path: root/Source/VCGeneration/VC.ssc

//-----------------------------------------------------------------------------
//
// Copyright (C) Microsoft Corporation.  All Rights Reserved.
//
//-----------------------------------------------------------------------------
using System;
using System.Collections;
using System.Collections.Generic;
using System.Diagnostics;
using System.Threading;
using System.IO;
using Microsoft.Boogie;
using Graphing;
using AI = Microsoft.AbstractInterpretationFramework;
using Microsoft.Contracts;
using Microsoft.Basetypes;
using Microsoft.Boogie.VCExprAST;


namespace VC
{
  using Bpl = Microsoft.Boogie;
  
  public class VCGen : ConditionGeneration
  {

    /// <summary>
    /// Constructor.  Initializes the theorem prover.
    /// </summary>
    public VCGen(Program! program, string/*?*/ logFilePath, bool appendLogFile)
      // throws ProverException
    {
      base(program);
      this.appendLogFile = appendLogFile;
      this.logFilePath = logFilePath;
      // base();
    }

    private static AssumeCmd! AssertTurnedIntoAssume(AssertCmd! assrt)
    {
      Expr! expr = assrt.Expr;

      switch (CommandLineOptions.Clo.UseSubsumption) {
        case CommandLineOptions.SubsumptionOption.Never:
          expr = Expr.True;
          break;
        case CommandLineOptions.SubsumptionOption.Always:
          break;
        case CommandLineOptions.SubsumptionOption.NotForQuantifiers:
          if (expr is QuantifierExpr) {
            expr = Expr.True;
          }
          break;
        default:
          assert false;  // unexpected case
      }

      return new AssumeCmd(assrt.tok, expr);
    }
    


   

    #region Soundness smoke tester
    class SmokeTester
    {
      VCGen! parent;
      Implementation! impl;
      Block! initial;
      Program! program;
      int id;
      Dictionary<Block!, Block!>! copies = new Dictionary<Block!, Block!>();
      Dictionary<Block!, bool>! visited = new Dictionary<Block!, bool>();
      VerifierCallback! callback;

      internal SmokeTester(VCGen! par, Implementation! i, Program! prog, VerifierCallback! callback)
      {
        parent = par;
        impl = i;
        initial = i.Blocks[0];
        program = prog;
        this.callback = callback;
      }

      internal void Copy()
      {
        CloneBlock(impl.Blocks[0]);
        initial = GetCopiedBlocks()[0];
      }

      internal void Test()
        throws UnexpectedProverOutputException;
      {
        DFS(initial);
      }

      void TopologicalSortImpl()
      {
        Graph<Block> dag = new Graph<Block>();
        dag.AddSource((!)impl.Blocks[0]); // there is always at least one node in the graph
        foreach (Block b in impl.Blocks)
        {
          GotoCmd gtc = b.TransferCmd as GotoCmd;
          if (gtc != null)
          {
            assume gtc.labelTargets != null;
            foreach (Block! dest in gtc.labelTargets)
            {
              dag.AddEdge(b,dest);
            }
          }
        }
        impl.Blocks = new List<Block!>();
        foreach (Block! b in dag.TopologicalSort()) {
          impl.Blocks.Add(b);
        }
      }

      void Emit()
      {
        TopologicalSortImpl();
        EmitImpl(impl, false);
      }

      // this one copies forward
      Block! CloneBlock(Block! b)
      {
        Block fake_res;
        if (copies.TryGetValue(b, out fake_res)) {
          return (!)fake_res;
        }
        Block! res;
        res = new Block(b.tok, b.Label, new CmdSeq(b.Cmds), null);
        copies[b] = res;
        if (b.TransferCmd is GotoCmd) {
          foreach (Block! ch in (!)((GotoCmd)b.TransferCmd).labelTargets) {
            CloneBlock(ch);
          }
        }
        foreach (Block! p in b.Predecessors) {
          res.Predecessors.Add(CloneBlock(p));
        }
        return res;
      }

      // this one copies backwards
      Block! CopyBlock(Block! b)
      {
        Block fake_res;
        if (copies.TryGetValue(b, out fake_res)) {
          // fake_res should be Block! but the compiler fails
          return (!)fake_res;
        }
        Block! res;
        CmdSeq seq = new CmdSeq();
        foreach (Cmd! c in b.Cmds) {
          AssertCmd turn = c as AssertCmd;
          if (!turnAssertIntoAssumes || turn == null) {
            seq.Add(c);
          } else {
            seq.Add(AssertTurnedIntoAssume(turn));
          }
        }
        res = new Block(b.tok, b.Label, seq, null);
        copies[b] = res;
        foreach (Block! p in b.Predecessors) {
          res.Predecessors.Add(CopyBlock(p));
        }
        return res;
      }

      List<Block!>! GetCopiedBlocks()
      {
        // the order of nodes in res is random (except for the first one, being the entry)
        List<Block!> res = new List<Block!>();
        res.Add(copies[initial]);

        foreach (KeyValuePair<Block!,Block!> kv in copies) {
          GotoCmd go = kv.Key.TransferCmd as GotoCmd;
          ReturnCmd ret = kv.Key.TransferCmd as ReturnCmd;
          if (kv.Key != initial) {
            res.Add(kv.Value);
          }
          if (go != null) {
            GotoCmd copy = new GotoCmd(go.tok, new StringSeq(), new BlockSeq());
            kv.Value.TransferCmd = copy;
            foreach (Block! b in (!)go.labelTargets) {
              Block c;
              if (copies.TryGetValue(b, out c)) {
                copy.AddTarget((!)c);
              }
            }
          } else if (ret != null) {
            kv.Value.TransferCmd = ret;
          } else {
            assume false;
          }
        }

        copies.Clear();

        return res;
      }

      // check if e is true, false, !true, !false
      // if so return true and the value of the expression in val
      bool BooleanEval(Expr! e, ref bool val)
      {
        LiteralExpr lit = e as LiteralExpr;
        NAryExpr call = e as NAryExpr;

        if (lit != null && lit.isBool) {
          val = lit.asBool;
          return true;
        } else if (call != null && 
                   call.Fun is UnaryOperator && 
                   ((UnaryOperator)call.Fun).Op == UnaryOperator.Opcode.Not &&
                   BooleanEval((!)call.Args[0], ref val)) {
          val = !val;
          return true;
        } 
        // this is for the 0bv32 != 0bv32 generated by vcc
        else if (call != null && 
                   call.Fun is BinaryOperator && 
                   ((BinaryOperator)call.Fun).Op == BinaryOperator.Opcode.Neq &&
                   call.Args[0] is LiteralExpr &&
                   ((!)call.Args[0]).Equals(call.Args[1]))
        {
          val = false;
          return true;
        }

        return false;
      }

      bool IsFalse(Expr! e)
      {
        bool val = false;
        return BooleanEval(e, ref val) && !val;
      }

      bool CheckUnreachable(Block! cur, CmdSeq! seq)
        throws UnexpectedProverOutputException;
      {
        foreach (Cmd cmd in seq) {
          AssertCmd assrt = cmd as AssertCmd;
          if (assrt != null && QKeyValue.FindBoolAttribute(assrt.Attributes, "PossiblyUnreachable"))
            return false;
        }

        DateTime start = DateTime.Now;
        if (CommandLineOptions.Clo.Trace) {
          System.Console.Write("    soundness smoke test #{0} ... ", id);
        }
        callback.OnProgress("smoke", id, id, 0.0);

        Token tok = new Token();
        tok.val = "soundness smoke test assertion";
        seq.Add(new AssertCmd(tok, Expr.False));
        Block! copy = CopyBlock(cur);
        copy.Cmds = seq;
        List<Block!>! backup = impl.Blocks;
        impl.Blocks = GetCopiedBlocks();
        copy.TransferCmd = new ReturnCmd(Token.NoToken);
        if (CommandLineOptions.Clo.TraceVerify) {
          System.Console.WriteLine();
          System.Console.WriteLine(" --- smoke #{0}, before passify", id);
          Emit();
        }
        parent.current_impl = impl;
        parent.PassifyImpl(impl, program);
        Hashtable! label2Absy;
        Checker! ch = parent.FindCheckerFor(impl, CommandLineOptions.Clo.SmokeTimeout);
        VCExpr! vc = parent.GenerateVC(impl, out label2Absy, ch);
        impl.Blocks = backup;

        if (CommandLineOptions.Clo.TraceVerify) {
          System.Console.WriteLine(" --- smoke #{0}, after passify", id);
          Emit();
        }
        ch.BeginCheck((!) impl.Name + "_smoke" + id++, vc, new ErrorHandler(label2Absy, this.callback));
        ch.ProverDone.WaitOne();
        ProverInterface.Outcome outcome = ch.ReadOutcome();
        parent.current_impl = null;

        DateTime end = DateTime.Now;
        TimeSpan elapsed = end - start;
        if (CommandLineOptions.Clo.Trace) {
          System.Console.WriteLine("  [{0} s] {1}", elapsed.TotalSeconds, 
            outcome == ProverInterface.Outcome.Valid ? "OOPS" : 
              "OK" + (outcome == ProverInterface.Outcome.Invalid ? "" : " (" + outcome + ")"));
        }

        if (outcome == ProverInterface.Outcome.Valid) {
          // copy it again, so we get the version with calls, assignments and such
          copy = CopyBlock(cur);
          copy.Cmds = seq;
          impl.Blocks = GetCopiedBlocks();
          TopologicalSortImpl();
          callback.OnUnreachableCode(impl);
          impl.Blocks = backup;
          return true;
        }
        return false;
      }

      const bool turnAssertIntoAssumes = false;

      void DFS(Block! cur)
        throws UnexpectedProverOutputException;
      {
        if (visited.ContainsKey(cur)) return;
        visited[cur] = true;

        CmdSeq! seq = new CmdSeq();
        foreach (Cmd! cmd_ in cur.Cmds) {
          Cmd! cmd = cmd_;
          AssertCmd assrt = cmd as AssertCmd;
          AssumeCmd assm = cmd as AssumeCmd;
          CallCmd call = cmd as CallCmd;

          bool assumeFalse = false;

          if (assrt != null) {
            // we're not going any further
            // it's clear the user expected unreachable code here
            // it's not clear where did he expect it, maybe it would be right to insert
            // a check just one command before
            if (IsFalse(assrt.Expr)) return;

            if (turnAssertIntoAssumes) {
              cmd = AssertTurnedIntoAssume(assrt);
            }
          } else if (assm != null) {
            if (IsFalse(assm.Expr)) assumeFalse = true;
          } else if (call != null) {
            foreach (Ensures! e in ((!)call.Proc).Ensures) {
              if (IsFalse(e.Condition)) assumeFalse = true;
            }
          }

          if (assumeFalse) {
            CheckUnreachable(cur, seq);
            return;
          }

          seq.Add(cmd);
        }

        
        GotoCmd go = cur.TransferCmd as GotoCmd;
        ReturnCmd ret = cur.TransferCmd as ReturnCmd;

        assume !(go!= null&&go.labelTargets==null&&go.labelNames!=null&&go.labelNames.Length>0) ;

        if (ret != null || (go != null && ((!)go.labelTargets).Length == 0)) {
          // we end in return, so there will be no more places to check
          CheckUnreachable(cur, seq);
        } else if (go != null) {
          bool needToCheck = true;
          // if all of our children have more than one parent, then
          // we're in the right place to check
          foreach (Block! target in (!)go.labelTargets) {
            if (target.Predecessors.Length == 1) {
              needToCheck = false;
            }
          }
          if (needToCheck) {
            CheckUnreachable(cur, seq);
          }
          foreach (Block! target in go.labelTargets) {
            DFS(target);
          }
        }
      }
      
      class ErrorHandler : ProverInterface.ErrorHandler {
        Hashtable! label2Absy;
        VerifierCallback! callback;
        
        public ErrorHandler(Hashtable! label2Absy, VerifierCallback! callback) {
          this.label2Absy = label2Absy;
          this.callback = callback;
        }
        
        public override Absy! Label2Absy(string! label) {
          int id = int.Parse(label);
          return (Absy!) label2Absy[id];
        }
        
        public override void OnProverWarning(string! msg) {
          this.callback.OnWarning(msg);
        }
      }
    }
    
    
    #endregion

    #region Splitter
    class Split
    {
      class BlockStats {
        public bool big_block;
        public int id;
        public double assertion_cost;
        public double assumption_cost; // before multiplier
        public double incomming_paths;
        public List<Block!>! virtual_successors = new List<Block!>();
        public List<Block!>! virtual_predecesors = new List<Block!>();
        public Dictionary<Block!,bool>? reachable_blocks;
        public readonly Block! block;

        public BlockStats(Block! b, int i)
        {
          block = b;
          assertion_cost = -1;
          id = i;
        }
      }

      readonly List<Block!>! blocks;
      readonly List<Block!>! big_blocks = new List<Block!>();
      readonly Dictionary<Block!, BlockStats!>! stats = new Dictionary<Block!, BlockStats!>();
      readonly int id;
      static int current_id;
      Block? split_block;
      bool assert_to_assume;
      List<Block!>! assumized_branches = new List<Block!>();
      public AssertCmd? first_assert;

      double score;
      bool score_computed;
      double total_cost;
      int assertion_count;
      double assertion_cost; // without multiplication by paths
      Hashtable/*TransferCmd->ReturnCmd*/! gotoCmdOrigins;
      VCGen! parent;
      Implementation! impl;

      Dictionary<Block!, Block!>! copies = new Dictionary<Block!, Block!>();
      bool doing_slice;
      double slice_initial_limit;
      double slice_limit;
      bool slice_pos;
      Dictionary<Block!, bool>! protected_from_assert_to_assume = new Dictionary<Block!,bool>();
      Dictionary<Block!, bool>! keep_at_all = new Dictionary<Block!,bool>();

      // async interface
      private Checker checker;
      private int splitNo;
      internal ErrorReporter reporter;

      public Split(List<Block!>! blocks, Hashtable/*TransferCmd->ReturnCmd*/! gotoCmdOrigins, VCGen! par, Implementation! impl)
      {
        this.blocks = blocks;
        this.gotoCmdOrigins = gotoCmdOrigins;
        this.parent = par;
        this.impl = impl;
        this.id = current_id++;
      }

      public double Cost
      {
        get {
          ComputeBestSplit();
          return total_cost;
        }
      }

      public bool LastChance
      {
        get {
          ComputeBestSplit();
          return assertion_count == 1 && score < 0;
        }
      }

      public string Stats
      {
        get {
          ComputeBestSplit();
          return string.Format("(cost:{0:0}/{1:0}{2})", total_cost, assertion_cost, LastChance ? " last" : "");
        }
      }

      public void DumpDot(int no)
      {
        using (System.IO.StreamWriter sw = System.IO.File.CreateText(string.Format("split.{0}.dot", no))) {
          sw.WriteLine("digraph G {");

          ComputeBestSplit();
          List<Block!> saved = assumized_branches;
          assumized_branches = new List<Block!>();
          DoComputeScore(false);
          assumized_branches = saved;

          foreach (Block! b in big_blocks) {
            BlockStats s = GetBlockStats(b);
            foreach (Block! t in s.virtual_successors) {
              sw.WriteLine("n{0} -> n{1};", s.id, GetBlockStats(t).id);
            }
            sw.WriteLine("n{0} [label=\"{1}:\\n({2:0.0}+{3:0.0})*{4:0.0}\"{5}];", 
                      s.id, b.Label, 
                      s.assertion_cost, s.assumption_cost, s.incomming_paths,
                      s.assertion_cost > 0 ? ",shape=box" : "");
       
          }
          sw.WriteLine("}");
          sw.Close();
        }

        string filename = string.Format("split.{0}.bpl", no);
        using (System.IO.StreamWriter sw = System.IO.File.CreateText(filename)) {
          int oldPrintUnstructured = CommandLineOptions.Clo.PrintUnstructured;
          CommandLineOptions.Clo.PrintUnstructured = 2;  // print only the unstructured program
          bool oldPrintDesugaringSetting = CommandLineOptions.Clo.PrintDesugarings;
          CommandLineOptions.Clo.PrintDesugarings = false;
          List<Block!> backup = impl.Blocks;
          impl.Blocks = blocks;
          impl.Emit(new TokenTextWriter(filename, sw, false), 0);
          impl.Blocks = backup;
          CommandLineOptions.Clo.PrintDesugarings = oldPrintDesugaringSetting;
          CommandLineOptions.Clo.PrintUnstructured = oldPrintUnstructured;
        }
      }

      int bsid;
      BlockStats! GetBlockStats(Block! b)
      {
        BlockStats s;
        if (!stats.TryGetValue(b, out s)) {
          s = new BlockStats(b, bsid++);
          stats[b] = s;
        }
        return (!)s;
      }

      double AssertionCost(PredicateCmd c)
      {
        return 1.0;
      }

      void CountAssertions(Block! b)
      {
        BlockStats s = GetBlockStats(b);
        if (s.assertion_cost >= 0) return; // already done
        s.big_block = true;
        s.assertion_cost = 0;
        s.assumption_cost = 0;
        foreach (Cmd c in b.Cmds) {
          if (c is AssertCmd) {
            double cost = AssertionCost((AssertCmd)c);
            s.assertion_cost += cost;
            assertion_count++;
            assertion_cost += cost;
          } else if (c is AssumeCmd) {
            s.assumption_cost += AssertionCost((AssumeCmd)c);
          }
        }
        foreach (Block! b in Exits(b)) {
          s.virtual_successors.Add(b);
        }
        if (s.virtual_successors.Count == 1) {
          Block next = s.virtual_successors[0];
          BlockStats se = GetBlockStats(next);
          CountAssertions(next);
          if (next.Predecessors.Length > 1 || se.virtual_successors.Count != 1) return;
          s.virtual_successors[0] = se.virtual_successors[0];
          s.assertion_cost += se.assertion_cost;
          s.assumption_cost += se.assumption_cost;
          se.big_block = false;
        }
      }

      Dictionary<Block!,bool>! ComputeReachableNodes(Block! b)
      {
        BlockStats s = GetBlockStats(b);
        if (s.reachable_blocks != null) {
          return s.reachable_blocks;
        }
        Dictionary<Block!, bool> blocks = new Dictionary<Block!, bool>();
        s.reachable_blocks = blocks;
        blocks[b] = true;
        foreach (Block! succ in Exits(b)) {
          foreach (Block! r in ComputeReachableNodes(succ).Keys) {
            blocks[r] = true;
          }
        }
        return blocks;
      }

      double ProverCost(double vc_cost)
      {
        return vc_cost * vc_cost;
      }

      void ComputeBestSplit()
      {
        if (score_computed) return;
        score_computed = true;

        assertion_count = 0;
        
        foreach (Block! b in blocks) {
          CountAssertions(b);
        }

        foreach (Block! b in blocks) {
          BlockStats bs = GetBlockStats(b);
          if (bs.big_block) {
            big_blocks.Add(b);
            foreach (Block! ch in bs.virtual_successors) {
              BlockStats chs = GetBlockStats(ch);
              if (!chs.big_block) {
                Console.WriteLine("non-big {0} accessed from {1}", ch, b);
                DumpDot(-1);
                assert false;
              }
              chs.virtual_predecesors.Add(b);
            }
          }
        }

        assumized_branches.Clear();
        total_cost = ProverCost(DoComputeScore(false));

        score = double.PositiveInfinity;
        Block? best_split = null;
        List<Block!>! saved_branches = new List<Block!>();

        foreach (Block! b in big_blocks) {
          GotoCmd gt = b.TransferCmd as GotoCmd;
          if (gt == null) continue;
          BlockSeq targ = (!)gt.labelTargets;
          if (targ.Length < 2) continue;
          // caution, we only consider two first exits

          double left0, right0, left1, right1;
          split_block = b;

          assumized_branches.Clear();
          assumized_branches.Add((!)targ[0]);
          left0 = DoComputeScore(true);
          right0 = DoComputeScore(false);

          assumized_branches.Clear();
          for (int idx = 1; idx < targ.Length; idx++) {
            assumized_branches.Add((!)targ[idx]);
          }
          left1 = DoComputeScore(true);
          right1 = DoComputeScore(false);

          double current_score = ProverCost(left1) + ProverCost(right1);
          double other_score = ProverCost(left0) + ProverCost(right0);

          if (other_score < current_score) {
            current_score = other_score;
            assumized_branches.Clear();
            assumized_branches.Add((!)targ[0]);
          }

          if (current_score < score) {
            score = current_score;
            best_split = split_block;
            saved_branches.Clear();
            saved_branches.AddRange(assumized_branches);
          }
        }

        if (CommandLineOptions.Clo.VcsPathSplitMult * score > total_cost) {
          split_block = null;
          score = -1;
        } else {
          assumized_branches = saved_branches;
          split_block = best_split;
        }
      }

      void UpdateIncommingPaths(BlockStats! s)
      {
        if (s.incomming_paths < 0.0) {
          int count = 0;
          s.incomming_paths = 0.0;
          if (!keep_at_all.ContainsKey(s.block)) return;
          foreach (Block! b in s.virtual_predecesors) {
            BlockStats! ch = GetBlockStats(b);
            UpdateIncommingPaths(ch);
            if (ch.incomming_paths > 0.0) {
              s.incomming_paths += ch.incomming_paths;
              count++;
            }
          }
          if (count > 1) {
            s.incomming_paths *= CommandLineOptions.Clo.VcsPathJoinMult;
          }
        }
      }

      void ComputeBlockSetsHelper(Block! b, bool allow_small)
      {
        if (keep_at_all.ContainsKey(b)) return;
        keep_at_all[b] = true;

        if (allow_small) {
          foreach (Block! ch in Exits(b)) {
            if (b == split_block && assumized_branches.Contains(ch)) continue;
            ComputeBlockSetsHelper(ch, allow_small);
          }
        } else {
          foreach (Block! ch in GetBlockStats(b).virtual_successors) {
            if (b == split_block && assumized_branches.Contains(ch)) continue;
            ComputeBlockSetsHelper(ch, allow_small);
          }
        }
      }

      void ComputeBlockSets(bool allow_small)
      {
        protected_from_assert_to_assume.Clear();
        keep_at_all.Clear();

        Debug.Assert(split_block == null || GetBlockStats(split_block).big_block);
        Debug.Assert(GetBlockStats(blocks[0]).big_block);

        if (assert_to_assume) {
          foreach (Block! b in allow_small ? blocks : big_blocks) {
            if (ComputeReachableNodes(b).ContainsKey((!)split_block)) {
              keep_at_all[b] = true;
            }
          }

          foreach (Block! b in assumized_branches) {
            foreach (Block! r in ComputeReachableNodes(b).Keys) {
              if (allow_small || GetBlockStats(r).big_block) {
                keep_at_all[r] = true;
                protected_from_assert_to_assume[r] = true;
              }
            }
          }
        } else {
          ComputeBlockSetsHelper(blocks[0], allow_small);
        }
      }

      bool ShouldAssumize(Block! b)
      {
         return assert_to_assume && !protected_from_assert_to_assume.ContainsKey(b);
      }

      double DoComputeScore(bool aa)
      {
        assert_to_assume = aa;
        ComputeBlockSets(false);

        foreach (Block! b in big_blocks) {
          GetBlockStats(b).incomming_paths = -1.0;
        }

        GetBlockStats(blocks[0]).incomming_paths = 1.0;

        double cost = 0.0;
        foreach (Block! b in big_blocks) {
          if (keep_at_all.ContainsKey(b)) {
            BlockStats s = GetBlockStats(b);
            UpdateIncommingPaths(s);
            double local = s.assertion_cost;
            if (ShouldAssumize(b)) {
              local = (s.assertion_cost + s.assumption_cost) * CommandLineOptions.Clo.VcsAssumeMult;
            } else {
              local = s.assumption_cost * CommandLineOptions.Clo.VcsAssumeMult + s.assertion_cost;
            }
            local = local + local * s.incomming_paths * CommandLineOptions.Clo.VcsPathCostMult;
            cost += local;
          }
        }
        
        return cost;
      }

      CmdSeq! SliceCmds(Block! b)
      {
        CmdSeq! seq = b.Cmds;
        if (!doing_slice && !ShouldAssumize(b)) return seq;
        CmdSeq! res = new CmdSeq();
        foreach (Cmd! c in seq) {
          AssertCmd a = c as AssertCmd;
          Cmd! the_new = c;
          bool swap = false;
          if (a != null) {
            if (doing_slice) {
              double cost = AssertionCost(a);
              bool first = (slice_limit - cost) >= 0 || slice_initial_limit == slice_limit;
              slice_limit -= cost;
              swap = slice_pos == first;
            } else if (assert_to_assume) {
              swap = true;
            } else {
              assert false;
            }

            if (swap) {
              the_new = AssertTurnedIntoAssume(a);
            }
          }
          res.Add(the_new);
        }
        return res;
      }

      Block! CloneBlock(Block! b)
      {
        Block res;
        if (copies.TryGetValue(b, out res)) {
          return (!)res;
        }
        res = new Block(b.tok, b.Label, SliceCmds(b), b.TransferCmd);
        GotoCmd gt = b.TransferCmd as GotoCmd;
        copies[b] = res;
        if (gt != null) {
          GotoCmd newGoto = new GotoCmd(gt.tok, new StringSeq(), new BlockSeq());
          res.TransferCmd = newGoto;
          int pos = 0;
          foreach (Block! ch in (!)gt.labelTargets) {
            assert doing_slice || 
                   (!assert_to_assume ==> (keep_at_all.ContainsKey(ch) || assumized_branches.Contains(ch)));
            if (doing_slice || 
                ((b != split_block || assumized_branches.Contains(ch) == assert_to_assume) &&
                 keep_at_all.ContainsKey(ch))) {
              newGoto.AddTarget(CloneBlock(ch));
            }
            pos++;
          }
        }
        return res;
      }

      Split! DoSplit()
      {
        copies.Clear();
        CloneBlock(blocks[0]);
        List<Block!> newBlocks = new List<Block!>();
        Hashtable newGotoCmdOrigins = new Hashtable();
        foreach (Block! b in blocks) {
          Block tmp;
          if (copies.TryGetValue(b, out tmp)) {
            newBlocks.Add((!)tmp);
            if (gotoCmdOrigins.ContainsKey(b)) {
              newGotoCmdOrigins[tmp] = gotoCmdOrigins[b];
            }

            foreach (Block! p in b.Predecessors) {
              Block tmp2;
              if (copies.TryGetValue(p, out tmp2)) {
                tmp.Predecessors.Add(tmp2);
              }
            }
          }
        }

        return new Split(newBlocks, newGotoCmdOrigins, parent, impl);
      }

      Split! SplitAt(int idx)
      {
        assert_to_assume = idx == 0;
        doing_slice = false;
        ComputeBlockSets(true);

        return DoSplit();
      }

      Split! SliceAsserts(double limit, bool pos)
      {
        slice_pos = pos;
        slice_limit = limit;
        slice_initial_limit = limit;
        doing_slice = true;
        Split! r = DoSplit();

        /*
        Console.WriteLine("split {0} / {1} -->", limit, pos);
        List<Block!> tmp = impl.Blocks;
        impl.Blocks = r.blocks;
        EmitImpl(impl, false);
        impl.Blocks = tmp;
        */

        return r;
      }

      void Print()
      {
        List<Block!> tmp = impl.Blocks;
        impl.Blocks = blocks;
        EmitImpl(impl, false);
        impl.Blocks = tmp;
      }

      public Counterexample! ToCounterexample()
      {
        BlockSeq trace = new BlockSeq();
        foreach (Block! b in blocks) {
          trace.Add(b);
        }
        foreach (Block! b in blocks) {
          foreach (Cmd! c in b.Cmds) {
            if (c is AssertCmd) {
              return AssertCmdToCounterexample((AssertCmd)c, (!)b.TransferCmd, trace, null, new Dictionary<Incarnation, Absy!>());
            }
          }
        }
        assume false;
      }

      public static List<Split!>! DoSplit(Split! initial, double max_cost, int max)
      {
        List<Split!> res = new List<Split!>();
        res.Add(initial);

        while (res.Count < max) {
          Split best = null;
          int best_idx = 0, pos = 0;
          foreach (Split! s in res) {
            s.ComputeBestSplit(); // TODO check total_cost first
            if (s.total_cost > max_cost && 
                (best == null || best.total_cost < s.total_cost) &&
                (s.assertion_count > 1 || s.split_block != null)) {
              best = s;
              best_idx = pos;
            }
            pos++;
          }

          if (best == null) break; // no split found

          Split! s0, s1;

          bool split_stats = CommandLineOptions.Clo.TraceVerify;

          if (split_stats) {
            Console.WriteLine("{0} {1} -->", best.split_block == null ? "SLICE" : ("SPLIT@" + best.split_block.Label), best.Stats);
            if (best.split_block != null) {
              GotoCmd g = best.split_block.TransferCmd as GotoCmd;
              if (g != null) {
                Console.Write("    exits: ");
                foreach (Block! b in (!)g.labelTargets) {
                  Console.Write("{0} ", b.Label);
                }
                Console.WriteLine("");
                Console.Write("    assumized: ");
                foreach (Block! b in best.assumized_branches) {
                  Console.Write("{0} ", b.Label);
                }
                Console.WriteLine("");
              }
            }
          }

          if (best.split_block != null) {
            s0 = best.SplitAt(0);
            s1 = best.SplitAt(1);
          } else {
            best.split_block = null;
            s0 = best.SliceAsserts(best.assertion_cost / 2, true);
            s1 = best.SliceAsserts(best.assertion_cost / 2, false);
          }

          if (true) {
            List<Block!> ss = new List<Block!>();
            ss.Add(s0.blocks[0]);
            ss.Add(s1.blocks[0]);
            try {
              best.SoundnessCheck(new Dictionary<PureCollections.Tuple!, bool>(), best.blocks[0], ss);
            } catch (System.Exception e) {
              Console.WriteLine(e);
              best.DumpDot(-1);
              s0.DumpDot(-2);
              s1.DumpDot(-3);
              assert false;
            }
          }

          if (split_stats) {
            s0.ComputeBestSplit();
            s1.ComputeBestSplit();
            Console.WriteLine("    --> {0}", s0.Stats);
            Console.WriteLine("    --> {0}", s1.Stats);
          }

          if (CommandLineOptions.Clo.TraceVerify) {
            best.Print();
          }

          res[best_idx] = s0;
          res.Add(s1);
        }

        return res;
      }

      public Checker! Checker 
      {
        get {
          assert checker != null;
          return checker;
        }
      }

      public WaitHandle ProverDone
      {
        get { 
          assert checker != null;
          return checker.ProverDone;
        }
      }

      public void ReadOutcome(ref Outcome cur_outcome, out bool prover_failed) 
        throws UnexpectedProverOutputException;
      {
        ProverInterface.Outcome outcome = ((!)checker).ReadOutcome();

        if (CommandLineOptions.Clo.Trace && splitNo >= 0) {
          System.Console.WriteLine("      --> split #{0} done,  [{1} s] {2}", splitNo, checker.ProverRunTime.TotalSeconds, outcome);
        }

        if (CommandLineOptions.Clo.VcsDumpSplits) {
          DumpDot(splitNo);
        }

        prover_failed = false;

        switch (outcome) {
          case ProverInterface.Outcome.Valid:
            return;
          case ProverInterface.Outcome.Invalid:
            cur_outcome = Outcome.Errors;
            return;
          case ProverInterface.Outcome.OutOfMemory:
            prover_failed = true;
            if (cur_outcome != Outcome.Errors && cur_outcome != Outcome.Inconclusive)
              cur_outcome = Outcome.OutOfMemory;
            return;
          case ProverInterface.Outcome.TimeOut:
            prover_failed = true;
            if (cur_outcome != Outcome.Errors && cur_outcome != Outcome.Inconclusive)
              cur_outcome = Outcome.TimedOut;
            return;
          case ProverInterface.Outcome.Undetermined:
            prover_failed = true;
            if (cur_outcome != Outcome.Errors)
              cur_outcome = Outcome.Inconclusive;
            return;
          default:
            assert false;
        }
      }

      public void BeginCheck(VerifierCallback! callback, int no, int timeout) 
      {
        splitNo = no;

        impl.Blocks = blocks;

        checker = parent.FindCheckerFor(impl, timeout);

        Hashtable/*<int, Absy!>*/! label2absy;
        VCExpr! vc = parent.GenerateVC(impl, out label2absy, checker);
        
        if (CommandLineOptions.Clo.vcVariety == CommandLineOptions.VCVariety.Local) {
          reporter = new ErrorReporterLocal(gotoCmdOrigins, label2absy, impl.Blocks, parent.incarnationOriginMap, callback);
        } else {
          reporter = new ErrorReporter(gotoCmdOrigins, label2absy, impl.Blocks, parent.incarnationOriginMap, callback);
        }
        
        if (CommandLineOptions.Clo.TraceVerify && no >= 0) 
        {
          Console.WriteLine("-- after split #{0}", no);
          Print();
        }

        string! desc = (!) impl.Name;
        if (no >= 0)
          desc += "_split" + no;
        checker.BeginCheck(desc, vc, reporter);

      }

      private void SoundnessCheck(Dictionary<PureCollections.Tuple!, bool>! cache, Block! orig, List<Block!>! copies)
      {
        {
          PureCollections.Tuple t = new PureCollections.Tuple(new PureCollections.Capacity(1 + copies.Count));
          int i = 0;
          t[i++] = orig;
          foreach (Block! b in copies) {
            t[i++] = b;
          }
          if (cache.ContainsKey(t)) { return; }
          cache[t] = true;
        }

        for (int i = 0; i < orig.Cmds.Length; ++i) {
          Cmd cmd = orig.Cmds[i];
          if (cmd is AssertCmd) {
            int found = 0;
            foreach (Block! c in copies) {
              if (c.Cmds[i] == cmd) {
                found++;
              }
            }
            if (found == 0) {
              throw new System.Exception(string.Format("missing assertion: {0}({1})", cmd.tok.filename, cmd.tok.line));
            }
          }
        }

        foreach (Block! exit in Exits(orig)) {
          List<Block!>! newcopies = new List<Block!>();
          foreach (Block! c in copies) {
            foreach (Block! cexit in Exits(c)) {
              if (cexit.Label == exit.Label) {
                newcopies.Add(cexit);
              }
            }
          }
          if (newcopies.Count == 0) {
            throw new System.Exception("missing exit " + exit.Label);
          }
          SoundnessCheck(cache, exit, newcopies);
        }
      }
    }
    #endregion


    protected VCExpr! GenerateVC(Implementation! impl, out Hashtable/*<int, Absy!>*/! label2absy, Checker! ch)
    {
      TypecheckingContext tc = new TypecheckingContext(null);
      impl.Typecheck(tc);

      label2absy = new Hashtable/*<int, Absy!>*/();
      VCExpr! vc;
      switch (CommandLineOptions.Clo.vcVariety) {
      case CommandLineOptions.VCVariety.Structured:
        vc = VCViaStructuredProgram(impl, label2absy, ch.TheoremProver.Context);
        break;
      case CommandLineOptions.VCVariety.Block:
        vc = FlatBlockVC(impl, label2absy, false, false, false, ch.TheoremProver.Context);
        break;
      case CommandLineOptions.VCVariety.BlockReach:
        vc = FlatBlockVC(impl, label2absy, false, true, false, ch.TheoremProver.Context);
        break;
      case CommandLineOptions.VCVariety.Local:
        vc = FlatBlockVC(impl, label2absy, true, false, false, ch.TheoremProver.Context);
        break;
      case CommandLineOptions.VCVariety.BlockNested:
        vc = NestedBlockVC(impl, label2absy, false, ch.TheoremProver.Context);
        break;
      case CommandLineOptions.VCVariety.BlockNestedReach:
        vc = NestedBlockVC(impl, label2absy, true, ch.TheoremProver.Context);
        break;
      case CommandLineOptions.VCVariety.Dag:
        if (((!)CommandLineOptions.Clo.TheProverFactory).SupportsDags) {
          vc = DagVC((!)impl.Blocks[0], label2absy, new Hashtable/*<Block, VCExpr!>*/(), ch.TheoremProver.Context);
        } else {
          vc = LetVC((!)impl.Blocks[0], label2absy, ch.TheoremProver.Context);
        }
        break;
      case CommandLineOptions.VCVariety.Doomed:
        vc = FlatBlockVC(impl, label2absy, false, false, true, ch.TheoremProver.Context);
        break;
      default:
        assert false;  // unexpected enumeration value
      }
      return vc;
    }

    void CheckIntAttributeOnImpl(Implementation! impl, string! name, ref int val)
    {
      if (!((!)impl.Proc).CheckIntAttribute(name, ref val) || !impl.CheckIntAttribute(name, ref val)) {
        Console.WriteLine("ignoring ill-formed {:{0} ...} attribute on {1}, parameter should be an int", name, impl.Name);
      }
    }

    
    public override Outcome VerifyImplementation(Implementation! impl, Program! program, VerifierCallback! callback)
      throws UnexpectedProverOutputException;
    {
      if (impl.SkipVerification) {
        return Outcome.Inconclusive; // not sure about this one
      } 

      callback.OnProgress("VCgen", 0, 0, 0.0);

      ConvertCFG2DAG(impl, program);

      SmokeTester smoke_tester = null;
      if (CommandLineOptions.Clo.SoundnessSmokeTest) {
        smoke_tester = new SmokeTester(this, impl, program, callback);
        smoke_tester.Copy();
      }

      Hashtable/*TransferCmd->ReturnCmd*/ gotoCmdOrigins = PassifyImpl(impl, program);

      double max_vc_cost = CommandLineOptions.Clo.VcsMaxCost;
      int tmp_max_vc_cost = -1, max_splits = CommandLineOptions.Clo.VcsMaxSplits, 
          max_kg_splits = CommandLineOptions.Clo.VcsMaxKeepGoingSplits;
      CheckIntAttributeOnImpl(impl, "vcs_max_cost", ref tmp_max_vc_cost);
      CheckIntAttributeOnImpl(impl, "vcs_max_splits", ref max_splits);
      CheckIntAttributeOnImpl(impl, "vcs_max_keep_going_splits", ref max_kg_splits);
      if (tmp_max_vc_cost >= 0) { 
        max_vc_cost = tmp_max_vc_cost; 
      }

      Outcome outcome = Outcome.Correct;

      int cores = CommandLineOptions.Clo.VcsCores;
      Stack<Split!> work = new Stack<Split!>();
      List<Split!> currently_running = new List<Split!>();
      ResetPredecessors(impl.Blocks);
      work.Push(new Split(impl.Blocks, gotoCmdOrigins, this, impl));

      bool keep_going = max_kg_splits > 1;
      int total = 0;
      int no = max_splits == 1 && !keep_going ? -1 : 0;
      bool first_round = true;
      bool do_splitting = keep_going || max_splits > 1; 
      double remaining_cost = 0.0, proven_cost = 0.0;

      if (do_splitting) {
        remaining_cost = work.Peek().Cost;
      }

      while (work.Count > 0 || currently_running.Count > 0) {
        bool prover_failed = false;
        Split! s;

        if (work.Count > 0 && currently_running.Count < cores) {
          s = work.Pop();

          if (first_round && max_splits > 1) {
            prover_failed = true;
            remaining_cost -= s.Cost;
          } else {
            if (CommandLineOptions.Clo.Trace && no >= 0) {
              System.Console.WriteLine("    checking split {1}/{2}, {3:0.00}%, {0} ...", 
                                   s.Stats, no + 1, total, 100 * proven_cost / (proven_cost + remaining_cost));
            }
            callback.OnProgress("VCprove", no < 0 ? 0 : no, total, proven_cost / (remaining_cost + proven_cost));

            s.BeginCheck(callback, no, 
              (keep_going && s.LastChance) ? CommandLineOptions.Clo.VcsFinalAssertTimeout :
                keep_going ? CommandLineOptions.Clo.VcsKeepGoingTimeout :
                             CommandLineOptions.Clo.ProverKillTime);

            no++;

            currently_running.Add(s);
          }
        } else {
          WaitHandle[] handles = new WaitHandle[currently_running.Count];
          for (int i = 0; i < currently_running.Count; ++i) {
            handles[i] = currently_running[i].ProverDone;
          }
          int index = WaitHandle.WaitAny(handles);
          s = currently_running[index];
          currently_running.RemoveAt(index);

          if (do_splitting) {
            remaining_cost -= s.Cost;
          }

          s.ReadOutcome(ref outcome, out prover_failed);

          if (do_splitting) {
            if (prover_failed) {
              // even if the prover fails, we have learned something, i.e., it is 
              // annoying to watch Boogie say Timeout, 0.00% a couple of times
              proven_cost += s.Cost / 100;
            } else {
              proven_cost += s.Cost;
            }
          }
          callback.OnProgress("VCprove", no < 0 ? 0 : no, total, proven_cost / (remaining_cost + proven_cost));

          if (prover_failed && !first_round && s.LastChance) {
            string! msg = "some timeout";
            if (s.reporter != null && s.reporter.resourceExceededMessage != null) {
              msg = s.reporter.resourceExceededMessage;
            }
            callback.OnCounterexample(s.ToCounterexample(), msg);
            outcome = Outcome.Errors;
            break;
          }

          assert prover_failed || outcome == Outcome.Correct || outcome == Outcome.Errors;
        }

        if (prover_failed) { 
          int splits = first_round && max_splits > 1 ? max_splits : max_kg_splits;

          if (splits > 1) {
            List<Split!> tmp = Split.DoSplit(s, max_vc_cost, splits);
            max_vc_cost = 1.0; // for future
            first_round = false;
            //tmp.Sort(new Comparison<Split!>(Split.Compare));
            foreach (Split! a in tmp) {
              work.Push(a);
              total++;
              remaining_cost += a.Cost;
            }
            if (outcome != Outcome.Errors) {
              outcome = Outcome.Correct;
            }
          } else {
            assert outcome != Outcome.Correct;
            if (outcome == Outcome.TimedOut) {
              string! msg = "some timeout";
              if (s.reporter != null && s.reporter.resourceExceededMessage != null) {
                msg = s.reporter.resourceExceededMessage;
              }
              callback.OnTimeout(msg);
            } else if (outcome == Outcome.OutOfMemory) {
              string! msg = "out of memory";
              if (s.reporter != null && s.reporter.resourceExceededMessage != null) {
                msg = s.reporter.resourceExceededMessage;
              }
              callback.OnOutOfMemory(msg);
            }

            break;
          }
        }
      }

      if (outcome == Outcome.Correct && smoke_tester != null) {
        smoke_tester.Test();
      }

      callback.OnProgress("done", 0, 0, 1.0);

      return outcome;
    }

    public class ErrorReporter : ProverInterface.ErrorHandler {
      Hashtable/*TransferCmd->ReturnCmd*/! gotoCmdOrigins;
      Hashtable/*<int, Absy!>*/! label2absy;
      List<Block!>! blocks;
      protected Dictionary<Incarnation, Absy!>! incarnationOriginMap;
      protected VerifierCallback! callback;
      internal string? resourceExceededMessage;
      static System.IO.TextWriter? modelWriter;
      
      public static TextWriter! ModelWriter {
        get {
          if (ErrorReporter.modelWriter == null)
            ErrorReporter.modelWriter = CommandLineOptions.Clo.PrintErrorModelFile == null ? Console.Out : new StreamWriter(CommandLineOptions.Clo.PrintErrorModelFile, false);
          return ErrorReporter.modelWriter;
        }
      } 
      
      public ErrorReporter(Hashtable/*TransferCmd->ReturnCmd*/! gotoCmdOrigins,
          Hashtable/*<int, Absy!>*/! label2absy,
          List<Block!>! blocks,
          Dictionary<Incarnation, Absy!>! incarnationOriginMap,
          VerifierCallback! callback)
      {
        this.gotoCmdOrigins = gotoCmdOrigins;
        this.label2absy = label2absy;
        this.blocks = blocks;
        this.incarnationOriginMap = incarnationOriginMap;
        this.callback = callback;
        // base();
      }
      
      public override void OnModel(IList<string!>! labels, ErrorModel errModel) {
        if (CommandLineOptions.Clo.PrintErrorModel >= 1 && errModel != null) {
            errModel.Print(ErrorReporter.ModelWriter);
            ErrorReporter.ModelWriter.Flush();
        }
        Hashtable traceNodes = new Hashtable();
        foreach (string! s in labels) {
          Absy! absy =Label2Absy(s); 
          if (traceNodes.ContainsKey(absy))
            System.Console.WriteLine("Warning: duplicate label: " + s + " read while tracing nodes");
          else
            traceNodes.Add(absy, null);
        }

        BlockSeq! trace = new BlockSeq();
        Block! entryBlock = (!) this.blocks[0];
        assert traceNodes.Contains(entryBlock);
        trace.Add(entryBlock);

        Counterexample newCounterexample = TraceCounterexample(entryBlock, traceNodes, trace, errModel, incarnationOriginMap);

        if (newCounterexample == null) return;
        
        #region Map passive program errors back to original program errors
        ReturnCounterexample returnExample = newCounterexample as ReturnCounterexample;
        if (returnExample != null)
        {
          foreach (Block! b in returnExample.Trace) {
            assume b.TransferCmd != null;
            ReturnCmd cmd = (ReturnCmd) gotoCmdOrigins[b.TransferCmd];
            if (cmd != null)
            {
              returnExample.FailingReturn = cmd;
              break;
            }
          }
        }
        #endregion
        callback.OnCounterexample(newCounterexample, null);
      }

      public override Absy! Label2Absy(string! label)
      {
        int id = int.Parse(label);
        return (Absy!) label2absy[id];
      }

      public override void OnResourceExceeded(string! msg)
      {
        resourceExceededMessage = msg;
      }
      
      public override void OnProverWarning(string! msg)
      {
        callback.OnWarning(msg);
      }
    }
    
    public class ErrorReporterLocal : ErrorReporter {
      public ErrorReporterLocal(Hashtable/*TransferCmd->ReturnCmd*/! gotoCmdOrigins,
          Hashtable/*<int, Absy!>*/! label2absy,
          List<Block!>! blocks,
          Dictionary<Incarnation, Absy!>! incarnationOriginMap,
          VerifierCallback! callback)
      {
        base(gotoCmdOrigins, label2absy, blocks, incarnationOriginMap, callback); // here for aesthetic purposes
      }

      public override void OnModel(IList<string!>! labels, ErrorModel errModel) {
        // We ignore the error model here for enhanced error message purposes.
        // It is only printed to the command line.
        if (CommandLineOptions.Clo.PrintErrorModel >= 1 && errModel != null) {
          if (CommandLineOptions.Clo.PrintErrorModelFile != null) {
            errModel.Print(ErrorReporter.ModelWriter);
            ErrorReporter.ModelWriter.Flush();
          }
        }
        List<Block!> traceNodes = new List<Block!>();
        List<AssertCmd!> assertNodes = new List<AssertCmd!>();
        foreach (string! s in labels) {
          Absy node = Label2Absy(s);
          if (node is Block) {
            Block b = (Block)node;
            traceNodes.Add(b);
          } else {
            AssertCmd a = (AssertCmd)node;
            assertNodes.Add(a);
          }
        }
        assert assertNodes.Count > 0;
        assert traceNodes.Count == assertNodes.Count;

        foreach (AssertCmd a in assertNodes) {
          // find the corresponding Block (assertNodes.Count is likely to be 1, or small in any case, so just do a linear search here)
          foreach (Block b in traceNodes) {
            if (b.Cmds.Has(a)) {
              BlockSeq trace = new BlockSeq();
              trace.Add(b);
              Counterexample newCounterexample = AssertCmdToCounterexample(a, (!)b.TransferCmd, trace, errModel, incarnationOriginMap);
              callback.OnCounterexample(newCounterexample, null);
              goto NEXT_ASSERT;
            }
          }
          assert false;  // there was no block that contains the assert
          NEXT_ASSERT: {}
        }
      }
    }

    protected void ConvertCFG2DAG(Implementation! impl, Program! program)
    {
      impl.PruneUnreachableBlocks();  // This is needed for VCVariety.BlockNested, and is otherwise just an optimization

      current_impl = impl;
      variable2SequenceNumber = new Hashtable/*Variable -> int*/();
      incarnationOriginMap = new Dictionary<Incarnation, Absy!>();

      #region Debug Tracing
      if (CommandLineOptions.Clo.TraceVerify) 
      {
        Console.WriteLine("original implementation");
        EmitImpl(impl, false);
      }
      #endregion

      #region Debug Tracing
      if (CommandLineOptions.Clo.TraceVerify) 
      {
        Console.WriteLine("after desugaring sugared commands like procedure calls");
        EmitImpl(impl, true);
      }
      #endregion

      ComputePredecessors(impl.Blocks);
      
      #region Convert program CFG into a DAG

      #region Use the graph library to figure out where the (natural) loops are

      #region Create the graph by adding the source node and each edge
      Graph<Block>! g = GraphFromImpl(impl);
      #endregion

      g.ComputeLoops(); // this is the call that does all of the processing
      if (!g.Reducible)
      {
        throw new VCGenException("Irreducible flow graphs are unsupported.");
      }

      #endregion

      #region Cut the backedges, push assert/assume statements from loop header into predecessors, change them all into assume statements at top of loop, introduce havoc statements
      foreach (Block! header in (!) g.Headers)
      {
        IDictionary<Block!,object> backEdgeNodes = new Dictionary<Block!,object>();
        foreach (Block! b in (!) g.BackEdgeNodes(header)) { backEdgeNodes.Add(b, null); }
      
        #region Find the (possibly empty) prefix of assert commands in the header, replace each assert with an assume of the same condition
        CmdSeq prefixOfPredicateCmdsInit = new CmdSeq();
        CmdSeq prefixOfPredicateCmdsMaintained = new CmdSeq();
        for (int i = 0, n = header.Cmds.Length; i < n; i++)
        {
          PredicateCmd a = header.Cmds[i] as PredicateCmd;
          if (a != null)
          {
            if (a is AssertCmd) {
              Bpl.AssertCmd c = (AssertCmd) a;
              Bpl.AssertCmd b = new Bpl.LoopInitAssertCmd(c.tok, c.Expr);
              b.ErrorData = c.ErrorData;
              prefixOfPredicateCmdsInit.Add(b);
              b = new Bpl.LoopInvMaintainedAssertCmd(c.tok, c.Expr);
              b.ErrorData = c.ErrorData;
              prefixOfPredicateCmdsMaintained.Add(b);
              header.Cmds[i] = new AssumeCmd(c.tok,c.Expr);
            } else {
              assert a is AssumeCmd;
              if (Bpl.CommandLineOptions.Clo.AlwaysAssumeFreeLoopInvariants) {
                // Usually, "free" stuff, like free loop invariants (and the assume statements
                // that stand for such loop invariants) are ignored on the checking side.  This
                // command-line option changes that behavior to always assume the conditions.
                prefixOfPredicateCmdsInit.Add(a);
                prefixOfPredicateCmdsMaintained.Add(a);
              }
            }
          }
          else if ( header.Cmds[i] is CommentCmd )
          {
            // ignore
          }
          else
          {
            break; // stop when an assignment statement (or any other non-predicate cmd) is encountered
          }
        }
        #endregion

        #region Copy the prefix of predicate commands into each predecessor. Do this *before* cutting the backedge!!
        for ( int predIndex = 0, n = header.Predecessors.Length; predIndex < n; predIndex++ )
        {
          Block! pred = (!)header.Predecessors[predIndex];
          
          // Create a block between header and pred for the predicate commands if header has more than one successor 
          // or if pred is a back edge node
          GotoCmd gotocmd = pred.TransferCmd as GotoCmd;
          if ((backEdgeNodes.ContainsKey(pred)) || (gotocmd != null && gotocmd.labelNames != null && gotocmd.labelNames.Length > 1))
          {
            Block! newBlock = CreateBlockBetween(predIndex, header);
            impl.Blocks.Add(newBlock);
            
            // if pred is a back edge node, then now newBlock is the back edge node
            if (backEdgeNodes.ContainsKey(pred))
            {
              backEdgeNodes.Remove(pred);
              backEdgeNodes.Add(newBlock,null);
            }
            
            pred = newBlock;
          } 
          // Add the predicate commands
          if (backEdgeNodes.ContainsKey(pred)){
            pred.Cmds.AddRange(prefixOfPredicateCmdsMaintained);
          }
          else {
            pred.Cmds.AddRange(prefixOfPredicateCmdsInit);
          }
        }
        #endregion

        #region Cut the back edge
        foreach (Block! backEdgeNode in (!)backEdgeNodes.Keys)
        {
          Debug.Assert(backEdgeNode.TransferCmd is GotoCmd,"An node was identified as the source for a backedge, but it does not have a goto command.");
          GotoCmd gtc = backEdgeNode.TransferCmd as GotoCmd;
          if (gtc != null && gtc.labelTargets != null && gtc.labelTargets.Length > 1 )
          {
            // then remove the backedge by removing the target block from the list of gotos
            BlockSeq remainingTargets = new BlockSeq();
            StringSeq remainingLabels = new StringSeq();
            assume gtc.labelNames != null;
            for (int i = 0, n = gtc.labelTargets.Length; i < n; i++)
            {
              if ( gtc.labelTargets[i] != header )
              {
                remainingTargets.Add(gtc.labelTargets[i]);
                remainingLabels.Add(gtc.labelNames[i]);
              }
            }
            gtc.labelTargets = remainingTargets;
            gtc.labelNames = remainingLabels;
          }
          else
          {
            // This backedge is the only out-going edge from this node.
            // Add an "assume false" statement to the end of the statements
            // inside of the block and change the goto command to a return command.
            AssumeCmd ac = new AssumeCmd(Token.NoToken,Expr.False);
            backEdgeNode.Cmds.Add(ac);
            backEdgeNode.TransferCmd = new ReturnCmd(Token.NoToken);
          }
          #region Remove the backedge node from the list of predecessor nodes in the header
          BlockSeq newPreds = new BlockSeq();
          foreach ( Block p in header.Predecessors )
          {
            if ( p != backEdgeNode )
              newPreds.Add(p);
          }
          header.Predecessors = newPreds;
          #endregion
        }
        #endregion

        #region Collect all variables that are assigned to in all of the natural loops for which this is the header
        VariableSeq varsToHavoc = new VariableSeq();
        foreach (Block! backEdgeNode in (!) g.BackEdgeNodes(header))
        {
          foreach ( Block! b in g.NaturalLoops(header,backEdgeNode) )
          {
            foreach ( Cmd! c in b.Cmds )
            {
              c.AddAssignedVariables(varsToHavoc);
            }
          }
        }
        IdentifierExprSeq havocExprs = new IdentifierExprSeq();
        foreach ( Variable! v in varsToHavoc )
        {
          IdentifierExpr ie = new IdentifierExpr(Token.NoToken, v);
          if(!havocExprs.Has(ie))
            havocExprs.Add(ie);
        }
        // pass the token of the enclosing loop header to the HavocCmd so we can reconstruct
        // the source location for this later on
        HavocCmd hc = new HavocCmd(header.tok,havocExprs);
        CmdSeq newCmds = new CmdSeq();
        newCmds.Add(hc);
        foreach ( Cmd c in header.Cmds )
        {
          newCmds.Add(c);
        }
        header.Cmds = newCmds;
        #endregion
      }
      #endregion
      #endregion Convert program CFG into a DAG
      
      #region Debug Tracing
      if (CommandLineOptions.Clo.TraceVerify) 
      {
        Console.WriteLine("after conversion into a DAG");
        EmitImpl(impl, true);
      }
      #endregion
    }

    protected Hashtable/*TransferCmd->ReturnCmd*/! PassifyImpl(Implementation! impl, Program! program)
    {
      Hashtable/*TransferCmd->ReturnCmd*/ gotoCmdOrigins = new Hashtable/*TransferCmd->ReturnCmd*/();
      Block/*?*/ exitBlock = GenerateUnifiedExit(impl, gotoCmdOrigins);
      
      #region Debug Tracing
      if (CommandLineOptions.Clo.TraceVerify) 
      {
        Console.WriteLine("after creating a unified exit block");
        EmitImpl(impl, true);
      }
      #endregion

      #region Insert pre- and post-conditions and where clauses as assume and assert statements
      {
        CmdSeq cc = new CmdSeq();
        // where clauses of global variables
        foreach (Declaration d in program.TopLevelDeclarations) {
          GlobalVariable gvar = d as GlobalVariable;
          if (gvar != null && gvar.TypedIdent.WhereExpr != null) {
            Cmd c = new AssumeCmd(gvar.tok, gvar.TypedIdent.WhereExpr);
            cc.Add(c);
          }
        }
        // where clauses of in- and out-parameters
        cc.AddRange(GetParamWhereClauses(impl));
        // where clauses of local variables
        foreach (Variable! lvar in impl.LocVars) {
          if (lvar.TypedIdent.WhereExpr != null) {
            Cmd c = new AssumeCmd(lvar.tok, lvar.TypedIdent.WhereExpr);
            cc.Add(c);
          }
        }

        InjectPreconditions(impl);
        //cc.AddRange(GetPre(impl));

        Block! entryBlock = (!) impl.Blocks[0];
        cc.AddRange(entryBlock.Cmds);
        entryBlock.Cmds = cc;
          
        InjectPostConditions(impl,exitBlock,gotoCmdOrigins);
        //CmdSeq! post = GetPost(impl);
        //exitBlock.Cmds.AddRange(post);
      }
      #endregion
      
      #region Debug Tracing
      if (CommandLineOptions.Clo.TraceVerify) 
      {
        Console.WriteLine("after inserting pre- and post-conditions");
        EmitImpl(impl, true);
      }
      #endregion

      AddBlocksBetween(impl);
      
      #region Debug Tracing
      if (CommandLineOptions.Clo.TraceVerify) 
      {
        Console.WriteLine("after adding empty blocks before all blocks with more than one predecessor");
        EmitImpl(impl, true);
      }
      #endregion
    
      Convert2PassiveCmd(impl);
      
      #region Peep-hole optimizations
      if (CommandLineOptions.Clo.RemoveEmptyBlocks){
        #region Get rid of empty blocks
        {
          Block! entryBlock = (!) impl.Blocks[0];
          RemoveEmptyBlocks(entryBlock);
          impl.PruneUnreachableBlocks();  
        }
        #endregion Get rid of empty blocks
        
        #region Debug Tracing
        if (CommandLineOptions.Clo.TraceVerify) 
        {
          Console.WriteLine("after peep-hole optimizations");
          EmitImpl(impl, true);
        }
        #endregion
      }
      #endregion Peep-hole optimizations

//      #region Constant Folding
//      #endregion
//      #region Debug Tracing
//      if (CommandLineOptions.Clo.TraceVerify) 
//      {
//        Console.WriteLine("after constant folding");
//        EmitImpl(impl, true);
//      }
//      #endregion

      return gotoCmdOrigins;
    }

    static Counterexample TraceCounterexample(Block! b, Hashtable! traceNodes, BlockSeq! trace, ErrorModel errModel, Dictionary<Incarnation, Absy!>! incarnationOriginMap)
    {
      // After translation, all potential errors come from asserts.
      CmdSeq! cmds = b.Cmds;
      TransferCmd! transferCmd = (!)b.TransferCmd;
      for (int i = 0; i < cmds.Length; i++)
      {
        Cmd! cmd = (!) cmds[i];
        
        // Skip if 'cmd' not contained in the trace or not an assert
        if (!(cmd is AssertCmd) || !traceNodes.Contains(cmd))
          continue;

        return AssertCmdToCounterexample((AssertCmd)cmd, transferCmd, trace, errModel, incarnationOriginMap);
      }
      
      GotoCmd gotoCmd = transferCmd as GotoCmd;
      if (gotoCmd != null)
      {
        foreach (Block! bb in (!)gotoCmd.labelTargets)
        {
          if (traceNodes.Contains(bb)){
            trace.Add(bb);
            return TraceCounterexample(bb, traceNodes, trace, errModel, incarnationOriginMap);
          }
        }
      }

      return null;

      // Debug.Fail("Could not find failing node.");
      // throw new Microsoft.Contracts.AssertException();
    }
    
    
    static void /*return printable error!*/ ApplyEnhancedErrorPrintingStrategy (Bpl.Expr! expr, Hashtable /*Variable -> Expr*/! incarnationMap, MiningStrategy errorDataEnhanced, ErrorModel! errModel, Dictionary<Expr!, object>! exprToPrintableValue, List<string!>! relatedInformation, bool printInternalStateDumpOnce, Dictionary<Incarnation, Absy!>! incarnationOriginMap) {
      if (errorDataEnhanced is ListOfMiningStrategies) {
        ListOfMiningStrategies loms = (ListOfMiningStrategies) errorDataEnhanced;
        List<MiningStrategy>! l = loms.msList;
        for (int i = 0; i < l.Count; i++) {
          MiningStrategy ms = l[i];
          if (ms != null) {
            ApplyEnhancedErrorPrintingStrategy(expr, incarnationMap, l[i], errModel, exprToPrintableValue, relatedInformation, false, incarnationOriginMap);
          }
        }
      }
      else if (errorDataEnhanced is EEDTemplate /*EDEverySubExpr*/) {
        EEDTemplate eedT = (EEDTemplate) errorDataEnhanced;
        string reason = eedT.reason;
        List<Bpl.Expr!> listOfExprs = eedT.exprList;
        if (listOfExprs != null) {
          List<string> holeFillers = new List<string>();
          for (int i = 0; i < listOfExprs.Count; i++) {
            bool alreadySet = false;
            foreach (KeyValuePair<Bpl.Expr!, object> kvp in exprToPrintableValue) {
              Bpl.Expr! e = kvp.Key;
              Bpl.Expr! f = listOfExprs[i];
              // the strings are compared instead of the actual expressions because 
              // the expressions might not be identical, but their print-out strings will be
              if (e.ToString() == f.ToString()) {
                object o = kvp.Value;
                if (o != null) {
                  holeFillers.Add(o.ToString());
                  alreadySet = true;
                  break;
                } 
              }
            }
            if (!alreadySet) {
              // no information about that Expression found, so put in <unknown>
              holeFillers.Add("<unknown>");
            }
          }
          reason = FormatReasonString(reason, holeFillers);
        }
        if (reason != null) {
          relatedInformation.Add("(related information): "+reason);
        }
      } else  {
        // define new templates here!
      } 
      
      if (printInternalStateDumpOnce) {
        ComputeAndTreatHeapSuccessions(incarnationMap, errModel, incarnationOriginMap, relatedInformation);

        // default action: print all values!
        foreach (KeyValuePair<Bpl.Expr!, object> kvp in exprToPrintableValue) {
          object o = kvp.Value;
          if (o != null) {
            // We do not want to print LiteralExprs because that gives things like 0 == 0.
            // If both arguments to the string.Format are the same it is also useless, 
            //   as that would print e.g. $a == $a.
            if (!(kvp.Key is LiteralExpr)&& kvp.Key.ToString() != o.ToString()) {
              string boogieExpr;
              // check whether we are handling BPL or SSC input
              if (CommandLineOptions.Clo.RunningBoogieOnSsc) {
                boogieExpr = Helpers.PrettyPrintBplExpr(kvp.Key);
              } else {
                boogieExpr = kvp.Key.ToString();
              }
              relatedInformation.Add("(internal state dump): "+string.Format("{0} == {1}", boogieExpr, o));
            }
          }
        }
      }
    }
    
    static void ComputeAndTreatHeapSuccessions(System.Collections.Hashtable! incarnationMap, ErrorModel! errModel, Dictionary<Incarnation, Absy!>! incarnationOriginMap, List<string!>! relatedInformation) {
      List<int> heapSuccList = ComputeHeapSuccessions(incarnationMap, errModel);
      TreatHeapSuccessions(heapSuccList, incarnationMap, errModel, incarnationOriginMap, relatedInformation);
    }
    
    static List<int> ComputeHeapSuccessions(System.Collections.Hashtable! incarnationMap, ErrorModel! errModel) {
      // find the heap variable
      Variable heap = null;
      ICollection ic = incarnationMap.Keys;
      foreach (object o in ic) {
        if (o is GlobalVariable) {
          GlobalVariable gv = (GlobalVariable) o;
          if (gv.Name == "$Heap") {
            heap = gv;
          }
        }
      }
      List<int> heapIdSuccession = new List<int>();
      if (heap == null) {
        // without knowing the name of the current heap we cannot create a heap succession!
      } else {
        object oHeap = incarnationMap[heap];
        if (oHeap != null) {
          string currentHeap = oHeap.ToString();
          int currentHeapId;
          if (errModel.identifierToPartition.TryGetValue(currentHeap, out currentHeapId)) {
            while (currentHeapId != -1) {
              if (!heapIdSuccession.Contains(currentHeapId)) {
                heapIdSuccession.Add(currentHeapId);
                currentHeapId = ComputePredecessorHeapId(currentHeapId, errModel);
              } else {
                // looping behavior, just stop here and do not add this value (again!)
                break;
              }
            }
          }
        }
      }
      if (heapIdSuccession.Count > 0) {
        int heapId = heapIdSuccession[heapIdSuccession.Count-1];
        List<string!> strl = errModel.partitionToIdentifiers[heapId];
        if (strl != null && strl.Contains("$Heap")) {
          // we have a proper succession of heaps that starts with $Heap
          return heapIdSuccession;
        } else {
          // no proper heap succession, not starting with $Heap!
          return null;
        }
      } else {
        // no heap succession found because either the $Heap does not have a current incarnation
        // or because (unlikely!) the model is somehow messed up
        return null;
      }
    }
    
    static int ComputePredecessorHeapId(int id, ErrorModel! errModel) {
      //check "$HeapSucc" and "store2" functions:
      List<int> heapSuccPredIdList = new List<int>();
      List<List<int>> heapSuccFunc;
      errModel.definedFunctions.TryGetValue("$HeapSucc", out heapSuccFunc);
      if (heapSuccFunc != null) {
        foreach (List<int> heapSuccFuncDef in heapSuccFunc) {
          // do not look at the else case of the function def, so check .Count
          if (heapSuccFuncDef != null && heapSuccFuncDef.Count == 3 && heapSuccFuncDef[1] == id) {
            // make sure each predecessor is put into the list at most once
            if (!heapSuccPredIdList.Contains(heapSuccFuncDef[0])) {
              heapSuccPredIdList.Add(heapSuccFuncDef[0]);
            }
          }
        }
      }
      List<int> store2PredIdList = new List<int>();;
      List<List<int>> store2Func;
      errModel.definedFunctions.TryGetValue("store2", out store2Func);
      if (store2Func != null) {
        foreach (List<int> store2FuncDef in store2Func) {
          // do not look at the else case of the function def, so check .Count
          if (store2FuncDef != null && store2FuncDef.Count == 5 && store2FuncDef[4] == id) {
            // make sure each predecessor is put into the list at most once
            if (!store2PredIdList.Contains(store2FuncDef[0])) {
              store2PredIdList.Add(store2FuncDef[0]);
            }
          }
        }
      }
      if (heapSuccPredIdList.Count + store2PredIdList.Count > 0) {
        if (store2PredIdList.Count == 1) {
          return store2PredIdList[0];
        } else if (store2PredIdList.Count == 0) {
          if (heapSuccPredIdList.Count == 1) {
            return heapSuccPredIdList[0];
          } else { //(heapSuccPredIdList.Count > 1)
            if (heapSuccPredIdList.Count == 2) {
              // if one of the 2 is a self-loop, take the other!
              if (heapSuccPredIdList[0] == id) {
                return heapSuccPredIdList[1];
              } else if (heapSuccPredIdList[1] == id) {
                return heapSuccPredIdList[0];
              } else {
                //no self-loop, two different predecessors, cannot choose
                return -1;
              }
            } else {
              // at least 3 different predecessors available, one of them could be a self-loop, but 
              // we cannot choose between the other 2 (or more) candidates
              return -1;
            }
          } 
        } else { 
          // more than one result in the succession coming from store2, no way 
          // to decide which is right, end here
          return -1;
        }
      } else {
        // no predecessor found
        return -1;
      }
    }
    
    static void TreatHeapSuccessions (List<int> heapSuccessionList, System.Collections.Hashtable! incarnationMap, ErrorModel! errModel, Dictionary<Incarnation, Absy!>! incarnationOriginMap, List<string!>! relatedInformation) {
      if (heapSuccessionList == null) {
        // empty list of heap successions, nothing we can do!
        return;
      }
      // primarily look for $o and $f (with skolem-id stuff) and then look where they were last changed!
      // find the o and f variables
      Variable dollarO = null;
      Variable dollarF = null;
      ICollection ic = incarnationMap.Keys;
      foreach (object o in ic) {
        if (o is BoundVariable) {
          BoundVariable bv = (BoundVariable) o;
          if (bv.Name == "$o") {
            dollarO = bv;
          }
          else if (bv.Name == "$f") {
            dollarF = bv;
          }
        }
      }
      if (dollarO == null || dollarF == null) {
        // without knowing the name of the current incarnation of $Heap, $o and $f we don't do anything here
      } else {
        object objO = incarnationMap[dollarO];
        object objF = incarnationMap[dollarF];
        if (objO != null && objF != null) {
          int zidO = errModel.identifierToPartition[objO.ToString()];
          int zidF = errModel.identifierToPartition[objF.ToString()];

          List<List<int>> select2Func = null;
          if (errModel.definedFunctions.TryGetValue("select2", out select2Func) && select2Func != null) {
            // check for all changes to $o.$f!
            List<int> heapsChangedOFZid = new List<int>();
            int oldValueZid = -1;
            int newValueZid = -1;
            
            for (int i = 0; i < heapSuccessionList.Count; i++) {
              bool foundValue = false;
              foreach (List<int> f in select2Func) {
                if (f != null && f.Count == 4 && f[0] == heapSuccessionList[i] && f[1] == zidO && f[2] == zidF) {
                  newValueZid = f[3];
                  foundValue = true;
                  break;
                }
              }
              if (!foundValue) {
                //    get default of the function once Leo&Nikolaj have changed it so the default is type correct
                //    for now treat it as a -1 !
                // the last element of select2Func is the else case, it has only 1 element, so grab that:
                // newValueZid = (select2Func[select2Func.Count-1])[0];
                newValueZid = -1;
              }
              
              if (oldValueZid != newValueZid) {
                // there was a change here, record that in the list:
                if (oldValueZid != -1) {
                  // don't record a change at the "initial" location, which refers to the $Heap in
                  // its current incarnation, and is marked by the oldValueZid being uninitialized
                  heapsChangedOFZid.Add(heapSuccessionList[i-1]);
                }
                oldValueZid = newValueZid;
              } 
            }
            
            foreach (int id in heapsChangedOFZid) {
              //get the heap name out of the errModel for this zid:
              List<string!> l = errModel.partitionToIdentifiers[id];
              List<string!> heaps = new List<string!>();
              if (l!=null) {
                foreach (string s in l) {
                  if (s.StartsWith("$Heap")) {
                    heaps.Add(s);
                  }
                }
              }
              // easy case first:
              if (heaps.Count == 1) {
                string heapName = heaps[0];
                // we have a string with the name of the heap, but we need to get the 
                // source location out of a map that uses Incarnations!
                
                ICollection incOrgMKeys = incarnationOriginMap.Keys;
                foreach (Incarnation inc in incOrgMKeys) {
                  if (inc!= null) {
                    if (inc.Name == heapName) {
                      Absy source = null;
                      incarnationOriginMap.TryGetValue(inc, out source);
                      if (source != null) {
                        if (source is Block) {
                          Block b = (Block) source;
                          string fileName = b.tok.filename;
                          if (fileName != null) {
                            fileName = fileName.Substring(fileName.LastIndexOf('\\') + 1);
                          }
                          relatedInformation.Add("(related information): Changed $o.$f here: " + fileName + "(" + b.tok.line + "," + b.tok.col + ")");
                        } else if (source is Cmd) {
                          Cmd c = (Cmd) source;
                          string fileName = c.tok.filename;
                          if (fileName != null) {
                            fileName = fileName.Substring(fileName.LastIndexOf('\\') + 1);
                          }
                          relatedInformation.Add("(related information) Changed $o.$f here: " + fileName + "(" + c.tok.line + "," + c.tok.col + ")");
                        } else {
                          assert false;
                        }
                      }
                    }
                  }
                }
              } else {
                // more involved! best use some of the above code and try to synchronize joint parts
                // here there is more than one "$Heap@i" in the partition, check if they all agree on one
                // source location or maybe if some of them are joins (i.e. blocks) that should be ignored
              }
              
            }
          }          
        }
      }
    }
    
    static string FormatReasonString (string reason, List<string> holeFillers) {
      if (holeFillers != null) {
        // in case all elements of holeFillers are "<unknown>" we can not say anything useful
        // so just say nothing and return null
        bool allUnknown = true;
        foreach (string s in holeFillers) {
          if (s != "<unknown>") {
            allUnknown = false;
            break;
          }
        }
        if (allUnknown) {
          return null;
        }
        string[] a = holeFillers.ToArray();
        reason = string.Format(reason, a);
      }
      return reason;
    }
    
    static object ValueFromZID (ErrorModel! errModel, int id) {
      return ValueFromZID(errModel, id, null);
    }

    static object ValueFromZID (ErrorModel! errModel, int id, string searchForAlternate) {
      object o = errModel.partitionToValue[id];
      if (o != null) {
        return o;
      } else {
        // more elaborate scheme to find something better, as in: look at the identifiers that
        // this partition maps to, or similar things!
        
        //treatment for 'null':
        int idForNull = -1;
        if (errModel.valueToPartition.TryGetValue("nullObject", out idForNull) && idForNull == id) {
          return "nullObject";
        }
        
        string returnStr = null;
        
        // "good identifiers" if there is no value found are 'unique consts' or 
        // '$in' parameters; '$in' parameters are treated, unclear how to get 'unique const' info
        List<string!> identifiers = errModel.partitionToIdentifiers[id];
        if (identifiers != null) {
          foreach (string s in identifiers)  {
            //$in parameters are (more) interesting than other identifiers, return the
            // first one found
            if (s.EndsWith("$in")) {
              returnStr = s;
              break;
            }
          }
        }
        
        // try to get mappings from one identifier to another if there are exactly 
        // two identifiers in the partition, where one of them is the identifier for which 
        // we search for alternate encodings (third parameter of the method) [or an incarnation
        // of such an identifier]
        if (returnStr == null && searchForAlternate != null && identifiers != null && identifiers.Count == 2) {
          if (identifiers[0] == searchForAlternate || identifiers[0].StartsWith(searchForAlternate + ".sk.")) {
            returnStr = identifiers[1];
          } else if (identifiers[1] == searchForAlternate || identifiers[1].StartsWith(searchForAlternate + ".sk.")) {
            returnStr = identifiers[0];
          }
        }
        
        if (returnStr != null) {
          return Helpers.BeautifyBplString(returnStr);
        }
        
        return null;
      }
    }
    
    static int TreatInterpretedFunction(string! functionName, List<int>! zargs, ErrorModel! errModel) {
      if (zargs.Count != 2) {
        //all interpreted functions are binary, so there have to be exactly two arguments
        return -1;
      }
      else {
        object arg0 =  ValueFromZID(errModel, zargs[0]);
        object arg1 = ValueFromZID(errModel, zargs[1]);
        if (arg0 is BigNum && arg1 is BigNum) {
          BigNum arg0i = (BigNum)arg0;
          BigNum arg1i = (BigNum)arg1;
          BigNum result;
          if (functionName == "+") {
            result = arg0i + arg1i;
          } else if (functionName == "-") {
            result = arg0i - arg1i;
          } else /*if (functionName == "*")*/ {
            result = arg0i * arg1i;
          }
          int returnId = -1;
          if (errModel.valueToPartition.TryGetValue(result, out returnId)) {
            return returnId;
          } else {
            return -1;
          }
        }
        else {
          //both arguments need to be integers for this to work!
          return -1;
        }
      }
    }
    
    static int TreatFunction (string! functionName, List<int>! zargs, bool undefined, ErrorModel! errModel) {
      List<List<int>> functionDef;
      if ((!errModel.definedFunctions.TryGetValue(functionName, out functionDef) && functionName != "+" && functionName != "-" && functionName != "*") || undefined) { 
        // no fitting function found or one of the arguments is undefined
        return -1;
      } else {
        if (functionName == "+" || functionName == "-" || functionName == "*") {
          return TreatInterpretedFunction(functionName, zargs, errModel);
        }
        assert functionDef != null;
        foreach (List<int> pWiseF in functionDef) {
          assert pWiseF != null;
          // else case in the function definition:
          if (pWiseF.Count == 1) {
            return pWiseF[0];
          }
          // number of arguments is exactly the right number
          assert zargs.Count == pWiseF.Count - 1;
          if (forall{int i in (0: zargs.Count); zargs[i] == pWiseF[i]}) {
            return pWiseF[pWiseF.Count - 1];
          }
        }
        // all functions should have an 'else ->' case defined, therefore this should be
        // unreachable code!
        assert false;
      }
    }
    
    //returned int is zID
    static int GetValuesFromModel (Bpl.Expr! expr, Hashtable /*Variable -> Expr*/! incarnationMap, ErrorModel! errModel, Dictionary<Bpl.Expr!, object>! exprToPrintableValue) 
      modifies exprToPrintableValue.*;
    {
      // call GetValuesFromModel on all proper subexpressions, returning their value, 
      // so they only have to be computed once!
      if (expr is LiteralExpr) {
        // nothing needs to be added to the exprToPrintableValue map, because e.g. 0 -> 0 is not interesting
        object o = ((LiteralExpr) expr).Val;
        if (o == null) {
          o = "nullObject";
        } 
        int idForExprVal;
        if (errModel.valueToPartition.TryGetValue(o, out idForExprVal)) {
          return idForExprVal;
        } else {
          return -1;
        }
      }
      else if (expr is IdentifierExpr) {
        // if the expression expr is in the incarnation map, then use its incarnation, 
        // otherwise just use the actual expression 
        string s = ((IdentifierExpr) expr).Name;
        object o = null;
        Variable v = ((IdentifierExpr) expr).Decl;
        if (v != null && incarnationMap.ContainsKey(v)) {
          if (incarnationMap[v] is IdentifierExpr!) {
            s = ((IdentifierExpr!) incarnationMap[v]).Name;
          } else if (incarnationMap[v] is LiteralExpr!) {
            o = ((LiteralExpr!) incarnationMap[v]).Val;
          }
        }
        // if o is not null, then we got a LiteralExpression, that needs separate treatment
        if (o == null) {
          // if the expression (respectively its incarnation) is mapped to some partition
          // then return that id, else return the error code -1
          if (errModel.identifierToPartition.ContainsKey(s)) {
            int i = errModel.identifierToPartition[s];
            // if the key is already in the map we can assume that it is the same map we would
            // get now and thus just ignore it
            if (!exprToPrintableValue.ContainsKey(expr)) {
              exprToPrintableValue.Add(expr, ValueFromZID(errModel, i, ((IdentifierExpr) expr).Name));
            }
            return i;
          } else {
            return -1;
          }
        } else if (errModel.valueToPartition.ContainsKey(o)) {
          int i = errModel.valueToPartition[o];
          if (!exprToPrintableValue.ContainsKey(expr))
            exprToPrintableValue.Add(expr, ValueFromZID(errModel, i));
          return i;
        } else {
          return -1;
        }
      }
      else if (expr is Bpl.NAryExpr) {
        Bpl.NAryExpr e = (Bpl.NAryExpr)expr;
        List<int> zargs = new List<int>();
        bool undefined = false;
        // do the recursion first
        foreach (Expr argument in ((NAryExpr) expr).Args) {
          int zid = -1;
          if (argument != null) {
            zid = GetValuesFromModel(argument, incarnationMap, errModel, exprToPrintableValue);
          }
          // if one of the arguments is 'undefined' then return -1 ('noZid') for this
          // but make sure the recursion is complete first1
          if (zid == -1) {
            undefined = true;
          }
          zargs.Add(zid);
        }
        IAppliable! fun = e.Fun;
        string functionName = fun.FunctionName; // PR: convert to select1, select2, etc in case of a map?
        // same as IndexedExpr:
        int id = TreatFunction(functionName, zargs, undefined, errModel);
        if (id != -1 && !exprToPrintableValue.ContainsKey(expr)) {
          exprToPrintableValue.Add(expr, ValueFromZID(errModel, id));
        }
        return id;
      } 
      else if (expr is Bpl.OldExpr) {
        //Bpl.OldExpr e = (Bpl.OldExpr)expr;
        // We do not know which heap is the old heap and what the latest state change was,
        // therefore we cannot return anything useful here!
        return -1;
      } 
      else if (expr is Bpl.QuantifierExpr) {
        Bpl.QuantifierExpr q = (Bpl.QuantifierExpr)expr;
        for (int i = 0; i < q.Dummies.Length; i++) {
          Bpl.Variable v = q.Dummies[i];
          if (v != null) {
            // add to the incarnation map a connection between the bound variable v
            // of the quantifier and its skolemized incarnation, if available,
            // i.e., search through the list of identifiers in the model and look for
            // v.sk.(q.SkolemId), only pick those that are directly associated to a value
            // DISCLAIMER: of course it is very well possible that one of these incarnations 
            // could be used without actually having a value, but it seems better to pick those
            // with a value, that is they are more likely to contribute useful information to 
            // the output
            List<Bpl.IdentifierExpr!> quantVarIncarnationList = new List<Bpl.IdentifierExpr!>();
            List<int> incarnationZidList = new List<int>();
            int numberOfNonNullValueIncarnations = 0;
            for (int j = 0; j < errModel.partitionToIdentifiers.Count; j++){
              List<string!> pti = errModel.partitionToIdentifiers[j];
              if (pti != null) {
                for (int k = 0; k < pti.Count; k++) {
                  // look for v.sk.(q.SkolemId)
                  // if there is more than one look at if there is exactly one with a non-null value
                  // associated, see above explanation
                  if (pti[k].StartsWith(v + ".sk." + q.SkolemId) && 
                      errModel.partitionToValue[errModel.identifierToPartition[pti[k]]] != null) {
                    quantVarIncarnationList.Add(new Bpl.IdentifierExpr(Bpl.Token.NoToken, pti[k], new Bpl.UnresolvedTypeIdentifier(Token.NoToken, "TName")));
                    incarnationZidList.Add(j);
                    if (errModel.partitionToValue[errModel.identifierToPartition[pti[k]]] != null) {
                      numberOfNonNullValueIncarnations++;
                    }
                  }
                }
              }
            }
            // only one such variable found, associate it with v
            if (quantVarIncarnationList.Count == 1) {
              incarnationMap[v] = quantVarIncarnationList[0];
            } else if (quantVarIncarnationList.Count > 1 && numberOfNonNullValueIncarnations == 1) {
              // if there are multiple candidate incarnations and exactly one of them has a value 
              // we can pick that one; otherwise it is not clear how to pick one out of multiple 
              // incarnations without a value or out of multiple incarnations with a value associated
              for (int n = 0; n < incarnationZidList.Count; n++) {
                if (errModel.partitionToValue[incarnationZidList[n]] != null) {
                  // quantVarIncarnationList and incarnationZidList are indexed in lockstep, so if
                  // for the associated zid the partitionToValue map is non-null then that is the one
                  // thus distinguished incarnation we want to put into the incarnationMap
                  incarnationMap[v] = quantVarIncarnationList[n];
                  break;
                }
              }
            }
          }
        }
        // generate the value of the body but do not return that outside
        GetValuesFromModel(q.Body, incarnationMap, errModel, exprToPrintableValue);
        // the quantifier cannot contribute any one value to the rest of the 
        // expression, thus just return -1
        return -1;
      } 
      else if (expr is Bpl.BvExtractExpr) {
        Bpl.BvExtractExpr ex = (Bpl.BvExtractExpr) expr;
        Bpl.Expr e0 = ex.Bitvector;
        Bpl.Expr e1 = new LiteralExpr(Token.NoToken, BigNum.FromInt(ex.Start));
        Bpl.Expr e2 = new LiteralExpr(Token.NoToken, BigNum.FromInt(ex.End));
        string functionName = "$bv_extract";
        List<int> zargs = new List<int>();
        bool undefined = false;
        
        int zid = -1;
        zid = GetValuesFromModel(e0, incarnationMap, errModel, exprToPrintableValue);
        if (zid == -1) {
          undefined = true;
        }
        zargs.Add(zid);
        
        zid = -1;
        zid = GetValuesFromModel(e1, incarnationMap, errModel, exprToPrintableValue);
        if (zid == -1) {
          undefined = true;
        }
        zargs.Add(zid);
        
        zid = -1;
        zid = GetValuesFromModel(e2, incarnationMap, errModel, exprToPrintableValue);
        if (zid == -1) {
          undefined = true;
        }
        zargs.Add(zid);
        
        //same as NAryExpr:
        int id = TreatFunction(functionName, zargs, undefined, errModel);
        if (id != -1 && !exprToPrintableValue.ContainsKey(expr)) {
          exprToPrintableValue.Add(expr, ValueFromZID(errModel, id));
        }
        return id;
      } 
      else if (expr is Bpl.BvConcatExpr) {
        // see comment above
        Bpl.BvConcatExpr bvc = (Bpl.BvConcatExpr) expr;
        string functionName = "$bv_concat";
        List<int> zargs = new List<int>();
        bool undefined = false;
        
        int zid = -1;
        zid = GetValuesFromModel(bvc.E0, incarnationMap, errModel, exprToPrintableValue);
        if (zid == -1) {
          undefined = true;
        }
        zargs.Add(zid);
        
        zid = -1;
        zid = GetValuesFromModel(bvc.E0, incarnationMap, errModel, exprToPrintableValue);
        if (zid == -1) {
          undefined = true;
        }
        zargs.Add(zid);
      
        //same as NAryExpr:
        int id = TreatFunction(functionName, zargs, undefined, errModel);
        if (id != -1 && !exprToPrintableValue.ContainsKey(expr)) {
          exprToPrintableValue.Add(expr, ValueFromZID(errModel, id));
        }
        return id;
      }
      else {
        assert false;  // unexpected Bpl.Expr
      }
      return -1;
    }

    static Counterexample! AssertCmdToCounterexample (AssertCmd! cmd, TransferCmd! transferCmd, BlockSeq! trace, ErrorModel errModel, Dictionary<Incarnation, Absy!>! incarnationOriginMap) {
      List<string!>! relatedInformation = new List<string!>();
      if (CommandLineOptions.Clo.EnhancedErrorMessages == 1) {
        if (cmd.OrigExpr != null && cmd.IncarnationMap != null && errModel != null) {
          
          // get all possible information first
          Dictionary<Expr!, object> exprToPrintableValue = new Dictionary<Expr!, object>();
          GetValuesFromModel(cmd.OrigExpr, cmd.IncarnationMap, errModel, exprToPrintableValue);
          // then apply the strategies
          ApplyEnhancedErrorPrintingStrategy(cmd.OrigExpr, cmd.IncarnationMap, cmd.ErrorDataEnhanced, errModel, exprToPrintableValue, relatedInformation, true, incarnationOriginMap);
        }
      }
      
      // See if it is a special assert inserted in translation
      if (cmd is AssertRequiresCmd)
      {
        AssertRequiresCmd! assertCmd = (AssertRequiresCmd)cmd;
        CallCounterexample cc = new CallCounterexample(trace, assertCmd.Call, assertCmd.Requires);
        cc.relatedInformation = relatedInformation;
        return cc;
      }
      else if (cmd is AssertEnsuresCmd)
      {
        AssertEnsuresCmd! assertCmd = (AssertEnsuresCmd)cmd;
        ReturnCounterexample rc = new ReturnCounterexample(trace, transferCmd, assertCmd.Ensures);
        rc.relatedInformation = relatedInformation;
        return rc;
      }
      else 
      {
        AssertCounterexample ac = new AssertCounterexample(trace, (AssertCmd)cmd);
        ac.relatedInformation = relatedInformation;
        return ac;
      }
    }
    
//    static void EmitImpl(Implementation! impl, bool printDesugarings) {
//      int oldPrintUnstructured = CommandLineOptions.Clo.PrintUnstructured;
//      CommandLineOptions.Clo.PrintUnstructured = 2;  // print only the unstructured program
//      bool oldPrintDesugaringSetting = CommandLineOptions.Clo.PrintDesugarings;
//      CommandLineOptions.Clo.PrintDesugarings = printDesugarings;
//      impl.Emit(new TokenTextWriter("<console>", Console.Out, false), 0);
//      CommandLineOptions.Clo.PrintDesugarings = oldPrintDesugaringSetting;
//      CommandLineOptions.Clo.PrintUnstructured = oldPrintUnstructured;
//    }

    static VCExpr! LetVC(Block! startBlock,
                         Hashtable/*<int, Absy!>*/! label2absy,
                         ProverContext! proverCtxt)
    {
      Hashtable/*<Block, LetVariable!>*/! blockVariables = new Hashtable/*<Block, LetVariable!!>*/();
      List<VCExprLetBinding!>! bindings = new List<VCExprLetBinding!>();
      VCExpr startCorrect = LetVC(startBlock, label2absy, blockVariables, bindings, proverCtxt);
      return proverCtxt.ExprGen.Let(bindings, startCorrect);
    }

    static VCExpr! LetVC(Block! block,
                         Hashtable/*<int, Absy!>*/! label2absy,
                         Hashtable/*<Block, VCExprVar!>*/! blockVariables,
                         List<VCExprLetBinding!>! bindings,
                         ProverContext! proverCtxt)
    {
      VCExpressionGenerator! gen = proverCtxt.ExprGen;
      VCExprVar v = (VCExprVar)blockVariables[block];
      if (v == null) {
        /*
         * For block A (= block), generate:
         *   LET_binding A_correct = wp(A_body, (/\ S \in Successors(A) :: S_correct))
         * with the side effect of adding the let bindings to "bindings" for any
         * successor not yet visited.
         */
        VCExpr SuccCorrect;
        GotoCmd gotocmd = block.TransferCmd as GotoCmd;
        if (gotocmd == null) {
          SuccCorrect = VCExpressionGenerator.True;
        } else {
          assert gotocmd.labelTargets != null;
          List<VCExpr!> SuccCorrectVars = new List<VCExpr!>(gotocmd.labelTargets.Length);
          foreach (Block! successor in gotocmd.labelTargets) {
            VCExpr s = LetVC(successor, label2absy, blockVariables, bindings, proverCtxt);
            SuccCorrectVars.Add(s);
          }
          SuccCorrect = gen.NAry(VCExpressionGenerator.AndOp, SuccCorrectVars);
        }

        VCContext context = new VCContext(label2absy, proverCtxt);
        VCExpr vc = Wlp.Block(block, SuccCorrect, context);
        
        v = gen.Variable(block.Label + "_correct", Bpl.Type.Bool);
        bindings.Add(gen.LetBinding(v, vc));
        blockVariables.Add(block, v);
      }
      return v;
    }

    static VCExpr! DagVC(Block! block,
                         Hashtable/*<int, Absy!>*/! label2absy,
                         Hashtable/*<Block, VCExpr!>*/! blockEquations,
                         ProverContext! proverCtxt)
    {
      VCExpressionGenerator! gen = proverCtxt.ExprGen;
      VCExpr vc = (VCExpr)blockEquations[block];
      if (vc != null) {
        return vc;
      }

      /* 
       * For block A (= block), generate:
       *   wp(A_body, (/\ S \in Successors(A) :: DagVC(S)))
       */
      VCExpr SuccCorrect = null;
      GotoCmd gotocmd = block.TransferCmd as GotoCmd;
      if (gotocmd != null)
      {
        foreach (Block! successor in (!)gotocmd.labelTargets) {
          VCExpr c = DagVC(successor, label2absy, blockEquations, proverCtxt);
          SuccCorrect = SuccCorrect == null ? c : gen.And(SuccCorrect, c);
        }
      }
      if (SuccCorrect == null) {
        SuccCorrect = VCExpressionGenerator.True;
      }

      VCContext context = new VCContext(label2absy, proverCtxt);
      vc = Wlp.Block(block, SuccCorrect, context);
      
      //  gen.MarkAsSharedFormula(vc);  PR: don't know yet what to do with this guy

      blockEquations.Add(block, vc);
      return vc;
    }

    static VCExpr! FlatBlockVC(Implementation! impl,
                              Hashtable/*<int, Absy!>*/! label2absy,
                              bool local, bool reach, bool doomed,
                              ProverContext! proverCtxt)
      requires local ==> !reach;  // "reach" must be false for local
    {
      VCExpressionGenerator! gen = proverCtxt.ExprGen;
      Hashtable/* Block --> VCExprVar */ BlkCorrect = BlockVariableMap(impl.Blocks, "_correct", gen);
      Hashtable/* Block --> VCExprVar */ BlkReached = reach ? BlockVariableMap(impl.Blocks, "_reached", gen) : null;

      List<Block!> blocks = impl.Blocks;
  // block sorting is now done on the VCExpr
  //    if (!local && ((!)CommandLineOptions.Clo.TheProverFactory).NeedsBlockSorting) {
  //      blocks = SortBlocks(blocks);
  //    }

      VCExpr proofObligation;
      if (!local) {
        proofObligation = (VCExprVar!)BlkCorrect[impl.Blocks[0]];
      } else {
        List<VCExpr!> conjuncts = new List<VCExpr!>(blocks.Count);
        foreach (Block! b in blocks) {
          VCExpr v = (VCExprVar!)BlkCorrect[b];
          conjuncts.Add(v);
        }
        proofObligation = gen.NAry(VCExpressionGenerator.AndOp, conjuncts);
      }

      VCContext! context = new VCContext(label2absy, proverCtxt);

      List<VCExprLetBinding!> programSemantics = new List<VCExprLetBinding!>(blocks.Count);
      foreach (Block! b in blocks) {
        /* 
         * In block mode,
         * For a return block A, generate:
         *   A_correct <== wp(A_body, true)  [post-condition has been translated into an assert]
         * For all other blocks, generate:
         *   A_correct <== wp(A_body, (/\ S \in Successors(A) :: S_correct))
         * 
         * In doomed mode, proceed as in block mode, except for a return block A, generate:
         *   A_correct <== wp(A_body, false)  [post-condition has been translated into an assert]
         *
         * In block reach mode, the wp(A_body,...) in the equations above change to:
         *   A_reached ==> wp(A_body,...)
         * and the conjunction above changes to:
         *   (/\ S \in Successors(A) :: S_correct \/ (\/ T \in Successors(A) && T != S :: T_reached))
         *
         * In local mode, generate:
         *   A_correct <== wp(A_body, true)
         */
        VCExpr! SuccCorrect;
        if (local) {
          SuccCorrect = VCExpressionGenerator.True;
        } else {
          SuccCorrect = SuccessorsCorrect(b, BlkCorrect, BlkReached, doomed, gen);
        }

        VCExpr wlp = Wlp.Block(b, SuccCorrect, context);
        if (BlkReached != null) {
          wlp = gen.Implies((VCExprVar!)BlkReached[b], wlp);
        }
        
        VCExprVar okVar = (VCExprVar!)BlkCorrect[b];
        VCExprLetBinding binding = gen.LetBinding(okVar, wlp);
        programSemantics.Add(binding);
      }

      return gen.Let(programSemantics, proofObligation);
    }
    
    private static Hashtable/* Block --> VCExprVar */! BlockVariableMap(List<Block!>! blocks, string! suffix,
                                                                        Microsoft.Boogie.VCExpressionGenerator! gen)
    {
      Hashtable/* Block --> VCExprVar */ map = new Hashtable/* Block --> (Let)Variable */();
      foreach (Block! b in blocks)
      {
        VCExprVar! v = gen.Variable(b.Label+suffix, Bpl.Type.Bool);
        map.Add(b, v);
      }
      return map;
    }

    private static VCExpr! SuccessorsCorrect(
        Block! b,
        Hashtable/* Block --> VCExprVar */! BlkCorrect,
        Hashtable/* Block --> VCExprVar */ BlkReached,
        bool doomed,
        Microsoft.Boogie.VCExpressionGenerator! gen)
    {
        VCExpr SuccCorrect = null;
        GotoCmd gotocmd = b.TransferCmd as GotoCmd;
        if (gotocmd != null)
        {
            foreach (Block! successor in (!)gotocmd.labelTargets)
            {
                // c := S_correct
                VCExpr c = (VCExprVar!)BlkCorrect[successor];
                if (BlkReached != null)
                {
                    // c := S_correct \/ Sibling0_reached \/ Sibling1_reached \/ ...;
                    foreach (Block! successorSibling in gotocmd.labelTargets)
                    {
                        if (successorSibling != successor)
                        {
                            c = gen.Or(c, (VCExprVar!)BlkReached[successorSibling]);
                        }
                    }
                }
                SuccCorrect = SuccCorrect == null ? c : gen.And(SuccCorrect, c);
            }
        }
        if (SuccCorrect == null) {
            return VCExpressionGenerator.True;
        } else if (doomed) {
            return VCExpressionGenerator.False;
        } else {
            return SuccCorrect;
        }
    }

    static VCExpr! NestedBlockVC(Implementation! impl,
                                Hashtable/*<int, Absy!>*/! label2absy,
                                bool reach,
                                ProverContext! proverCtxt)
      requires impl.Blocks.Count != 0;
    {
      VCExpressionGenerator! gen = proverCtxt.ExprGen;
      Graph<Block>! g = GraphFromImpl(impl);

      Hashtable/* Block --> VCExprVar */ BlkCorrect = BlockVariableMap(impl.Blocks, "_correct", gen);
      Hashtable/* Block --> VCExprVar */ BlkReached = reach ? BlockVariableMap(impl.Blocks, "_reached", gen) : null;

      Block! startBlock = (!) impl.Blocks[0];
      VCExpr proofObligation = (VCExprVar!)BlkCorrect[startBlock];

      VCContext! context = new VCContext(label2absy, proverCtxt);
      
      Hashtable/*Block->int*/ totalOrder = new Hashtable/*Block->int*/();
      {
        List<Block!> blocks = impl.Blocks;
     // block sorting is now done on the VCExpr
     //   if (((!)CommandLineOptions.Clo.TheProverFactory).NeedsBlockSorting) {
     //     blocks = SortBlocks(blocks);
     //   }
        int i = 0;
        foreach (Block b in blocks) {
          totalOrder[b] = i;
          i++;
        }
      }
      
      VCExprLetBinding programSemantics = NestedBlockEquation((!)impl.Blocks[0], BlkCorrect, BlkReached, totalOrder, context, g, gen);
      List<VCExprLetBinding!> ps = new List<VCExprLetBinding!>(1);
      ps.Add(programSemantics);
      
      return gen.Let(ps, proofObligation);
    }

    private static VCExprLetBinding! NestedBlockEquation(Block! b,
        Hashtable/*Block-->VCExprVar*/! BlkCorrect,
        Hashtable/*Block-->VCExprVar*/ BlkReached,
        Hashtable/*Block->int*/! totalOrder,
        VCContext! context,
        Graph<Block>! g,
        Microsoft.Boogie.VCExpressionGenerator! gen)
    {
        /*
        * For a block b, return:
        *   LET_BINDING b_correct = wp(b_body, X)
        * where X is:
        *   LET (THOSE d \in DirectDominates(b) :: BlockEquation(d))
        *   IN (/\ s \in Successors(b) :: s_correct)
        * 
        * When the VC-expression generator does not support LET expresions, this
        * will eventually turn into:
        *   b_correct <== wp(b_body, X)
        * where X is:
        *   (/\ s \in Successors(b) :: s_correct)
        *   <==
        *   (/\ d \in DirectDominatees(b) :: BlockEquation(d))
        *
        * In both cases above, if BlkReached is non-null, then the wp expression
        * is instead:
        *   b_reached ==> wp(b_body, X)
        */

        VCExpr! SuccCorrect = SuccessorsCorrect(b, BlkCorrect, null, false, gen);

        List<VCExprLetBinding!> bindings = new List<VCExprLetBinding!>();
        foreach (Block! dominee in GetSortedBlocksImmediatelyDominatedBy(g, b, totalOrder))
        {
            VCExprLetBinding c = NestedBlockEquation(dominee, BlkCorrect, BlkReached, totalOrder, context, g, gen);
            bindings.Add(c);
        }

        VCExpr X = gen.Let(bindings, SuccCorrect);
        VCExpr wlp = Wlp.Block(b, X, context);
        if (BlkReached != null) {
          wlp = gen.Implies((VCExprVar!)BlkReached[b], wlp);
        }
        VCExprVar okVar = (VCExprVar!)BlkCorrect[b];
        return gen.LetBinding(okVar, wlp);
    }

    /// <summary>
    /// Returns a list of g.ImmediatelyDominatedBy(b), but in a sorted order, hoping to steer around
    /// the nondeterminism problems we've been seeing by using just this call.
    /// </summary>
    static List<Block!>! GetSortedBlocksImmediatelyDominatedBy(Graph<Block>! g, Block! b, Hashtable/*Block->int*/! totalOrder) {
      List<Block!> list = new List<Block!>();
      foreach (Block! dominee in g.ImmediatelyDominatedBy(b)) {
        list.Add(dominee);
      }
      list.Sort(new Comparison<Block!>(delegate (Block! x, Block! y) {return (int)(!)totalOrder[x] - (int)(!)totalOrder[y];} ));
      return list;
    }
    
    static VCExpr! VCViaStructuredProgram
                  (Implementation! impl, Hashtable/*<int, Absy!>*/! label2absy,
                   ProverContext! proverCtxt)
    {
      #region Convert block structure back to a "regular expression"
      RE! r = DAG2RE.Transform((!)impl.Blocks[0]);
      #endregion

      VCContext! ctxt = new VCContext(label2absy, proverCtxt);
      #region Send wlp(program,true) to Simplify
      return Wlp.RegExpr(r, VCExpressionGenerator.True, ctxt);
      #endregion
    }

    /// <summary> 
    /// Remove the empty blocks reachable from the block.
    /// It changes the visiting state of the blocks, so that if you want to visit again the blocks, you have to reset them...
    /// </summary>
    static BlockSeq! RemoveEmptyBlocks(Block! b)
    {
      assert b.TraversingStatus == Block.VisitState.ToVisit;
      BlockSeq retVal = removeEmptyBlocksWorker(b, true);
      return retVal;
    }

    private static BlockSeq! removeEmptyBlocksWorker(Block! b, bool startNode)
    {
      BlockSeq bs = new BlockSeq();
      GotoCmd gtc = b.TransferCmd as GotoCmd;

      // b has no successors
      if (gtc == null || gtc.labelTargets == null || gtc.labelTargets.Length == 0) 
      {        
        if (b.Cmds.Length != 0){ // only empty blocks are removed...
          bs.Add(b);
        }
        return bs;
      }
      else if(b.TraversingStatus == Block.VisitState.ToVisit)  // if b has some successors and we have not seen it so far...
      { 
        b.TraversingStatus = Block.VisitState.BeingVisited;

        // recursively call this method on each successor
        // merge result into a *set* of blocks
        Dictionary<Block,bool> mergedSuccessors = new Dictionary<Block,bool>();
        foreach (Block! dest in gtc.labelTargets){
          BlockSeq! ys = removeEmptyBlocksWorker(dest, false);
          foreach (Block successor in ys){
            if (!mergedSuccessors.ContainsKey(successor))
              mergedSuccessors.Add(successor,true);
          }
        }
        b.TraversingStatus = Block.VisitState.AlreadyVisited;

        BlockSeq setOfSuccessors = new BlockSeq();
        foreach (Block d in mergedSuccessors.Keys)
          setOfSuccessors.Add(d);
        if (b.Cmds.Length == 0 && !startNode)
          return setOfSuccessors;
        // otherwise, update the list of successors of b to be the blocks in setOfSuccessors
        gtc.labelTargets = setOfSuccessors;
        gtc.labelNames = new StringSeq();
        foreach (Block! d in setOfSuccessors)
          gtc.labelNames.Add(d.Label);
        return new BlockSeq(b);
      }
      else // b has some successors, but we are already visiting it, or we have already visited it...
      {
        return new BlockSeq(b);
      }
    }

    static Graph<Block>! GraphFromImpl(Implementation! impl) {
      Graph<Block>! g = new Graph<Block>();
      g.AddSource((!)impl.Blocks[0]); // there is always at least one node in the graph
      foreach (Block! b in impl.Blocks)
      {
        GotoCmd gtc = b.TransferCmd as GotoCmd;
        if (gtc != null)
        {
          foreach (Block! dest in (!)gtc.labelTargets)
          {
            g.AddEdge(b,dest);
          }
        }
      }
      return g;
    }


    static void DumpMap(Hashtable /*Variable->Expr*/! map) {
      foreach (DictionaryEntry de in map) {
        Variable! v = (Variable!)de.Key;
        Expr! e = (Expr!)de.Value;
        Console.Write("  ");
        v.Emit(new TokenTextWriter("<console>", Console.Out, false), 0);
        Console.Write("  --> ");
        e.Emit(new TokenTextWriter("<console>", Console.Out, false));
        Console.WriteLine();
      }
    }
  }
}