private List <EnvironmentState> _stateEnv = new List <EnvironmentState>(); // how to link up the corresponding concrete states for easy access? e.g., given abstract tuple, get the concrete predicates being abstracted
/**
*
*/
public AbstractState(ConcreteLocation rstate, List <EnvironmentState> estates)
: base("", UInt32.MaxValue, false)
{
this._stateRef = rstate;
this._stateEnv = estates;
this._concretization = null;
}
public Transition(ConcreteLocation p)
{
this.Parent = p;
// todo next: switch if not int type: , Controller.Instance.IndexType
Expr hidxinner = Controller.Instance.Z3.MkIntConst("h");
this.TransitionTermGlobal = (BoolExpr)this.makeTransitionTerm(null, hidxinner, null); // no local vars
this.TransitionTerm = (BoolExpr)this.makeTransitionTerm(this.Parent, hidxinner, null); // with local vars
}
/**
*
*/
private void Dispose(bool disposing)
{
// Check to see if Dispose has already been called.
if (!this._dispose)
{
// If disposing equals true, dispose all managed and unmanaged resources.
if (disposing)
{
// Dispose managed resources.
this._label = null;
this._stateRef = null;
this._stateEnv = null;
}
}
this._dispose = true;
}
public Transition(ConcreteLocation p, Expr guard, Expr reset, List <AState> nextStates)
: this(p, nextStates)
{
this.Guard = guard;
this._reset = reset;
}
public Transition(ConcreteLocation p, Expr guard, Expr reset) : this(p)
{
this.Guard = guard;
this._reset = reset;
}
public Transition(ConcreteLocation p, List <AState> nextStates) : this(p)
{
this._nextStates = nextStates;
}
public Transition(ConcreteLocation p, AState nextState, AbstractTransitionType t)
: this(p, nextState)
{
this._type = t;
}
/**
* Make terms corresponding to pre and post-state for a transition (can be local or global transition)
*/
public Expr makeTransitionTerm(ConcreteLocation l, Expr idx, params uint[] paramList)
{
uint N = 0;
uint quant = 0;
uint k = 0;
if (paramList != null && paramList.Length > 0)
{
N = paramList[0];
if (paramList.Length > 1)
{
k = paramList[1];
}
if (paramList.Length > 2)
{
quant = paramList[2];
}
}
List <BoolExpr> locInvariant = new List <BoolExpr>();
if (l != null)
{
locInvariant.Add((BoolExpr)l.StatePredicate); // discrete location prestate (e.g., loc[i] = 1)
}
if (this.NextStates.Count > 0)
{
locInvariant.Add((BoolExpr)this.ToTerm()); // discrete location post-state (e.g., loc'[i] = 2)
}
// add guard, if one exists
if (this.Guard != null)
{
locInvariant.Add((BoolExpr)this.Guard);
}
if (l != null)
{
// add invariant, if one exists
if (l.Invariant != null)
{
locInvariant.Add((BoolExpr)l.Invariant);
}
// add stopping condition, if one exists
if (l.Stop != null)
{
locInvariant.Add((BoolExpr)l.Stop);
}
}
List <String> globalVariableResets = new List <String>(); // global variables not reset
List <String> indexVariableResets = new List <String>(); // indexed variables of process moving that are not reset
List <String> universalIndexVariableResets = new List <String>(); // universally quantified indexed variables that are reset
if (this.Reset != null)
{
locInvariant.Add((BoolExpr)this.Reset);
globalVariableResets = Controller.Instance.Z3.findGlobalVariableResets(this.Reset);
indexVariableResets = Controller.Instance.Z3.findIndexedVariableResets(this.Reset);
}
else
{
// global variable was not mentioned since reset is null: add it to the identity global variables (g' = g)
globalVariableResets = Controller.Instance.Z3.findGlobalVariableResets(null);
indexVariableResets = Controller.Instance.Z3.findIndexedVariableResets(null);
}
if (this.UGuard != null)
{
universalIndexVariableResets = Controller.Instance.Z3.findIndexedVariableResetsNeg(this.UGuard);
}
Expr locInvariantAnd = null;
// create conjunction of pre-state and post-state conditions
if (locInvariant.Count > 0)
{
locInvariantAnd = Controller.Instance.Z3.MkAnd(locInvariant.ToArray());
}
Expr identity;
if (l == null)
{
// TODO NEXT: GLOBAL INDEXED VARIABLE COULD CAUSE RESETS / "be the process moving"
int i = 0;
Expr gidx = null;
foreach (var v in Controller.Instance.GlobalVariables)
{
if (Controller.Instance.Sys.Variables.Find(
delegate(Variable gv)
{
return(gv.Name == v.Key);
}).Type == Variable.VarType.index && Controller.Instance.Z3.findTerm(this.Reset, v.Value, true))
{
gidx = v.Value;
i++;
}
// TODO: need to refactor forall identity to allow multiple processes moving, for now throw exception if it happens
if (i > 1)
{
throw new Exception("Error: too many global index variables used.");
}
}
identity = Controller.Instance.Sys.forallIdentity(gidx, globalVariableResets, indexVariableResets, universalIndexVariableResets, this.UGuard, N); // no process moves if no location
}
else
{
identity = Controller.Instance.Sys.forallIdentity(idx, globalVariableResets, indexVariableResets, universalIndexVariableResets, this.UGuard, N);
}
if (locInvariantAnd == null && N == 0)
{
locInvariantAnd = identity;
}
else if (N == 0)
{
locInvariantAnd = Controller.Instance.Z3.MkAnd((BoolExpr)locInvariantAnd, (BoolExpr)identity);
}
if (l != null && N == 0)
{
locInvariantAnd = locInvariantAnd.Substitute(Controller.Instance.Indices["i"], idx); // replace i by h
BoolExpr idxConstraint = Controller.Instance.Z3.MkAnd(Controller.Instance.Z3.MkGe((ArithExpr)idx, (ArithExpr)Controller.Instance.IntOne), Controller.Instance.Z3.MkLe((ArithExpr)idx, (ArithExpr)Controller.Instance.IndexN));
// add quantifiers based on pre-state and post-state, using implies vs. and options and indexing options
switch (Controller.Instance.IndexOption)
{
case Controller.IndexOptionType.naturalOneToN:
switch (Controller.Instance.ExistsOption)
{
case Controller.ExistsOptionType.and:
locInvariantAnd = Controller.Instance.Z3.MkAnd(idxConstraint, (BoolExpr)locInvariantAnd); // 1 <= h <= N, enforce identity for all other processes not moving
break;
case Controller.ExistsOptionType.implies:
default:
locInvariantAnd = Controller.Instance.Z3.MkImplies(idxConstraint, (BoolExpr)locInvariantAnd); // 1 <= h <= N, enforce identity for all other processes not moving
break;
}
break;
case Controller.IndexOptionType.enumeration:
case Controller.IndexOptionType.integer:
default:
//locInvariantAnd = locInvariantAnd & z3.forallIdentity(hidx, globalVariableResets, indexVariableResets);
break;
}
}
if (N == 0)
{
// todo: add quantifier: check if correct
}
else
{
List <BoolExpr> transAll = new List <BoolExpr>();
// expand quantifier manually
for (uint i = 1; i <= N; i++)
{
Expr numidx = Controller.Instance.Z3.MkInt(i);
//Expr trans = locInvariantAnd.Substitute(idx, numidx); // instantiate i
//transAll.Add(z3.MkAnd(z3.MkEq(idx, numidx), (BoolExpr)locInvariantAnd)); // simply set symbol idx = value idx
BoolExpr copy = (BoolExpr)Controller.Instance.Z3.copyExpr(locInvariantAnd);
foreach (var v in Controller.Instance.Sys.Variables)
{
copy = (BoolExpr)copy.Substitute(Controller.Instance.GlobalVariables[v.Name], Controller.Instance.Sys.GlobalReachValues[new Tuple <string, uint>(v.Name, k)]); // substitute to constant (needed for doing q.e.)
copy = (BoolExpr)copy.Substitute(Controller.Instance.GlobalVariablesPrimed[v.Name], Controller.Instance.Sys.GlobalReachValues[new Tuple <string, uint>(v.Name, k + 1)]); // substitute to constant (needed for doing q.e.)
}
foreach (var v in Controller.Instance.Sys.HybridAutomata[0].Variables) // TODO: generalize
{
//copy.Substitute(z3.MkApp(v.Value, idx), z3.MkApp(v.Value, numidx)); // substitute to function
idx = Controller.Instance.Z3.MkIntConst("i");
copy = (BoolExpr)copy.Substitute(Controller.Instance.Z3.MkApp(v.Value, idx), Controller.Instance.Sys.ReachValues[new Tuple <string, uint, uint>(v.Name, k, i)]); // substitute to constant (needed for doing q.e.)
copy = (BoolExpr)copy.Substitute(Controller.Instance.Z3.MkApp(v.ValuePrimed, idx), Controller.Instance.Sys.ReachValues[new Tuple <string, uint, uint>(v.Name, k + 1, i)]); // substitute to constant (needed for doing q.e.)
}
copy = (BoolExpr)copy.Substitute(idx, numidx); // must be outside variable loop
copy = Controller.Instance.Z3.MkAnd(copy, (BoolExpr)Controller.Instance.Sys.forallIdentity(Controller.Instance.Z3.MkInt(i), globalVariableResets, indexVariableResets, universalIndexVariableResets, this.UGuard, N));
for (uint j = 1; j <= N; j++)
{
if (j == i)
{
continue;
}
foreach (var v in Controller.Instance.Sys.HybridAutomata[0].Variables) // TODO: generalize
{
copy = (BoolExpr)copy.Substitute(Controller.Instance.Z3.MkApp(v.Value, Controller.Instance.Z3.MkInt(j)), Controller.Instance.Sys.ReachValues[new Tuple <string, uint, uint>(v.Name, k, j)]); // substitute to constant (needed for doing q.e.)
copy = (BoolExpr)copy.Substitute(Controller.Instance.Z3.MkApp(v.ValuePrimed, Controller.Instance.Z3.MkInt(j)), Controller.Instance.Sys.ReachValues[new Tuple <string, uint, uint>(v.Name, k + 1, j)]); // substitute to constant (needed for doing q.e.)
}
}
transAll.Add(copy);
}
locInvariantAnd = Controller.Instance.Z3.MkOr(transAll.ToArray());
}
return(locInvariantAnd);
}
public Transition(ConcreteLocation p, AState nextState) : this(p)
{
this._nextStates = new List <AState>();
this._nextStates.Add(nextState);
}
/// <summary>
/// Compute post from pre
/// </summary>
/// <param name="pre"></param>
/// <returns></returns>
public Expr MakePost(Expr pre)
{
KeyValuePair <Transition, Expr> postKey = new KeyValuePair <Transition, Expr>(this, pre);
if (Transition.CachePost.ContainsKey(postKey))
{
return(CachePost[postKey]);
}
Expr idx = Controller.Instance.Indices["i"];
ConcreteLocation l = this.Parent;
List <BoolExpr> resets = new List <BoolExpr>();
resets.Add((BoolExpr)pre); // add prestate
if (this.NextStates.Count > 0)
{
resets.Add((BoolExpr)this.ToTerm()); // discrete location post-state (e.g., loc'[i] = 2)
}
List <String> globalVariableResets = new List <String>(); // global variables not reset
List <String> indexVariableResets = new List <String>(); // indexed variables of process moving that are not reset
List <String> universalIndexVariableResets = new List <String>(); // universally quantified indexed variables that are reset
if (this.Reset != null)
{
resets.Add((BoolExpr)this.Reset);
globalVariableResets = Controller.Instance.Z3.findGlobalVariableResets(this.Reset);
indexVariableResets = Controller.Instance.Z3.findIndexedVariableResets(this.Reset);
}
else
{
// global variable was not mentioned since reset is null: add it to the identity global variables (g' = g)
globalVariableResets = Controller.Instance.Z3.findGlobalVariableResets(null);
indexVariableResets = Controller.Instance.Z3.findIndexedVariableResets(null);
}
if (this.UGuard != null) // TODO: handle univerasl resets (assume none for now)
{
universalIndexVariableResets = Controller.Instance.Z3.findIndexedVariableResetsNeg(this.UGuard);
}
Expr resetAnd = null;
// create conjunction of pre-state and post-state conditions
if (resets.Count > 0)
{
resetAnd = Controller.Instance.Z3.MkAnd(resets.ToArray());
}
Expr identity;
if (l == null)
{
// TODO NEXT: GLOBAL INDEXED VARIABLE COULD CAUSE RESETS / "be the process moving"
int i = 0;
Expr gidx = null;
foreach (var v in Controller.Instance.GlobalVariables)
{
if (Controller.Instance.Sys.Variables.Find(
delegate(Variable gv)
{
return(gv.Name == v.Key);
}).Type == Variable.VarType.index && Controller.Instance.Z3.findTerm(this.Reset, v.Value, true))
{
gidx = v.Value;
i++;
}
// TODO: need to refactor forall identity to allow multiple processes moving, for now throw exception if it happens
if (i > 1)
{
throw new Exception("Error: too many global index variables used.");
}
}
identity = Controller.Instance.Sys.forallIdentityPost(gidx, globalVariableResets, indexVariableResets, universalIndexVariableResets, this.UGuard, 0); // no process moves if no location
}
else
{
identity = Controller.Instance.Sys.forallIdentityPost(idx, globalVariableResets, indexVariableResets, universalIndexVariableResets, this.UGuard, 0);
}
resetAnd = Controller.Instance.Z3.MkAnd((BoolExpr)resetAnd, (BoolExpr)identity);
resetAnd = Controller.Instance.Z3.copyExpr(resetAnd);
// short circuit
/*
* if (this.Reset == null && Controller.Instance.Sys.Variables.Count == 0)
* {
* return resetAnd;
* }
*/
// replace all function declarations with constants (e.g., (q i) => (qi), where qi is a constant, instead of a function)
List <Expr> bound = new List <Expr>();
// TODO: use this.Parent.Parent.Parent, etc to access hybrid automata, holism, etc (will make generalizing to compositions easier)
foreach (var v in Controller.Instance.Sys.HybridAutomata[0].Variables)
{
Expr varConst = Controller.Instance.Z3.MkConst(v.Name + "_" + "i", v.TypeSort);
Expr varConstPost = Controller.Instance.Z3.MkConst(v.NamePrimed + "_" + "i", v.TypeSort);
resetAnd = resetAnd.Substitute(Controller.Instance.Z3.MkApp(v.Value, idx), varConst);
resetAnd = resetAnd.Substitute(Controller.Instance.Z3.MkApp(v.ValuePrimed, idx), varConstPost);
bound.Add(varConst);
}
foreach (var v in Controller.Instance.GlobalVariables.Values)
{
bound.Add(v);
}
//Expr post = Controller.Instance.Z3.MkExists(new Expr[] { idx }, (BoolExpr)resetAnd);
Expr post = Controller.Instance.Z3.MkExists(bound.ToArray(), (BoolExpr)resetAnd);
// HACK: replace all location names with their values...
foreach (var loc in Controller.Instance.Sys.HybridAutomata[0].Locations)
{
post = post.Substitute(loc.LabelExpr, loc.BitVectorExpr);
}
post = post.Substitute(Controller.Instance.IndexN, Controller.Instance.Z3.MkInt(Controller.Instance.IndexNValue));
Tactic tqe = Controller.Instance.Z3.Repeat(Controller.Instance.Z3.MkTactic("qe"));
Goal g = Controller.Instance.Z3.MkGoal();
List <BoolExpr> remAss = Controller.Instance.Z3.Assumptions.FindAll(a => a.IsQuantifier); // todo: add type constraints to constant (q_i) instead of functions (q i)
Controller.Instance.Z3.Assumptions.RemoveAll(a => a.IsQuantifier); // otherwise q.e. will fail
g.Assert(Controller.Instance.Z3.Assumptions.ToArray());
Controller.Instance.Z3.Assumptions.AddRange(remAss); // add back
g.Assert(Controller.Instance.Z3.AssumptionsUniversal.ToArray());
g.Assert((BoolExpr)post);
g = g.Simplify();
ApplyResult ar = tqe.Apply(g);
List <BoolExpr> postStates = new List <BoolExpr>();
foreach (var sg in ar.Subgoals)
{
postStates.AddRange(sg.Formulas);
}
postStates.RemoveAll(fa => Controller.Instance.Z3.Assumptions.Contains(fa));
postStates.RemoveAll(fa => Controller.Instance.Z3.AssumptionsUniversal.Contains(fa));
post = Controller.Instance.Z3.MkAnd(postStates.ToArray());
// HACK: replace all location values with their names...
foreach (var loc in Controller.Instance.Sys.HybridAutomata[0].Locations)
{
post = post.Substitute(loc.BitVectorExpr, loc.LabelExpr);
}
// convert constants back to functions
foreach (var v in Controller.Instance.Sys.HybridAutomata[0].Variables)
{
Expr varConst = Controller.Instance.Z3.MkConst(v.Name + "_" + "i", v.TypeSort);
Expr varConstPost = Controller.Instance.Z3.MkConst(v.NamePrimed + "_" + "i", v.TypeSort);
post = post.Substitute(varConst, Controller.Instance.Z3.MkApp(v.Value, idx));
post = post.Substitute(varConstPost, Controller.Instance.Z3.MkApp(v.ValuePrimed, idx));
}
Controller.Instance.Z3.unprimeAllVariables(ref post); // unprime
System.Console.WriteLine("POST: " + post.ToString());
// cache result
CachePost.Add(postKey, post);
return(post);
}
public Expr MakeReset(Expr idx, uint N, uint k)
{
ConcreteLocation l = this.Parent;
List <BoolExpr> resets = new List <BoolExpr>();
if (this.NextStates.Count > 0)
{
resets.Add((BoolExpr)this.ToTerm()); // discrete location post-state (e.g., loc'[i] = 2)
}
List <String> globalVariableResets = new List <String>(); // global variables not reset
List <String> indexVariableResets = new List <String>(); // indexed variables of process moving that are not reset
List <String> universalIndexVariableResets = new List <String>(); // universally quantified indexed variables that are reset
if (this.Reset != null)
{
resets.Add((BoolExpr)this.Reset);
globalVariableResets = Controller.Instance.Z3.findGlobalVariableResets(this.Reset);
indexVariableResets = Controller.Instance.Z3.findIndexedVariableResets(this.Reset);
}
else
{
// global variable was not mentioned since reset is null: add it to the identity global variables (g' = g)
globalVariableResets = Controller.Instance.Z3.findGlobalVariableResets(null);
indexVariableResets = Controller.Instance.Z3.findIndexedVariableResets(null);
}
if (this.UGuard != null)
{
universalIndexVariableResets = Controller.Instance.Z3.findIndexedVariableResetsNeg(this.UGuard);
}
Expr resetAnd = null;
// create conjunction of pre-state and post-state conditions
if (resets.Count > 0)
{
resetAnd = Controller.Instance.Z3.MkAnd(resets.ToArray());
}
Expr identity;
if (l == null)
{
// TODO NEXT: GLOBAL INDEXED VARIABLE COULD CAUSE RESETS / "be the process moving"
int i = 0;
Expr gidx = null;
foreach (var v in Controller.Instance.GlobalVariables)
{
if (Controller.Instance.Sys.Variables.Find(
delegate(Variable gv)
{
return(gv.Name == v.Key);
}).Type == Variable.VarType.index && Controller.Instance.Z3.findTerm(this.Reset, v.Value, true))
{
gidx = v.Value;
i++;
}
// TODO: need to refactor forall identity to allow multiple processes moving, for now throw exception if it happens
if (i > 1)
{
throw new Exception("Error: too many global index variables used.");
}
}
identity = Controller.Instance.Sys.forallIdentity(gidx, globalVariableResets, indexVariableResets, universalIndexVariableResets, this.UGuard, N); // no process moves if no location
}
else
{
identity = Controller.Instance.Sys.forallIdentity(idx, globalVariableResets, indexVariableResets, universalIndexVariableResets, this.UGuard, N);
}
if (resetAnd == null && N == 0)
{
resetAnd = identity;
}
else if (N == 0)
{
resetAnd = Controller.Instance.Z3.MkAnd((BoolExpr)resetAnd, (BoolExpr)identity);
}
List <BoolExpr> transAll = new List <BoolExpr>();
// expand quantifier manually
for (uint i = 1; i <= N; i++)
{
Expr numidx = Controller.Instance.Z3.MkInt(i);
//Expr trans = locInvariantAnd.Substitute(idx, numidx); // instantiate i
//transAll.Add(z3.MkAnd(z3.MkEq(idx, numidx), (BoolExpr)locInvariantAnd)); // simply set symbol idx = value idx
BoolExpr copy = (BoolExpr)Controller.Instance.Z3.copyExpr(resetAnd);
idx = Controller.Instance.Z3.MkIntConst("i");
foreach (var v in Controller.Instance.Sys.HybridAutomata[0].Variables) // TODO: generalize
{
//copy.Substitute(z3.MkApp(v.Value, idx), z3.MkApp(v.Value, numidx)); // substitute to function
copy = (BoolExpr)copy.Substitute(Controller.Instance.IndexedVariables[new KeyValuePair <string, string>(v.Name, idx.ToString())], Controller.Instance.Sys.ReachValues[new Tuple <string, uint, uint>(v.Name, k, i)]); // substitute to constant (needed for doing q.e.)
copy = (BoolExpr)copy.Substitute(Controller.Instance.IndexedVariablesPrimed[new KeyValuePair <string, string>(v.Name + Controller.PRIME_SUFFIX, idx.ToString())], Controller.Instance.Sys.ReachValues[new Tuple <string, uint, uint>(v.Name, k + 1, i)]); // substitute to constant (needed for doing q.e.)
}
copy = (BoolExpr)copy.Substitute(idx, numidx); // must be outside loop
copy = Controller.Instance.Z3.MkAnd(copy, (BoolExpr)Controller.Instance.Sys.forallIdentity(Controller.Instance.Z3.MkInt(i), globalVariableResets, indexVariableResets, universalIndexVariableResets, this.UGuard, N));
foreach (var v in Controller.Instance.Sys.HybridAutomata[0].Variables) // TODO: generalize
{
//copy.Substitute(z3.MkApp(v.Value, idx), z3.MkApp(v.Value, numidx)); // substitute to function
copy = (BoolExpr)copy.Substitute(Controller.Instance.Z3.MkApp(v.Value, Controller.Instance.Z3.MkInt(i)), Controller.Instance.Sys.ReachValues[new Tuple <string, uint, uint>(v.Name, k, i)]); // substitute to constant (needed for doing q.e.)
copy = (BoolExpr)copy.Substitute(Controller.Instance.Z3.MkApp(v.ValuePrimed, Controller.Instance.Z3.MkInt(i)), Controller.Instance.Sys.ReachValues[new Tuple <string, uint, uint>(v.Name, k + 1, i)]); // substitute to constant (needed for doing q.e.)
}
// todo: check order of operations
foreach (var v in Controller.Instance.Sys.Variables)
{
copy = (BoolExpr)copy.Substitute(Controller.Instance.GlobalVariables[v.Name], Controller.Instance.Sys.GlobalReachValues[new Tuple <string, uint>(v.Name, k)]); // substitute to constant (needed for doing q.e.)
copy = (BoolExpr)copy.Substitute(Controller.Instance.GlobalVariablesPrimed[v.Name], Controller.Instance.Sys.GlobalReachValues[new Tuple <string, uint>(v.Name, k + 1)]); // substitute to constant (needed for doing q.e.)
}
for (uint j = 1; j <= N; j++)
{
if (j == i)
{
continue;
}
foreach (var v in Controller.Instance.Sys.HybridAutomata[0].Variables) // TODO: generalize
{
copy = (BoolExpr)copy.Substitute(Controller.Instance.Z3.MkApp(v.Value, Controller.Instance.Z3.MkInt(j)), Controller.Instance.Sys.ReachValues[new Tuple <string, uint, uint>(v.Name, k, j)]); // substitute to constant (needed for doing q.e.)
copy = (BoolExpr)copy.Substitute(Controller.Instance.Z3.MkApp(v.ValuePrimed, Controller.Instance.Z3.MkInt(j)), Controller.Instance.Sys.ReachValues[new Tuple <string, uint, uint>(v.Name, k + 1, j)]); // substitute to constant (needed for doing q.e.)
}
}
transAll.Add(copy);
}
resetAnd = Controller.Instance.Z3.MkOr(transAll.ToArray());
return(resetAnd);
}
