+      SCC<string> dummy = new SCC<string>();
+      foreach (var scc in SCCs)
+      {
+        StagesDAG.AddEdge(scc, dummy);
+      }
+    }
+
+    private void ConstructAnnotationDependenceGraph()
+    {
+      if (CommandLineOptions.Clo.Trace)
+      {
+        Console.WriteLine("Annotation dependence analysis: Building dependence graph");
+      }
+
+      IAnnotationReachabilityChecker reachabilityChecker;
+      
+      if(CommandLineOptions.Clo.StagedHoudiniReachabilityAnalysis) {
+        reachabilityChecker = new AnnotationReachabilityChecker(prog, AllAnnotationIdentifiers());
+      } else {
+        reachabilityChecker = new DummyAnnotationReachabilityChecker();
+      }
+
+      AnnotationDependences = new Graph<string>();
+      foreach (var c in AllAnnotationIdentifiers())
+      {
+        AnnotationDependences.AddEdge(c, c);
+        foreach (var vd in annotationDependsOn[c])
+        {
+          if (variableDirectlyReferredToByAnnotations.ContainsKey(vd))
+          {
+            foreach (var d in variableDirectlyReferredToByAnnotations[vd])
+            {
+              if(reachabilityChecker.MayReach(d, c))
+              {
+                AnnotationDependences.AddEdge(c, d);
+              }
+            }
+          }
+        }
+      }
+
+      if(CommandLineOptions.Clo.StagedHoudiniMergeIgnoredAnnotations) {
+        MergeIgnoredAnnotations();
+      }
+
+    }
+
+    private void MergeIgnoredAnnotations()
+    {
+      var IgnoredAnnotationsToVariables = new Dictionary<string, HashSet<Variable>>();
+      foreach(var c in AllAnnotationIdentifiers()) {
+        IgnoredAnnotationsToVariables[c] = new HashSet<Variable>();
+      }
+      foreach(var ci in AnnotationInstances()) {
+        if(!IgnoredAnnotationsToVariables.ContainsKey(ci.AnnotationIdentifier)) {
+          continue;
+        }
+        VariableCollector vc = new VariableCollector();
+        vc.Visit(ci.Expr);
+        if(vc.usedVars.Select(Item => varDepAnalyser.VariableRelevantToAnalysis(Item, ci.Proc)).Count() != 0) {
+          continue;
+        }
+        foreach(var v in vc.usedVars) {
+          if(varDepAnalyser.Ignoring(v, ci.Proc)) {
+            IgnoredAnnotationsToVariables[ci.AnnotationIdentifier].Add(v);
+          }
+        }
+      }
+      foreach(var c in IgnoredAnnotationsToVariables.Keys) {
+        foreach(var d in IgnoredAnnotationsToVariables.Keys) {
+          if(c == d) {
+            continue;
+          }
+          if(IgnoredAnnotationsToVariables[c].Equals(IgnoredAnnotationsToVariables[d])) {
+            AnnotationDependences.AddEdge(c, d);
+          }
+        }
+      }
+    }
+
+
+
+    private void DetermineAnnotationVariableDependences()
+    {
+      if (CommandLineOptions.Clo.Trace)
+      {
+        Console.WriteLine("Annotation dependence analysis: Working out what annotations depend on");
+      }
+      annotationDependsOn = new Dictionary<string, HashSet<VariableDescriptor>>();
+      variableDirectlyReferredToByAnnotations = new Dictionary<VariableDescriptor, HashSet<string>>();
+      foreach (var c in AllAnnotationIdentifiers())
+      {
+        annotationDependsOn[c] = new HashSet<VariableDescriptor>();
+      }
+
+      foreach(var annotationInstance in AnnotationInstances()) {
+        AddDependences(annotationInstance);
+      }
+
+    }
+
+    private IEnumerable<AnnotationInstance> AnnotationInstances()
+    {
+      foreach (var impl in prog.Implementations)
+      {
+        foreach (PredicateCmd p in impl.Blocks.SelectMany(Item => Item.Cmds).OfType<PredicateCmd>())
+        {
+          string c;
+          if(Houdini.MatchCandidate(p.Expr, CandidateIdentifiers, out c)) {
+            yield return new AnnotationInstance(c, impl.Name, p.Expr);
+          } else if((p is AssertCmd) && QKeyValue.FindBoolAttribute(p.Attributes, "originated_from_invariant")) {
+            var tag = GetTagFromNonCandidateAttributes(p.Attributes);
+            if (tag != null) {
+              yield return new AnnotationInstance(tag, impl.Name, p.Expr);
+            }
+          }
+        }
+      }
+
+      foreach (var proc in prog.NonInlinedProcedures())
+      {
+        foreach (Requires r in proc.Requires)
+        {
+          string c;
+          if(Houdini.MatchCandidate(r.Condition, CandidateIdentifiers, out c)) {
+            yield return new AnnotationInstance(c, proc.Name, r.Condition);
+          } else {
+            var tag = GetTagFromNonCandidateAttributes(r.Attributes);
+            if (tag != null) {
+              yield return new AnnotationInstance(tag, proc.Name, r.Condition);
+            }
+          }
+        }
+        foreach (Ensures e in proc.Ensures)
+        {
+          string c;
+          if(Houdini.MatchCandidate(e.Condition, CandidateIdentifiers, out c)) {
+            yield return new AnnotationInstance(c, proc.Name, e.Condition);
+          } else {
+            var tag = GetTagFromNonCandidateAttributes(e.Attributes);
+            if (tag != null) {
+              yield return new AnnotationInstance(tag, proc.Name, e.Condition);
+            }
+          }
+        }
+      }
+    }
+
+    internal static string GetTagFromNonCandidateAttributes(QKeyValue Attributes)
+    {
+      string tag = QKeyValue.FindStringAttribute(Attributes, "staged_houdini_tag");
+      return tag;
+    }
+
+    private bool FindInDAG(Graph<SCC<string>> DAG, SCC<string> toFind, SCC<string> start) {
+      if (toFind == start) {
+        return true;
+      }
+      foreach (var n in DAG.Successors(start)) {
+        if (FindInDAG(DAG, toFind, n)) {
+          return true;
+        }
+      }
+      return false;
+    }
+
+    private void AddDependences(AnnotationInstance ci) {
+      VariableCollector vc = new VariableCollector();
+      vc.VisitExpr(ci.Expr);
+
+      foreach (var v in vc.usedVars.Where(Item => varDepAnalyser.VariableRelevantToAnalysis(Item, ci.Proc))) {
+        VariableDescriptor vd =
+          varDepAnalyser.MakeDescriptor(ci.Proc, v);
+        if (!variableDirectlyReferredToByAnnotations.ContainsKey(vd)) {
+          variableDirectlyReferredToByAnnotations[vd] = new HashSet<string>();
+        }
+        variableDirectlyReferredToByAnnotations[vd].Add(ci.AnnotationIdentifier);
+
+        foreach (var w in varDepAnalyser.DependsOn(vd)) {
+          annotationDependsOn[ci.AnnotationIdentifier].Add(w);
+        }
+      }
+    }
+
+    private bool IsStageDependence(SCC<string> Src, SCC<string> Dst) {
+      foreach (var c in Src) {
+        foreach (var d in AnnotationDependences.Successors(c)) {
+          if (Dst.Contains(d)) {
+            return true;
+          }
+        }
+      }
+      return false;
+    }
+
+
+    public void dump() {
+
+      if(CommandLineOptions.Clo.DebugStagedHoudini) {
+        varDepAnalyser.dump();
+
+        Console.WriteLine("Annotations and the variables they depend on");
+        Console.WriteLine("============================================");
+        foreach (var entry in annotationDependsOn) {
+          Console.WriteLine(entry.Key + " <- ");
+          foreach (var vd in entry.Value) {
+            Console.WriteLine("  " + vd + ", ");
+          }
+        }
+
+        Console.WriteLine("");
+
+        Console.WriteLine("Variables and the annotations that directly refer to them");
+        Console.WriteLine("========================================================");
+        foreach (var entry in variableDirectlyReferredToByAnnotations) {
+          Console.WriteLine(entry.Key + " <- ");
+          foreach (var annotation in entry.Value) {
+            Console.WriteLine("  " + annotation + ", ");
+          }
+        }
+
+        Console.WriteLine("");
+
+        Console.WriteLine("Annotation dependence graph");
+        Console.WriteLine("==========================");
+        foreach (var c in AnnotationDependences.Nodes) {
+          Console.WriteLine(c + " <- ");
+          foreach (var d in AnnotationDependences.Successors(c)) {
+            Console.WriteLine("  " + d);
+          }
+        }
+      }
+
+      Console.WriteLine("");
+
+      Console.WriteLine("Strongly connected components");
+      Console.WriteLine("=============================");
+
+      List<SCC<string>> Components = StagesDAG.TopologicalSort().ToList();
+
+      for (int i = 0; i < Components.Count(); i++) {
+        Console.Write(i + ": ");
+        DumpSCC(Components[i]);
+        Console.WriteLine(); Console.WriteLine();
+      }
+
+      Console.WriteLine("Stages DAG");
+      Console.WriteLine("==========");
+      for (int i = 0; i < Components.Count(); i++) {
+        Console.Write(i + " -> { ");
+        bool first = true;
+        foreach (var d in StagesDAG.Successors(Components[i])) {
+          if (first) {
+            first = false;
+          }
+          else {
+            Console.Write(", ");
+          }
+          Console.Write(Components.IndexOf(d));
+        }
+        Console.WriteLine(" }");
+      }
+    
+    }
+
+    private static void DumpSCC(SCC<string> component) {
+      var sortedComponent = component.ToList();
+      sortedComponent.Sort();
+      Console.Write("{ ");
+      bool first = true;
+      foreach (var s in sortedComponent) {
+        if (first) {
+          first = false;
+        }
+        else {
+          Console.Write(", ");
+        }
+        Console.Write(s);
+      }
+      Console.Write(" }");
+    }
+
+    private bool OnlyRefersToConstants(Expr e) {
+      VariableCollector vc = new VariableCollector();
+      vc.Visit(e);
+      return vc.usedVars.OfType<Constant>().Count() == vc.usedVars.Count();
+    }
+
+    private IEnumerable<string> GetNonCandidateAnnotations() {
+      var Result = new HashSet<string>();
+      int Counter = 0;
+      foreach(var Assertion in prog.Blocks().SelectMany(Item => Item.Cmds).
+        OfType<AssertCmd>()) {
+
+        string unused;
+        if (Houdini.MatchCandidate(Assertion.Expr, CandidateIdentifiers, out unused)) {
+          continue;
+        }
+
+        if (!QKeyValue.FindBoolAttribute(Assertion.Attributes, "originated_from_invariant")) {
+          continue;
+        }
+
+        if (OnlyRefersToConstants(Assertion.Expr)) {
+          continue;
+        }
+
+        string Tag = "staged_houdini_tag_" + Counter;
+        Result.Add(Tag);
+        Assertion.Attributes = new QKeyValue(Token.NoToken, "staged_houdini_tag", 
+          new List<object> { Tag }, Assertion.Attributes);
+        Counter++;
+      }
+      
+      foreach(var Req in prog.NonInlinedProcedures().SelectMany(Item => Item.Requires)) {
+
+        string unused;
+        if (Houdini.MatchCandidate(Req.Condition, CandidateIdentifiers, out unused)) {
+          continue;
+        }
+
+        if (OnlyRefersToConstants(Req.Condition)) {
+          continue;
+        }
+
+        string Tag = "staged_houdini_tag_" + Counter;
+        Result.Add(Tag);
+        Req.Attributes = new QKeyValue(Token.NoToken, "staged_houdini_tag", 
+          new List<object> { Tag }, Req.Attributes);
+        Counter++;
+
+      }
+
+      foreach(var Ens in prog.NonInlinedProcedures().SelectMany(Item => Item.Ensures)) {
+
+        string unused;
+        if (Houdini.MatchCandidate(Ens.Condition, CandidateIdentifiers, out unused)) {
+          continue;
+        }
+
+        if (OnlyRefersToConstants(Ens.Condition)) {
+          continue;
+        }
+
+        string Tag = "staged_houdini_tag_" + Counter;
+        Result.Add(Tag);
+        Ens.Attributes = new QKeyValue(Token.NoToken, "staged_houdini_tag", 
+          new List<object> { Tag }, Ens.Attributes);
+        Counter++;
+
+      }
+
+      return Result;
+    }
+
+    private IEnumerable<string> GetCandidates() {
+      return prog.Variables.Where(Item =>
+        QKeyValue.FindBoolAttribute(Item.Attributes, "existential")).Select(Item => Item.Name);
+    }
+
+
+    public StagedHoudiniPlan ApplyStages() {
+
+        if (NoStages())
+        {
+          Debug.Assert(false);
+          var TrivialGraph = new Graph<ScheduledStage>();
+          TrivialGraph.AddSource(new ScheduledStage(0, new HashSet<string>()));
+          return new StagedHoudiniPlan(TrivialGraph);
+        }
+
+        #region Assign annotations to stages at a given level of granularity
+      
+        switch(CommandLineOptions.Clo.StagedHoudini) {
+          case COARSE_STAGES:
+            Plan = ComputeCoarseStages();
+            break;
+          case FINE_STAGES:
+            Plan = ComputeFineStages();
+            break;
+          case BALANCED_STAGES:
+            Plan = ComputeBalancedStages();
+            break;
+          default:
+            Debug.Assert(false);
+            Plan = null;
+            break;
+        }
+
+        foreach(var c in AllAnnotationIdentifiers()) {
+          Debug.Assert(Plan.StageForAnnotation(c) != null);
+        }
+        #endregion
+
+        #region Generate boolean variables to control stages
+        var stageToActiveBoolean = new Dictionary<int, Constant>();
+        var stageToCompleteBoolean = new Dictionary<int, Constant>();
+
+        foreach (var stage in Plan)
+        {
+            var stageActive = new Constant(Token.NoToken,
+                new TypedIdent(Token.NoToken, "_stage_" + stage.GetId() + "_active", Type.Bool),
+                false);
+            stageActive.AddAttribute("stage_active", new object[] { new LiteralExpr(Token.NoToken, BigNum.FromInt(stage.GetId())) });
+            prog.AddTopLevelDeclaration(stageActive);
+            stageToActiveBoolean[stage.GetId()] = stageActive;
+
+            var stageComplete = new Constant(Token.NoToken, 
+                new TypedIdent(Token.NoToken, "_stage_" + stage.GetId() + "_complete", Type.Bool),
+                false);
+            stageComplete.AddAttribute("stage_complete", new object[] { new LiteralExpr(Token.NoToken, BigNum.FromInt(stage.GetId())) });
+            prog.AddTopLevelDeclaration(stageComplete);
+            stageToCompleteBoolean[stage.GetId()] = stageComplete;
+        }
+        #endregion
+
+        #region Adapt annotation assertions to take account of stages
+        foreach (var b in prog.Implementations.Select(Item => Item.Blocks).SelectMany(Item => Item))
+        {
+            List<Cmd> newCmds = new List<Cmd>();
+            foreach (var cmd in b.Cmds)
+            {
+                var a = cmd as AssertCmd;
+                string c;
+                if (a != null) {
+                    if (Houdini.MatchCandidate(a.Expr, CandidateIdentifiers, out c))
+                    {
+                        newCmds.Add(new AssertCmd(a.tok, Houdini.AddConditionToCandidate(a.Expr,
+                            Expr.Ident(stageToActiveBoolean[Plan.StageForAnnotation(c).GetId()]), c), a.Attributes));
+                        newCmds.Add(new AssumeCmd(a.tok, Houdini.AddConditionToCandidate(a.Expr,
+                            Expr.Ident(stageToCompleteBoolean[Plan.StageForAnnotation(c).GetId()]), c), a.Attributes));
+                    } else if (QKeyValue.FindBoolAttribute(a.Attributes, "originated_from_invariant")) {
+                        string tag = GetTagFromNonCandidateAttributes(a.Attributes);
+                        if (tag == null) {
+                          newCmds.Add(a);
+                        } else {
+                          newCmds.Add(new AssertCmd(a.tok, Expr.Imp(
+                              Expr.Ident(stageToActiveBoolean[Plan.StageForAnnotation(tag).GetId()]), a.Expr),
+                              a.Attributes));
+                          newCmds.Add(new AssumeCmd(a.tok, Expr.Imp(
+                              Expr.Ident(stageToCompleteBoolean[Plan.StageForAnnotation(tag).GetId()]), a.Expr),
+                              a.Attributes));
+                        }
+                    }
+                }
+                else
+                {
+                    newCmds.Add(cmd);
+                }
+            }
+            b.Cmds = newCmds;
+        }
+        #endregion
+
+        #region Adapt pre/postconditions to take account of stages
+        foreach (var p in prog.NonInlinedProcedures())
+        {
+
+          #region Handle the preconditions
+          {
+            List<Requires> newRequires = new List<Requires>();
+            foreach(Requires r in p.Requires) {
+              string c;
+              if (Houdini.MatchCandidate(r.Condition, CandidateIdentifiers, out c)) {
+                newRequires.Add(new Requires(r.tok, false, 
+                  Houdini.AddConditionToCandidate(r.Condition,
+                  Expr.Ident(stageToActiveBoolean[Plan.StageForAnnotation(c).GetId()]), c),
+                  r.Comment, r.Attributes));
+                newRequires.Add(new Requires(r.tok, true, 
+                  Houdini.AddConditionToCandidate(r.Condition,
+                  Expr.Ident(stageToCompleteBoolean[Plan.StageForAnnotation(c).GetId()]), c),
+                  r.Comment, r.Attributes));
+              } else {
+                string tag = GetTagFromNonCandidateAttributes(r.Attributes);
+                if (tag == null) {
+                  newRequires.Add(r);
+                } else {
+                  newRequires.Add(new Requires(r.tok, false, 
+                    Expr.Imp(Expr.Ident(stageToActiveBoolean[Plan.StageForAnnotation(tag).GetId()]), r.Condition),
+                    r.Comment, r.Attributes));
+                  newRequires.Add(new Requires(r.tok, true, 
+                    Expr.Imp(Expr.Ident(stageToCompleteBoolean[Plan.StageForAnnotation(tag).GetId()]), r.Condition),
+                    r.Comment, r.Attributes));
+                }
+              }
+            }
+            p.Requires = newRequires;
+          }
+          #endregion
+
+          #region Handle the postconditions
+          {
+            List<Ensures> newEnsures = new List<Ensures>();
+            foreach(Ensures e in p.Ensures) {
+              string c;
+              if (Houdini.MatchCandidate(e.Condition, CandidateIdentifiers, out c)) {
+                int stage = Plan.StageForAnnotation(c).GetId();
+                newEnsures.Add(new Ensures(e.tok, false, 
+                  Houdini.AddConditionToCandidate(e.Condition,
+                  Expr.Ident(stageToActiveBoolean[stage]), c),
+                  e.Comment, e.Attributes));
+                newEnsures.Add(new Ensures(e.tok, true, 
+                  Houdini.AddConditionToCandidate(e.Condition,
+                  Expr.Ident(stageToCompleteBoolean[stage]), c),
+                  e.Comment, e.Attributes));
+              } else {
+                string tag = GetTagFromNonCandidateAttributes(e.Attributes);
+                if (tag == null) {
+                  newEnsures.Add(e);
+                } else {
+                  newEnsures.Add(new Ensures(e.tok, false, 
+                    Expr.Imp(Expr.Ident(stageToActiveBoolean[Plan.StageForAnnotation(tag).GetId()]), e.Condition),
+                    e.Comment, e.Attributes));
+                  newEnsures.Add(new Ensures(e.tok, true, 
+                    Expr.Imp(Expr.Ident(stageToCompleteBoolean[Plan.StageForAnnotation(tag).GetId()]), e.Condition),
+                    e.Comment, e.Attributes));
+                }
+              }
+            }
+            p.Ensures = newEnsures;
+          }
+          #endregion
+
+        }
+        #endregion
+
+        return Plan;
+
+    }
+
+    private int FindLargestStage() {
+      return StagesDAG.Nodes.Select(Item => Item.Count()).Max();
+    }
+
+
+    private StagedHoudiniPlan ComputeCoarseStages()
+    {
+        foreach(var n in StagesDAG.Nodes) {
+          Debug.Assert(!StagesDAG.Successors(n).Contains(n));
+        }
+
+        Graph<ScheduledStage> Dependences = new Graph<ScheduledStage>();
+
+        var done = new Dictionary<SCC<string>, ScheduledStage>();
+        done[GetStartNodeOfStagesDAG()] = new ScheduledStage(0, new HashSet<string>());
+
+        for(int stageId = 1; done.Count() != StagesDAG.Nodes.Count(); stageId++)
+        {
+            var Stage = new ScheduledStage(stageId, new HashSet<string>());
+            HashSet<SCC<string>> AssignedToThisStage = new HashSet<SCC<string>>();
+
+            foreach (var n in StagesDAG.Nodes.Where(Item => !done.ContainsKey(Item)))
+            {
+              if(StagesDAG.Successors(n).Where(Item => !done.ContainsKey(Item)).Count() == 0) {
+                foreach(var s in StagesDAG.Successors(n)) {
+                  Debug.Assert(s != n);
+                  Debug.Assert(Stage != done[s]);
+                  Dependences.AddEdge(Stage, done[s]);
+                }
+                foreach (var a in n)
+                {
+                  Stage.AddAnnotation(a);
+                }
+                AssignedToThisStage.Add(n);
+              }
+            }
+
+            foreach(var n in AssignedToThisStage) {
+              done[n] = Stage;
+            }
+        }
+        return new StagedHoudiniPlan(Dependences);
+    }
+
+    private StagedHoudiniPlan ComputeBalancedStages()
+    {
+      Graph<ScheduledStage> Dependences = new Graph<ScheduledStage>();
+      var done = new Dictionary<SCC<string>, ScheduledStage>();
+      done[GetStartNodeOfStagesDAG()] = new ScheduledStage(0, new HashSet<string>());
+
+      int maxStageSize = 200;
+
+      for(int stageId = 1; done.Count() != StagesDAG.Nodes.Count(); stageId++)
+      {
+        int stageSize = 0;
+        ScheduledStage Stage = new ScheduledStage(stageId, new HashSet<string>());
+        HashSet<SCC<string>> AddedToThisStage = new HashSet<SCC<string>>();
+
+        foreach (var n in StagesDAG.Nodes.Where(Item => !done.ContainsKey(Item)))
+        {
+          if(stageSize + n.Count() > maxStageSize) {
+            continue;
+          }
+          if(StagesDAG.Successors(n).Where(Item => !done.ContainsKey(Item)).Count() == 0) {
+            foreach (var c in n)
+            {
+              Stage.AddAnnotation(c);
+              stageSize++;
+            }
+            foreach(var s in StagesDAG.Successors(n)) {
+              Dependences.AddEdge(Stage, done[s]);
+            }
+            AddedToThisStage.Add(n);
+          }
+        }
+        foreach(var n in AddedToThisStage) {
+          done[n] = Stage;
+        }
+        if(stageSize == 0) {
+          maxStageSize *= 2;
+        }
+      }
+      return new StagedHoudiniPlan(Dependences);
+    }
+
+    private StagedHoudiniPlan ComputeFineStages()
+    {
+      Graph<ScheduledStage> Dependences = new Graph<ScheduledStage>();
+      var done = new Dictionary<SCC<string>, ScheduledStage>();
+
+      List<SCC<string>> components = StagesDAG.TopologicalSort().ToList();
+      components.Reverse();
+
+      for (int i = 0; i < components.Count(); i++)
+      {
+        ScheduledStage Stage = new ScheduledStage(i, new HashSet<string>());
+        done[components[i]] = Stage;
+        foreach (var c in components[i])
+        {
+          Stage.AddAnnotation(c);
+        }
+        foreach(var s in StagesDAG.Successors(components[i])) {
+          Dependences.AddEdge(Stage, done[s]);
+        }
+      }
+      return new StagedHoudiniPlan(Dependences);
+    }
+
+    private SCC<string> GetStartNodeOfStagesDAG()
+    {
+      return StagesDAG.Nodes.Where(Item => StagesDAG.Successors(Item).Count() == 0).
+        ToList()[0];
+    }
+
+    private bool NoStages()
+    {
+        return AllAnnotationIdentifiers().Count() == 0 || StagesDAG.Nodes.Count() == 0;
+    }
+  }
+
+  interface IAnnotationReachabilityChecker {
+    bool MayReach(string c, string d);
+  }
+
+  class DummyAnnotationReachabilityChecker : IAnnotationReachabilityChecker {
+    public bool MayReach(string c, string d) {
+      return true;
+    }
+  }
+
+  class AnnotationReachabilityChecker : IAnnotationReachabilityChecker {
+
+    private enum PrePost {
+      PRE, POST
+    }
+
+    private Program prog;
+    private IEnumerable<string> AnnotationIdentifiers;
+    private IInterproceduralReachabilityGraph reachabilityGraph;
+    private Dictionary<string, HashSet<object>> annotationToOccurences;
+
+    internal AnnotationReachabilityChecker(Program prog, IEnumerable<string> AnnotationIdentifiers) {
+      this.prog = prog;
+      this.AnnotationIdentifiers = AnnotationIdentifiers;
+      this.reachabilityGraph = new InterproceduralReachabilityGraph(prog);
+      this.annotationToOccurences = new Dictionary<string,HashSet<object>>();
+
+      // Add all annotation occurrences in blocks
+      foreach(Block b in prog.Blocks()) {
+        foreach(var assertCmd in b.Cmds.OfType<AssertCmd>()) {
+          string c;
+          if(Houdini.MatchCandidate(assertCmd.Expr, AnnotationIdentifiers, out c)) {
+            AddAnnotationOccurrence(c, b);
+          } else {
+            var tag = AnnotationDependenceAnalyser.GetTagFromNonCandidateAttributes(assertCmd.Attributes);
+            if (tag != null) {
+              AddAnnotationOccurrence(tag, b);
+            }
+          }
+        }
+      }
+
+      // Add all annotation occurrences in pre and post conditions
+      foreach(var proc in prog.NonInlinedProcedures()) {
+        foreach(Requires r in proc.Requires) {
+          string c;
+          if(Houdini.MatchCandidate(r.Condition, AnnotationIdentifiers, out c)) {
+            AddAnnotationOccurrence(c, new Tuple<string, PrePost>(proc.Name, PrePost.PRE));
+          } else {
+            string tag = AnnotationDependenceAnalyser.GetTagFromNonCandidateAttributes(r.Attributes);
+            if(tag != null) {
+              AddAnnotationOccurrence(tag, new Tuple<string, PrePost>(proc.Name, PrePost.PRE));
+            }
+          }
+        }
+        foreach(Ensures e in proc.Ensures) {
+          string c;
+          if(Houdini.MatchCandidate(e.Condition, AnnotationIdentifiers, out c)) {
+            AddAnnotationOccurrence(c, new Tuple<string, PrePost>(proc.Name, PrePost.POST));
+          } else {
+            string tag = AnnotationDependenceAnalyser.GetTagFromNonCandidateAttributes(e.Attributes);
+            if(tag != null) {
+              AddAnnotationOccurrence(tag, new Tuple<string, PrePost>(proc.Name, PrePost.PRE));
+            }
+          }
+        }
+      }
+      
+    }
+
+    private void AddAnnotationOccurrence(string c, object o) {
+      Debug.Assert(o is Block || o is Tuple<string, PrePost>);
+      if(!annotationToOccurences.ContainsKey(c)) {
+        annotationToOccurences[c] = new HashSet<object>();
+      }
+      annotationToOccurences[c].Add(o);
+    }
+
+    public bool MayReach(string c, string d) {
+      foreach(object cOccurrence in annotationToOccurences[c]) {
+        foreach(object dOccurrence in annotationToOccurences[d]) {
+          if(OccurrencesMayReach(cOccurrence, dOccurrence)) {
+            return true;
+          }
+        }
+      }
+      return false;
+    }
+
+    private bool OccurrencesMayReach(object cOccurrence, object dOccurrence) {
+      Debug.Assert(cOccurrence is Block || cOccurrence is Tuple<string, PrePost>);
+      Debug.Assert(dOccurrence is Block || dOccurrence is Tuple<string, PrePost>);
+
+      Block cInterproceduralBlock = GetInterproceduralBlock(cOccurrence);
+      Block dInterproceduralBlock = GetInterproceduralBlock(dOccurrence);
+
+      return reachabilityGraph.MayReach(cInterproceduralBlock, dInterproceduralBlock);
+
+    }
+
+    private Block GetInterproceduralBlock(object cOccurrence)
+    {
+      Debug.Assert(cOccurrence is Block || cOccurrence is Tuple<string, PrePost>);
+
+      var stringPrePostPair = cOccurrence as Tuple<string, PrePost>;
+      if(stringPrePostPair != null) {
+        if(stringPrePostPair.Item2 == PrePost.PRE) {
+          return reachabilityGraph.GetNewEntryBlock(stringPrePostPair.Item1);
+        } else {
+          return reachabilityGraph.GetNewExitBlock(stringPrePostPair.Item1);
+        }
+      }
+
+      return reachabilityGraph.GetNewBlock((Block)cOccurrence);
+
+    }
+  }
+
+  class AnnotationInstance {
+    public string AnnotationIdentifier;
+    public string Proc;
+    public Expr Expr;
+
+    internal AnnotationInstance(string AnnotationIdentifier, string Proc, Expr Expr) {
+      this.AnnotationIdentifier = AnnotationIdentifier;
+      this.Proc = Proc;
+      this.Expr = Expr;
+    }
+  }
+
+}
diff --git a/Source/Houdini/Checker.cs b/Source/Houdini/Checker.cs
index 30056d99..73842019 100644
--- a/Source/Houdini/Checker.cs
+++ b/Source/Houdini/Checker.cs
@@ -1,456 +1,457 @@
-//-----------------------------------------------------------------------------

-//

-// Copyright (C) Microsoft Corporation.  All Rights Reserved.

-//

-//-----------------------------------------------------------------------------

-using System;

-using System.Diagnostics.Contracts;

-using System.Collections.Generic;

-using Microsoft.Boogie;

-using Microsoft.Boogie.VCExprAST;

-using Microsoft.Basetypes;

-using System.Collections;

-using System.IO;

-using System.Threading;

-using VC;

-using System.Linq;

-

-namespace Microsoft.Boogie.Houdini {

-  public class ExistentialConstantCollector : ReadOnlyVisitor {

-      public static void CollectHoudiniConstants(Houdini houdini, Implementation impl, out ExistentialConstantCollector collector)

-      {

-          collector = new ExistentialConstantCollector(houdini);

-          collector.impl = impl;

-          collector.VisitImplementation(impl);

-      }

-

-    private ExistentialConstantCollector(Houdini houdini) {

-      this.houdini = houdini;

-      this.houdiniAssertConstants = new HashSet<Variable>();

-      this.houdiniAssumeConstants = new HashSet<Variable>();

-

-      this.explainNegative = new HashSet<Variable>();

-      this.explainPositive = new HashSet<Variable>();

-      this.constToControl = new Dictionary<string, Tuple<Variable, Variable>>();

-    }

-    private Houdini houdini;

-    public HashSet<Variable> houdiniAssertConstants;

-    public HashSet<Variable> houdiniAssumeConstants;

-

-    // Explain Houdini stuff

-    public HashSet<Variable> explainPositive;

-    public HashSet<Variable> explainNegative;

-    public Dictionary<string, Tuple<Variable, Variable>> constToControl;

-    Implementation impl;

-

-    public override Cmd VisitAssertRequiresCmd(AssertRequiresCmd node) {

-      AddHoudiniConstant(node);

-      return base.VisitAssertRequiresCmd(node);

-    }

-    public override Cmd VisitAssertEnsuresCmd(AssertEnsuresCmd node) {

-      AddHoudiniConstant(node);

-      return base.VisitAssertEnsuresCmd(node);

-    }

-    public override Cmd VisitAssertCmd(AssertCmd node) {

-      AddHoudiniConstant(node);

-      return base.VisitAssertCmd(node);

-    }

-    public override Cmd VisitAssumeCmd(AssumeCmd node) {

-      AddHoudiniConstant(node);

-      return base.VisitAssumeCmd(node);

-    }

-    private void AddHoudiniConstant(AssertCmd assertCmd)

-    {

-        Variable houdiniConstant;

-        if (houdini.MatchCandidate(assertCmd.Expr, out houdiniConstant))

-            houdiniAssertConstants.Add(houdiniConstant);

-        

-        if (houdiniConstant != null && CommandLineOptions.Clo.ExplainHoudini && !constToControl.ContainsKey(houdiniConstant.Name))

-        {

-            // For each houdini constant c, create two more constants c_pos and c_neg.

-            // Then change the asserted condition (c ==> \phi) to

-            // (c ==> (c_pos && (\phi || \not c_neg))

-            var control = createNewExplainConstants(houdiniConstant);

-            assertCmd.Expr = houdini.InsertCandidateControl(assertCmd.Expr, control.Item1, control.Item2);

-            explainPositive.Add(control.Item1);

-            explainNegative.Add(control.Item2);

-            constToControl.Add(houdiniConstant.Name, control);

-        }

-    }

-    private void AddHoudiniConstant(AssumeCmd assumeCmd)

-    {

-        Variable houdiniConstant;

-        if (houdini.MatchCandidate(assumeCmd.Expr, out houdiniConstant))

-            houdiniAssumeConstants.Add(houdiniConstant);

-    }

-    private Tuple<Variable, Variable> createNewExplainConstants(Variable v)

-    {

-        Contract.Assert(impl != null);

-        Contract.Assert(CommandLineOptions.Clo.ExplainHoudini);

-        Variable v1 = new Constant(Token.NoToken, new TypedIdent(Token.NoToken, string.Format("{0}_{1}_{2}", v.Name, impl.Name, "pos"), Microsoft.Boogie.BasicType.Bool));

-        Variable v2 = new Constant(Token.NoToken, new TypedIdent(Token.NoToken, string.Format("{0}_{1}_{2}", v.Name, impl.Name, "neg"), Microsoft.Boogie.BasicType.Bool));

-

-        return Tuple.Create(v1, v2);

-    }

-  }

-

-

-

-  public class HoudiniSession {

-

-    public class HoudiniStatistics {

-      public double proverTime = 0;

-      public int numProverQueries = 0;

-      public double unsatCoreProverTime = 0;

-      public int numUnsatCoreProverQueries = 0;

-      public int numUnsatCorePrunings = 0;

-    }

-

-    public string descriptiveName;

-    public HoudiniStatistics stats;

-    private VCExpr conjecture;

-    private ProverInterface.ErrorHandler handler;

-    ConditionGeneration.CounterexampleCollector collector;

-    HashSet<Variable> unsatCoreSet;

-    HashSet<Variable> houdiniConstants;

-    public HashSet<Variable> houdiniAssertConstants;

-    private HashSet<Variable> houdiniAssumeConstants;

-    

-    // Extra constants created for ExplainHoudini

-    private HashSet<Variable> explainConstantsPositive;

-    private HashSet<Variable> explainConstantsNegative;

-    private Dictionary<string, Tuple<Variable, Variable>> constantToControl;

-

-    public bool InUnsatCore(Variable constant) {

-      if (unsatCoreSet == null)

-        return true;

-      if (unsatCoreSet.Contains(constant))

-        return true;

-      stats.numUnsatCorePrunings++;

-      return false;

-    }

-

-    public HoudiniSession(Houdini houdini, VCGen vcgen, ProverInterface proverInterface, Program program, Implementation impl, HoudiniStatistics stats, int taskID = -1) {

-      this.descriptiveName = impl.Name;

-      this.stats = stats;

-      collector = new ConditionGeneration.CounterexampleCollector();

-      collector.OnProgress("HdnVCGen", 0, 0, 0.0);

-

-      vcgen.ConvertCFG2DAG(impl, taskID: taskID);

-      ModelViewInfo mvInfo;

-      var gotoCmdOrigins = vcgen.PassifyImpl(impl, out mvInfo);

-

-      ExistentialConstantCollector ecollector;

-      ExistentialConstantCollector.CollectHoudiniConstants(houdini, impl, out ecollector);

-      this.houdiniAssertConstants = ecollector.houdiniAssertConstants;

-      this.houdiniAssumeConstants = ecollector.houdiniAssumeConstants;

-      this.explainConstantsNegative = ecollector.explainNegative;

-      this.explainConstantsPositive = ecollector.explainPositive;

-      this.constantToControl = ecollector.constToControl;

-

-      houdiniConstants = new HashSet<Variable>();

-      houdiniConstants.UnionWith(houdiniAssertConstants);

-      houdiniConstants.UnionWith(houdiniAssumeConstants);

-

-      var exprGen = proverInterface.Context.ExprGen;

-      VCExpr controlFlowVariableExpr = CommandLineOptions.Clo.UseLabels ? null : exprGen.Integer(BigNum.ZERO);

-

-      Dictionary<int, Absy> label2absy;

-      conjecture = vcgen.GenerateVC(impl, controlFlowVariableExpr, out label2absy, proverInterface.Context);

-      if (!CommandLineOptions.Clo.UseLabels) {

-        VCExpr controlFlowFunctionAppl = exprGen.ControlFlowFunctionApplication(exprGen.Integer(BigNum.ZERO), exprGen.Integer(BigNum.ZERO));

-        VCExpr eqExpr = exprGen.Eq(controlFlowFunctionAppl, exprGen.Integer(BigNum.FromInt(impl.Blocks[0].UniqueId)));

-        conjecture = exprGen.Implies(eqExpr, conjecture);

-      }

-

-      Macro macro = new Macro(Token.NoToken, descriptiveName, new List<Variable>(), new Formal(Token.NoToken, new TypedIdent(Token.NoToken, "", Type.Bool), false));

-      proverInterface.DefineMacro(macro, conjecture);

-      conjecture = exprGen.Function(macro);

-

-      if (CommandLineOptions.Clo.vcVariety == CommandLineOptions.VCVariety.Local) {

-        handler = new VCGen.ErrorReporterLocal(gotoCmdOrigins, label2absy, impl.Blocks, vcgen.incarnationOriginMap, collector, mvInfo, proverInterface.Context, program);

-      }

-      else {

-        handler = new VCGen.ErrorReporter(gotoCmdOrigins, label2absy, impl.Blocks, vcgen.incarnationOriginMap, collector, mvInfo, proverInterface.Context, program);

-      }

-

-    }

-

-    private VCExpr BuildAxiom(ProverInterface proverInterface, Dictionary<Variable, bool> currentAssignment) {

-      ProverContext proverContext = proverInterface.Context;

-      Boogie2VCExprTranslator exprTranslator = proverContext.BoogieExprTranslator;

-      VCExpressionGenerator exprGen = proverInterface.VCExprGen;

-

-      VCExpr expr = VCExpressionGenerator.True;

-

-      foreach (KeyValuePair<Variable, bool> kv in currentAssignment) {

-        Variable constant = kv.Key;

-        VCExprVar exprVar = exprTranslator.LookupVariable(constant);

-        if (kv.Value) {

-          expr = exprGen.And(expr, exprVar);

-        }

-        else {

-          expr = exprGen.And(expr, exprGen.Not(exprVar));

-        }

-      }

-

-      if (CommandLineOptions.Clo.ExplainHoudini)

-      {

-          // default values for ExplainHoudini control variables

-          foreach (var constant in explainConstantsNegative.Concat(explainConstantsPositive))

-          {

-              expr = exprGen.And(expr, exprTranslator.LookupVariable(constant));

-          }

-      }

-

-      /*

-      foreach (Variable constant in this.houdiniConstants) {

-        VCExprVar exprVar = exprTranslator.LookupVariable(constant);

-        if (currentAssignment[constant]) {

-          expr = exprGen.And(expr, exprVar);

-        }

-        else {

-          expr = exprGen.And(expr, exprGen.Not(exprVar));

-        }

-      }

-       */

-

-      if(CommandLineOptions.Clo.Trace) {

-        Console.WriteLine("Houdini assignment axiom: " + expr);

-      }

-

-      return expr;

-    }

-

-    public ProverInterface.Outcome Verify(ProverInterface proverInterface, Dictionary<Variable, bool> assignment, out List<Counterexample> errors, int taskID = -1) {

-      collector.examples.Clear();

-

-      if (CommandLineOptions.Clo.Trace) {

-        Console.WriteLine("Verifying " + descriptiveName);

-      }

-      DateTime now = DateTime.UtcNow;

-

-      VCExpr vc = proverInterface.VCExprGen.Implies(BuildAxiom(proverInterface, assignment), conjecture);

-      proverInterface.BeginCheck(descriptiveName, vc, handler);

-      ProverInterface.Outcome proverOutcome = proverInterface.CheckOutcome(handler, taskID: taskID);

-

-      double queryTime = (DateTime.UtcNow - now).TotalSeconds;

-      stats.proverTime += queryTime;

-      stats.numProverQueries++;

-      if (CommandLineOptions.Clo.Trace) {

-        Console.WriteLine("Time taken = " + queryTime);

-      }

-

-      errors = collector.examples;

-      return proverOutcome;

-    }

-

-    // MAXSAT

-    public void Explain(ProverInterface proverInterface, 

-        Dictionary<Variable, bool> assignment, Variable refutedConstant)

-    {

-        Contract.Assert(CommandLineOptions.Clo.ExplainHoudini);

-

-        collector.examples.Clear();

-

-        // debugging

-        houdiniAssertConstants.Iter(v => System.Diagnostics.Debug.Assert(assignment.ContainsKey(v)));

-        houdiniAssumeConstants.Iter(v => System.Diagnostics.Debug.Assert(assignment.ContainsKey(v)));

-        Contract.Assert(assignment.ContainsKey(refutedConstant));

-        Contract.Assert(houdiniAssertConstants.Contains(refutedConstant));

-

-        var hardAssumptions = new List<VCExpr>();

-        var softAssumptions = new List<VCExpr>();

-

-        Boogie2VCExprTranslator exprTranslator = proverInterface.Context.BoogieExprTranslator;

-        VCExpressionGenerator exprGen = proverInterface.VCExprGen;

-        var controlExpr = VCExpressionGenerator.True;

-

-        foreach (var tup in assignment)

-        {

-            Variable constant = tup.Key;

-            VCExprVar exprVar = exprTranslator.LookupVariable(constant);

-            var val = tup.Value;

-

-            if (houdiniAssumeConstants.Contains(constant))

-            {

-                if (tup.Value)

-                    hardAssumptions.Add(exprVar);

-                else

-                    // Previously removed assumed candidates are the soft constraints

-                    softAssumptions.Add(exprVar);

-            }

-            else if (houdiniAssertConstants.Contains(constant))

-            {

-                if (constant == refutedConstant)

-                    hardAssumptions.Add(exprVar);

-                else

-                    hardAssumptions.Add(exprGen.Not(exprVar));

-            }

-            else

-            {

-                if (tup.Value)

-                    hardAssumptions.Add(exprVar);

-                else

-                    hardAssumptions.Add(exprGen.Not(exprVar));

-            }

-

-            // For an asserted condition (c ==> \phi), 

-            // ExplainHoudini's extra control constants (c_pos, c_neg) are used as follows:

-            //   (true, true): "assert \phi"

-            //   (false, _): "assert false"

-            //   (true, false): "assert true"

-            if (constant != refutedConstant && constantToControl.ContainsKey(constant.Name))

-            {

-                var posControl = constantToControl[constant.Name].Item1;

-                var negControl = constantToControl[constant.Name].Item2;

-

-                // Handle self-recursion

-                if (houdiniAssertConstants.Contains(constant) && houdiniAssumeConstants.Contains(constant))

-                {

-                    // disable this assert

-                    controlExpr = exprGen.And(controlExpr, exprGen.And(exprTranslator.LookupVariable(posControl), exprGen.Not(exprTranslator.LookupVariable(negControl))));

-                }

-                else

-                {

-                    // default values for control variables

-                    controlExpr = exprGen.And(controlExpr, exprGen.And(exprTranslator.LookupVariable(posControl), exprTranslator.LookupVariable(negControl)));

-                }

-            }

-        }

-

-        hardAssumptions.Add(exprGen.Not(conjecture));

-

-        // default values for control variables

-        Contract.Assert(constantToControl.ContainsKey(refutedConstant.Name));

-        var pc = constantToControl[refutedConstant.Name].Item1;

-        var nc = constantToControl[refutedConstant.Name].Item2;

-

-        var controlExprNoop = exprGen.And(controlExpr,

-            exprGen.And(exprTranslator.LookupVariable(pc), exprTranslator.LookupVariable(nc)));

-

-        var controlExprFalse = exprGen.And(controlExpr,

-            exprGen.And(exprGen.Not(exprTranslator.LookupVariable(pc)), exprGen.Not(exprTranslator.LookupVariable(nc))));

-

-        if (CommandLineOptions.Clo.Trace)

-        {

-            Console.WriteLine("Verifying (MaxSat) " + descriptiveName);

-        }

-        DateTime now = DateTime.UtcNow;

-

-        var el = CommandLineOptions.Clo.ProverCCLimit;

-        CommandLineOptions.Clo.ProverCCLimit = 1;

-

-        var outcome = ProverInterface.Outcome.Undetermined;

-

-        do

-        {

-            List<int> unsatisfiedSoftAssumptions;

-

-            hardAssumptions.Add(controlExprNoop);

-            outcome = proverInterface.CheckAssumptions(hardAssumptions, softAssumptions, out unsatisfiedSoftAssumptions, handler);

-            hardAssumptions.RemoveAt(hardAssumptions.Count - 1);

-

-            if (outcome == ProverInterface.Outcome.TimeOut || outcome == ProverInterface.Outcome.OutOfMemory || outcome == ProverInterface.Outcome.Undetermined)

-                break;

-

-            var reason = new HashSet<string>();

-            unsatisfiedSoftAssumptions.Iter(i => reason.Add(softAssumptions[i].ToString()));

-            if (CommandLineOptions.Clo.Trace)

-            {

-                Console.Write("Reason for removal of {0}: ", refutedConstant.Name);

-                reason.Iter(r => Console.Write("{0} ", r));

-                Console.WriteLine();

-            }

-

-            // Get rid of those constants from the "reason" that can even make

-            // "assert false" pass

-

-            hardAssumptions.Add(controlExprFalse);

-            var softAssumptions2 = new List<VCExpr>();

-            for (int i = 0; i < softAssumptions.Count; i++)

-            {

-                if (unsatisfiedSoftAssumptions.Contains(i))

-                {

-                    softAssumptions2.Add(softAssumptions[i]);

-                    continue;

-                }

-                hardAssumptions.Add(softAssumptions[i]);

-            }

-

-            var unsatisfiedSoftAssumptions2 = new List<int>();

-            outcome = proverInterface.CheckAssumptions(hardAssumptions, softAssumptions2, out unsatisfiedSoftAssumptions2, handler);

-

-            if (outcome == ProverInterface.Outcome.TimeOut || outcome == ProverInterface.Outcome.OutOfMemory || outcome == ProverInterface.Outcome.Undetermined)

-                break;

-

-            unsatisfiedSoftAssumptions2.Iter(i => reason.Remove(softAssumptions2[i].ToString()));

-            var reason1 = new HashSet<string>(); //these are the reasons for inconsistency

-            unsatisfiedSoftAssumptions2.Iter(i => reason1.Add(softAssumptions2[i].ToString()));

-

-            if (CommandLineOptions.Clo.Trace)

-            {

-                Console.Write("Revised reason for removal of {0}: ", refutedConstant.Name);

-                reason.Iter(r => Console.Write("{0} ", r));

-                Console.WriteLine();

-            }

-            foreach (var r in reason)

-            {

-                Houdini.explainHoudiniDottyFile.WriteLine("{0} -> {1} [ label = \"{2}\" color=red ];", refutedConstant.Name, r, descriptiveName);

-            }

-            //also add the removed reasons using dotted edges (requires- x != 0, requires- x == 0 ==> assert x != 0)

-            foreach (var r in reason1)

-            {

-                Houdini.explainHoudiniDottyFile.WriteLine("{0} -> {1} [ label = \"{2}\" color=blue style=dotted ];", refutedConstant.Name, r, descriptiveName);

-            }

-        } while (false);

-

-        if (outcome == ProverInterface.Outcome.TimeOut || outcome == ProverInterface.Outcome.OutOfMemory || outcome == ProverInterface.Outcome.Undetermined)

-        {

-            Houdini.explainHoudiniDottyFile.WriteLine("{0} -> {1} [ label = \"{2}\" color=red ];", refutedConstant.Name, "TimeOut", descriptiveName);

-        }

-

-        CommandLineOptions.Clo.ProverCCLimit = el;

-

-        double queryTime = (DateTime.UtcNow - now).TotalSeconds;

-        stats.proverTime += queryTime;

-        stats.numProverQueries++;

-        if (CommandLineOptions.Clo.Trace)

-        {

-            Console.WriteLine("Time taken = " + queryTime);

-        }

-    }

-

-    public void UpdateUnsatCore(ProverInterface proverInterface, Dictionary<Variable, bool> assignment)

-    {

-      DateTime now = DateTime.UtcNow;

-

-      Boogie2VCExprTranslator exprTranslator = proverInterface.Context.BoogieExprTranslator;

-      proverInterface.Push();

-      proverInterface.Assert(conjecture, false);

-      foreach (var v in assignment.Keys) {

-        if (assignment[v]) continue;

-        proverInterface.Assert(exprTranslator.LookupVariable(v), false);

-      }

-      List<Variable> assumptionVars = new List<Variable>();

-      List<VCExpr> assumptionExprs = new List<VCExpr>();

-      foreach (var v in assignment.Keys) {

-        if (!assignment[v]) continue;

-        assumptionVars.Add(v);

-        assumptionExprs.Add(exprTranslator.LookupVariable(v));

-      }

-      List<int> unsatCore;

-      ProverInterface.Outcome tmp = proverInterface.CheckAssumptions(assumptionExprs, out unsatCore, handler);

-      System.Diagnostics.Debug.Assert(tmp == ProverInterface.Outcome.Valid);

-      unsatCoreSet = new HashSet<Variable>();

-      foreach (int i in unsatCore)

-        unsatCoreSet.Add(assumptionVars[i]);

-      proverInterface.Pop();

-

-      double unsatCoreQueryTime = (DateTime.UtcNow - now).TotalSeconds;

-      stats.unsatCoreProverTime += unsatCoreQueryTime;

-      stats.numUnsatCoreProverQueries++;

-    }

-

-  }

+//-----------------------------------------------------------------------------
+//
+// Copyright (C) Microsoft Corporation.  All Rights Reserved.
+//
+//-----------------------------------------------------------------------------
+using System;
+using System.Diagnostics.Contracts;
+using System.Collections.Generic;
+using Microsoft.Boogie;
+using Microsoft.Boogie.VCExprAST;
+using Microsoft.Basetypes;
+using System.Collections;
+using System.IO;
+using System.Threading;
+using VC;
+using System.Linq;
+
+namespace Microsoft.Boogie.Houdini {
+  public class ExistentialConstantCollector : ReadOnlyVisitor {
+      public static void CollectHoudiniConstants(Houdini houdini, Implementation impl, out ExistentialConstantCollector collector)
+      {
+          collector = new ExistentialConstantCollector(houdini);
+          collector.impl = impl;
+          collector.VisitImplementation(impl);
+      }
+
+    private ExistentialConstantCollector(Houdini houdini) {
+      this.houdini = houdini;
+      this.houdiniAssertConstants = new HashSet<Variable>();
+      this.houdiniAssumeConstants = new HashSet<Variable>();
+
+      this.explainNegative = new HashSet<Variable>();
+      this.explainPositive = new HashSet<Variable>();
+      this.constToControl = new Dictionary<string, Tuple<Variable, Variable>>();
+    }
+    private Houdini houdini;
+    public HashSet<Variable> houdiniAssertConstants;
+    public HashSet<Variable> houdiniAssumeConstants;
+
+    // Explain Houdini stuff
+    public HashSet<Variable> explainPositive;
+    public HashSet<Variable> explainNegative;
+    public Dictionary<string, Tuple<Variable, Variable>> constToControl;
+    Implementation impl;
+
+    public override Cmd VisitAssertRequiresCmd(AssertRequiresCmd node) {
+      AddHoudiniConstant(node);
+      return base.VisitAssertRequiresCmd(node);
+    }
+    public override Cmd VisitAssertEnsuresCmd(AssertEnsuresCmd node) {
+      AddHoudiniConstant(node);
+      return base.VisitAssertEnsuresCmd(node);
+    }
+    public override Cmd VisitAssertCmd(AssertCmd node) {
+      AddHoudiniConstant(node);
+      return base.VisitAssertCmd(node);
+    }
+    public override Cmd VisitAssumeCmd(AssumeCmd node) {
+      AddHoudiniConstant(node);
+      return base.VisitAssumeCmd(node);
+    }
+    private void AddHoudiniConstant(AssertCmd assertCmd)
+    {
+        Variable houdiniConstant;
+        if (houdini.MatchCandidate(assertCmd.Expr, out houdiniConstant))
+            houdiniAssertConstants.Add(houdiniConstant);
+        
+        if (houdiniConstant != null && CommandLineOptions.Clo.ExplainHoudini && !constToControl.ContainsKey(houdiniConstant.Name))
+        {
+            // For each houdini constant c, create two more constants c_pos and c_neg.
+            // Then change the asserted condition (c ==> \phi) to
+            // (c ==> (c_pos && (\phi || \not c_neg))
+            var control = createNewExplainConstants(houdiniConstant);
+            assertCmd.Expr = houdini.InsertCandidateControl(assertCmd.Expr, control.Item1, control.Item2);
+            explainPositive.Add(control.Item1);
+            explainNegative.Add(control.Item2);
+            constToControl.Add(houdiniConstant.Name, control);
+        }
+    }
+    private void AddHoudiniConstant(AssumeCmd assumeCmd)
+    {
+        Variable houdiniConstant;
+        if (houdini.MatchCandidate(assumeCmd.Expr, out houdiniConstant))
+            houdiniAssumeConstants.Add(houdiniConstant);
+    }
+    private Tuple<Variable, Variable> createNewExplainConstants(Variable v)
+    {
+        Contract.Assert(impl != null);
+        Contract.Assert(CommandLineOptions.Clo.ExplainHoudini);
+        Variable v1 = new Constant(Token.NoToken, new TypedIdent(Token.NoToken, string.Format("{0}_{1}_{2}", v.Name, impl.Name, "pos"), Microsoft.Boogie.BasicType.Bool));
+        Variable v2 = new Constant(Token.NoToken, new TypedIdent(Token.NoToken, string.Format("{0}_{1}_{2}", v.Name, impl.Name, "neg"), Microsoft.Boogie.BasicType.Bool));
+
+        return Tuple.Create(v1, v2);
+    }
+  }
+
+
+
+  public class HoudiniSession {
+
+    public class HoudiniStatistics {
+      public double proverTime = 0;
+      public int numProverQueries = 0;
+      public double unsatCoreProverTime = 0;
+      public int numUnsatCoreProverQueries = 0;
+      public int numUnsatCorePrunings = 0;
+    }
+
+    public string descriptiveName;
+    public HoudiniStatistics stats;
+    private VCExpr conjecture;
+    private ProverInterface.ErrorHandler handler;
+    ConditionGeneration.CounterexampleCollector collector;
+    HashSet<Variable> unsatCoreSet;
+    HashSet<Variable> houdiniConstants;
+    public HashSet<Variable> houdiniAssertConstants;
+    private HashSet<Variable> houdiniAssumeConstants;
+    
+    // Extra constants created for ExplainHoudini
+    private HashSet<Variable> explainConstantsPositive;
+    private HashSet<Variable> explainConstantsNegative;
+    private Dictionary<string, Tuple<Variable, Variable>> constantToControl;
+
+    public bool InUnsatCore(Variable constant) {
+      if (unsatCoreSet == null)
+        return true;
+      if (unsatCoreSet.Contains(constant))
+        return true;
+      stats.numUnsatCorePrunings++;
+      return false;
+    }
+
+    public HoudiniSession(Houdini houdini, VCGen vcgen, ProverInterface proverInterface, Program program, Implementation impl, HoudiniStatistics stats, int taskID = -1) {
+      this.descriptiveName = impl.Name;
+      this.stats = stats;
+      collector = new ConditionGeneration.CounterexampleCollector();
+      collector.OnProgress("HdnVCGen", 0, 0, 0.0);
+
+      vcgen.ConvertCFG2DAG(impl, taskID: taskID);
+      ModelViewInfo mvInfo;
+      var gotoCmdOrigins = vcgen.PassifyImpl(impl, out mvInfo);
+
+      ExistentialConstantCollector ecollector;
+      ExistentialConstantCollector.CollectHoudiniConstants(houdini, impl, out ecollector);
+      this.houdiniAssertConstants = ecollector.houdiniAssertConstants;
+      this.houdiniAssumeConstants = ecollector.houdiniAssumeConstants;
+      this.explainConstantsNegative = ecollector.explainNegative;
+      this.explainConstantsPositive = ecollector.explainPositive;
+      this.constantToControl = ecollector.constToControl;
+
+      houdiniConstants = new HashSet<Variable>();
+      houdiniConstants.UnionWith(houdiniAssertConstants);
+      houdiniConstants.UnionWith(houdiniAssumeConstants);
+
+      var exprGen = proverInterface.Context.ExprGen;
+      VCExpr controlFlowVariableExpr = CommandLineOptions.Clo.UseLabels ? null : exprGen.Integer(BigNum.ZERO);
+
+      Dictionary<int, Absy> label2absy;
+      conjecture = vcgen.GenerateVC(impl, controlFlowVariableExpr, out label2absy, proverInterface.Context);
+      if (!CommandLineOptions.Clo.UseLabels) {
+        VCExpr controlFlowFunctionAppl = exprGen.ControlFlowFunctionApplication(exprGen.Integer(BigNum.ZERO), exprGen.Integer(BigNum.ZERO));
+        VCExpr eqExpr = exprGen.Eq(controlFlowFunctionAppl, exprGen.Integer(BigNum.FromInt(impl.Blocks[0].UniqueId)));
+        conjecture = exprGen.Implies(eqExpr, conjecture);
+      }
+
+      Macro macro = new Macro(Token.NoToken, descriptiveName, new List<Variable>(), new Formal(Token.NoToken, new TypedIdent(Token.NoToken, "", Type.Bool), false));
+      proverInterface.DefineMacro(macro, conjecture);
+      conjecture = exprGen.Function(macro);
+
+      if (CommandLineOptions.Clo.vcVariety == CommandLineOptions.VCVariety.Local) {
+        handler = new VCGen.ErrorReporterLocal(gotoCmdOrigins, label2absy, impl.Blocks, vcgen.incarnationOriginMap, collector, mvInfo, proverInterface.Context, program);
+      }
+      else {
+        handler = new VCGen.ErrorReporter(gotoCmdOrigins, label2absy, impl.Blocks, vcgen.incarnationOriginMap, collector, mvInfo, proverInterface.Context, program);
+      }
+
+    }
+
+    private VCExpr BuildAxiom(ProverInterface proverInterface, Dictionary<Variable, bool> currentAssignment) {
+      ProverContext proverContext = proverInterface.Context;
+      Boogie2VCExprTranslator exprTranslator = proverContext.BoogieExprTranslator;
+      VCExpressionGenerator exprGen = proverInterface.VCExprGen;
+
+      VCExpr expr = VCExpressionGenerator.True;
+
+      foreach (KeyValuePair<Variable, bool> kv in currentAssignment) {
+        Variable constant = kv.Key;
+        VCExprVar exprVar = exprTranslator.LookupVariable(constant);
+        if (kv.Value) {
+          expr = exprGen.And(expr, exprVar);
+        }
+        else {
+          expr = exprGen.And(expr, exprGen.Not(exprVar));
+        }
+      }
+
+      if (CommandLineOptions.Clo.ExplainHoudini)
+      {
+          // default values for ExplainHoudini control variables
+          foreach (var constant in explainConstantsNegative.Concat(explainConstantsPositive))
+          {
+              expr = exprGen.And(expr, exprTranslator.LookupVariable(constant));
+          }
+      }
+
+      /*
+      foreach (Variable constant in this.houdiniConstants) {
+        VCExprVar exprVar = exprTranslator.LookupVariable(constant);
+        if (currentAssignment[constant]) {
+          expr = exprGen.And(expr, exprVar);
+        }
+        else {
+          expr = exprGen.And(expr, exprGen.Not(exprVar));
+        }
+      }
+       */
+
+      if(CommandLineOptions.Clo.Trace) {
+        Console.WriteLine("Houdini assignment axiom: " + expr);
+      }
+
+      return expr;
+    }
+
+    public ProverInterface.Outcome Verify(ProverInterface proverInterface, Dictionary<Variable, bool> assignment, out List<Counterexample> errors, int taskID = -1) {
+      collector.examples.Clear();
+
+      if (CommandLineOptions.Clo.Trace) {
+        Console.WriteLine("Verifying " + descriptiveName);
+      }
+      DateTime now = DateTime.UtcNow;
+
+      VCExpr vc = proverInterface.VCExprGen.Implies(BuildAxiom(proverInterface, assignment), conjecture);
+      proverInterface.BeginCheck(descriptiveName, vc, handler);
+      ProverInterface.Outcome proverOutcome = proverInterface.CheckOutcome(handler, taskID: taskID);
+
+      double queryTime = (DateTime.UtcNow - now).TotalSeconds;
+      stats.proverTime += queryTime;
+      stats.numProverQueries++;
+      if (CommandLineOptions.Clo.Trace) {
+        Console.WriteLine("Outcome = " + proverOutcome);
+        Console.WriteLine("Time taken = " + queryTime);
+      }
+
+      errors = collector.examples;
+      return proverOutcome;
+    }
+
+    // MAXSAT
+    public void Explain(ProverInterface proverInterface, 
+        Dictionary<Variable, bool> assignment, Variable refutedConstant)
+    {
+        Contract.Assert(CommandLineOptions.Clo.ExplainHoudini);
+
+        collector.examples.Clear();
+
+        // debugging
+        houdiniAssertConstants.Iter(v => System.Diagnostics.Debug.Assert(assignment.ContainsKey(v)));
+        houdiniAssumeConstants.Iter(v => System.Diagnostics.Debug.Assert(assignment.ContainsKey(v)));
+        Contract.Assert(assignment.ContainsKey(refutedConstant));
+        Contract.Assert(houdiniAssertConstants.Contains(refutedConstant));
+
+        var hardAssumptions = new List<VCExpr>();
+        var softAssumptions = new List<VCExpr>();
+
+        Boogie2VCExprTranslator exprTranslator = proverInterface.Context.BoogieExprTranslator;
+        VCExpressionGenerator exprGen = proverInterface.VCExprGen;
+        var controlExpr = VCExpressionGenerator.True;
+
+        foreach (var tup in assignment)
+        {
+            Variable constant = tup.Key;
+            VCExprVar exprVar = exprTranslator.LookupVariable(constant);
+            var val = tup.Value;
+
+            if (houdiniAssumeConstants.Contains(constant))
+            {
+                if (tup.Value)
+                    hardAssumptions.Add(exprVar);
+                else
+                    // Previously removed assumed candidates are the soft constraints
+                    softAssumptions.Add(exprVar);
+            }
+            else if (houdiniAssertConstants.Contains(constant))
+            {
+                if (constant == refutedConstant)
+                    hardAssumptions.Add(exprVar);
+                else
+                    hardAssumptions.Add(exprGen.Not(exprVar));
+            }
+            else
+            {
+                if (tup.Value)
+                    hardAssumptions.Add(exprVar);
+                else
+                    hardAssumptions.Add(exprGen.Not(exprVar));
+            }
+
+            // For an asserted condition (c ==> \phi), 
+            // ExplainHoudini's extra control constants (c_pos, c_neg) are used as follows:
+            //   (true, true): "assert \phi"
+            //   (false, _): "assert false"
+            //   (true, false): "assert true"
+            if (constant != refutedConstant && constantToControl.ContainsKey(constant.Name))
+            {
+                var posControl = constantToControl[constant.Name].Item1;
+                var negControl = constantToControl[constant.Name].Item2;
+
+                // Handle self-recursion
+                if (houdiniAssertConstants.Contains(constant) && houdiniAssumeConstants.Contains(constant))
+                {
+                    // disable this assert
+                    controlExpr = exprGen.And(controlExpr, exprGen.And(exprTranslator.LookupVariable(posControl), exprGen.Not(exprTranslator.LookupVariable(negControl))));
+                }
+                else
+                {
+                    // default values for control variables
+                    controlExpr = exprGen.And(controlExpr, exprGen.And(exprTranslator.LookupVariable(posControl), exprTranslator.LookupVariable(negControl)));
+                }
+            }
+        }
+
+        hardAssumptions.Add(exprGen.Not(conjecture));
+
+        // default values for control variables
+        Contract.Assert(constantToControl.ContainsKey(refutedConstant.Name));
+        var pc = constantToControl[refutedConstant.Name].Item1;
+        var nc = constantToControl[refutedConstant.Name].Item2;
+
+        var controlExprNoop = exprGen.And(controlExpr,
+            exprGen.And(exprTranslator.LookupVariable(pc), exprTranslator.LookupVariable(nc)));
+
+        var controlExprFalse = exprGen.And(controlExpr,
+            exprGen.And(exprGen.Not(exprTranslator.LookupVariable(pc)), exprGen.Not(exprTranslator.LookupVariable(nc))));
+
+        if (CommandLineOptions.Clo.Trace)
+        {
+            Console.WriteLine("Verifying (MaxSat) " + descriptiveName);
+        }
+        DateTime now = DateTime.UtcNow;
+
+        var el = CommandLineOptions.Clo.ProverCCLimit;
+        CommandLineOptions.Clo.ProverCCLimit = 1;
+
+        var outcome = ProverInterface.Outcome.Undetermined;
+
+        do
+        {
+            List<int> unsatisfiedSoftAssumptions;
+
+            hardAssumptions.Add(controlExprNoop);
+            outcome = proverInterface.CheckAssumptions(hardAssumptions, softAssumptions, out unsatisfiedSoftAssumptions, handler);
+            hardAssumptions.RemoveAt(hardAssumptions.Count - 1);
+
+            if (outcome == ProverInterface.Outcome.TimeOut || outcome == ProverInterface.Outcome.OutOfMemory || outcome == ProverInterface.Outcome.Undetermined)
+                break;
+
+            var reason = new HashSet<string>();
+            unsatisfiedSoftAssumptions.Iter(i => reason.Add(softAssumptions[i].ToString()));
+            if (CommandLineOptions.Clo.Trace)
+            {
+                Console.Write("Reason for removal of {0}: ", refutedConstant.Name);
+                reason.Iter(r => Console.Write("{0} ", r));
+                Console.WriteLine();
+            }
+
+            // Get rid of those constants from the "reason" that can even make
+            // "assert false" pass
+
+            hardAssumptions.Add(controlExprFalse);
+            var softAssumptions2 = new List<VCExpr>();
+            for (int i = 0; i < softAssumptions.Count; i++)
+            {
+                if (unsatisfiedSoftAssumptions.Contains(i))
+                {
+                    softAssumptions2.Add(softAssumptions[i]);
+                    continue;
+                }
+                hardAssumptions.Add(softAssumptions[i]);
+            }
+
+            var unsatisfiedSoftAssumptions2 = new List<int>();
+            outcome = proverInterface.CheckAssumptions(hardAssumptions, softAssumptions2, out unsatisfiedSoftAssumptions2, handler);
+
+            if (outcome == ProverInterface.Outcome.TimeOut || outcome == ProverInterface.Outcome.OutOfMemory || outcome == ProverInterface.Outcome.Undetermined)
+                break;
+
+            unsatisfiedSoftAssumptions2.Iter(i => reason.Remove(softAssumptions2[i].ToString()));
+            var reason1 = new HashSet<string>(); //these are the reasons for inconsistency
+            unsatisfiedSoftAssumptions2.Iter(i => reason1.Add(softAssumptions2[i].ToString()));
+
+            if (CommandLineOptions.Clo.Trace)
+            {
+                Console.Write("Revised reason for removal of {0}: ", refutedConstant.Name);
+                reason.Iter(r => Console.Write("{0} ", r));
+                Console.WriteLine();
+            }
+            foreach (var r in reason)
+            {
+                Houdini.explainHoudiniDottyFile.WriteLine("{0} -> {1} [ label = \"{2}\" color=red ];", refutedConstant.Name, r, descriptiveName);
+            }
+            //also add the removed reasons using dotted edges (requires- x != 0, requires- x == 0 ==> assert x != 0)
+            foreach (var r in reason1)
+            {
+                Houdini.explainHoudiniDottyFile.WriteLine("{0} -> {1} [ label = \"{2}\" color=blue style=dotted ];", refutedConstant.Name, r, descriptiveName);
+            }
+        } while (false);
+
+        if (outcome == ProverInterface.Outcome.TimeOut || outcome == ProverInterface.Outcome.OutOfMemory || outcome == ProverInterface.Outcome.Undetermined)
+        {
+            Houdini.explainHoudiniDottyFile.WriteLine("{0} -> {1} [ label = \"{2}\" color=red ];", refutedConstant.Name, "TimeOut", descriptiveName);
+        }
+
+        CommandLineOptions.Clo.ProverCCLimit = el;
+
+        double queryTime = (DateTime.UtcNow - now).TotalSeconds;
+        stats.proverTime += queryTime;
+        stats.numProverQueries++;
+        if (CommandLineOptions.Clo.Trace)
+        {
+            Console.WriteLine("Time taken = " + queryTime);
+        }
+    }
+
+    public void UpdateUnsatCore(ProverInterface proverInterface, Dictionary<Variable, bool> assignment)
+    {
+      DateTime now = DateTime.UtcNow;
+
+      Boogie2VCExprTranslator exprTranslator = proverInterface.Context.BoogieExprTranslator;
+      proverInterface.Push();
+      proverInterface.Assert(conjecture, false);
+      foreach (var v in assignment.Keys) {
+        if (assignment[v]) continue;
+        proverInterface.Assert(exprTranslator.LookupVariable(v), false);
+      }
+      List<Variable> assumptionVars = new List<Variable>();
+      List<VCExpr> assumptionExprs = new List<VCExpr>();
+      foreach (var v in assignment.Keys) {
+        if (!assignment[v]) continue;
+        assumptionVars.Add(v);
+        assumptionExprs.Add(exprTranslator.LookupVariable(v));
+      }
+      List<int> unsatCore;
+      ProverInterface.Outcome tmp = proverInterface.CheckAssumptions(assumptionExprs, out unsatCore, handler);
+      System.Diagnostics.Debug.Assert(tmp == ProverInterface.Outcome.Valid);
+      unsatCoreSet = new HashSet<Variable>();
+      foreach (int i in unsatCore)
+        unsatCoreSet.Add(assumptionVars[i]);
+      proverInterface.Pop();
+
+      double unsatCoreQueryTime = (DateTime.UtcNow - now).TotalSeconds;
+      stats.unsatCoreProverTime += unsatCoreQueryTime;
+      stats.numUnsatCoreProverQueries++;
+    }
+
+  }
 }
\ No newline at end of file
diff --git a/Source/Houdini/ConcurrentHoudini.cs b/Source/Houdini/ConcurrentHoudini.cs
index bfc7cbc1..e13fa802 100644
--- a/Source/Houdini/ConcurrentHoudini.cs
+++ b/Source/Houdini/ConcurrentHoudini.cs
@@ -1,104 +1,104 @@
-using System;

-using System.IO;

-using System.Collections.Generic;

-using System.Collections.Concurrent;

-using System.Diagnostics;

-using System.Diagnostics.Contracts;

-using System.Text.RegularExpressions;

-using System.Linq;

-using VC;

-

-namespace Microsoft.Boogie.Houdini

-{

-  public class ConcurrentHoudini : Houdini

-  {

-

-    protected int taskID;

-

-    private static ConcurrentDictionary<string, RefutedAnnotation> refutedSharedAnnotations;

-

-    public static ConcurrentDictionary<string, RefutedAnnotation> RefutedSharedAnnotations { get { return refutedSharedAnnotations; } }

-

-    public ConcurrentHoudini(int taskId, Program program, HoudiniSession.HoudiniStatistics stats, string cexTraceFile = "houdiniCexTrace.txt") {

-      Contract.Assert(taskId >= 0);

-      this.program = program;

-      this.cexTraceFile = cexTraceFile;

-      this.taskID = taskId;

-      Initialize(program, stats);

-    }

-

-    static ConcurrentHoudini()

-    {

-      refutedSharedAnnotations = new ConcurrentDictionary<string, RefutedAnnotation>();

-    }

-

-    protected override bool ExchangeRefutedAnnotations()

-    {

-      int count = 0;

-

-      if (CommandLineOptions.Clo.DebugConcurrentHoudini)

-        Console.WriteLine("# number of shared refuted annotations: " + refutedSharedAnnotations.Count);

-

-      foreach (string key in refutedSharedAnnotations.Keys) {

-        KeyValuePair<Variable, bool> kv = currentHoudiniState.Assignment.FirstOrDefault(entry => entry.Key.Name.Equals(key) && entry.Value);

-

-        if (kv.Key != null) {

-          RefutedAnnotation ra = null;

-          Implementation refutationSite = null;

-

-          foreach (var r in program.Implementations) {

-            if (r.Name.Equals(refutedSharedAnnotations[key].RefutationSite.Name)) {

-              refutationSite = r;

-              break;

-            }

-          }

-          Debug.Assert(refutationSite != null);

-

-          if (refutedSharedAnnotations[key].Kind == RefutedAnnotationKind.REQUIRES) {

-            Procedure proc = null;

-            foreach (var p in program.Procedures) {

-              if (p.Name.Equals(refutedSharedAnnotations[key].CalleeProc.Name)) {

-                proc = p;

-                break;

-              }

-            }

-            Debug.Assert(proc != null);

-            ra = RefutedAnnotation.BuildRefutedRequires(kv.Key, proc, refutationSite);

-          } else if (refutedSharedAnnotations[key].Kind == RefutedAnnotationKind.ENSURES)

-            ra = RefutedAnnotation.BuildRefutedEnsures(kv.Key, refutationSite);

-          else if (refutedSharedAnnotations[key].Kind == RefutedAnnotationKind.ASSERT)

-            ra = RefutedAnnotation.BuildRefutedAssert(kv.Key, refutationSite);

-          Debug.Assert(ra != null);

-

-          if (CommandLineOptions.Clo.DebugConcurrentHoudini)

-            Console.WriteLine("(+) " + ra.Constant + "," + ra.Kind + "," + ra.CalleeProc + "," + ra.RefutationSite);

-

-          AddRelatedToWorkList(ra);

-          UpdateAssignment(ra);

-          count++;

-        }

-      }

-

-      return count > 0 ? true : false;

-    }

-

-    protected override void ShareRefutedAnnotation(RefutedAnnotation refutedAnnotation) {

-      refutedSharedAnnotations.TryAdd(refutedAnnotation.Constant.Name, refutedAnnotation);

-    }

-

-    protected override void ApplyRefutedSharedAnnotations() {

-      if (refutedSharedAnnotations.Count > 0) {

-        foreach (var v in currentHoudiniState.Assignment.Keys.ToList()) {

-          if (refutedSharedAnnotations.ContainsKey(v.Name)) {

-            currentHoudiniState.Assignment[v] = false;

-          }

-        }

-      }

-    }

-

-    protected override int GetTaskID() {

-      return taskID;

-    }

-

-  }

-}

+using System;
+using System.IO;
+using System.Collections.Generic;
+using System.Collections.Concurrent;
+using System.Diagnostics;
+using System.Diagnostics.Contracts;
+using System.Text.RegularExpressions;
+using System.Linq;
+using VC;
+
+namespace Microsoft.Boogie.Houdini
+{
+  public class ConcurrentHoudini : Houdini
+  {
+
+    protected int taskID;
+
+    private static ConcurrentDictionary<string, RefutedAnnotation> refutedSharedAnnotations;
+
+    public static ConcurrentDictionary<string, RefutedAnnotation> RefutedSharedAnnotations { get { return refutedSharedAnnotations; } }
+
+    public ConcurrentHoudini(int taskId, Program program, HoudiniSession.HoudiniStatistics stats, string cexTraceFile = "houdiniCexTrace.txt") {
+      Contract.Assert(taskId >= 0);
+      this.program = program;
+      this.cexTraceFile = cexTraceFile;
+      this.taskID = taskId;
+      Initialize(program, stats);
+    }
+
+    static ConcurrentHoudini()
+    {
+      refutedSharedAnnotations = new ConcurrentDictionary<string, RefutedAnnotation>();
+    }
+
+    protected override bool ExchangeRefutedAnnotations()
+    {
+      int count = 0;
+
+      if (CommandLineOptions.Clo.DebugConcurrentHoudini)
+        Console.WriteLine("# number of shared refuted annotations: " + refutedSharedAnnotations.Count);
+
+      foreach (string key in refutedSharedAnnotations.Keys) {
+        KeyValuePair<Variable, bool> kv = currentHoudiniState.Assignment.FirstOrDefault(entry => entry.Key.Name.Equals(key) && entry.Value);
+
+        if (kv.Key != null) {
+          RefutedAnnotation ra = null;
+          Implementation refutationSite = null;
+
+          foreach (var r in program.Implementations) {
+            if (r.Name.Equals(refutedSharedAnnotations[key].RefutationSite.Name)) {
+              refutationSite = r;
+              break;
+            }
+          }
+          Debug.Assert(refutationSite != null);
+
+          if (refutedSharedAnnotations[key].Kind == RefutedAnnotationKind.REQUIRES) {
+            Procedure proc = null;
+            foreach (var p in program.Procedures) {
+              if (p.Name.Equals(refutedSharedAnnotations[key].CalleeProc.Name)) {
+                proc = p;
+                break;
+              }
+            }
+            Debug.Assert(proc != null);
+            ra = RefutedAnnotation.BuildRefutedRequires(kv.Key, proc, refutationSite);
+          } else if (refutedSharedAnnotations[key].Kind == RefutedAnnotationKind.ENSURES)
+            ra = RefutedAnnotation.BuildRefutedEnsures(kv.Key, refutationSite);
+          else if (refutedSharedAnnotations[key].Kind == RefutedAnnotationKind.ASSERT)
+            ra = RefutedAnnotation.BuildRefutedAssert(kv.Key, refutationSite);
+          Debug.Assert(ra != null);
+
+          if (CommandLineOptions.Clo.DebugConcurrentHoudini)
+            Console.WriteLine("(+) " + ra.Constant + "," + ra.Kind + "," + ra.CalleeProc + "," + ra.RefutationSite);
+
+          AddRelatedToWorkList(ra);
+          UpdateAssignment(ra);
+          count++;
+        }
+      }
+
+      return count > 0 ? true : false;
+    }
+
+    protected override void ShareRefutedAnnotation(RefutedAnnotation refutedAnnotation) {
+      refutedSharedAnnotations.TryAdd(refutedAnnotation.Constant.Name, refutedAnnotation);
+    }
+
+    protected override void ApplyRefutedSharedAnnotations() {
+      if (refutedSharedAnnotations.Count > 0) {
+        foreach (var v in currentHoudiniState.Assignment.Keys.ToList()) {
+          if (refutedSharedAnnotations.ContainsKey(v.Name)) {
+            currentHoudiniState.Assignment[v] = false;
+          }
+        }
+      }
+    }
+
+    protected override int GetTaskID() {
+      return taskID;
+    }
+
+  }
+}
diff --git a/Source/Houdini/Houdini.cs b/Source/Houdini/Houdini.cs
index 986d0fff..4c4ab5aa 100644
--- a/Source/Houdini/Houdini.cs
+++ b/Source/Houdini/Houdini.cs
@@ -1,1328 +1,1330 @@
-//-----------------------------------------------------------------------------

-//

-// Copyright (C) Microsoft Corporation.  All Rights Reserved.

-//

-//-----------------------------------------------------------------------------

-using System;

-using System.Diagnostics.Contracts;

-using System.Collections.Generic;

-using Microsoft.Boogie;

-using Microsoft.Boogie.VCExprAST;

-using VC;

-using System.Collections;

-using System.IO;

-using Microsoft.Boogie.GraphUtil;

-using System.Linq;

-using System.Diagnostics;

-

-namespace Microsoft.Boogie.Houdini {

-

-  internal class ReadOnlyDictionary<K, V> {

-    private Dictionary<K, V> dictionary;

-    public ReadOnlyDictionary(Dictionary<K, V> dictionary) {

-      this.dictionary = dictionary;

-    }

-

-    public Dictionary<K, V>.KeyCollection Keys {

-      get { return this.dictionary.Keys; }

-    }

-

-    public bool TryGetValue(K k, out V v) {

-      return this.dictionary.TryGetValue(k, out v);

-    }

-

-    public bool ContainsKey(K k) {

-      return this.dictionary.ContainsKey(k);

-    }

-  }

-

-  public abstract class HoudiniObserver {

-    public virtual void UpdateStart(Program program, int numConstants) { }

-    public virtual void UpdateIteration() { }

-    public virtual void UpdateImplementation(Implementation implementation) { }

-    public virtual void UpdateAssignment(Dictionary<Variable, bool> assignment) { }

-    public virtual void UpdateOutcome(ProverInterface.Outcome outcome) { }

-    public virtual void UpdateEnqueue(Implementation implementation) { }

-    public virtual void UpdateDequeue() { }

-    public virtual void UpdateConstant(string constantName) { }

-    public virtual void UpdateEnd(bool isNormalEnd) { }

-    public virtual void UpdateFlushStart() { }

-    public virtual void UpdateFlushFinish() { }

-    public virtual void SeeException(string msg) { }

-  }

-

-  public class IterationTimer<K> {

-    private Dictionary<K, List<double>> times;

-

-    public IterationTimer() {

-      times = new Dictionary<K, List<double>>();

-    }

-

-    public void AddTime(K key, double timeMS) {

-      List<double> oldList;

-      times.TryGetValue(key, out oldList);

-      if (oldList == null) {

-        oldList = new List<double>();

-      }

-      else {

-        times.Remove(key);

-      }

-      oldList.Add(timeMS);

-      times.Add(key, oldList);

-    }

-

-    public void PrintTimes(TextWriter wr) {

-      wr.WriteLine("Total procedures: {0}", times.Count);

-      double total = 0;

-      int totalIters = 0;

-      foreach (KeyValuePair<K, List<double>> kv in times) {

-        int curIter = 0;

-        wr.WriteLine("Times for {0}:", kv.Key);

-        foreach (double v in kv.Value) {

-          wr.WriteLine("  ({0})\t{1}ms", curIter, v);

-          total += v;

-          curIter++;

-        }

-        totalIters += curIter;

-      }

-      total = total / 1000.0;

-      wr.WriteLine("Total time: {0} (s)", total);

-      wr.WriteLine("Avg: {0} (s/iter)", total / totalIters);

-    }

-  }

-

-  public class HoudiniTimer : HoudiniObserver {

-    private DateTime startT;

-    private Implementation curImp;

-    private IterationTimer<string> times;

-    private TextWriter wr;

-

-    public HoudiniTimer(TextWriter wr) {

-      this.wr = wr;

-      times = new IterationTimer<string>();

-    }

-    public override void UpdateIteration() {

-      startT = DateTime.UtcNow;

-    }

-    public override void UpdateImplementation(Implementation implementation) {

-      curImp = implementation;

-    }

-    public override void UpdateOutcome(ProverInterface.Outcome o) {

-      Contract.Assert(curImp != null);

-      DateTime endT = DateTime.UtcNow;

-      times.AddTime(curImp.Name, (endT - startT).TotalMilliseconds); // assuming names are unique

-    }

-    public void PrintTimes() {

-      wr.WriteLine("-----------------------------------------");

-      wr.WriteLine("Times for each iteration for each procedure");

-      wr.WriteLine("-----------------------------------------");

-      times.PrintTimes(wr);

-    }

-  }

-

-  public class HoudiniTextReporter : HoudiniObserver {

-    private TextWriter wr;

-    private int currentIteration = -1;

-

-    public HoudiniTextReporter(TextWriter wr) {

-      this.wr = wr;

-    }

-    public override void UpdateStart(Program program, int numConstants) {

-      wr.WriteLine("Houdini started:" + program.ToString() + " #constants: " + numConstants.ToString());

-      currentIteration = -1;

-      wr.Flush();

-    }

-    public override void UpdateIteration() {

-      currentIteration++;

-      wr.WriteLine("---------------------------------------");

-      wr.WriteLine("Houdini iteration #" + currentIteration);

-      wr.Flush();

-    }

-    public override void UpdateImplementation(Implementation implementation) {

-      wr.WriteLine("implementation under analysis :" + implementation.Name);

-      wr.Flush();

-    }

-    public override void UpdateAssignment(Dictionary<Variable, bool> assignment) {

-      bool firstTime = true;

-      wr.Write("assignment under analysis : axiom (");

-      foreach (KeyValuePair<Variable, bool> kv in assignment) {

-        if (!firstTime) wr.Write(" && "); else firstTime = false;

-        string valString; // ugliness to get it lower cased

-        if (kv.Value) valString = "true"; else valString = "false";

-        wr.Write(kv.Key + " == " + valString);

-      }

-      wr.WriteLine(");");

-      wr.Flush();

-    }

-    public override void UpdateOutcome(ProverInterface.Outcome outcome) {

-      wr.WriteLine("analysis outcome :" + outcome);

-      wr.Flush();

-    }

-    public override void UpdateEnqueue(Implementation implementation) {

-      wr.WriteLine("worklist enqueue :" + implementation.Name);

-      wr.Flush();

-    }

-    public override void UpdateDequeue() {

-      wr.WriteLine("worklist dequeue");

-      wr.Flush();

-    }

-    public override void UpdateConstant(string constantName) {

-      wr.WriteLine("constant disabled : " + constantName);

-      wr.Flush();

-    }

-    public override void UpdateEnd(bool isNormalEnd) {

-      wr.WriteLine("Houdini ended: " + (isNormalEnd ? "Normal" : "Abnormal"));

-      wr.WriteLine("Number of iterations: " + (this.currentIteration + 1));

-      wr.Flush();

-    }

-    public override void UpdateFlushStart() {

-      wr.WriteLine("***************************************");

-      wr.WriteLine("Flushing remaining implementations");

-      wr.Flush();

-    }

-    public override void UpdateFlushFinish() {

-      wr.WriteLine("***************************************");

-      wr.WriteLine("Flushing finished");

-      wr.Flush();

-    }

-    public override void SeeException(string msg) {

-      wr.WriteLine("Caught exception: " + msg);

-      wr.Flush();

-    }

-

-  }

-

-  public abstract class ObservableHoudini {

-    private List<HoudiniObserver> observers = new List<HoudiniObserver>();

-

-    public void AddObserver(HoudiniObserver observer) {

-      if (!observers.Contains(observer))

-        observers.Add(observer);

-    }

-    private delegate void NotifyDelegate(HoudiniObserver observer);

-

-    private void Notify(NotifyDelegate notifyDelegate) {

-      foreach (HoudiniObserver observer in observers) {

-        notifyDelegate(observer);

-      }

-    }

-    protected void NotifyStart(Program program, int numConstants) {

-      NotifyDelegate notifyDelegate = (NotifyDelegate)delegate(HoudiniObserver r) { r.UpdateStart(program, numConstants); };

-      Notify(notifyDelegate);

-    }

-    protected void NotifyIteration() {

-      Notify((NotifyDelegate)delegate(HoudiniObserver r) { r.UpdateIteration(); });

-    }

-    protected void NotifyImplementation(Implementation implementation) {

-      Notify((NotifyDelegate)delegate(HoudiniObserver r) { r.UpdateImplementation(implementation); });

-    }

-    protected void NotifyAssignment(Dictionary<Variable, bool> assignment) {

-      Notify((NotifyDelegate)delegate(HoudiniObserver r) { r.UpdateAssignment(assignment); });

-    }

-    protected void NotifyOutcome(ProverInterface.Outcome outcome) {

-      Notify((NotifyDelegate)delegate(HoudiniObserver r) { r.UpdateOutcome(outcome); });

-    }

-    protected void NotifyEnqueue(Implementation implementation) {

-      Notify((NotifyDelegate)delegate(HoudiniObserver r) { r.UpdateEnqueue(implementation); });

-    }

-    protected void NotifyDequeue() {

-      Notify((NotifyDelegate)delegate(HoudiniObserver r) { r.UpdateDequeue(); });

-    }

-    protected void NotifyConstant(string constantName) {

-      Notify((NotifyDelegate)delegate(HoudiniObserver r) { r.UpdateConstant(constantName); });

-    }

-    protected void NotifyEnd(bool isNormalEnd) {

-      Notify((NotifyDelegate)delegate(HoudiniObserver r) { r.UpdateEnd(isNormalEnd); });

-    }

-    protected void NotifyFlushStart() {

-      Notify((NotifyDelegate)delegate(HoudiniObserver r) { r.UpdateFlushStart(); });

-    }

-    protected void NotifyFlushFinish() {

-      Notify((NotifyDelegate)delegate(HoudiniObserver r) { r.UpdateFlushFinish(); });

-    }

-

-    protected void NotifyException(string msg) {

-      Notify((NotifyDelegate)delegate(HoudiniObserver r) { r.SeeException(msg); });

-    }

-  }

-

-  public class InlineEnsuresVisitor : ReadOnlyVisitor {

-      public override Ensures VisitEnsures(Ensures ensures)

-      {

-          if (!ensures.Free)

-          {

-              ensures.Attributes = new QKeyValue(Token.NoToken, "InlineAssume", new List<object>(), ensures.Attributes);

-          }

-          return base.VisitEnsures(ensures);

-      }

-  }

-

-  public class Houdini : ObservableHoudini {

-    protected Program program;

-    protected HashSet<Variable> houdiniConstants;

-    protected VCGen vcgen;

-    protected ProverInterface proverInterface;

-    protected Graph<Implementation> callGraph;

-    protected HashSet<Implementation> vcgenFailures;

-    protected HoudiniState currentHoudiniState;

-    protected CrossDependencies crossDependencies;

-    internal ReadOnlyDictionary<Implementation, HoudiniSession> houdiniSessions;

-

-    protected string cexTraceFile;

-

-    public HoudiniState CurrentHoudiniState { get { return currentHoudiniState; } }    

-

-    public static TextWriter explainHoudiniDottyFile;

-

-    protected Houdini() { }

-

-    public Houdini(Program program, HoudiniSession.HoudiniStatistics stats, string cexTraceFile = "houdiniCexTrace.txt") {

-      this.program = program;

-      this.cexTraceFile = cexTraceFile;

-      Initialize(program, stats);

-    }

-

-    protected void Initialize(Program program, HoudiniSession.HoudiniStatistics stats)

-    {

-        if (CommandLineOptions.Clo.Trace)

-            Console.WriteLine("Collecting existential constants...");

-        this.houdiniConstants = CollectExistentialConstants();

-

-        if (CommandLineOptions.Clo.Trace)

-            Console.WriteLine("Building call graph...");

-        this.callGraph = Program.BuildCallGraph(program);

-        if (CommandLineOptions.Clo.Trace)

-            Console.WriteLine("Number of implementations = {0}", callGraph.Nodes.Count);

-

-        if (CommandLineOptions.Clo.HoudiniUseCrossDependencies)

-        {

-            if (CommandLineOptions.Clo.Trace) Console.WriteLine("Computing procedure cross dependencies ...");

-            this.crossDependencies = new CrossDependencies(this.houdiniConstants);

-            this.crossDependencies.Visit(program);

-        }

-

-        Inline();

-        /*

-        {

-            int oldPrintUnstructured = CommandLineOptions.Clo.PrintUnstructured;

-            CommandLineOptions.Clo.PrintUnstructured = 1;

-            using (TokenTextWriter stream = new TokenTextWriter("houdini_inline.bpl"))

-            {

-                program.Emit(stream);

-            }

-            CommandLineOptions.Clo.PrintUnstructured = oldPrintUnstructured;

-        }

-        */

-

-        this.vcgen = new VCGen(program, CommandLineOptions.Clo.SimplifyLogFilePath, CommandLineOptions.Clo.SimplifyLogFileAppend, new List<Checker>());

-        this.proverInterface = ProverInterface.CreateProver(program, CommandLineOptions.Clo.SimplifyLogFilePath, CommandLineOptions.Clo.SimplifyLogFileAppend, CommandLineOptions.Clo.ProverKillTime, taskID: GetTaskID());

-

-        vcgenFailures = new HashSet<Implementation>();

-        Dictionary<Implementation, HoudiniSession> houdiniSessions = new Dictionary<Implementation, HoudiniSession>();

-        if (CommandLineOptions.Clo.Trace)

-            Console.WriteLine("Beginning VC generation for Houdini...");

-        foreach (Implementation impl in callGraph.Nodes)

-        {

-            try

-            {

-                if (CommandLineOptions.Clo.Trace)

-                    Console.WriteLine("Generating VC for {0}", impl.Name);

-                HoudiniSession session = new HoudiniSession(this, vcgen, proverInterface, program, impl, stats, taskID: GetTaskID());

-                houdiniSessions.Add(impl, session);

-            }

-            catch (VCGenException)

-            {

-                if (CommandLineOptions.Clo.Trace)

-                    Console.WriteLine("VC generation failed");

-                vcgenFailures.Add(impl);

-            }

-        }

-        this.houdiniSessions = new ReadOnlyDictionary<Implementation, HoudiniSession>(houdiniSessions);

-

-        if (CommandLineOptions.Clo.ExplainHoudini)

-        {

-            // Print results of ExplainHoudini to a dotty file

-            explainHoudiniDottyFile = new StreamWriter("explainHoudini.dot");

-            explainHoudiniDottyFile.WriteLine("digraph explainHoudini {");

-            foreach (var constant in houdiniConstants)

-                explainHoudiniDottyFile.WriteLine("{0} [ label = \"{0}\" color=black ];", constant.Name);

-            explainHoudiniDottyFile.WriteLine("TimeOut [label = \"TimeOut\" color=red ];");

-        }

-    }

-

-    protected void Inline() {

-      if (CommandLineOptions.Clo.InlineDepth <= 0)

-        return;

-

-      foreach (Implementation impl in callGraph.Nodes) {

-        InlineEnsuresVisitor inlineEnsuresVisitor = new InlineEnsuresVisitor();

-        inlineEnsuresVisitor.Visit(impl);

-      }

-

-      foreach (Implementation impl in callGraph.Nodes) {

-        impl.OriginalBlocks = impl.Blocks;

-        impl.OriginalLocVars = impl.LocVars;

-      }

-      foreach (Implementation impl in callGraph.Nodes) {

-        CommandLineOptions.Inlining savedOption = CommandLineOptions.Clo.ProcedureInlining;

-        CommandLineOptions.Clo.ProcedureInlining = CommandLineOptions.Inlining.Spec;

-        Inliner.ProcessImplementationForHoudini(program, impl);

-        CommandLineOptions.Clo.ProcedureInlining = savedOption;

-      }

-      foreach (Implementation impl in callGraph.Nodes) {

-        impl.OriginalBlocks = null;

-        impl.OriginalLocVars = null;

-      }

-

-      Graph<Implementation> oldCallGraph = callGraph;

-      callGraph = new Graph<Implementation>();

-      foreach (Implementation impl in oldCallGraph.Nodes) {

-        callGraph.AddSource(impl);

-      }

-      foreach (Tuple<Implementation, Implementation> edge in oldCallGraph.Edges) {

-        callGraph.AddEdge(edge.Item1, edge.Item2);

-      }

-      int count = CommandLineOptions.Clo.InlineDepth;

-      while (count > 0) {

-        foreach (Implementation impl in oldCallGraph.Nodes) {

-          List<Implementation> newNodes = new List<Implementation>();

-          foreach (Implementation succ in callGraph.Successors(impl)) {

-            newNodes.AddRange(oldCallGraph.Successors(succ));

-          }

-          foreach (Implementation newNode in newNodes) {

-            callGraph.AddEdge(impl, newNode);

-          }

-        }

-        count--;

-      }

-    }

-

-    protected HashSet<Variable> CollectExistentialConstants() {

-      HashSet<Variable> existentialConstants = new HashSet<Variable>();

-      foreach (var constant in program.Constants) {

-        bool result = false;

-        if (constant.CheckBooleanAttribute("existential", ref result)) {

-          if (result == true)

-            existentialConstants.Add(constant);

-        }

-      }

-      return existentialConstants;

-    }

-

-      // Compute dependencies between candidates

-    public class CrossDependencies : ReadOnlyVisitor

-    {

-        public CrossDependencies(HashSet<Variable> constants)

-        {

-            this.constants = constants;

-        }

-

-        public override Program VisitProgram(Program node)

-        {

-            assumedInImpl = new Dictionary<string, HashSet<Implementation>>();

-            return base.VisitProgram(node);

-        }

-

-        public override Implementation VisitImplementation(Implementation node)

-        {

-            curImpl = node;

-            return base.VisitImplementation(node);

-        }

-

-        public override Cmd VisitAssumeCmd(AssumeCmd node)

-        {

-            return base.VisitAssumeCmd(node);

-        }

-

-        public override Variable VisitVariable(Variable node)

-        {

-            if (node is Constant)

-            {

-                var constant = node as Constant;

-                if (constants.Contains(constant))

-                {

-                    if (!assumedInImpl.ContainsKey(constant.Name))

-                        assumedInImpl[constant.Name] = new HashSet<Implementation>();

-                    assumedInImpl[constant.Name].Add(curImpl);

-                }

-            }

-            return base.VisitVariable(node);

-        }

-

-        HashSet<Variable> constants;

-        Implementation curImpl;

-

-        // contant -> set of implementations that have an assume command with that constant

-        public Dictionary<string, HashSet<Implementation>> assumedInImpl { get; private set; }

-    }

-    

-    protected WorkQueue BuildWorkList(Program program) {

-      // adding implementations to the workqueue from the bottom of the call graph upwards

-      WorkQueue queue = new WorkQueue();

-      StronglyConnectedComponents<Implementation> sccs =

-        new StronglyConnectedComponents<Implementation>(callGraph.Nodes,

-          new Adjacency<Implementation>(callGraph.Predecessors),

-          new Adjacency<Implementation>(callGraph.Successors));

-      sccs.Compute();

-      foreach (SCC<Implementation> scc in sccs) {

-        foreach (Implementation impl in scc) {

-          if (vcgenFailures.Contains(impl)) continue;

-          queue.Enqueue(impl);

-        }

-      }

-      if (CommandLineOptions.Clo.ReverseHoudiniWorklist)

-          queue = queue.Reverse();

-      return queue;      

-      /*

-      Queue<Implementation> queue = new Queue<Implementation>();

-      foreach (Declaration decl in program.TopLevelDeclarations) {

-        Implementation impl = decl as Implementation;

-        if (impl == null || impl.SkipVerification) continue;

-        queue.Enqueue(impl);

-      }

-      return queue;

-       */

-    }

-

-    public static bool MatchCandidate(Expr boogieExpr, IEnumerable<string> candidates, out string candidateConstant) {

-      candidateConstant = null;

-      NAryExpr e = boogieExpr as NAryExpr;

-      if (e != null && e.Fun is BinaryOperator && ((BinaryOperator)e.Fun).Op == BinaryOperator.Opcode.Imp) {

-        Expr antecedent = e.Args[0];

-        Expr consequent = e.Args[1];

-

-        IdentifierExpr id = antecedent as IdentifierExpr;

-        if (id != null && id.Decl is Constant && candidates.Contains(id.Decl.Name)) {

-          candidateConstant = id.Decl.Name;

-          return true;

-        }

-

-        if (MatchCandidate(consequent, candidates, out candidateConstant))

-          return true;

-      }

-      return false;

-    }

-

-    public static bool GetCandidateWithoutConstant(Expr boogieExpr, IEnumerable<string> candidates, out string candidateConstant, out Expr exprWithoutConstant) {

-      candidateConstant = null;

-      exprWithoutConstant = null;

-      NAryExpr e = boogieExpr as NAryExpr;

-      if (e != null && e.Fun is BinaryOperator && ((BinaryOperator)e.Fun).Op == BinaryOperator.Opcode.Imp) {

-        Expr antecedent = e.Args[0];

-        Expr consequent = e.Args[1];

-

-        IdentifierExpr id = antecedent as IdentifierExpr;

-        if (id != null && id.Decl is Constant && candidates.Contains(id.Decl.Name)) {

-          candidateConstant = id.Decl.Name;

-          exprWithoutConstant = consequent;

-          return true;

-        }

-

-        if (GetCandidateWithoutConstant(consequent, candidates, out candidateConstant, out exprWithoutConstant))

-          exprWithoutConstant = Expr.Imp(antecedent, exprWithoutConstant);

-          return true;

-      }

-      return false;

-    }

-

-    private static Expr AddConditionToCandidateRec(Expr boogieExpr, Expr condition, string candidateConstant, List<Expr> implicationStack)

-    {

-        NAryExpr e = boogieExpr as NAryExpr;

-        if (e != null && e.Fun is BinaryOperator && ((BinaryOperator)e.Fun).Op == BinaryOperator.Opcode.Imp)

-        {

-            Expr antecedent = e.Args[0];

-            Expr consequent = e.Args[1];

-

-            IdentifierExpr id = antecedent as IdentifierExpr;

-            if (id != null && id.Decl is Constant && id.Decl.Name.Equals(candidateConstant))

-            {

-                Expr result = Expr.Imp(antecedent, Expr.Imp(condition, consequent));

-                implicationStack.Reverse();

-                foreach (var expr in implicationStack)

-                {

-                    result = Expr.Imp(expr, result);

-                }

-                return result;

-            }

-

-            implicationStack.Add(antecedent);

-            return AddConditionToCandidateRec(consequent, condition, candidateConstant,

-                implicationStack);

-        }

-        return boogieExpr;

-    }

-

-    public static Expr AddConditionToCandidate(Expr boogieExpr, Expr condition, string candidateConstant)

-    {

-        return AddConditionToCandidateRec(boogieExpr, condition, candidateConstant, new List<Expr>());

-    }

-

-    public bool MatchCandidate(Expr boogieExpr, out Variable candidateConstant) {

-      candidateConstant = null;

-      string candidateString;

-      if(MatchCandidate(boogieExpr, houdiniConstants.Select(item => item.Name), out candidateString)) {

-        candidateConstant = houdiniConstants.Where(item => item.Name.Equals(candidateString)).ToList()[0];

-        return true;

-      }

-      return false;

-    }

-

-    public bool MatchCandidate(Expr boogieExpr, out string candidateConstant) {

-      return MatchCandidate(boogieExpr, houdiniConstants.Select(item => item.Name), out candidateConstant);

-    }

-

-    // For Explain houdini: it decorates the condition \phi as (vpos && (\phi || \not vneg))

-    // Precondition: MatchCandidate returns true

-    public Expr InsertCandidateControl(Expr boogieExpr, Variable vpos, Variable vneg)

-    {

-        Contract.Assert(CommandLineOptions.Clo.ExplainHoudini);

-

-        NAryExpr e = boogieExpr as NAryExpr;

-        if (e != null && e.Fun is BinaryOperator && ((BinaryOperator)e.Fun).Op == BinaryOperator.Opcode.Imp)

-        {

-            Expr antecedent = e.Args[0];

-            Expr consequent = e.Args[1];

-

-            IdentifierExpr id = antecedent as IdentifierExpr;

-            if (id != null && id.Decl is Constant && houdiniConstants.Contains((Constant)id.Decl))

-            {

-                return Expr.Imp(antecedent, Expr.And(Expr.Ident(vpos), Expr.Or(consequent, Expr.Not(Expr.Ident(vneg)))));

-            }

-

-            return Expr.Imp(antecedent, InsertCandidateControl(consequent, vpos, vneg));

-        }

-        Contract.Assert(false);

-        return null;

-    }

-

-    protected Dictionary<Variable, bool> BuildAssignment(HashSet<Variable> constants) {

-      Dictionary<Variable, bool> initial = new Dictionary<Variable, bool>();

-      foreach (var constant in constants)

-        initial.Add(constant, true);

-      return initial;

-    }

-

-    private bool IsOutcomeNotHoudini(ProverInterface.Outcome outcome, List<Counterexample> errors) {

-      switch (outcome) {

-        case ProverInterface.Outcome.Valid:

-          return false;

-        case ProverInterface.Outcome.Invalid:

-          Contract.Assume(errors != null);

-          foreach (Counterexample error in errors) {

-            if (ExtractRefutedAnnotation(error) == null)

-              return true;

-          }

-          return false;

-        default:

-          return true;

-      }

-    }

-

-    // Record most current non-candidate errors found

-    // Return true if there was at least one non-candidate error

-    protected bool UpdateHoudiniOutcome(HoudiniOutcome houdiniOutcome,

-                                      Implementation implementation,

-                                      ProverInterface.Outcome outcome,

-                                      List<Counterexample> errors) {

-      string implName = implementation.Name;

-      houdiniOutcome.implementationOutcomes.Remove(implName);

-      List<Counterexample> nonCandidateErrors = new List<Counterexample>();

-

-      if (outcome == ProverInterface.Outcome.Invalid) {

-          foreach (Counterexample error in errors) {

-            if (ExtractRefutedAnnotation(error) == null)

-              nonCandidateErrors.Add(error);

-          }

-      }

-      houdiniOutcome.implementationOutcomes.Add(implName, new VCGenOutcome(outcome, nonCandidateErrors));

-      return nonCandidateErrors.Count > 0;

-    }

-

-    protected void FlushWorkList(int stage, IEnumerable<int> completedStages) {

-      this.NotifyFlushStart();

-      while (currentHoudiniState.WorkQueue.Count > 0) {

-        this.NotifyIteration();

-

-        currentHoudiniState.Implementation = currentHoudiniState.WorkQueue.Peek();

-        this.NotifyImplementation(currentHoudiniState.Implementation);

-

-        HoudiniSession session;

-        houdiniSessions.TryGetValue(currentHoudiniState.Implementation, out session);

-        List<Counterexample> errors;

-        ProverInterface.Outcome outcome = TryCatchVerify(session, stage, completedStages, out errors);

-        UpdateHoudiniOutcome(currentHoudiniState.Outcome, currentHoudiniState.Implementation, outcome, errors);

-        this.NotifyOutcome(outcome);

-

-        currentHoudiniState.WorkQueue.Dequeue();

-        this.NotifyDequeue();

-      }

-      this.NotifyFlushFinish();

-    }

-

-    protected void UpdateAssignment(RefutedAnnotation refAnnot) {

-      if (CommandLineOptions.Clo.Trace) {

-        Console.WriteLine("Removing " + refAnnot.Constant);

-        using (var cexWriter = new System.IO.StreamWriter(cexTraceFile, true))

-            cexWriter.WriteLine("Removing " + refAnnot.Constant);

-      }

-      currentHoudiniState.Assignment.Remove(refAnnot.Constant);

-      currentHoudiniState.Assignment.Add(refAnnot.Constant, false);

-      this.NotifyConstant(refAnnot.Constant.Name);

-    }

-

-    protected void AddRelatedToWorkList(RefutedAnnotation refutedAnnotation) {

-      Contract.Assume(currentHoudiniState.Implementation != null);

-      foreach (Implementation implementation in FindImplementationsToEnqueue(refutedAnnotation, refutedAnnotation.RefutationSite)) {

-        if (!currentHoudiniState.isBlackListed(implementation.Name)) {

-          currentHoudiniState.WorkQueue.Enqueue(implementation);

-          this.NotifyEnqueue(implementation);

-        }

-      }

-    }

-

-    // Updates the worklist and current assignment

-    // @return true if the current function is dequeued

-    protected bool UpdateAssignmentWorkList(ProverInterface.Outcome outcome,

-                                          List<Counterexample> errors) {

-      Contract.Assume(currentHoudiniState.Implementation != null);

-      bool dequeue = true;

-

-      switch (outcome) {

-        case ProverInterface.Outcome.Valid:

-          //yeah, dequeue

-          break;

-

-        case ProverInterface.Outcome.Invalid:

-            Contract.Assume(errors != null);

-

-            foreach (Counterexample error in errors) {

-              RefutedAnnotation refutedAnnotation = ExtractRefutedAnnotation(error);

-              if (refutedAnnotation != null) {

-                // some candidate annotation removed

-                ShareRefutedAnnotation(refutedAnnotation);

-                AddRelatedToWorkList(refutedAnnotation);

-                UpdateAssignment(refutedAnnotation);

-                dequeue = false;

-                #region Extra debugging output

-                if (CommandLineOptions.Clo.Trace) {

-                  using (var cexWriter = new System.IO.StreamWriter(cexTraceFile, true)) {

-                    cexWriter.WriteLine("Counter example for " + refutedAnnotation.Constant);

-                    cexWriter.Write(error.ToString());

-                    cexWriter.WriteLine();

-                    using (var writer = new Microsoft.Boogie.TokenTextWriter(cexWriter, /*pretty=*/ false))

-                      foreach (Microsoft.Boogie.Block blk in error.Trace)

-                        blk.Emit(writer, 15);

-                    //cexWriter.WriteLine(); 

-                  }

-                }

-                #endregion

-              }

-            }

-              

-            if (ExchangeRefutedAnnotations()) dequeue = false;

-

-            break;

-        default:

-            if (CommandLineOptions.Clo.Trace) {

-                Console.WriteLine("Timeout/Spaceout while verifying " + currentHoudiniState.Implementation.Name);

-            }

-            HoudiniSession houdiniSession;

-            houdiniSessions.TryGetValue(currentHoudiniState.Implementation, out houdiniSession);

-            foreach (Variable v in houdiniSession.houdiniAssertConstants) {

-                if (CommandLineOptions.Clo.Trace) {

-                    Console.WriteLine("Removing " + v);

-                }

-                currentHoudiniState.Assignment.Remove(v);

-                currentHoudiniState.Assignment.Add(v, false);

-                this.NotifyConstant(v.Name);

-            }

-            currentHoudiniState.addToBlackList(currentHoudiniState.Implementation.Name);

-            break;

-      }

-      

-      return dequeue;

-    }

-

-    // This method is a hook used by ConcurrentHoudini to

-    // exchange refuted annotations with other Houdini engines.

-    // If the method returns true, this indicates that at least

-    // one new refutation was received from some other engine.

-    // In the base class we thus return false.

-    protected virtual bool ExchangeRefutedAnnotations() {

-      return false;

-    }

-

-    // This method is a hook used by ConcurrentHoudini to

-    // apply a set of existing refuted annotations at the

-    // start of inference.

-    protected virtual void ApplyRefutedSharedAnnotations() {

-      // Empty in base class; can be overridden.

-    }

-

-    // This method is a hook used by ConcurrentHoudini to

-    // broadcast to other Houdini engines the fact that an

-    // annotation was refuted.

-    protected virtual void ShareRefutedAnnotation(RefutedAnnotation refutedAnnotation) {

-      // Empty in base class; can be overridden.

-    }

-

-    // Hook for ConcurrentHoudini, which requires a task id.

-    // Non-concurrent Houdini has -1 as a task id

-    protected virtual int GetTaskID() {

-      return -1;

-    }

-

-    public class WorkQueue {

-      private Queue<Implementation> queue;

-      private HashSet<Implementation> set;

-      public WorkQueue() {

-        queue = new Queue<Implementation>();

-        set = new HashSet<Implementation>();

-      }

-      public void Enqueue(Implementation impl) {

-        if (set.Contains(impl))

-          return;

-        queue.Enqueue(impl);

-        set.Add(impl);

-      }

-      public Implementation Dequeue() {

-        Implementation impl = queue.Dequeue();

-        set.Remove(impl);

-        return impl;

-      }

-      public Implementation Peek() {

-        return queue.Peek();

-      }

-      public int Count {

-        get { return queue.Count; }

-      }

-      public bool Contains(Implementation impl) {

-        return set.Contains(impl);

-      }

-      public WorkQueue Reverse()

-      {

-          var ret = new WorkQueue();

-          foreach (var impl in queue.Reverse())

-              ret.Enqueue(impl);

-          return ret;

-      }

-    }

-

-    public class HoudiniState {

-      public WorkQueue _workQueue;

-      public HashSet<string> blackList;

-      public Dictionary<Variable, bool> _assignment;

-      public Implementation _implementation;

-      public HoudiniOutcome _outcome;

-

-      public HoudiniState(WorkQueue workQueue, Dictionary<Variable, bool> currentAssignment) {

-        this._workQueue = workQueue;

-        this._assignment = currentAssignment;

-        this._implementation = null;

-        this._outcome = new HoudiniOutcome();

-        this.blackList = new HashSet<string>();

-      }

-

-      public WorkQueue WorkQueue {

-        get { return this._workQueue; }

-      }

-      public Dictionary<Variable, bool> Assignment {

-        get { return this._assignment; }

-      }

-      public Implementation Implementation {

-        get { return this._implementation; }

-        set { this._implementation = value; }

-      }

-      public HoudiniOutcome Outcome {

-        get { return this._outcome; }

-      }

-      public bool isBlackListed(string funcName) {

-        return blackList.Contains(funcName);

-      }

-      public void addToBlackList(string funcName) {

-        blackList.Add(funcName);

-      }

-    }

-

-    public HoudiniOutcome PerformHoudiniInference(int stage = 0, 

-                                                  IEnumerable<int> completedStages = null,

-                                                  Dictionary<string, bool> initialAssignment = null) {

-      this.NotifyStart(program, houdiniConstants.Count);

-

-      currentHoudiniState = new HoudiniState(BuildWorkList(program), BuildAssignment(houdiniConstants));

-

-      if(initialAssignment != null) {

-        foreach(var v in CurrentHoudiniState.Assignment.Keys.ToList()) {

-          CurrentHoudiniState.Assignment[v] = initialAssignment[v.Name];

-        }

-      }

-

-      ApplyRefutedSharedAnnotations();

-

-      foreach (Implementation impl in vcgenFailures) {

-        currentHoudiniState.addToBlackList(impl.Name);

-      }

-

-      while (currentHoudiniState.WorkQueue.Count > 0) {

-        this.NotifyIteration();

-

-        currentHoudiniState.Implementation = currentHoudiniState.WorkQueue.Peek();

-        this.NotifyImplementation(currentHoudiniState.Implementation);

-

-        HoudiniSession session;

-        this.houdiniSessions.TryGetValue(currentHoudiniState.Implementation, out session);

-        HoudiniVerifyCurrent(session, stage, completedStages);

-      }

-

-      this.NotifyEnd(true);

-      Dictionary<string, bool> assignment = new Dictionary<string, bool>();

-      foreach (var x in currentHoudiniState.Assignment)

-        assignment[x.Key.Name] = x.Value;

-      currentHoudiniState.Outcome.assignment = assignment;

-      return currentHoudiniState.Outcome;

-    }

-

-    public void Close() {

-      vcgen.Close();

-      proverInterface.Close();

-      if (CommandLineOptions.Clo.ExplainHoudini)

-      {

-          explainHoudiniDottyFile.WriteLine("};");

-          explainHoudiniDottyFile.Close();

-      }

-    }

-

-    private int NumberOfStages()

-    {

-      int result = 1;

-      foreach(var c in program.Constants) {

-        result = Math.Max(result, 1 + QKeyValue.FindIntAttribute(c.Attributes, "stage_active", -1));

-      }

-      return result;

-    }

-

-    private List<Implementation> FindImplementationsToEnqueue(RefutedAnnotation refutedAnnotation, Implementation currentImplementation) {

-      HoudiniSession session;

-      List<Implementation> implementations = new List<Implementation>();

-      switch (refutedAnnotation.Kind) {

-        case RefutedAnnotationKind.REQUIRES:

-              foreach (Implementation callee in callGraph.Successors(currentImplementation))

-              {

-                  if (vcgenFailures.Contains(callee)) continue;

-                  houdiniSessions.TryGetValue(callee, out session);

-                  Contract.Assume(callee.Proc != null);

-                  if (callee.Proc.Equals(refutedAnnotation.CalleeProc) && session.InUnsatCore(refutedAnnotation.Constant))

-                      implementations.Add(callee);

-              }

-          break;

-        case RefutedAnnotationKind.ENSURES:

-          foreach (Implementation caller in callGraph.Predecessors(currentImplementation))

-          {

-              if (vcgenFailures.Contains(caller)) continue;

-              houdiniSessions.TryGetValue(caller, out session);

-              if (session.InUnsatCore(refutedAnnotation.Constant))

-                  implementations.Add(caller);

-          }

-          break;

-        case RefutedAnnotationKind.ASSERT: //the implementation is already in queue

-          if (CommandLineOptions.Clo.HoudiniUseCrossDependencies && crossDependencies.assumedInImpl.ContainsKey(refutedAnnotation.Constant.Name))

-          {

-              foreach (var impl in crossDependencies.assumedInImpl[refutedAnnotation.Constant.Name])

-              {

-                  if (vcgenFailures.Contains(impl)) continue;

-                  houdiniSessions.TryGetValue(impl, out session);

-                  if (session.InUnsatCore(refutedAnnotation.Constant))

-                      implementations.Add(impl);

-              }

-          }

-          break;

-        default:

-          throw new Exception("Unknown Refuted annotation kind:" + refutedAnnotation.Kind);

-      }

-      return implementations;

-    }

-

-    public enum RefutedAnnotationKind { REQUIRES, ENSURES, ASSERT };

-

-    public class RefutedAnnotation {

-      private Variable _constant;

-      private RefutedAnnotationKind _kind;

-      private Procedure _callee;

-      private Implementation _refutationSite;

-

-      private RefutedAnnotation(Variable constant, RefutedAnnotationKind kind, Procedure callee, Implementation refutationSite) {

-        this._constant = constant;

-        this._kind = kind;

-        this._callee = callee;

-        this._refutationSite = refutationSite;

-      }

-      public RefutedAnnotationKind Kind {

-        get { return this._kind; }

-      }

-      public Variable Constant {

-        get { return this._constant; }

-      }

-      public Procedure CalleeProc {

-        get { return this._callee; }

-      }

-      public Implementation RefutationSite {

-        get { return this._refutationSite; }

-      }

-      public static RefutedAnnotation BuildRefutedRequires(Variable constant, Procedure callee, Implementation refutationSite) {

-        return new RefutedAnnotation(constant, RefutedAnnotationKind.REQUIRES, callee, refutationSite);

-      }

-      public static RefutedAnnotation BuildRefutedEnsures(Variable constant, Implementation refutationSite) {

-        return new RefutedAnnotation(constant, RefutedAnnotationKind.ENSURES, null, refutationSite);

-      }

-      public static RefutedAnnotation BuildRefutedAssert(Variable constant, Implementation refutationSite) {

-        return new RefutedAnnotation(constant, RefutedAnnotationKind.ASSERT, null, refutationSite);

-      }

-

-      public override int GetHashCode()

-      {

-        unchecked {

-          int hash = 17;

-          hash = hash * 23 + this.Constant.GetHashCode();

-          hash = hash * 23 + this.Kind.GetHashCode();

-          if (this.CalleeProc != null)

-            hash = hash * 23 + this.CalleeProc.GetHashCode();

-          hash = hash * 23 + this.RefutationSite.GetHashCode();

-          return hash;

-        }

-      }

-

-      public override bool Equals(object obj) {

-        bool result = true;

-        var other = obj as RefutedAnnotation;

-

-        if (other == null) {

-          result = false;

-        } else {

-          result = result && String.Equals(other.Constant, this.Constant);

-          result = result && String.Equals(other.Kind, this.Kind);

-          if (other.CalleeProc != null && this.CalleeProc != null)

-            result = result && String.Equals(other.CalleeProc, this.CalleeProc);

-          result = result && String.Equals(other.RefutationSite, this.RefutationSite);

-        }

-

-        return result;

-      }

-    }

-

-    private void PrintRefutedCall(CallCounterexample err, XmlSink xmlOut) {

-      Expr cond = err.FailingRequires.Condition;

-      Variable houdiniConst;

-      if (MatchCandidate(cond, out houdiniConst)) {

-        xmlOut.WriteError("precondition violation", err.FailingCall.tok, err.FailingRequires.tok, err.Trace);

-      }

-    }

-

-    private void PrintRefutedReturn(ReturnCounterexample err, XmlSink xmlOut) {

-      Expr cond = err.FailingEnsures.Condition;

-      Variable houdiniConst;

-      if (MatchCandidate(cond, out houdiniConst)) {

-        xmlOut.WriteError("postcondition violation", err.FailingReturn.tok, err.FailingEnsures.tok, err.Trace);

-      }

-    }

-

-    private void PrintRefutedAssert(AssertCounterexample err, XmlSink xmlOut) {

-      Expr cond = err.FailingAssert.OrigExpr;

-      Variable houdiniConst;

-      if (MatchCandidate(cond, out houdiniConst)) {

-        xmlOut.WriteError("postcondition violation", err.FailingAssert.tok, err.FailingAssert.tok, err.Trace);

-      }

-    }

-

-    protected void DebugRefutedCandidates(Implementation curFunc, List<Counterexample> errors) {

-      XmlSink xmlRefuted = CommandLineOptions.Clo.XmlRefuted;

-      if (xmlRefuted != null && errors != null) {

-        DateTime start = DateTime.UtcNow;

-        xmlRefuted.WriteStartMethod(curFunc.ToString(), start);

-

-        foreach (Counterexample error in errors) {

-          CallCounterexample ce = error as CallCounterexample;

-          if (ce != null) PrintRefutedCall(ce, xmlRefuted);

-          ReturnCounterexample re = error as ReturnCounterexample;

-          if (re != null) PrintRefutedReturn(re, xmlRefuted);

-          AssertCounterexample ae = error as AssertCounterexample;

-          if (ae != null) PrintRefutedAssert(ae, xmlRefuted);

-        }

-

-        DateTime end = DateTime.UtcNow;

-        xmlRefuted.WriteEndMethod("errors", end, end.Subtract(start));

-      }

-    }

-

-    private RefutedAnnotation ExtractRefutedAnnotation(Counterexample error) {

-      Variable houdiniConstant;

-      CallCounterexample callCounterexample = error as CallCounterexample;

-      if (callCounterexample != null) {

-        Procedure failingProcedure = callCounterexample.FailingCall.Proc;

-        Requires failingRequires = callCounterexample.FailingRequires;

-        if (MatchCandidate(failingRequires.Condition, out houdiniConstant)) {

-          Contract.Assert(houdiniConstant != null);

-          return RefutedAnnotation.BuildRefutedRequires(houdiniConstant, failingProcedure, currentHoudiniState.Implementation);

-        }

-      }

-      ReturnCounterexample returnCounterexample = error as ReturnCounterexample;

-      if (returnCounterexample != null) {

-        Ensures failingEnsures = returnCounterexample.FailingEnsures;

-        if (MatchCandidate(failingEnsures.Condition, out houdiniConstant)) {

-          Contract.Assert(houdiniConstant != null);

-          return RefutedAnnotation.BuildRefutedEnsures(houdiniConstant, currentHoudiniState.Implementation);

-        }

-      }

-      AssertCounterexample assertCounterexample = error as AssertCounterexample;

-      if (assertCounterexample != null) {

-        AssertCmd failingAssert = assertCounterexample.FailingAssert;

-        if (MatchCandidate(failingAssert.OrigExpr, out houdiniConstant)) {

-          Contract.Assert(houdiniConstant != null);

-          return RefutedAnnotation.BuildRefutedAssert(houdiniConstant, currentHoudiniState.Implementation);

-        }

-      }

-

-      return null;

-    }

-

-    private ProverInterface.Outcome TryCatchVerify(HoudiniSession session, int stage, IEnumerable<int> completedStages, out List<Counterexample> errors) {

-      ProverInterface.Outcome outcome;

-      try {

-        outcome = session.Verify(proverInterface, GetAssignmentWithStages(stage, completedStages), out errors, taskID: GetTaskID());

-      }

-      catch (UnexpectedProverOutputException upo) {

-        Contract.Assume(upo != null);

-        errors = null;

-        outcome = ProverInterface.Outcome.Undetermined;

-      }

-      return outcome;

-    }

-

-    protected Dictionary<Variable, bool> GetAssignmentWithStages(int currentStage, IEnumerable<int> completedStages)

-    {

-      Dictionary<Variable, bool> result = new Dictionary<Variable, bool>(currentHoudiniState.Assignment);

-      foreach (var c in program.Constants)

-      {

-        int stageActive = QKeyValue.FindIntAttribute(c.Attributes, "stage_active", -1);

-        if (stageActive != -1)

-        {

-          result[c] = (stageActive == currentStage);

-        }

-        int stageComplete = QKeyValue.FindIntAttribute(c.Attributes, "stage_complete", -1);

-        if (stageComplete != -1)

-        {

-          result[c] = (completedStages.Contains(stageComplete));

-        }

-      }

-      return result;

-    }

-

-    private void HoudiniVerifyCurrent(HoudiniSession session, int stage, IEnumerable<int> completedStages) {

-      while (true) {

-        this.NotifyAssignment(currentHoudiniState.Assignment);

-

-        //check the VC with the current assignment

-        List<Counterexample> errors;

-        ProverInterface.Outcome outcome = TryCatchVerify(session, stage, completedStages, out errors);

-        this.NotifyOutcome(outcome);

-

-        DebugRefutedCandidates(currentHoudiniState.Implementation, errors);

-

-        #region Explain Houdini

-        if (CommandLineOptions.Clo.ExplainHoudini && outcome == ProverInterface.Outcome.Invalid)

-        {

-            Contract.Assume(errors != null);

-            // make a copy of this variable

-            errors = new List<Counterexample>(errors);

-            var refutedAnnotations = new List<RefutedAnnotation>();

-            foreach (Counterexample error in errors)

-            {

-                RefutedAnnotation refutedAnnotation = ExtractRefutedAnnotation(error);

-                if (refutedAnnotation == null || refutedAnnotation.Kind == RefutedAnnotationKind.ASSERT) continue;

-                refutedAnnotations.Add(refutedAnnotation);

-            }

-            foreach (var refutedAnnotation in refutedAnnotations)

-            {

-                session.Explain(proverInterface, currentHoudiniState.Assignment, refutedAnnotation.Constant);

-            }

-        }

-        #endregion

-

-        if (UpdateHoudiniOutcome(currentHoudiniState.Outcome, currentHoudiniState.Implementation, outcome, errors)) { // abort

-          currentHoudiniState.WorkQueue.Dequeue();

-          this.NotifyDequeue();

-          FlushWorkList(stage, completedStages);

-          return;

-        }

-        else if (UpdateAssignmentWorkList(outcome, errors)) {

-          if (CommandLineOptions.Clo.UseUnsatCoreForContractInfer && outcome == ProverInterface.Outcome.Valid)

-            session.UpdateUnsatCore(proverInterface, currentHoudiniState.Assignment);

-          currentHoudiniState.WorkQueue.Dequeue();

-          this.NotifyDequeue();

-          return;

-        }

-      } 

-    }

-

-    /// <summary>

-    /// Transforms given program based on Houdini outcome.  If a constant is assigned "true",

-    /// any preconditions or postconditions guarded by the constant are made free, and any assertions 

-    /// guarded by the constant are replaced with assumptions.

-    /// 

-    /// If a constant is assigned "false", any preconditions or postconditions

-    /// guarded by the constant are replaced with "true", and assertions guarded by the constant

-    /// are removed.

-    /// 

-    /// In addition, all Houdini constants are removed from the program.

-    /// </summary>

-    public static void ApplyAssignment(Program prog, HoudiniOutcome outcome) {

-

-      var Candidates = prog.TopLevelDeclarations.OfType<Constant>().Where

-            (Item => QKeyValue.FindBoolAttribute(Item.Attributes, "existential")).Select(Item => Item.Name);

-

-      // Treat all assertions

-      // TODO: do we need to also consider assumptions?

-      foreach (Block block in prog.Implementations.Select(item => item.Blocks).SelectMany(item => item)) {

-        List<Cmd> newCmds = new List<Cmd>();

-        foreach (Cmd cmd in block.Cmds) {

-          string c;

-          AssertCmd assertCmd = cmd as AssertCmd;

-          if (assertCmd != null && MatchCandidate(assertCmd.Expr, Candidates, out c)) {

-            var cVar = outcome.assignment.Keys.Where(item => item.Equals(c)).ToList()[0];

-            if (outcome.assignment[cVar]) {

-              Dictionary<Variable, Expr> cToTrue = new Dictionary<Variable, Expr>();

-              Variable cVarProg = prog.Variables.Where(item => item.Name.Equals(c)).ToList()[0];

-              cToTrue[cVarProg] = Expr.True;

-              newCmds.Add(new AssumeCmd(assertCmd.tok,

-                Substituter.Apply(Substituter.SubstitutionFromHashtable(cToTrue), assertCmd.Expr),

-                assertCmd.Attributes));

-            }

-          }

-          else {

-            newCmds.Add(cmd);

-          }

-        }

-        block.Cmds = newCmds;

-      }

-

-      foreach (var proc in prog.Procedures) {

-        List<Requires> newRequires = new List<Requires>();

-        foreach (Requires r in proc.Requires) {

-          string c;

-          if (MatchCandidate(r.Condition, Candidates, out c)) {

-            var cVar = outcome.assignment.Keys.Where(item => item.Equals(c)).ToList()[0];

-            if (outcome.assignment[cVar]) {

-              Variable cVarProg = prog.Variables.Where(item => item.Name.Equals(c)).ToList()[0];

-              Dictionary<Variable, Expr> subst = new Dictionary<Variable, Expr>();

-              subst[cVarProg] = Expr.True;

-              newRequires.Add(new Requires(Token.NoToken, true,

-                Substituter.Apply(Substituter.SubstitutionFromHashtable(subst), r.Condition),

-                r.Comment, r.Attributes));

-            }

-          }

-          else {

-            newRequires.Add(r);

-          }

-        }

-        proc.Requires = newRequires;

-

-        List<Ensures> newEnsures = new List<Ensures>();

-        foreach (Ensures e in proc.Ensures) {

-          string c;

-          if (MatchCandidate(e.Condition, Candidates, out c)) {

-            var cVar = outcome.assignment.Keys.Where(item => item.Equals(c)).ToList()[0];

-            if (outcome.assignment[cVar]) {

-              Variable cVarProg = prog.Variables.Where(item => item.Name.Equals(c)).ToList()[0];

-              Dictionary<Variable, Expr> subst = new Dictionary<Variable, Expr>();

-              subst[cVarProg] = Expr.True;

-              newEnsures.Add(new Ensures(Token.NoToken, true,

-                Substituter.Apply(Substituter.SubstitutionFromHashtable(subst), e.Condition),

-                e.Comment, e.Attributes));

-            }

-          }

-          else {

-            newEnsures.Add(e);

-          }

-        }

-        proc.Ensures = newEnsures;

-      }

-

-      // Remove the existential constants

-      prog.RemoveTopLevelDeclarations(item => (item is Constant) && 

-               (Candidates.Any(item2 => item2.Equals((item as Constant).Name))));

-    }

-

-  }

-

-  public class VCGenOutcome {

-    public VCGen.Outcome outcome;

-    public List<Counterexample> errors;

-    public VCGenOutcome(ProverInterface.Outcome outcome, List<Counterexample> errors) {

-      this.outcome = ConditionGeneration.ProverInterfaceOutcomeToConditionGenerationOutcome(outcome);

-      this.errors = errors;

-    }

-  }

-

-  public class HoudiniOutcome {

-    // final assignment

-    public Dictionary<string, bool> assignment = new Dictionary<string, bool>();

-    // boogie errors

-    public Dictionary<string, VCGenOutcome> implementationOutcomes = new Dictionary<string, VCGenOutcome>();

-

-    // statistics 

-

-    private int CountResults(VCGen.Outcome outcome) {

-      int outcomeCount = 0;

-      foreach (VCGenOutcome verifyOutcome in implementationOutcomes.Values) {

-        if (verifyOutcome.outcome == outcome)

-          outcomeCount++;

-      }

-      return outcomeCount;

-    }

-

-    private List<string> ListOutcomeMatches(VCGen.Outcome outcome) {

-      List<string> result = new List<string>();

-      foreach (KeyValuePair<string, VCGenOutcome> kvpair in implementationOutcomes) {

-        if (kvpair.Value.outcome == outcome)

-          result.Add(kvpair.Key);

-      }

-      return result;

-    }

-

-    public int ErrorCount {

-      get {

-        return CountResults(VCGen.Outcome.Errors);

-      }

-    }

-    public int Verified {

-      get {

-        return CountResults(VCGen.Outcome.Correct);

-      }

-    }

-    public int Inconclusives {

-      get {

-        return CountResults(VCGen.Outcome.Inconclusive);

-      }

-    }

-    public int TimeOuts {

-      get {

-        return CountResults(VCGen.Outcome.TimedOut);

-      }

-    }

-    public List<string> ListOfTimeouts {

-      get {

-        return ListOutcomeMatches(VCGen.Outcome.TimedOut);

-      }

-    }

-    public List<string> ListOfInconclusives {

-      get {

-        return ListOutcomeMatches(VCGen.Outcome.Inconclusive);

-      }

-    }

-    public List<string> ListOfErrors {

-      get {

-        return ListOutcomeMatches(VCGen.Outcome.Errors);

-      }

-    }

-  }

-

-}

+//-----------------------------------------------------------------------------
+//
+// Copyright (C) Microsoft Corporation.  All Rights Reserved.
+//
+//-----------------------------------------------------------------------------
+using System;
+using System.Diagnostics.Contracts;
+using System.Collections.Generic;
+using Microsoft.Boogie;
+using Microsoft.Boogie.VCExprAST;
+using VC;
+using System.Collections;
+using System.IO;
+using Microsoft.Boogie.GraphUtil;
+using System.Linq;
+using System.Diagnostics;
+
+namespace Microsoft.Boogie.Houdini {
+
+  internal class ReadOnlyDictionary<K, V> {
+    private Dictionary<K, V> dictionary;
+    public ReadOnlyDictionary(Dictionary<K, V> dictionary) {
+      this.dictionary = dictionary;
+    }
+
+    public Dictionary<K, V>.KeyCollection Keys {
+      get { return this.dictionary.Keys; }
+    }
+
+    public bool TryGetValue(K k, out V v) {
+      return this.dictionary.TryGetValue(k, out v);
+    }
+
+    public bool ContainsKey(K k) {
+      return this.dictionary.ContainsKey(k);
+    }
+  }
+
+  public abstract class HoudiniObserver {
+    public virtual void UpdateStart(Program program, int numConstants) { }
+    public virtual void UpdateIteration() { }
+    public virtual void UpdateImplementation(Implementation implementation) { }
+    public virtual void UpdateAssignment(Dictionary<Variable, bool> assignment) { }
+    public virtual void UpdateOutcome(ProverInterface.Outcome outcome) { }
+    public virtual void UpdateEnqueue(Implementation implementation) { }
+    public virtual void UpdateDequeue() { }
+    public virtual void UpdateConstant(string constantName) { }
+    public virtual void UpdateEnd(bool isNormalEnd) { }
+    public virtual void UpdateFlushStart() { }
+    public virtual void UpdateFlushFinish() { }
+    public virtual void SeeException(string msg) { }
+  }
+
+  public class IterationTimer<K> {
+    private Dictionary<K, List<double>> times;
+
+    public IterationTimer() {
+      times = new Dictionary<K, List<double>>();
+    }
+
+    public void AddTime(K key, double timeMS) {
+      List<double> oldList;
+      times.TryGetValue(key, out oldList);
+      if (oldList == null) {
+        oldList = new List<double>();
+      }
+      else {
+        times.Remove(key);
+      }
+      oldList.Add(timeMS);
+      times.Add(key, oldList);
+    }
+
+    public void PrintTimes(TextWriter wr) {
+      wr.WriteLine("Total procedures: {0}", times.Count);
+      double total = 0;
+      int totalIters = 0;
+      foreach (KeyValuePair<K, List<double>> kv in times) {
+        int curIter = 0;
+        wr.WriteLine("Times for {0}:", kv.Key);
+        foreach (double v in kv.Value) {
+          wr.WriteLine("  ({0})\t{1}ms", curIter, v);
+          total += v;
+          curIter++;
+        }
+        totalIters += curIter;
+      }
+      total = total / 1000.0;
+      wr.WriteLine("Total time: {0} (s)", total);
+      wr.WriteLine("Avg: {0} (s/iter)", total / totalIters);
+    }
+  }
+
+  public class HoudiniTimer : HoudiniObserver {
+    private DateTime startT;
+    private Implementation curImp;
+    private IterationTimer<string> times;
+    private TextWriter wr;
+
+    public HoudiniTimer(TextWriter wr) {
+      this.wr = wr;
+      times = new IterationTimer<string>();
+    }
+    public override void UpdateIteration() {
+      startT = DateTime.UtcNow;
+    }
+    public override void UpdateImplementation(Implementation implementation) {
+      curImp = implementation;
+    }
+    public override void UpdateOutcome(ProverInterface.Outcome o) {
+      Contract.Assert(curImp != null);
+      DateTime endT = DateTime.UtcNow;
+      times.AddTime(curImp.Name, (endT - startT).TotalMilliseconds); // assuming names are unique
+    }
+    public void PrintTimes() {
+      wr.WriteLine("-----------------------------------------");
+      wr.WriteLine("Times for each iteration for each procedure");
+      wr.WriteLine("-----------------------------------------");
+      times.PrintTimes(wr);
+    }
+  }
+
+  public class HoudiniTextReporter : HoudiniObserver {
+    private TextWriter wr;
+    private int currentIteration = -1;
+
+    public HoudiniTextReporter(TextWriter wr) {
+      this.wr = wr;
+    }
+    public override void UpdateStart(Program program, int numConstants) {
+      wr.WriteLine("Houdini started:" + program.ToString() + " #constants: " + numConstants.ToString());
+      currentIteration = -1;
+      wr.Flush();
+    }
+    public override void UpdateIteration() {
+      currentIteration++;
+      wr.WriteLine("---------------------------------------");
+      wr.WriteLine("Houdini iteration #" + currentIteration);
+      wr.Flush();
+    }
+    public override void UpdateImplementation(Implementation implementation) {
+      wr.WriteLine("implementation under analysis :" + implementation.Name);
+      wr.Flush();
+    }
+    public override void UpdateAssignment(Dictionary<Variable, bool> assignment) {
+      bool firstTime = true;
+      wr.Write("assignment under analysis : axiom (");
+      foreach (KeyValuePair<Variable, bool> kv in assignment) {
+        if (!firstTime) wr.Write(" && "); else firstTime = false;
+        string valString; // ugliness to get it lower cased
+        if (kv.Value) valString = "true"; else valString = "false";
+        wr.Write(kv.Key + " == " + valString);
+      }
+      wr.WriteLine(");");
+      wr.Flush();
+    }
+    public override void UpdateOutcome(ProverInterface.Outcome outcome) {
+      wr.WriteLine("analysis outcome :" + outcome);
+      wr.Flush();
+    }
+    public override void UpdateEnqueue(Implementation implementation) {
+      wr.WriteLine("worklist enqueue :" + implementation.Name);
+      wr.Flush();
+    }
+    public override void UpdateDequeue() {
+      wr.WriteLine("worklist dequeue");
+      wr.Flush();
+    }
+    public override void UpdateConstant(string constantName) {
+      wr.WriteLine("constant disabled : " + constantName);
+      wr.Flush();
+    }
+    public override void UpdateEnd(bool isNormalEnd) {
+      wr.WriteLine("Houdini ended: " + (isNormalEnd ? "Normal" : "Abnormal"));
+      wr.WriteLine("Number of iterations: " + (this.currentIteration + 1));
+      wr.Flush();
+    }
+    public override void UpdateFlushStart() {
+      wr.WriteLine("***************************************");
+      wr.WriteLine("Flushing remaining implementations");
+      wr.Flush();
+    }
+    public override void UpdateFlushFinish() {
+      wr.WriteLine("***************************************");
+      wr.WriteLine("Flushing finished");
+      wr.Flush();
+    }
+    public override void SeeException(string msg) {
+      wr.WriteLine("Caught exception: " + msg);
+      wr.Flush();
+    }
+
+  }
+
+  public abstract class ObservableHoudini {
+    private List<HoudiniObserver> observers = new List<HoudiniObserver>();
+
+    public void AddObserver(HoudiniObserver observer) {
+      if (!observers.Contains(observer))
+        observers.Add(observer);
+    }
+    private delegate void NotifyDelegate(HoudiniObserver observer);
+
+    private void Notify(NotifyDelegate notifyDelegate) {
+      foreach (HoudiniObserver observer in observers) {
+        notifyDelegate(observer);
+      }
+    }
+    protected void NotifyStart(Program program, int numConstants) {
+      NotifyDelegate notifyDelegate = (NotifyDelegate)delegate(HoudiniObserver r) { r.UpdateStart(program, numConstants); };
+      Notify(notifyDelegate);
+    }
+    protected void NotifyIteration() {
+      Notify((NotifyDelegate)delegate(HoudiniObserver r) { r.UpdateIteration(); });
+    }
+    protected void NotifyImplementation(Implementation implementation) {
+      Notify((NotifyDelegate)delegate(HoudiniObserver r) { r.UpdateImplementation(implementation); });
+    }
+    protected void NotifyAssignment(Dictionary<Variable, bool> assignment) {
+      Notify((NotifyDelegate)delegate(HoudiniObserver r) { r.UpdateAssignment(assignment); });
+    }
+    protected void NotifyOutcome(ProverInterface.Outcome outcome) {
+      Notify((NotifyDelegate)delegate(HoudiniObserver r) { r.UpdateOutcome(outcome); });
+    }
+    protected void NotifyEnqueue(Implementation implementation) {
+      Notify((NotifyDelegate)delegate(HoudiniObserver r) { r.UpdateEnqueue(implementation); });
+    }
+    protected void NotifyDequeue() {
+      Notify((NotifyDelegate)delegate(HoudiniObserver r) { r.UpdateDequeue(); });
+    }
+    protected void NotifyConstant(string constantName) {
+      Notify((NotifyDelegate)delegate(HoudiniObserver r) { r.UpdateConstant(constantName); });
+    }
+    protected void NotifyEnd(bool isNormalEnd) {
+      Notify((NotifyDelegate)delegate(HoudiniObserver r) { r.UpdateEnd(isNormalEnd); });
+    }
+    protected void NotifyFlushStart() {
+      Notify((NotifyDelegate)delegate(HoudiniObserver r) { r.UpdateFlushStart(); });
+    }
+    protected void NotifyFlushFinish() {
+      Notify((NotifyDelegate)delegate(HoudiniObserver r) { r.UpdateFlushFinish(); });
+    }
+
+    protected void NotifyException(string msg) {
+      Notify((NotifyDelegate)delegate(HoudiniObserver r) { r.SeeException(msg); });
+    }
+  }
+
+  public class InlineEnsuresVisitor : ReadOnlyVisitor {
+      public override Ensures VisitEnsures(Ensures ensures)
+      {
+          if (!ensures.Free)
+          {
+              ensures.Attributes = new QKeyValue(Token.NoToken, "InlineAssume", new List<object>(), ensures.Attributes);
+          }
+          return base.VisitEnsures(ensures);
+      }
+  }
+
+  public class Houdini : ObservableHoudini {
+    protected Program program;
+    protected HashSet<Variable> houdiniConstants;
+    protected VCGen vcgen;
+    protected ProverInterface proverInterface;
+    protected Graph<Implementation> callGraph;
+    protected HashSet<Implementation> vcgenFailures;
+    protected HoudiniState currentHoudiniState;
+    protected CrossDependencies crossDependencies;
+    internal ReadOnlyDictionary<Implementation, HoudiniSession> houdiniSessions;
+
+    protected string cexTraceFile;
+
+    public HoudiniState CurrentHoudiniState { get { return currentHoudiniState; } }    
+
+    public static TextWriter explainHoudiniDottyFile;
+
+    protected Houdini() { }
+
+    public Houdini(Program program, HoudiniSession.HoudiniStatistics stats, string cexTraceFile = "houdiniCexTrace.txt") {
+      this.program = program;
+      this.cexTraceFile = cexTraceFile;
+      Initialize(program, stats);
+    }
+
+    protected void Initialize(Program program, HoudiniSession.HoudiniStatistics stats)
+    {
+        if (CommandLineOptions.Clo.Trace)
+            Console.WriteLine("Collecting existential constants...");
+        this.houdiniConstants = CollectExistentialConstants();
+
+        if (CommandLineOptions.Clo.Trace)
+            Console.WriteLine("Building call graph...");
+        this.callGraph = Program.BuildCallGraph(program);
+        if (CommandLineOptions.Clo.Trace)
+            Console.WriteLine("Number of implementations = {0}", callGraph.Nodes.Count);
+
+        if (CommandLineOptions.Clo.HoudiniUseCrossDependencies)
+        {
+            if (CommandLineOptions.Clo.Trace) Console.WriteLine("Computing procedure cross dependencies ...");
+            this.crossDependencies = new CrossDependencies(this.houdiniConstants);
+            this.crossDependencies.Visit(program);
+        }
+
+        Inline();
+        /*
+        {
+            int oldPrintUnstructured = CommandLineOptions.Clo.PrintUnstructured;
+            CommandLineOptions.Clo.PrintUnstructured = 1;
+            using (TokenTextWriter stream = new TokenTextWriter("houdini_inline.bpl"))
+            {
+                program.Emit(stream);
+            }
+            CommandLineOptions.Clo.PrintUnstructured = oldPrintUnstructured;
+        }
+        */
+
+        this.vcgen = new VCGen(program, CommandLineOptions.Clo.SimplifyLogFilePath, CommandLineOptions.Clo.SimplifyLogFileAppend, new List<Checker>());
+        this.proverInterface = ProverInterface.CreateProver(program, CommandLineOptions.Clo.SimplifyLogFilePath, CommandLineOptions.Clo.SimplifyLogFileAppend, CommandLineOptions.Clo.ProverKillTime, taskID: GetTaskID());
+
+        vcgenFailures = new HashSet<Implementation>();
+        Dictionary<Implementation, HoudiniSession> houdiniSessions = new Dictionary<Implementation, HoudiniSession>();
+        if (CommandLineOptions.Clo.Trace)
+            Console.WriteLine("Beginning VC generation for Houdini...");
+        foreach (Implementation impl in callGraph.Nodes)
+        {
+            try
+            {
+                if (CommandLineOptions.Clo.Trace)
+                    Console.WriteLine("Generating VC for {0}", impl.Name);
+                HoudiniSession session = new HoudiniSession(this, vcgen, proverInterface, program, impl, stats, taskID: GetTaskID());
+                houdiniSessions.Add(impl, session);
+            }
+            catch (VCGenException)
+            {
+                if (CommandLineOptions.Clo.Trace)
+                    Console.WriteLine("VC generation failed");
+                vcgenFailures.Add(impl);
+            }
+        }
+        this.houdiniSessions = new ReadOnlyDictionary<Implementation, HoudiniSession>(houdiniSessions);
+
+        if (CommandLineOptions.Clo.ExplainHoudini)
+        {
+            // Print results of ExplainHoudini to a dotty file
+            explainHoudiniDottyFile = new StreamWriter("explainHoudini.dot");
+            explainHoudiniDottyFile.WriteLine("digraph explainHoudini {");
+            foreach (var constant in houdiniConstants)
+                explainHoudiniDottyFile.WriteLine("{0} [ label = \"{0}\" color=black ];", constant.Name);
+            explainHoudiniDottyFile.WriteLine("TimeOut [label = \"TimeOut\" color=red ];");
+        }
+    }
+
+    protected void Inline() {
+      if (CommandLineOptions.Clo.InlineDepth <= 0)
+        return;
+
+      foreach (Implementation impl in callGraph.Nodes) {
+        InlineEnsuresVisitor inlineEnsuresVisitor = new InlineEnsuresVisitor();
+        inlineEnsuresVisitor.Visit(impl);
+      }
+
+      foreach (Implementation impl in callGraph.Nodes) {
+        impl.OriginalBlocks = impl.Blocks;
+        impl.OriginalLocVars = impl.LocVars;
+      }
+      foreach (Implementation impl in callGraph.Nodes) {
+        CommandLineOptions.Inlining savedOption = CommandLineOptions.Clo.ProcedureInlining;
+        CommandLineOptions.Clo.ProcedureInlining = CommandLineOptions.Inlining.Spec;
+        Inliner.ProcessImplementationForHoudini(program, impl);
+        CommandLineOptions.Clo.ProcedureInlining = savedOption;
+      }
+      foreach (Implementation impl in callGraph.Nodes) {
+        impl.OriginalBlocks = null;
+        impl.OriginalLocVars = null;
+      }
+
+      Graph<Implementation> oldCallGraph = callGraph;
+      callGraph = new Graph<Implementation>();
+      foreach (Implementation impl in oldCallGraph.Nodes) {
+        callGraph.AddSource(impl);
+      }
+      foreach (Tuple<Implementation, Implementation> edge in oldCallGraph.Edges) {
+        callGraph.AddEdge(edge.Item1, edge.Item2);
+      }
+      int count = CommandLineOptions.Clo.InlineDepth;
+      while (count > 0) {
+        foreach (Implementation impl in oldCallGraph.Nodes) {
+          List<Implementation> newNodes = new List<Implementation>();
+          foreach (Implementation succ in callGraph.Successors(impl)) {
+            newNodes.AddRange(oldCallGraph.Successors(succ));
+          }
+          foreach (Implementation newNode in newNodes) {
+            callGraph.AddEdge(impl, newNode);
+          }
+        }
+        count--;
+      }
+    }
+
+    protected HashSet<Variable> CollectExistentialConstants() {
+      HashSet<Variable> existentialConstants = new HashSet<Variable>();
+      foreach (var constant in program.Constants) {
+        bool result = false;
+        if (constant.CheckBooleanAttribute("existential", ref result)) {
+          if (result == true)
+            existentialConstants.Add(constant);
+        }
+      }
+      return existentialConstants;
+    }
+
+      // Compute dependencies between candidates
+    public class CrossDependencies : ReadOnlyVisitor
+    {
+        public CrossDependencies(HashSet<Variable> constants)
+        {
+            this.constants = constants;
+        }
+
+        public override Program VisitProgram(Program node)
+        {
+            assumedInImpl = new Dictionary<string, HashSet<Implementation>>();
+            return base.VisitProgram(node);
+        }
+
+        public override Implementation VisitImplementation(Implementation node)
+        {
+            curImpl = node;
+            return base.VisitImplementation(node);
+        }
+
+        public override Cmd VisitAssumeCmd(AssumeCmd node)
+        {
+            return base.VisitAssumeCmd(node);
+        }
+
+        public override Variable VisitVariable(Variable node)
+        {
+            if (node is Constant)
+            {
+                var constant = node as Constant;
+                if (constants.Contains(constant))
+                {
+                    if (!assumedInImpl.ContainsKey(constant.Name))
+                        assumedInImpl[constant.Name] = new HashSet<Implementation>();
+                    assumedInImpl[constant.Name].Add(curImpl);
+                }
+            }
+            return base.VisitVariable(node);
+        }
+
+        HashSet<Variable> constants;
+        Implementation curImpl;
+
+        // contant -> set of implementations that have an assume command with that constant
+        public Dictionary<string, HashSet<Implementation>> assumedInImpl { get; private set; }
+    }
+    
+    protected WorkQueue BuildWorkList(Program program) {
+      // adding implementations to the workqueue from the bottom of the call graph upwards
+      WorkQueue queue = new WorkQueue();
+      StronglyConnectedComponents<Implementation> sccs =
+        new StronglyConnectedComponents<Implementation>(callGraph.Nodes,
+          new Adjacency<Implementation>(callGraph.Predecessors),
+          new Adjacency<Implementation>(callGraph.Successors));
+      sccs.Compute();
+      foreach (SCC<Implementation> scc in sccs) {
+        foreach (Implementation impl in scc) {
+          if (vcgenFailures.Contains(impl)) continue;
+          queue.Enqueue(impl);
+        }
+      }
+      if (CommandLineOptions.Clo.ReverseHoudiniWorklist)
+          queue = queue.Reverse();
+      return queue;      
+      /*
+      Queue<Implementation> queue = new Queue<Implementation>();
+      foreach (Declaration decl in program.TopLevelDeclarations) {
+        Implementation impl = decl as Implementation;
+        if (impl == null || impl.SkipVerification) continue;
+        queue.Enqueue(impl);
+      }
+      return queue;
+       */
+    }
+
+    public static bool MatchCandidate(Expr boogieExpr, IEnumerable<string> candidates, out string candidateConstant) {
+      candidateConstant = null;
+      NAryExpr e = boogieExpr as NAryExpr;
+      if (e != null && e.Fun is BinaryOperator && ((BinaryOperator)e.Fun).Op == BinaryOperator.Opcode.Imp) {
+        Expr antecedent = e.Args[0];
+        Expr consequent = e.Args[1];
+
+        IdentifierExpr id = antecedent as IdentifierExpr;
+        if (id != null && id.Decl is Constant && candidates.Contains(id.Decl.Name)) {
+          candidateConstant = id.Decl.Name;
+          return true;
+        }
+
+        if (MatchCandidate(consequent, candidates, out candidateConstant))
+          return true;
+      }
+      return false;
+    }
+
+    public static bool GetCandidateWithoutConstant(Expr boogieExpr, IEnumerable<string> candidates, out string candidateConstant, out Expr exprWithoutConstant) {
+      candidateConstant = null;
+      exprWithoutConstant = null;
+      NAryExpr e = boogieExpr as NAryExpr;
+      if (e != null && e.Fun is BinaryOperator && ((BinaryOperator)e.Fun).Op == BinaryOperator.Opcode.Imp) {
+        Expr antecedent = e.Args[0];
+        Expr consequent = e.Args[1];
+
+        IdentifierExpr id = antecedent as IdentifierExpr;
+        if (id != null && id.Decl is Constant && candidates.Contains(id.Decl.Name)) {
+          candidateConstant = id.Decl.Name;
+          exprWithoutConstant = consequent;
+          return true;
+        }
+
+        if (GetCandidateWithoutConstant(consequent, candidates, out candidateConstant, out exprWithoutConstant))
+        {
+            exprWithoutConstant = Expr.Imp(antecedent, exprWithoutConstant);
+            return true;
+        }
+      }
+      return false;
+    }
+
+    private static Expr AddConditionToCandidateRec(Expr boogieExpr, Expr condition, string candidateConstant, List<Expr> implicationStack)
+    {
+        NAryExpr e = boogieExpr as NAryExpr;
+        if (e != null && e.Fun is BinaryOperator && ((BinaryOperator)e.Fun).Op == BinaryOperator.Opcode.Imp)
+        {
+            Expr antecedent = e.Args[0];
+            Expr consequent = e.Args[1];
+
+            IdentifierExpr id = antecedent as IdentifierExpr;
+            if (id != null && id.Decl is Constant && id.Decl.Name.Equals(candidateConstant))
+            {
+                Expr result = Expr.Imp(antecedent, Expr.Imp(condition, consequent));
+                implicationStack.Reverse();
+                foreach (var expr in implicationStack)
+                {
+                    result = Expr.Imp(expr, result);
+                }
+                return result;
+            }
+
+            implicationStack.Add(antecedent);
+            return AddConditionToCandidateRec(consequent, condition, candidateConstant,
+                implicationStack);
+        }
+        return boogieExpr;
+    }
+
+    public static Expr AddConditionToCandidate(Expr boogieExpr, Expr condition, string candidateConstant)
+    {
+        return AddConditionToCandidateRec(boogieExpr, condition, candidateConstant, new List<Expr>());
+    }
+
+    public bool MatchCandidate(Expr boogieExpr, out Variable candidateConstant) {
+      candidateConstant = null;
+      string candidateString;
+      if(MatchCandidate(boogieExpr, houdiniConstants.Select(item => item.Name), out candidateString)) {
+        candidateConstant = houdiniConstants.Where(item => item.Name.Equals(candidateString)).ToList()[0];
+        return true;
+      }
+      return false;
+    }
+
+    public bool MatchCandidate(Expr boogieExpr, out string candidateConstant) {
+      return MatchCandidate(boogieExpr, houdiniConstants.Select(item => item.Name), out candidateConstant);
+    }
+
+    // For Explain houdini: it decorates the condition \phi as (vpos && (\phi || \not vneg))
+    // Precondition: MatchCandidate returns true
+    public Expr InsertCandidateControl(Expr boogieExpr, Variable vpos, Variable vneg)
+    {
+        Contract.Assert(CommandLineOptions.Clo.ExplainHoudini);
+
+        NAryExpr e = boogieExpr as NAryExpr;
+        if (e != null && e.Fun is BinaryOperator && ((BinaryOperator)e.Fun).Op == BinaryOperator.Opcode.Imp)
+        {
+            Expr antecedent = e.Args[0];
+            Expr consequent = e.Args[1];
+
+            IdentifierExpr id = antecedent as IdentifierExpr;
+            if (id != null && id.Decl is Constant && houdiniConstants.Contains((Constant)id.Decl))
+            {
+                return Expr.Imp(antecedent, Expr.And(Expr.Ident(vpos), Expr.Or(consequent, Expr.Not(Expr.Ident(vneg)))));
+            }
+
+            return Expr.Imp(antecedent, InsertCandidateControl(consequent, vpos, vneg));
+        }
+        Contract.Assert(false);
+        return null;
+    }
+
+    protected Dictionary<Variable, bool> BuildAssignment(HashSet<Variable> constants) {
+      Dictionary<Variable, bool> initial = new Dictionary<Variable, bool>();
+      foreach (var constant in constants)
+        initial.Add(constant, true);
+      return initial;
+    }
+
+    private bool IsOutcomeNotHoudini(ProverInterface.Outcome outcome, List<Counterexample> errors) {
+      switch (outcome) {
+        case ProverInterface.Outcome.Valid:
+          return false;
+        case ProverInterface.Outcome.Invalid:
+          Contract.Assume(errors != null);
+          foreach (Counterexample error in errors) {
+            if (ExtractRefutedAnnotation(error) == null)
+              return true;
+          }
+          return false;
+        default:
+          return true;
+      }
+    }
+
+    // Record most current non-candidate errors found
+    // Return true if there was at least one non-candidate error
+    protected bool UpdateHoudiniOutcome(HoudiniOutcome houdiniOutcome,
+                                      Implementation implementation,
+                                      ProverInterface.Outcome outcome,
+                                      List<Counterexample> errors) {
+      string implName = implementation.Name;
+      houdiniOutcome.implementationOutcomes.Remove(implName);
+      List<Counterexample> nonCandidateErrors = new List<Counterexample>();
+
+      if (outcome == ProverInterface.Outcome.Invalid) {
+          foreach (Counterexample error in errors) {
+            if (ExtractRefutedAnnotation(error) == null)
+              nonCandidateErrors.Add(error);
+          }
+      }
+      houdiniOutcome.implementationOutcomes.Add(implName, new VCGenOutcome(outcome, nonCandidateErrors));
+      return nonCandidateErrors.Count > 0;
+    }
+
+    protected void FlushWorkList(int stage, IEnumerable<int> completedStages) {
+      this.NotifyFlushStart();
+      while (currentHoudiniState.WorkQueue.Count > 0) {
+        this.NotifyIteration();
+
+        currentHoudiniState.Implementation = currentHoudiniState.WorkQueue.Peek();
+        this.NotifyImplementation(currentHoudiniState.Implementation);
+
+        HoudiniSession session;
+        houdiniSessions.TryGetValue(currentHoudiniState.Implementation, out session);
+        List<Counterexample> errors;
+        ProverInterface.Outcome outcome = TryCatchVerify(session, stage, completedStages, out errors);
+        UpdateHoudiniOutcome(currentHoudiniState.Outcome, currentHoudiniState.Implementation, outcome, errors);
+        this.NotifyOutcome(outcome);
+
+        currentHoudiniState.WorkQueue.Dequeue();
+        this.NotifyDequeue();
+      }
+      this.NotifyFlushFinish();
+    }
+
+    protected void UpdateAssignment(RefutedAnnotation refAnnot) {
+      if (CommandLineOptions.Clo.Trace) {
+        Console.WriteLine("Removing " + refAnnot.Constant);
+        using (var cexWriter = new System.IO.StreamWriter(cexTraceFile, true))
+            cexWriter.WriteLine("Removing " + refAnnot.Constant);
+      }
+      currentHoudiniState.Assignment.Remove(refAnnot.Constant);
+      currentHoudiniState.Assignment.Add(refAnnot.Constant, false);
+      this.NotifyConstant(refAnnot.Constant.Name);
+    }
+
+    protected void AddRelatedToWorkList(RefutedAnnotation refutedAnnotation) {
+      Contract.Assume(currentHoudiniState.Implementation != null);
+      foreach (Implementation implementation in FindImplementationsToEnqueue(refutedAnnotation, refutedAnnotation.RefutationSite)) {
+        if (!currentHoudiniState.isBlackListed(implementation.Name)) {
+          currentHoudiniState.WorkQueue.Enqueue(implementation);
+          this.NotifyEnqueue(implementation);
+        }
+      }
+    }
+
+    // Updates the worklist and current assignment
+    // @return true if the current function is dequeued
+    protected bool UpdateAssignmentWorkList(ProverInterface.Outcome outcome,
+                                          List<Counterexample> errors) {
+      Contract.Assume(currentHoudiniState.Implementation != null);
+      bool dequeue = true;
+
+      switch (outcome) {
+        case ProverInterface.Outcome.Valid:
+          //yeah, dequeue
+          break;
+
+        case ProverInterface.Outcome.Invalid:
+            Contract.Assume(errors != null);
+
+            foreach (Counterexample error in errors) {
+              RefutedAnnotation refutedAnnotation = ExtractRefutedAnnotation(error);
+              if (refutedAnnotation != null) {
+                // some candidate annotation removed
+                ShareRefutedAnnotation(refutedAnnotation);
+                AddRelatedToWorkList(refutedAnnotation);
+                UpdateAssignment(refutedAnnotation);
+                dequeue = false;
+                #region Extra debugging output
+                if (CommandLineOptions.Clo.Trace) {
+                  using (var cexWriter = new System.IO.StreamWriter(cexTraceFile, true)) {
+                    cexWriter.WriteLine("Counter example for " + refutedAnnotation.Constant);
+                    cexWriter.Write(error.ToString());
+                    cexWriter.WriteLine();
+                    using (var writer = new Microsoft.Boogie.TokenTextWriter(cexWriter, /*pretty=*/ false))
+                      foreach (Microsoft.Boogie.Block blk in error.Trace)
+                        blk.Emit(writer, 15);
+                    //cexWriter.WriteLine(); 
+                  }
+                }
+                #endregion
+              }
+            }
+              
+            if (ExchangeRefutedAnnotations()) dequeue = false;
+
+            break;
+        default:
+            if (CommandLineOptions.Clo.Trace) {
+                Console.WriteLine("Timeout/Spaceout while verifying " + currentHoudiniState.Implementation.Name);
+            }
+            HoudiniSession houdiniSession;
+            houdiniSessions.TryGetValue(currentHoudiniState.Implementation, out houdiniSession);
+            foreach (Variable v in houdiniSession.houdiniAssertConstants) {
+                if (CommandLineOptions.Clo.Trace) {
+                    Console.WriteLine("Removing " + v);
+                }
+                currentHoudiniState.Assignment.Remove(v);
+                currentHoudiniState.Assignment.Add(v, false);
+                this.NotifyConstant(v.Name);
+            }
+            currentHoudiniState.addToBlackList(currentHoudiniState.Implementation.Name);
+            break;
+      }
+      
+      return dequeue;
+    }
+
+    // This method is a hook used by ConcurrentHoudini to
+    // exchange refuted annotations with other Houdini engines.
+    // If the method returns true, this indicates that at least
+    // one new refutation was received from some other engine.
+    // In the base class we thus return false.
+    protected virtual bool ExchangeRefutedAnnotations() {
+      return false;
+    }
+
+    // This method is a hook used by ConcurrentHoudini to
+    // apply a set of existing refuted annotations at the
+    // start of inference.
+    protected virtual void ApplyRefutedSharedAnnotations() {
+      // Empty in base class; can be overridden.
+    }
+
+    // This method is a hook used by ConcurrentHoudini to
+    // broadcast to other Houdini engines the fact that an
+    // annotation was refuted.
+    protected virtual void ShareRefutedAnnotation(RefutedAnnotation refutedAnnotation) {
+      // Empty in base class; can be overridden.
+    }
+
+    // Hook for ConcurrentHoudini, which requires a task id.
+    // Non-concurrent Houdini has -1 as a task id
+    protected virtual int GetTaskID() {
+      return -1;
+    }
+
+    public class WorkQueue {
+      private Queue<Implementation> queue;
+      private HashSet<Implementation> set;
+      public WorkQueue() {
+        queue = new Queue<Implementation>();
+        set = new HashSet<Implementation>();
+      }
+      public void Enqueue(Implementation impl) {
+        if (set.Contains(impl))
+          return;
+        queue.Enqueue(impl);
+        set.Add(impl);
+      }
+      public Implementation Dequeue() {
+        Implementation impl = queue.Dequeue();
+        set.Remove(impl);
+        return impl;
+      }
+      public Implementation Peek() {
+        return queue.Peek();
+      }
+      public int Count {
+        get { return queue.Count; }
+      }
+      public bool Contains(Implementation impl) {
+        return set.Contains(impl);
+      }
+      public WorkQueue Reverse()
+      {
+          var ret = new WorkQueue();
+          foreach (var impl in queue.Reverse())
+              ret.Enqueue(impl);
+          return ret;
+      }
+    }
+
+    public class HoudiniState {
+      public WorkQueue _workQueue;
+      public HashSet<string> blackList;
+      public Dictionary<Variable, bool> _assignment;
+      public Implementation _implementation;
+      public HoudiniOutcome _outcome;
+
+      public HoudiniState(WorkQueue workQueue, Dictionary<Variable, bool> currentAssignment) {
+        this._workQueue = workQueue;
+        this._assignment = currentAssignment;
+        this._implementation = null;
+        this._outcome = new HoudiniOutcome();
+        this.blackList = new HashSet<string>();
+      }
+
+      public WorkQueue WorkQueue {
+        get { return this._workQueue; }
+      }
+      public Dictionary<Variable, bool> Assignment {
+        get { return this._assignment; }
+      }
+      public Implementation Implementation {
+        get { return this._implementation; }
+        set { this._implementation = value; }
+      }
+      public HoudiniOutcome Outcome {
+        get { return this._outcome; }
+      }
+      public bool isBlackListed(string funcName) {
+        return blackList.Contains(funcName);
+      }
+      public void addToBlackList(string funcName) {
+        blackList.Add(funcName);
+      }
+    }
+
+    public HoudiniOutcome PerformHoudiniInference(int stage = 0, 
+                                                  IEnumerable<int> completedStages = null,
+                                                  Dictionary<string, bool> initialAssignment = null) {
+      this.NotifyStart(program, houdiniConstants.Count);
+
+      currentHoudiniState = new HoudiniState(BuildWorkList(program), BuildAssignment(houdiniConstants));
+
+      if(initialAssignment != null) {
+        foreach(var v in CurrentHoudiniState.Assignment.Keys.ToList()) {
+          CurrentHoudiniState.Assignment[v] = initialAssignment[v.Name];
+        }
+      }
+
+      ApplyRefutedSharedAnnotations();
+
+      foreach (Implementation impl in vcgenFailures) {
+        currentHoudiniState.addToBlackList(impl.Name);
+      }
+
+      while (currentHoudiniState.WorkQueue.Count > 0) {
+        this.NotifyIteration();
+
+        currentHoudiniState.Implementation = currentHoudiniState.WorkQueue.Peek();
+        this.NotifyImplementation(currentHoudiniState.Implementation);
+
+        HoudiniSession session;
+        this.houdiniSessions.TryGetValue(currentHoudiniState.Implementation, out session);
+        HoudiniVerifyCurrent(session, stage, completedStages);
+      }
+
+      this.NotifyEnd(true);
+      Dictionary<string, bool> assignment = new Dictionary<string, bool>();
+      foreach (var x in currentHoudiniState.Assignment)
+        assignment[x.Key.Name] = x.Value;
+      currentHoudiniState.Outcome.assignment = assignment;
+      return currentHoudiniState.Outcome;
+    }
+
+    public void Close() {
+      vcgen.Close();
+      proverInterface.Close();
+      if (CommandLineOptions.Clo.ExplainHoudini)
+      {
+          explainHoudiniDottyFile.WriteLine("};");
+          explainHoudiniDottyFile.Close();
+      }
+    }
+
+    private int NumberOfStages()
+    {
+      int result = 1;
+      foreach(var c in program.Constants) {
+        result = Math.Max(result, 1 + QKeyValue.FindIntAttribute(c.Attributes, "stage_active", -1));
+      }
+      return result;
+    }
+
+    private List<Implementation> FindImplementationsToEnqueue(RefutedAnnotation refutedAnnotation, Implementation currentImplementation) {
+      HoudiniSession session;
+      List<Implementation> implementations = new List<Implementation>();
+      switch (refutedAnnotation.Kind) {
+        case RefutedAnnotationKind.REQUIRES:
+              foreach (Implementation callee in callGraph.Successors(currentImplementation))
+              {
+                  if (vcgenFailures.Contains(callee)) continue;
+                  houdiniSessions.TryGetValue(callee, out session);
+                  Contract.Assume(callee.Proc != null);
+                  if (callee.Proc.Equals(refutedAnnotation.CalleeProc) && session.InUnsatCore(refutedAnnotation.Constant))
+                      implementations.Add(callee);
+              }
+          break;
+        case RefutedAnnotationKind.ENSURES:
+          foreach (Implementation caller in callGraph.Predecessors(currentImplementation))
+          {
+              if (vcgenFailures.Contains(caller)) continue;
+              houdiniSessions.TryGetValue(caller, out session);
+              if (session.InUnsatCore(refutedAnnotation.Constant))
+                  implementations.Add(caller);
+          }
+          break;
+        case RefutedAnnotationKind.ASSERT: //the implementation is already in queue
+          if (CommandLineOptions.Clo.HoudiniUseCrossDependencies && crossDependencies.assumedInImpl.ContainsKey(refutedAnnotation.Constant.Name))
+          {
+              foreach (var impl in crossDependencies.assumedInImpl[refutedAnnotation.Constant.Name])
+              {
+                  if (vcgenFailures.Contains(impl)) continue;
+                  houdiniSessions.TryGetValue(impl, out session);
+                  if (session.InUnsatCore(refutedAnnotation.Constant))
+                      implementations.Add(impl);
+              }
+          }
+          break;
+        default:
+          throw new Exception("Unknown Refuted annotation kind:" + refutedAnnotation.Kind);
+      }
+      return implementations;
+    }
+
+    public enum RefutedAnnotationKind { REQUIRES, ENSURES, ASSERT };
+
+    public class RefutedAnnotation {
+      private Variable _constant;
+      private RefutedAnnotationKind _kind;
+      private Procedure _callee;
+      private Implementation _refutationSite;
+
+      private RefutedAnnotation(Variable constant, RefutedAnnotationKind kind, Procedure callee, Implementation refutationSite) {
+        this._constant = constant;
+        this._kind = kind;
+        this._callee = callee;
+        this._refutationSite = refutationSite;
+      }
+      public RefutedAnnotationKind Kind {
+        get { return this._kind; }
+      }
+      public Variable Constant {
+        get { return this._constant; }
+      }
+      public Procedure CalleeProc {
+        get { return this._callee; }
+      }
+      public Implementation RefutationSite {
+        get { return this._refutationSite; }
+      }
+      public static RefutedAnnotation BuildRefutedRequires(Variable constant, Procedure callee, Implementation refutationSite) {
+        return new RefutedAnnotation(constant, RefutedAnnotationKind.REQUIRES, callee, refutationSite);
+      }
+      public static RefutedAnnotation BuildRefutedEnsures(Variable constant, Implementation refutationSite) {
+        return new RefutedAnnotation(constant, RefutedAnnotationKind.ENSURES, null, refutationSite);
+      }
+      public static RefutedAnnotation BuildRefutedAssert(Variable constant, Implementation refutationSite) {
+        return new RefutedAnnotation(constant, RefutedAnnotationKind.ASSERT, null, refutationSite);
+      }
+
+      public override int GetHashCode()
+      {
+        unchecked {
+          int hash = 17;
+          hash = hash * 23 + this.Constant.GetHashCode();
+          hash = hash * 23 + this.Kind.GetHashCode();
+          if (this.CalleeProc != null)
+            hash = hash * 23 + this.CalleeProc.GetHashCode();
+          hash = hash * 23 + this.RefutationSite.GetHashCode();
+          return hash;
+        }
+      }
+
+      public override bool Equals(object obj) {
+        bool result = true;
+        var other = obj as RefutedAnnotation;
+
+        if (other == null) {
+          result = false;
+        } else {
+          result = result && String.Equals(other.Constant, this.Constant);
+          result = result && String.Equals(other.Kind, this.Kind);
+          if (other.CalleeProc != null && this.CalleeProc != null)
+            result = result && String.Equals(other.CalleeProc, this.CalleeProc);
+          result = result && String.Equals(other.RefutationSite, this.RefutationSite);
+        }
+
+        return result;
+      }
+    }
+
+    private void PrintRefutedCall(CallCounterexample err, XmlSink xmlOut) {
+      Expr cond = err.FailingRequires.Condition;
+      Variable houdiniConst;
+      if (MatchCandidate(cond, out houdiniConst)) {
+        xmlOut.WriteError("precondition violation", err.FailingCall.tok, err.FailingRequires.tok, err.Trace);
+      }
+    }
+
+    private void PrintRefutedReturn(ReturnCounterexample err, XmlSink xmlOut) {
+      Expr cond = err.FailingEnsures.Condition;
+      Variable houdiniConst;
+      if (MatchCandidate(cond, out houdiniConst)) {
+        xmlOut.WriteError("postcondition violation", err.FailingReturn.tok, err.FailingEnsures.tok, err.Trace);
+      }
+    }
+
+    private void PrintRefutedAssert(AssertCounterexample err, XmlSink xmlOut) {
+      Expr cond = err.FailingAssert.OrigExpr;
+      Variable houdiniConst;
+      if (MatchCandidate(cond, out houdiniConst)) {
+        xmlOut.WriteError("postcondition violation", err.FailingAssert.tok, err.FailingAssert.tok, err.Trace);
+      }
+    }
+
+    protected void DebugRefutedCandidates(Implementation curFunc, List<Counterexample> errors) {
+      XmlSink xmlRefuted = CommandLineOptions.Clo.XmlRefuted;
+      if (xmlRefuted != null && errors != null) {
+        DateTime start = DateTime.UtcNow;
+        xmlRefuted.WriteStartMethod(curFunc.ToString(), start);
+
+        foreach (Counterexample error in errors) {
+          CallCounterexample ce = error as CallCounterexample;
+          if (ce != null) PrintRefutedCall(ce, xmlRefuted);
+          ReturnCounterexample re = error as ReturnCounterexample;
+          if (re != null) PrintRefutedReturn(re, xmlRefuted);
+          AssertCounterexample ae = error as AssertCounterexample;
+          if (ae != null) PrintRefutedAssert(ae, xmlRefuted);
+        }
+
+        DateTime end = DateTime.UtcNow;
+        xmlRefuted.WriteEndMethod("errors", end, end.Subtract(start));
+      }
+    }
+
+    private RefutedAnnotation ExtractRefutedAnnotation(Counterexample error) {
+      Variable houdiniConstant;
+      CallCounterexample callCounterexample = error as CallCounterexample;
+      if (callCounterexample != null) {
+        Procedure failingProcedure = callCounterexample.FailingCall.Proc;
+        Requires failingRequires = callCounterexample.FailingRequires;
+        if (MatchCandidate(failingRequires.Condition, out houdiniConstant)) {
+          Contract.Assert(houdiniConstant != null);
+          return RefutedAnnotation.BuildRefutedRequires(houdiniConstant, failingProcedure, currentHoudiniState.Implementation);
+        }
+      }
+      ReturnCounterexample returnCounterexample = error as ReturnCounterexample;
+      if (returnCounterexample != null) {
+        Ensures failingEnsures = returnCounterexample.FailingEnsures;
+        if (MatchCandidate(failingEnsures.Condition, out houdiniConstant)) {
+          Contract.Assert(houdiniConstant != null);
+          return RefutedAnnotation.BuildRefutedEnsures(houdiniConstant, currentHoudiniState.Implementation);
+        }
+      }
+      AssertCounterexample assertCounterexample = error as AssertCounterexample;
+      if (assertCounterexample != null) {
+        AssertCmd failingAssert = assertCounterexample.FailingAssert;
+        if (MatchCandidate(failingAssert.OrigExpr, out houdiniConstant)) {
+          Contract.Assert(houdiniConstant != null);
+          return RefutedAnnotation.BuildRefutedAssert(houdiniConstant, currentHoudiniState.Implementation);
+        }
+      }
+
+      return null;
+    }
+
+    private ProverInterface.Outcome TryCatchVerify(HoudiniSession session, int stage, IEnumerable<int> completedStages, out List<Counterexample> errors) {
+      ProverInterface.Outcome outcome;
+      try {
+        outcome = session.Verify(proverInterface, GetAssignmentWithStages(stage, completedStages), out errors, taskID: GetTaskID());
+      }
+      catch (UnexpectedProverOutputException upo) {
+        Contract.Assume(upo != null);
+        errors = null;
+        outcome = ProverInterface.Outcome.Undetermined;
+      }
+      return outcome;
+    }
+
+    protected Dictionary<Variable, bool> GetAssignmentWithStages(int currentStage, IEnumerable<int> completedStages)
+    {
+      Dictionary<Variable, bool> result = new Dictionary<Variable, bool>(currentHoudiniState.Assignment);
+      foreach (var c in program.Constants)
+      {
+        int stageActive = QKeyValue.FindIntAttribute(c.Attributes, "stage_active", -1);
+        if (stageActive != -1)
+        {
+          result[c] = (stageActive == currentStage);
+        }
+        int stageComplete = QKeyValue.FindIntAttribute(c.Attributes, "stage_complete", -1);
+        if (stageComplete != -1)
+        {
+          result[c] = (completedStages.Contains(stageComplete));
+        }
+      }
+      return result;
+    }
+
+    private void HoudiniVerifyCurrent(HoudiniSession session, int stage, IEnumerable<int> completedStages) {
+      while (true) {
+        this.NotifyAssignment(currentHoudiniState.Assignment);
+
+        //check the VC with the current assignment
+        List<Counterexample> errors;
+        ProverInterface.Outcome outcome = TryCatchVerify(session, stage, completedStages, out errors);
+        this.NotifyOutcome(outcome);
+
+        DebugRefutedCandidates(currentHoudiniState.Implementation, errors);
+
+        #region Explain Houdini
+        if (CommandLineOptions.Clo.ExplainHoudini && outcome == ProverInterface.Outcome.Invalid)
+        {
+            Contract.Assume(errors != null);
+            // make a copy of this variable
+            errors = new List<Counterexample>(errors);
+            var refutedAnnotations = new List<RefutedAnnotation>();
+            foreach (Counterexample error in errors)
+            {
+                RefutedAnnotation refutedAnnotation = ExtractRefutedAnnotation(error);
+                if (refutedAnnotation == null || refutedAnnotation.Kind == RefutedAnnotationKind.ASSERT) continue;
+                refutedAnnotations.Add(refutedAnnotation);
+            }
+            foreach (var refutedAnnotation in refutedAnnotations)
+            {
+                session.Explain(proverInterface, currentHoudiniState.Assignment, refutedAnnotation.Constant);
+            }
+        }
+        #endregion
+
+        if (UpdateHoudiniOutcome(currentHoudiniState.Outcome, currentHoudiniState.Implementation, outcome, errors)) { // abort
+          currentHoudiniState.WorkQueue.Dequeue();
+          this.NotifyDequeue();
+          FlushWorkList(stage, completedStages);
+          return;
+        }
+        else if (UpdateAssignmentWorkList(outcome, errors)) {
+          if (CommandLineOptions.Clo.UseUnsatCoreForContractInfer && outcome == ProverInterface.Outcome.Valid)
+            session.UpdateUnsatCore(proverInterface, currentHoudiniState.Assignment);
+          currentHoudiniState.WorkQueue.Dequeue();
+          this.NotifyDequeue();
+          return;
+        }
+      } 
+    }
+
+    /// <summary>
+    /// Transforms given program based on Houdini outcome.  If a constant is assigned "true",
+    /// any preconditions or postconditions guarded by the constant are made free, and any assertions 
+    /// guarded by the constant are replaced with assumptions.
+    /// 
+    /// If a constant is assigned "false", any preconditions or postconditions
+    /// guarded by the constant are replaced with "true", and assertions guarded by the constant
+    /// are removed.
+    /// 
+    /// In addition, all Houdini constants are removed from the program.
+    /// </summary>
+    public static void ApplyAssignment(Program prog, HoudiniOutcome outcome) {
+
+      var Candidates = prog.TopLevelDeclarations.OfType<Constant>().Where
+            (Item => QKeyValue.FindBoolAttribute(Item.Attributes, "existential")).Select(Item => Item.Name);
+
+      // Treat all assertions
+      // TODO: do we need to also consider assumptions?
+      foreach (Block block in prog.Implementations.Select(item => item.Blocks).SelectMany(item => item)) {
+        List<Cmd> newCmds = new List<Cmd>();
+        foreach (Cmd cmd in block.Cmds) {
+          string c;
+          AssertCmd assertCmd = cmd as AssertCmd;
+          if (assertCmd != null && MatchCandidate(assertCmd.Expr, Candidates, out c)) {
+            var cVar = outcome.assignment.Keys.Where(item => item.Equals(c)).ToList()[0];
+            if (outcome.assignment[cVar]) {
+              Dictionary<Variable, Expr> cToTrue = new Dictionary<Variable, Expr>();
+              Variable cVarProg = prog.Variables.Where(item => item.Name.Equals(c)).ToList()[0];
+              cToTrue[cVarProg] = Expr.True;
+              newCmds.Add(new AssumeCmd(assertCmd.tok,
+                Substituter.Apply(Substituter.SubstitutionFromHashtable(cToTrue), assertCmd.Expr),
+                assertCmd.Attributes));
+            }
+          }
+          else {
+            newCmds.Add(cmd);
+          }
+        }
+        block.Cmds = newCmds;
+      }
+
+      foreach (var proc in prog.Procedures) {
+        List<Requires> newRequires = new List<Requires>();
+        foreach (Requires r in proc.Requires) {
+          string c;
+          if (MatchCandidate(r.Condition, Candidates, out c)) {
+            var cVar = outcome.assignment.Keys.Where(item => item.Equals(c)).ToList()[0];
+            if (outcome.assignment[cVar]) {
+              Variable cVarProg = prog.Variables.Where(item => item.Name.Equals(c)).ToList()[0];
+              Dictionary<Variable, Expr> subst = new Dictionary<Variable, Expr>();
+              subst[cVarProg] = Expr.True;
+              newRequires.Add(new Requires(Token.NoToken, true,
+                Substituter.Apply(Substituter.SubstitutionFromHashtable(subst), r.Condition),
+                r.Comment, r.Attributes));
+            }
+          }
+          else {
+            newRequires.Add(r);
+          }
+        }
+        proc.Requires = newRequires;
+
+        List<Ensures> newEnsures = new List<Ensures>();
+        foreach (Ensures e in proc.Ensures) {
+          string c;
+          if (MatchCandidate(e.Condition, Candidates, out c)) {
+            var cVar = outcome.assignment.Keys.Where(item => item.Equals(c)).ToList()[0];
+            if (outcome.assignment[cVar]) {
+              Variable cVarProg = prog.Variables.Where(item => item.Name.Equals(c)).ToList()[0];
+              Dictionary<Variable, Expr> subst = new Dictionary<Variable, Expr>();
+              subst[cVarProg] = Expr.True;
+              newEnsures.Add(new Ensures(Token.NoToken, true,
+                Substituter.Apply(Substituter.SubstitutionFromHashtable(subst), e.Condition),
+                e.Comment, e.Attributes));
+            }
+          }
+          else {
+            newEnsures.Add(e);
+          }
+        }
+        proc.Ensures = newEnsures;
+      }
+
+      // Remove the existential constants
+      prog.RemoveTopLevelDeclarations(item => (item is Constant) && 
+               (Candidates.Any(item2 => item2.Equals((item as Constant).Name))));
+    }
+
+  }
+
+  public class VCGenOutcome {
+    public VCGen.Outcome outcome;
+    public List<Counterexample> errors;
+    public VCGenOutcome(ProverInterface.Outcome outcome, List<Counterexample> errors) {
+      this.outcome = ConditionGeneration.ProverInterfaceOutcomeToConditionGenerationOutcome(outcome);
+      this.errors = errors;
+    }
+  }
+
+  public class HoudiniOutcome {
+    // final assignment
+    public Dictionary<string, bool> assignment = new Dictionary<string, bool>();
+    // boogie errors
+    public Dictionary<string, VCGenOutcome> implementationOutcomes = new Dictionary<string, VCGenOutcome>();
+
+    // statistics 
+
+    private int CountResults(VCGen.Outcome outcome) {
+      int outcomeCount = 0;
+      foreach (VCGenOutcome verifyOutcome in implementationOutcomes.Values) {
+        if (verifyOutcome.outcome == outcome)
+          outcomeCount++;
+      }
+      return outcomeCount;
+    }
+
+    private List<string> ListOutcomeMatches(VCGen.Outcome outcome) {
+      List<string> result = new List<string>();
+      foreach (KeyValuePair<string, VCGenOutcome> kvpair in implementationOutcomes) {
+        if (kvpair.Value.outcome == outcome)
+          result.Add(kvpair.Key);
+      }
+      return result;
+    }
+
+    public int ErrorCount {
+      get {
+        return CountResults(VCGen.Outcome.Errors);
+      }
+    }
+    public int Verified {
+      get {
+        return CountResults(VCGen.Outcome.Correct);
+      }
+    }
+    public int Inconclusives {
+      get {
+        return CountResults(VCGen.Outcome.Inconclusive);
+      }
+    }
+    public int TimeOuts {
+      get {
+        return CountResults(VCGen.Outcome.TimedOut);
+      }
+    }
+    public List<string> ListOfTimeouts {
+      get {
+        return ListOutcomeMatches(VCGen.Outcome.TimedOut);
+      }
+    }
+    public List<string> ListOfInconclusives {
+      get {
+        return ListOutcomeMatches(VCGen.Outcome.Inconclusive);
+      }
+    }
+    public List<string> ListOfErrors {
+      get {
+        return ListOutcomeMatches(VCGen.Outcome.Errors);
+      }
+    }
+  }
+
+}
diff --git a/Source/Houdini/Houdini.csproj b/Source/Houdini/Houdini.csproj
index dcb42ef7..43612142 100644
--- a/Source/Houdini/Houdini.csproj
+++ b/Source/Houdini/Houdini.csproj
@@ -1,154 +1,154 @@
-<?xml version="1.0" encoding="utf-8"?>

-<Project ToolsVersion="4.0" DefaultTargets="Build" xmlns="http://schemas.microsoft.com/developer/msbuild/2003">

-  <PropertyGroup>

-    <Configuration Condition=" '$(Configuration)' == '' ">Debug</Configuration>

-    <Platform Condition=" '$(Platform)' == '' ">AnyCPU</Platform>

-    <ProductVersion>8.0.30703</ProductVersion>

-    <SchemaVersion>2.0</SchemaVersion>

-    <ProjectGuid>{CF41E903-78EB-43BA-A355-E5FEB5ECECD4}</ProjectGuid>

-    <OutputType>Library</OutputType>

-    <AppDesignerFolder>Properties</AppDesignerFolder>

-    <RootNamespace>Microsoft.Boogie.Houdini</RootNamespace>

-    <AssemblyName>Houdini</AssemblyName>

-    <TargetFrameworkVersion>v4.0</TargetFrameworkVersion>

-    <FileAlignment>512</FileAlignment>

-    <CodeContractsAssemblyMode>0</CodeContractsAssemblyMode>

-  </PropertyGroup>

-  <PropertyGroup Condition=" '$(Configuration)|$(Platform)' == 'Debug|AnyCPU' ">

-    <DebugSymbols>true</DebugSymbols>

-    <DebugType>full</DebugType>

-    <Optimize>false</Optimize>

-    <OutputPath>bin\Debug\</OutputPath>

-    <DefineConstants>DEBUG;TRACE</DefineConstants>

-    <ErrorReport>prompt</ErrorReport>

-    <WarningLevel>4</WarningLevel>

-  </PropertyGroup>

-  <PropertyGroup Condition=" '$(Configuration)|$(Platform)' == 'Release|AnyCPU' ">

-    <DebugType>pdbonly</DebugType>

-    <Optimize>true</Optimize>

-    <OutputPath>bin\Release\</OutputPath>

-    <DefineConstants>TRACE</DefineConstants>

-    <ErrorReport>prompt</ErrorReport>

-    <WarningLevel>4</WarningLevel>

-  </PropertyGroup>

-  <PropertyGroup>

-    <SignAssembly>true</SignAssembly>

-  </PropertyGroup>

-  <PropertyGroup>

-    <AssemblyOriginatorKeyFile>..\InterimKey.snk</AssemblyOriginatorKeyFile>

-  </PropertyGroup>

-  <PropertyGroup Condition="'$(Configuration)|$(Platform)' == 'Checked|AnyCPU'">

-    <OutputPath>bin\Checked\</OutputPath>

-    <CodeContractsEnableRuntimeChecking>True</CodeContractsEnableRuntimeChecking>

-    <CodeContractsRuntimeOnlyPublicSurface>False</CodeContractsRuntimeOnlyPublicSurface>

-    <CodeContractsRuntimeThrowOnFailure>True</CodeContractsRuntimeThrowOnFailure>

-    <CodeContractsRuntimeCallSiteRequires>False</CodeContractsRuntimeCallSiteRequires>

-    <CodeContractsRuntimeSkipQuantifiers>False</CodeContractsRuntimeSkipQuantifiers>

-    <CodeContractsRunCodeAnalysis>False</CodeContractsRunCodeAnalysis>

-    <CodeContractsNonNullObligations>False</CodeContractsNonNullObligations>

-    <CodeContractsBoundsObligations>False</CodeContractsBoundsObligations>

-    <CodeContractsArithmeticObligations>False</CodeContractsArithmeticObligations>

-    <CodeContractsEnumObligations>False</CodeContractsEnumObligations>

-    <CodeContractsRedundantAssumptions>False</CodeContractsRedundantAssumptions>

-    <CodeContractsRunInBackground>True</CodeContractsRunInBackground>

-    <CodeContractsShowSquigglies>False</CodeContractsShowSquigglies>

-    <CodeContractsUseBaseLine>False</CodeContractsUseBaseLine>

-    <CodeContractsEmitXMLDocs>False</CodeContractsEmitXMLDocs>

-    <CodeContractsCustomRewriterAssembly>

-    </CodeContractsCustomRewriterAssembly>

-    <CodeContractsCustomRewriterClass>

-    </CodeContractsCustomRewriterClass>

-    <CodeContractsLibPaths>

-    </CodeContractsLibPaths>

-    <CodeContractsExtraRewriteOptions>

-    </CodeContractsExtraRewriteOptions>

-    <CodeContractsExtraAnalysisOptions>

-    </CodeContractsExtraAnalysisOptions>

-    <CodeContractsBaseLineFile>

-    </CodeContractsBaseLineFile>

-    <CodeContractsCacheAnalysisResults>False</CodeContractsCacheAnalysisResults>

-    <CodeContractsRuntimeCheckingLevel>Full</CodeContractsRuntimeCheckingLevel>

-    <CodeContractsReferenceAssembly>Build</CodeContractsReferenceAssembly>

-    <CodeContractsAnalysisWarningLevel>0</CodeContractsAnalysisWarningLevel>

-    <WarningLevel>4</WarningLevel>

-    <Optimize>false</Optimize>

-  </PropertyGroup>

-  <PropertyGroup Condition="'$(Configuration)|$(Platform)' == 'QED|AnyCPU'">

-    <DebugSymbols>true</DebugSymbols>

-    <OutputPath>bin\QED\</OutputPath>

-    <DefineConstants>DEBUG;TRACE</DefineConstants>

-    <DebugType>full</DebugType>

-    <PlatformTarget>AnyCPU</PlatformTarget>

-    <ErrorReport>prompt</ErrorReport>

-    <CodeAnalysisRuleSet>MinimumRecommendedRules.ruleset</CodeAnalysisRuleSet>

-  </PropertyGroup>

-  <ItemGroup>

-    <Reference Include="System" />

-    <Reference Include="System.Core" />

-    <Reference Include="System.Xml.Linq" />

-    <Reference Include="System.Data.DataSetExtensions" />

-    <Reference Include="Microsoft.CSharp" />

-    <Reference Include="System.Data" />

-    <Reference Include="System.Xml" />

-  </ItemGroup>

-  <ItemGroup>

-    <Compile Include="..\version.cs">

-      <Link>version.cs</Link>

-    </Compile>

-    <Compile Include="AbstractHoudini.cs" />

-    <Compile Include="Checker.cs" />

-    <Compile Include="AnnotationDependenceAnalyser.cs" />

-    <Compile Include="Houdini.cs" />

-    <Compile Include="StagedHoudini.cs" />

-    <Compile Include="ConcurrentHoudini.cs" />

-  </ItemGroup>

-  <ItemGroup>

-    <ProjectReference Include="..\Basetypes\Basetypes.csproj">

-      <Project>{43DFAD18-3E35-4558-9BE2-CAFF6B5BA8A0}</Project>

-      <Name>Basetypes</Name>

-    </ProjectReference>

-    <ProjectReference Include="..\CodeContractsExtender\CodeContractsExtender.csproj">

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-    <ProjectReference Include="..\Core\Core.csproj">

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-      <Name>Core</Name>

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-    <ProjectReference Include="..\Graph\Graph.csproj">

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-      <Project>{ACEF88D5-DADD-46DA-BAE1-2144D63F4C83}</Project>

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-    <ProjectReference Include="..\Provers\SMTLib\SMTLib.csproj">

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-    <ProjectReference Include="..\VCExpr\VCExpr.csproj">

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-      <Name>VCExpr</Name>

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-    <ProjectReference Include="..\VCGeneration\VCGeneration.csproj">

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-  <ItemGroup>

-    <Folder Include="Properties\" />

-  </ItemGroup>

-  <Import Project="$(MSBuildToolsPath)\Microsoft.CSharp.targets" />

-  <!-- To modify your build process, add your task inside one of the targets below and uncomment it. 

-       Other similar extension points exist, see Microsoft.Common.targets.

-  <Target Name="BeforeBuild">

-  </Target>

-  <Target Name="AfterBuild">

-  </Target>

-  -->

+<?xml version="1.0" encoding="utf-8"?>
+<Project ToolsVersion="4.0" DefaultTargets="Build" xmlns="http://schemas.microsoft.com/developer/msbuild/2003">
+  <PropertyGroup>
+    <Configuration Condition=" '$(Configuration)' == '' ">Debug</Configuration>
+    <Platform Condition=" '$(Platform)' == '' ">AnyCPU</Platform>
+    <ProductVersion>8.0.30703</ProductVersion>
+    <SchemaVersion>2.0</SchemaVersion>
+    <ProjectGuid>{CF41E903-78EB-43BA-A355-E5FEB5ECECD4}</ProjectGuid>
+    <OutputType>Library</OutputType>
+    <AppDesignerFolder>Properties</AppDesignerFolder>
+    <RootNamespace>Microsoft.Boogie.Houdini</RootNamespace>
+    <AssemblyName>BoogieHoudini</AssemblyName>
+    <TargetFrameworkVersion>v4.0</TargetFrameworkVersion>
+    <FileAlignment>512</FileAlignment>
+    <CodeContractsAssemblyMode>0</CodeContractsAssemblyMode>
+  </PropertyGroup>
+  <PropertyGroup Condition=" '$(Configuration)|$(Platform)' == 'Debug|AnyCPU' ">
+    <DebugSymbols>true</DebugSymbols>
+    <DebugType>full</DebugType>
+    <Optimize>false</Optimize>
+    <OutputPath>bin\Debug\</OutputPath>
+    <DefineConstants>DEBUG;TRACE</DefineConstants>
+    <ErrorReport>prompt</ErrorReport>
+    <WarningLevel>4</WarningLevel>
+  </PropertyGroup>
+  <PropertyGroup Condition=" '$(Configuration)|$(Platform)' == 'Release|AnyCPU' ">
+    <DebugType>pdbonly</DebugType>
+    <Optimize>true</Optimize>
+    <OutputPath>bin\Release\</OutputPath>
+    <DefineConstants>TRACE</DefineConstants>
+    <ErrorReport>prompt</ErrorReport>
+    <WarningLevel>4</WarningLevel>
+  </PropertyGroup>
+  <PropertyGroup>
+    <SignAssembly>true</SignAssembly>
+  </PropertyGroup>
+  <PropertyGroup>
+    <AssemblyOriginatorKeyFile>..\InterimKey.snk</AssemblyOriginatorKeyFile>
+  </PropertyGroup>
+  <PropertyGroup Condition="'$(Configuration)|$(Platform)' == 'Checked|AnyCPU'">
+    <OutputPath>bin\Checked\</OutputPath>
+    <CodeContractsEnableRuntimeChecking>True</CodeContractsEnableRuntimeChecking>
+    <CodeContractsRuntimeOnlyPublicSurface>False</CodeContractsRuntimeOnlyPublicSurface>
+    <CodeContractsRuntimeThrowOnFailure>True</CodeContractsRuntimeThrowOnFailure>
+    <CodeContractsRuntimeCallSiteRequires>False</CodeContractsRuntimeCallSiteRequires>
+    <CodeContractsRuntimeSkipQuantifiers>False</CodeContractsRuntimeSkipQuantifiers>
+    <CodeContractsRunCodeAnalysis>False</CodeContractsRunCodeAnalysis>
+    <CodeContractsNonNullObligations>False</CodeContractsNonNullObligations>
+    <CodeContractsBoundsObligations>False</CodeContractsBoundsObligations>
+    <CodeContractsArithmeticObligations>False</CodeContractsArithmeticObligations>
+    <CodeContractsEnumObligations>False</CodeContractsEnumObligations>
+    <CodeContractsRedundantAssumptions>False</CodeContractsRedundantAssumptions>
+    <CodeContractsRunInBackground>True</CodeContractsRunInBackground>
+    <CodeContractsShowSquigglies>False</CodeContractsShowSquigglies>
+    <CodeContractsUseBaseLine>False</CodeContractsUseBaseLine>
+    <CodeContractsEmitXMLDocs>False</CodeContractsEmitXMLDocs>
+    <CodeContractsCustomRewriterAssembly>
+    </CodeContractsCustomRewriterAssembly>
+    <CodeContractsCustomRewriterClass>
+    </CodeContractsCustomRewriterClass>
+    <CodeContractsLibPaths>
+    </CodeContractsLibPaths>
+    <CodeContractsExtraRewriteOptions>
+    </CodeContractsExtraRewriteOptions>
+    <CodeContractsExtraAnalysisOptions>
+    </CodeContractsExtraAnalysisOptions>
+    <CodeContractsBaseLineFile>
+    </CodeContractsBaseLineFile>
+    <CodeContractsCacheAnalysisResults>False</CodeContractsCacheAnalysisResults>
+    <CodeContractsRuntimeCheckingLevel>Full</CodeContractsRuntimeCheckingLevel>
+    <CodeContractsReferenceAssembly>Build</CodeContractsReferenceAssembly>
+    <CodeContractsAnalysisWarningLevel>0</CodeContractsAnalysisWarningLevel>
+    <WarningLevel>4</WarningLevel>
+    <Optimize>false</Optimize>
+  </PropertyGroup>
+  <PropertyGroup Condition="'$(Configuration)|$(Platform)' == 'QED|AnyCPU'">
+    <DebugSymbols>true</DebugSymbols>
+    <OutputPath>bin\QED\</OutputPath>
+    <DefineConstants>DEBUG;TRACE</DefineConstants>
+    <DebugType>full</DebugType>
+    <PlatformTarget>AnyCPU</PlatformTarget>
+    <ErrorReport>prompt</ErrorReport>
+    <CodeAnalysisRuleSet>MinimumRecommendedRules.ruleset</CodeAnalysisRuleSet>
+  </PropertyGroup>
+  <ItemGroup>
+    <Reference Include="System" />
+    <Reference Include="System.Core" />
+    <Reference Include="System.Xml.Linq" />
+    <Reference Include="System.Data.DataSetExtensions" />
+    <Reference Include="Microsoft.CSharp" />
+    <Reference Include="System.Data" />
+    <Reference Include="System.Xml" />
+  </ItemGroup>
+  <ItemGroup>
+    <Compile Include="..\version.cs">
+      <Link>version.cs</Link>
+    </Compile>
+    <Compile Include="AbstractHoudini.cs" />
+    <Compile Include="Checker.cs" />
+    <Compile Include="AnnotationDependenceAnalyser.cs" />
+    <Compile Include="Houdini.cs" />
+    <Compile Include="StagedHoudini.cs" />
+    <Compile Include="ConcurrentHoudini.cs" />
+  </ItemGroup>
+  <ItemGroup>
+    <ProjectReference Include="..\Basetypes\Basetypes.csproj">
+      <Project>{43DFAD18-3E35-4558-9BE2-CAFF6B5BA8A0}</Project>
+      <Name>Basetypes</Name>
+    </ProjectReference>
+    <ProjectReference Include="..\CodeContractsExtender\CodeContractsExtender.csproj">
+      <Project>{ACCC0156-0921-43ED-8F67-AD8BDC8CDE31}</Project>
+      <Name>CodeContractsExtender</Name>
+    </ProjectReference>
+    <ProjectReference Include="..\Core\Core.csproj">
+      <Project>{B230A69C-C466-4065-B9C1-84D80E76D802}</Project>
+      <Name>Core</Name>
+    </ProjectReference>
+    <ProjectReference Include="..\Graph\Graph.csproj">
+      <Project>{69A2B0B8-BCAC-4101-AE7A-556FCC58C06E}</Project>
+      <Name>Graph</Name>
+    </ProjectReference>
+    <ProjectReference Include="..\Model\Model.csproj">
+      <Project>{ACEF88D5-DADD-46DA-BAE1-2144D63F4C83}</Project>
+      <Name>Model</Name>
+    </ProjectReference>
+    <ProjectReference Include="..\ParserHelper\ParserHelper.csproj">
+      <Project>{FCD3AC7F-9DFD-46C8-AB1E-09F0B0F16DC5}</Project>
+      <Name>ParserHelper</Name>
+    </ProjectReference>
+    <ProjectReference Include="..\Provers\SMTLib\SMTLib.csproj">
+      <Project>{9B163AA3-36BC-4AFB-88AB-79BC9E97E401}</Project>
+      <Name>SMTLib</Name>
+    </ProjectReference>
+    <ProjectReference Include="..\VCExpr\VCExpr.csproj">
+      <Project>{56FFDBCA-7D14-43B8-A6CA-22A20E417EE1}</Project>
+      <Name>VCExpr</Name>
+    </ProjectReference>
+    <ProjectReference Include="..\VCGeneration\VCGeneration.csproj">
+      <Project>{E1F10180-C7B9-4147-B51F-FA1B701966DC}</Project>
+      <Name>VCGeneration</Name>
+    </ProjectReference>
+  </ItemGroup>
+  <ItemGroup>
+    <Folder Include="Properties\" />
+  </ItemGroup>
+  <Import Project="$(MSBuildToolsPath)\Microsoft.CSharp.targets" />
+  <!-- To modify your build process, add your task inside one of the targets below and uncomment it. 
+       Other similar extension points exist, see Microsoft.Common.targets.
+  <Target Name="BeforeBuild">
+  </Target>
+  <Target Name="AfterBuild">
+  </Target>
+  -->
 </Project>
\ No newline at end of file
diff --git a/Source/Houdini/StagedHoudini.cs b/Source/Houdini/StagedHoudini.cs
index 27481e4f..964321c7 100644
--- a/Source/Houdini/StagedHoudini.cs
+++ b/Source/Houdini/StagedHoudini.cs
@@ -1,427 +1,427 @@
-using System;

-using System.Collections.Generic;

-using System.Linq;

-using System.Text;

-using System.Diagnostics.Contracts;

-using System.Diagnostics;

-using System.Threading.Tasks;

-using System.Threading;

-using Microsoft.Boogie;

-using Microsoft.Boogie.GraphUtil;

-

-namespace Microsoft.Boogie.Houdini

-{

-  public class StagedHoudini

-  {

-

-    private Program program;

-    private HoudiniSession.HoudiniStatistics houdiniStats;

-    private Func<string, Program> ProgramFromFile;

-    private StagedHoudiniPlan plan;

-    private List<Houdini>[] houdiniInstances;

-    private List<StagedHoudiniTask> tasks = new List<StagedHoudiniTask>();

-    private Dictionary<ScheduledStage, HoudiniOutcome> outcomes = new Dictionary<ScheduledStage,HoudiniOutcome>();

-

-    private const string tempFilename = "__stagedHoudiniTemp.bpl";

-

-    public StagedHoudini(Program program, HoudiniSession.HoudiniStatistics houdiniStats, Func<string, Program> ProgramFromFile) {

-      this.program = program;

-      this.houdiniStats = houdiniStats;

-      this.ProgramFromFile = ProgramFromFile;

-      this.houdiniInstances = new List<Houdini>[CommandLineOptions.Clo.StagedHoudiniThreads];

-      for (int i = 0; i < CommandLineOptions.Clo.StagedHoudiniThreads; i++) {

-        houdiniInstances[i] = new List<Houdini>();

-      }

-

-      BreakApartConjunctionsInAnnotations();

-

-      var annotationDependenceAnalyser = new AnnotationDependenceAnalyser(program);

-      annotationDependenceAnalyser.Analyse();

-      this.plan = annotationDependenceAnalyser.ApplyStages();

-      if (CommandLineOptions.Clo.Trace)

-      {

-        annotationDependenceAnalyser.dump();

-

-        if(CommandLineOptions.Clo.DebugStagedHoudini) {

-          Console.WriteLine("Plan\n====\n");

-          if(plan == null) {

-            Console.WriteLine("No plan, as there were no stages");

-          } else {

-            Console.WriteLine(this.plan);

-          }

-        }

-        

-        EmitProgram("staged.bpl");

-      }

-    }

-

-    private void BreakApartConjunctionsInAnnotations()

-    {

-      // StagedHoudini works on a syntactic basis, so that

-      // if x and y occur in the same annotation, any annotation

-      // referring to either x or y will be in the same stage

-      // as this annotation.  It is thus desirable to separate

-      // conjunctive annotations into multiple annotations,

-      // to reduce these syntactic dependencies.

-

-      foreach(var b in program.Blocks()) {

-        List<Cmd> newCmds = new List<Cmd>();

-        foreach(var c in b.Cmds) {

-          var assertion = c as AssertCmd;

-          if (assertion != null) {

-            foreach(var e in BreakIntoConjuncts(assertion.Expr)) {

-              newCmds.Add(new AssertCmd(assertion.tok, e, assertion.Attributes));

-            }

-          } else {

-            newCmds.Add(c);

-          }

-        }

-        b.Cmds = newCmds;

-      }

-

-      foreach(var proc in program.Procedures) {

-        {

-          var newRequires = new List<Requires>();

-          foreach(var r in proc.Requires) {

-            foreach(var c in BreakIntoConjuncts(r.Condition)) {

-              newRequires.Add(new Requires(r.tok, r.Free, c, r.Comment, r.Attributes));

-            }

-          }

-          proc.Requires = newRequires;

-        }

-        {

-          var newEnsures = new List<Ensures>();

-          foreach(var e in proc.Ensures) {

-            foreach(var c in BreakIntoConjuncts(e.Condition)) {

-              newEnsures.Add(new Ensures(e.tok, e.Free, c, e.Comment, e.Attributes));

-            }

-          }

-          proc.Ensures = newEnsures;

-        }

-      }

-    }

-

-    private List<Expr> BreakIntoConjuncts(Expr expr)

-    {

-      var nary = expr as NAryExpr;

-      if(nary == null) {

-        return new List<Expr> { expr };

-      }

-      var fun = nary.Fun as BinaryOperator;

-      if(fun == null || (fun.Op != BinaryOperator.Opcode.And)) {

-        return new List<Expr> { expr };

-      }

-      var result = new List<Expr>();

-      result.AddRange(BreakIntoConjuncts(nary.Args[0]));

-      result.AddRange(BreakIntoConjuncts(nary.Args[1]));

-      return result;

-    }

-

-    private bool NoStages() {

-      return plan == null;

-    }

-

-    public HoudiniOutcome PerformStagedHoudiniInference()

-    {

-

-      if (NoStages()) {

-        Houdini houdini = new Houdini(program, houdiniStats);

-        return houdini.PerformHoudiniInference();

-      }

-

-      EmitProgram(tempFilename);

-

-      #region Prepare the tasks, but do not launch them

-      foreach (var s in plan) {

-        Debug.Assert(!plan.GetDependences(s).Contains(s));

-        tasks.Add(new StagedHoudiniTask(s, new Task(o => {

-          ExecuteStage((ScheduledStage)o);

-        }, s, TaskCreationOptions.LongRunning)));

-      }

-      #endregion

-

-      #region Launch the tasks, and wait for them to finish

-      foreach (var t in tasks) {

-        t.parallelTask.Start();

-      }

-      Task.WaitAll(tasks.Select(Item => Item.parallelTask).ToArray());

-      int count = 0;

-      foreach(var h in houdiniInstances) {

-        if(h.Count() > 0) {

-          count++;

-          System.Diagnostics.Debug.Assert(h.Count() == 1);

-          h[0].Close();

-        }

-      }

-      #endregion

-

-      return UnifyOutcomes();

-

-    }

-

-    private HoudiniOutcome UnifyOutcomes()

-    {

-      HoudiniOutcome result = new HoudiniOutcome();

-      var scheduledStages = outcomes.Keys.ToList();

-

-      result.assignment = new Dictionary<string,bool>();

-      foreach(var c in outcomes[scheduledStages[0]].assignment.Keys) {

-        result.assignment[c] = outcomes.Select(Item => Item.Value).Select(Item => Item.assignment[c]).All(Item => Item);

-      }

-

-      result.implementationOutcomes = new Dictionary<string,VCGenOutcome>();

-      foreach(var p in outcomes[scheduledStages[0]].implementationOutcomes.Keys) {

-        var unifiedImplementationOutcome = outcomes[scheduledStages[0]].implementationOutcomes[p];

-        for(int i = 1; i < scheduledStages.Count(); i++) {

-          unifiedImplementationOutcome = ChooseOutcome(unifiedImplementationOutcome,

-                                                        outcomes[scheduledStages[i]].implementationOutcomes[p]);

-        }

-        result.implementationOutcomes[p] = unifiedImplementationOutcome;

-      }

-

-      return result;

-    }

-

-    private void ExecuteStage(ScheduledStage s)

-    {

-      Task.WaitAll(tasks.Where(

-        Item => plan.GetDependences(s).Contains(Item.stage)).

-          Select(Item => Item.parallelTask).ToArray());

-

-      if(s.Count() == 0) {

-        // This is the trivial first stage, so don't launch Houdini;

-        // give this a null outcome

-        return;

-      }

-

-      List<Houdini> h = AcquireHoudiniInstance();

-

-      if (h.Count() == 0)

-      {

-        h.Add(new Houdini(ProgramFromFile(tempFilename), new HoudiniSession.HoudiniStatistics(), "houdiniCexTrace_" + s.GetId() + ".txt"));

-      }

-

-      System.Diagnostics.Debug.Assert(h.Count() == 1);

-

-      Dictionary<string, bool> mergedAssignment = null;

-

-      List<Dictionary<string, bool>> relevantAssignments;

-      IEnumerable<int> completedStages;

-      lock (outcomes)

-      {

-        relevantAssignments =

-        outcomes.Where(Item => plan.Contains(Item.Key)).

-          Select(Item => Item.Value).

-            Select(Item => Item.assignment).ToList();

-        completedStages = plan.GetDependences(s).Select(Item => Item.GetId());

-      }

-

-      if (relevantAssignments.Count() > 0)

-      {

-        mergedAssignment = new Dictionary<string, bool>();

-        foreach (var v in relevantAssignments[0].Keys)

-        {

-          mergedAssignment[v] = relevantAssignments.Select(Item => Item[v]).ToList().All(Item => Item);

-        }

-      }

-

-      HoudiniOutcome outcome = h[0].PerformHoudiniInference(

-        s.GetId(),

-        completedStages,

-        mergedAssignment);

-

-      lock (outcomes)

-      {

-        outcomes[s] = outcome;

-      }

-

-      ReleaseHoudiniInstance(h);

-

-    }

-

-    private static void ReleaseHoudiniInstance(List<Houdini> h)

-    {

-      Monitor.Exit(h);

-    }

-

-    private List<Houdini> AcquireHoudiniInstance()

-    {

-      while(true) {

-        foreach (var houdini in houdiniInstances) {

-          if (Monitor.TryEnter(houdini)) {

-            return houdini;

-          }

-          Thread.Sleep(20);

-        }

-      }

-    }

-

-    private void EmitProgram(string filename)

-    {

-      using (TokenTextWriter writer = new TokenTextWriter(filename, true))

-      {

-        int oldPrintUnstructured = CommandLineOptions.Clo.PrintUnstructured;

-        CommandLineOptions.Clo.PrintUnstructured = 2;

-        program.Emit(writer);

-        CommandLineOptions.Clo.PrintUnstructured = oldPrintUnstructured;

-      }

-    }

-

-  

-    private static VCGenOutcome ChooseOutcome(VCGenOutcome o1, VCGenOutcome o2) {

-      var vcOutcome1 = o1.outcome;

-      var vcOutcome2 = o2.outcome;

-

-      if(vcOutcome1 == vcOutcome2) {

-        return o1;

-      }

-

-      // Errors trump everything else

-      if(vcOutcome1 == VC.ConditionGeneration.Outcome.Errors) {

-        return o1;

-      }

-      if(vcOutcome2 == VC.ConditionGeneration.Outcome.Errors) {

-        return o2;

-      }

-

-      // If one outcome is Correct, return the other in case it is "worse"

-      if(vcOutcome1 == VC.ConditionGeneration.Outcome.Correct) {

-        return o2;

-      }

-      if(vcOutcome2 == VC.ConditionGeneration.Outcome.Correct) {

-        return o1;

-      }

-

-      // Neither outcome is correct, so if one outcome is ReachedBound, return the other in case it is "worse"

-      if(vcOutcome1 == VC.ConditionGeneration.Outcome.ReachedBound) {

-        return o2;

-      }

-      if(vcOutcome2 == VC.ConditionGeneration.Outcome.ReachedBound) {

-        return o1;

-      }

-

-      // Both outcomes must be timeout or memout; arbitrarily choose the first

-      return o1;

-    }

-

-    internal class StagedHoudiniTask {

-      internal ScheduledStage stage;

-      internal Task parallelTask;

-      internal StagedHoudiniTask(ScheduledStage stage, Task parallelTask) {

-        this.stage = stage;

-        this.parallelTask = parallelTask;

-      }

-    }

-  

-  }

-

-  public class StagedHoudiniPlan : IEnumerable<ScheduledStage> {

-

-    private Graph<ScheduledStage> ScheduledStages;

-    private Dictionary<string, ScheduledStage> AnnotationToStage;

-

-    internal StagedHoudiniPlan(Graph<ScheduledStage> ScheduledStages) {

-      this.ScheduledStages = ScheduledStages;

-      this.AnnotationToStage = new Dictionary<string, ScheduledStage>();

-      foreach(var s in this) {

-        Debug.Assert(!GetDependences(s).Contains(s));

-      }

-    }

-

-    public IEnumerable<ScheduledStage> GetDependences(ScheduledStage s) {

-      IEnumerable<ScheduledStage> result;

-      lock(ScheduledStages) {

-        result = ScheduledStages.Successors(s);

-      }

-      return result;

-    }

-

-

-    private static int CompareStages(ScheduledStage s1, ScheduledStage s2) {

-      if(s1.GetId() < s2.GetId()) {

-        return -1;

-      }

-      if(s2.GetId() < s1.GetId()) {

-        return 1;

-      }

-      return 0;

-    }

-

-    public IEnumerator<ScheduledStage> GetEnumerator() {

-      List<ScheduledStage> sortedStages = ScheduledStages.Nodes.ToList();

-      sortedStages.Sort(CompareStages);

-      return sortedStages.GetEnumerator();

-    }

-

-    System.Collections.IEnumerator System.Collections.IEnumerable.GetEnumerator()

-    {

-        return this.GetEnumerator();

-    }

-

-    internal ScheduledStage StageForAnnotation(string c) {

-      if(AnnotationToStage.ContainsKey(c)) {

-        return AnnotationToStage[c];

-      }

-      foreach(var s in ScheduledStages.Nodes) {

-        if(s.ContainsAnnotation(c)) {

-          AnnotationToStage[c] = s;

-          return s;

-        }

-      }

-      return null;

-    }

-

-    public override string ToString()

-    {

-      string result = "";

-      foreach(ScheduledStage s in this) {

-        result += "Stage " + s;

-        

-        result += " depends on stages: ";

-        foreach(var id in GetDependences(s).Select(Item => Item.GetId())) {

-          result += id + " ";

-        }

-        result += "\n";

-      }

-      return result;

-    }

-  }

-

-  public class ScheduledStage {

-    private int Id;

-    private HashSet<string> Annotations;

-

-    public ScheduledStage(int Id, HashSet<string> Annotations) {

-      this.Id = Id;

-      this.Annotations = Annotations;

-    }

-

-    internal void AddAnnotation(string a) {

-      Annotations.Add(a);

-    }

-

-    internal bool ContainsAnnotation(string a) {

-      return Annotations.Contains(a);

-    }

-

-    public int GetId() {

-      return Id;

-    }

-

-    public int Count() {

-      return Annotations.Count();

-    }

-

-    public override string ToString()

-    {

-      string result = "ID: " + Id + "{ ";

-      foreach(var c in Annotations) {

-        result += c + " ";

-      }

-      result += "}\n";

-      return result;

-    }

-  }

-

-

-}

+using System;
+using System.Collections.Generic;
+using System.Linq;
+using System.Text;
+using System.Diagnostics.Contracts;
+using System.Diagnostics;
+using System.Threading.Tasks;
+using System.Threading;
+using Microsoft.Boogie;
+using Microsoft.Boogie.GraphUtil;
+
+namespace Microsoft.Boogie.Houdini
+{
+  public class StagedHoudini
+  {
+
+    private Program program;
+    private HoudiniSession.HoudiniStatistics houdiniStats;
+    private Func<string, Program> ProgramFromFile;
+    private StagedHoudiniPlan plan;
+    private List<Houdini>[] houdiniInstances;
+    private List<StagedHoudiniTask> tasks = new List<StagedHoudiniTask>();
+    private Dictionary<ScheduledStage, HoudiniOutcome> outcomes = new Dictionary<ScheduledStage,HoudiniOutcome>();
+
+    private const string tempFilename = "__stagedHoudiniTemp.bpl";
+
+    public StagedHoudini(Program program, HoudiniSession.HoudiniStatistics houdiniStats, Func<string, Program> ProgramFromFile) {
+      this.program = program;
+      this.houdiniStats = houdiniStats;
+      this.ProgramFromFile = ProgramFromFile;
+      this.houdiniInstances = new List<Houdini>[CommandLineOptions.Clo.StagedHoudiniThreads];
+      for (int i = 0; i < CommandLineOptions.Clo.StagedHoudiniThreads; i++) {
+        houdiniInstances[i] = new List<Houdini>();
+      }
+
+      BreakApartConjunctionsInAnnotations();
+
+      var annotationDependenceAnalyser = new AnnotationDependenceAnalyser(program);
+      annotationDependenceAnalyser.Analyse();
+      this.plan = annotationDependenceAnalyser.ApplyStages();
+      if (CommandLineOptions.Clo.Trace)
+      {
+        annotationDependenceAnalyser.dump();
+
+        if(CommandLineOptions.Clo.DebugStagedHoudini) {
+          Console.WriteLine("Plan\n====\n");
+          if(plan == null) {
+            Console.WriteLine("No plan, as there were no stages");
+          } else {
+            Console.WriteLine(this.plan);
+          }
+        }
+        
+        EmitProgram("staged.bpl");
+      }
+    }
+
+    private void BreakApartConjunctionsInAnnotations()
+    {
+      // StagedHoudini works on a syntactic basis, so that
+      // if x and y occur in the same annotation, any annotation
+      // referring to either x or y will be in the same stage
+      // as this annotation.  It is thus desirable to separate
+      // conjunctive annotations into multiple annotations,
+      // to reduce these syntactic dependencies.
+
+      foreach(var b in program.Blocks()) {
+        List<Cmd> newCmds = new List<Cmd>();
+        foreach(var c in b.Cmds) {
+          var assertion = c as AssertCmd;
+          if (assertion != null) {
+            foreach(var e in BreakIntoConjuncts(assertion.Expr)) {
+              newCmds.Add(new AssertCmd(assertion.tok, e, assertion.Attributes));
+            }
+          } else {
+            newCmds.Add(c);
+          }
+        }
+        b.Cmds = newCmds;
+      }
+
+      foreach(var proc in program.Procedures) {
+        {
+          var newRequires = new List<Requires>();
+          foreach(var r in proc.Requires) {
+            foreach(var c in BreakIntoConjuncts(r.Condition)) {
+              newRequires.Add(new Requires(r.tok, r.Free, c, r.Comment, r.Attributes));
+            }
+          }
+          proc.Requires = newRequires;
+        }
+        {
+          var newEnsures = new List<Ensures>();
+          foreach(var e in proc.Ensures) {
+            foreach(var c in BreakIntoConjuncts(e.Condition)) {
+              newEnsures.Add(new Ensures(e.tok, e.Free, c, e.Comment, e.Attributes));
+            }
+          }
+          proc.Ensures = newEnsures;
+        }
+      }
+    }
+
+    private List<Expr> BreakIntoConjuncts(Expr expr)
+    {
+      var nary = expr as NAryExpr;
+      if(nary == null) {
+        return new List<Expr> { expr };
+      }
+      var fun = nary.Fun as BinaryOperator;
+      if(fun == null || (fun.Op != BinaryOperator.Opcode.And)) {
+        return new List<Expr> { expr };
+      }
+      var result = new List<Expr>();
+      result.AddRange(BreakIntoConjuncts(nary.Args[0]));
+      result.AddRange(BreakIntoConjuncts(nary.Args[1]));
+      return result;
+    }
+
+    private bool NoStages() {
+      return plan == null;
+    }
+
+    public HoudiniOutcome PerformStagedHoudiniInference()
+    {
+
+      if (NoStages()) {
+        Houdini houdini = new Houdini(program, houdiniStats);
+        return houdini.PerformHoudiniInference();
+      }
+
+      EmitProgram(tempFilename);
+
+      #region Prepare the tasks, but do not launch them
+      foreach (var s in plan) {
+        Debug.Assert(!plan.GetDependences(s).Contains(s));
+        tasks.Add(new StagedHoudiniTask(s, new Task(o => {
+          ExecuteStage((ScheduledStage)o);
+        }, s, TaskCreationOptions.LongRunning)));
+      }
+      #endregion
+
+      #region Launch the tasks, and wait for them to finish
+      foreach (var t in tasks) {
+        t.parallelTask.Start();
+      }
+      Task.WaitAll(tasks.Select(Item => Item.parallelTask).ToArray());
+      int count = 0;
+      foreach(var h in houdiniInstances) {
+        if(h.Count() > 0) {
+          count++;
+          System.Diagnostics.Debug.Assert(h.Count() == 1);
+          h[0].Close();
+        }
+      }
+      #endregion
+
+      return UnifyOutcomes();
+
+    }
+
+    private HoudiniOutcome UnifyOutcomes()
+    {
+      HoudiniOutcome result = new HoudiniOutcome();
+      var scheduledStages = outcomes.Keys.ToList();
+
+      result.assignment = new Dictionary<string,bool>();
+      foreach(var c in outcomes[scheduledStages[0]].assignment.Keys) {
+        result.assignment[c] = outcomes.Select(Item => Item.Value).Select(Item => Item.assignment[c]).All(Item => Item);
+      }
+
+      result.implementationOutcomes = new Dictionary<string,VCGenOutcome>();
+      foreach(var p in outcomes[scheduledStages[0]].implementationOutcomes.Keys) {
+        var unifiedImplementationOutcome = outcomes[scheduledStages[0]].implementationOutcomes[p];
+        for(int i = 1; i < scheduledStages.Count(); i++) {
+          unifiedImplementationOutcome = ChooseOutcome(unifiedImplementationOutcome,
+                                                        outcomes[scheduledStages[i]].implementationOutcomes[p]);
+        }
+        result.implementationOutcomes[p] = unifiedImplementationOutcome;
+      }
+
+      return result;
+    }
+
+    private void ExecuteStage(ScheduledStage s)
+    {
+      Task.WaitAll(tasks.Where(
+        Item => plan.GetDependences(s).Contains(Item.stage)).
+          Select(Item => Item.parallelTask).ToArray());
+
+      if(s.Count() == 0) {
+        // This is the trivial first stage, so don't launch Houdini;
+        // give this a null outcome
+        return;
+      }
+
+      List<Houdini> h = AcquireHoudiniInstance();
+
+      if (h.Count() == 0)
+      {
+        h.Add(new Houdini(ProgramFromFile(tempFilename), new HoudiniSession.HoudiniStatistics(), "houdiniCexTrace_" + s.GetId() + ".txt"));
+      }
+
+      System.Diagnostics.Debug.Assert(h.Count() == 1);
+
+      Dictionary<string, bool> mergedAssignment = null;
+
+      List<Dictionary<string, bool>> relevantAssignments;
+      IEnumerable<int> completedStages;
+      lock (outcomes)
+      {
+        relevantAssignments =
+        outcomes.Where(Item => plan.Contains(Item.Key)).
+          Select(Item => Item.Value).
+            Select(Item => Item.assignment).ToList();
+        completedStages = plan.GetDependences(s).Select(Item => Item.GetId());
+      }
+
+      if (relevantAssignments.Count() > 0)
+      {
+        mergedAssignment = new Dictionary<string, bool>();
+        foreach (var v in relevantAssignments[0].Keys)
+        {
+          mergedAssignment[v] = relevantAssignments.Select(Item => Item[v]).ToList().All(Item => Item);
+        }
+      }
+
+      HoudiniOutcome outcome = h[0].PerformHoudiniInference(
+        s.GetId(),
+        completedStages,
+        mergedAssignment);
+
+      lock (outcomes)
+      {
+        outcomes[s] = outcome;
+      }
+
+      ReleaseHoudiniInstance(h);
+
+    }
+
+    private static void ReleaseHoudiniInstance(List<Houdini> h)
+    {
+      Monitor.Exit(h);
+    }
+
+    private List<Houdini> AcquireHoudiniInstance()
+    {
+      while(true) {
+        foreach (var houdini in houdiniInstances) {
+          if (Monitor.TryEnter(houdini)) {
+            return houdini;
+          }
+          Thread.Sleep(20);
+        }
+      }
+    }
+
+    private void EmitProgram(string filename)
+    {
+      using (TokenTextWriter writer = new TokenTextWriter(filename, true))
+      {
+        int oldPrintUnstructured = CommandLineOptions.Clo.PrintUnstructured;
+        CommandLineOptions.Clo.PrintUnstructured = 2;
+        program.Emit(writer);
+        CommandLineOptions.Clo.PrintUnstructured = oldPrintUnstructured;
+      }
+    }
+
+  
+    private static VCGenOutcome ChooseOutcome(VCGenOutcome o1, VCGenOutcome o2) {
+      var vcOutcome1 = o1.outcome;
+      var vcOutcome2 = o2.outcome;
+
+      if(vcOutcome1 == vcOutcome2) {
+        return o1;
+      }
+
+      // Errors trump everything else
+      if(vcOutcome1 == VC.ConditionGeneration.Outcome.Errors) {
+        return o1;
+      }
+      if(vcOutcome2 == VC.ConditionGeneration.Outcome.Errors) {
+        return o2;
+      }
+
+      // If one outcome is Correct, return the other in case it is "worse"
+      if(vcOutcome1 == VC.ConditionGeneration.Outcome.Correct) {
+        return o2;
+      }
+      if(vcOutcome2 == VC.ConditionGeneration.Outcome.Correct) {
+        return o1;
+      }
+
+      // Neither outcome is correct, so if one outcome is ReachedBound, return the other in case it is "worse"
+      if(vcOutcome1 == VC.ConditionGeneration.Outcome.ReachedBound) {
+        return o2;
+      }
+      if(vcOutcome2 == VC.ConditionGeneration.Outcome.ReachedBound) {
+        return o1;
+      }
+
+      // Both outcomes must be timeout or memout; arbitrarily choose the first
+      return o1;
+    }
+
+    internal class StagedHoudiniTask {
+      internal ScheduledStage stage;
+      internal Task parallelTask;
+      internal StagedHoudiniTask(ScheduledStage stage, Task parallelTask) {
+        this.stage = stage;
+        this.parallelTask = parallelTask;
+      }
+    }
+  
+  }
+
+  public class StagedHoudiniPlan : IEnumerable<ScheduledStage> {
+
+    private Graph<ScheduledStage> ScheduledStages;
+    private Dictionary<string, ScheduledStage> AnnotationToStage;
+
+    internal StagedHoudiniPlan(Graph<ScheduledStage> ScheduledStages) {
+      this.ScheduledStages = ScheduledStages;
+      this.AnnotationToStage = new Dictionary<string, ScheduledStage>();
+      foreach(var s in this) {
+        Debug.Assert(!GetDependences(s).Contains(s));
+      }
+    }
+
+    public IEnumerable<ScheduledStage> GetDependences(ScheduledStage s) {
+      IEnumerable<ScheduledStage> result;
+      lock(ScheduledStages) {
+        result = ScheduledStages.Successors(s);
+      }
+      return result;
+    }
+
+
+    private static int CompareStages(ScheduledStage s1, ScheduledStage s2) {
+      if(s1.GetId() < s2.GetId()) {
+        return -1;
+      }
+      if(s2.GetId() < s1.GetId()) {
+        return 1;
+      }
+      return 0;
+    }
+
+    public IEnumerator<ScheduledStage> GetEnumerator() {
+      List<ScheduledStage> sortedStages = ScheduledStages.Nodes.ToList();
+      sortedStages.Sort(CompareStages);
+      return sortedStages.GetEnumerator();
+    }
+
+    System.Collections.IEnumerator System.Collections.IEnumerable.GetEnumerator()
+    {
+        return this.GetEnumerator();
+    }
+
+    internal ScheduledStage StageForAnnotation(string c) {
+      if(AnnotationToStage.ContainsKey(c)) {
+        return AnnotationToStage[c];
+      }
+      foreach(var s in ScheduledStages.Nodes) {
+        if(s.ContainsAnnotation(c)) {
+          AnnotationToStage[c] = s;
+          return s;
+        }
+      }
+      return null;
+    }
+
+    public override string ToString()
+    {
+      string result = "";
+      foreach(ScheduledStage s in this) {
+        result += "Stage " + s;
+        
+        result += " depends on stages: ";
+        foreach(var id in GetDependences(s).Select(Item => Item.GetId())) {
+          result += id + " ";
+        }
+        result += "\n";
+      }
+      return result;
+    }
+  }
+
+  public class ScheduledStage {
+    private int Id;
+    private HashSet<string> Annotations;
+
+    public ScheduledStage(int Id, HashSet<string> Annotations) {
+      this.Id = Id;
+      this.Annotations = Annotations;
+    }
+
+    internal void AddAnnotation(string a) {
+      Annotations.Add(a);
+    }
+
+    internal bool ContainsAnnotation(string a) {
+      return Annotations.Contains(a);
+    }
+
+    public int GetId() {
+      return Id;
+    }
+
+    public int Count() {
+      return Annotations.Count();
+    }
+
+    public override string ToString()
+    {
+      string result = "ID: " + Id + "{ ";
+      foreach(var c in Annotations) {
+        result += c + " ";
+      }
+      result += "}\n";
+      return result;
+    }
+  }
+
+
+}