/** Create a symbolic transformer. */
public Transformer CreateTransformer(FuncDecl[] _RelParams, Term[] _IndParams, Term _Formula)
{
Transformer t = new Transformer();
t.RelParams = _RelParams;
t.IndParams = _IndParams;
t.Formula = _Formula;
t.owner = this;
return t;
}
/** Create a relation (nullary relational transformer) */
public Transformer CreateRelation(Term[] _IndParams, Term _Formula)
{
return CreateTransformer(new FuncDecl[0], _IndParams, _Formula);
}
/** Assert a background axiom. Background axioms can be used to provide the
* theory of auxilliary functions or relations. All symbols appearing in
* background axioms are considered global, and may appear in both transformer
* and relational solutions. Semantically, a solution to the RPFP gives
* an interpretation of the unknown relations for each interpretation of the
* auxilliary symbols that is consistent with the axioms. Axioms should be
* asserted before any calls to Push. They cannot be de-asserted by Pop. */
public void AssertAxiom(Term t)
{
ctx.AddAxiom(t);
}
private Term ExtractSmallerVCsRec(TermDict< Term> memo, Term t, List<Term> small, Term lbl = null)
{
Term res;
if (memo.TryGetValue(t, out res))
return res;
var kind = t.GetKind();
if (kind == TermKind.App)
{
var f = t.GetAppDecl();
if (f.GetKind() == DeclKind.Implies){
var lhs = t.GetAppArgs()[0];
if(lhs.GetKind() == TermKind.App){
var r = lhs.GetAppDecl();
if (r.GetKind() == DeclKind.And)
{
Term q = t.GetAppArgs()[1];
var lhsargs = lhs.GetAppArgs();
for (int i = lhsargs.Length-1; i >= 0; --i)
{
q = ctx.MkImplies(lhsargs[i], q);
}
res = ExtractSmallerVCsRec(memo, q, small,lbl);
goto done;
}
if (r.GetKind() == DeclKind.Label)
{
var arg = lhs;
arg = lhs.GetAppArgs()[0];
if (!(arg.GetKind() == TermKind.App && arg.GetAppDecl().GetKind() == DeclKind.Uninterpreted))
goto normal;
if (!(annotationInfo.ContainsKey(arg.GetAppDecl().GetDeclName()) && annotationInfo[arg.GetAppDecl().GetDeclName()].type == AnnotationInfo.AnnotationType.LoopInvariant))
goto normal;
var sm = ctx.MkImplies(lhs, ExtractSmallerVCsRec(memo, t.GetAppArgs()[1], small));
if (lbl != null)
sm = ctx.MkImplies(lbl, sm);
small.Add(sm);
res = ctx.MkTrue();
goto done;
}
if (r.GetKind() == DeclKind.Uninterpreted)
{
var arg = lhs;
if (!(annotationInfo.ContainsKey(arg.GetAppDecl().GetDeclName()) && annotationInfo[arg.GetAppDecl().GetDeclName()].type == AnnotationInfo.AnnotationType.LoopInvariant))
goto normal;
var sm = ctx.MkImplies(lhs,ExtractSmallerVCsRec(memo,t.GetAppArgs()[1],small));
if (lbl != null)
sm = ctx.MkImplies(lbl, sm);
small.Add(sm);
res = ctx.MkTrue();
goto done;
}
}
normal:
Term newlbl = null;
if (lhs.IsLabel() && lhs.GetAppArgs()[0] == ctx.MkTrue())
newlbl = lhs;
res = ctx.MkImplies(lhs,ExtractSmallerVCsRec(memo,t.GetAppArgs()[1],small,newlbl));
}
else if (f.GetKind() == DeclKind.And)
{
res = ctx.MkApp(f,t.GetAppArgs().Select(x => ExtractSmallerVCsRec(memo, x, small)).ToArray());
}
else
res = t;
}
else
res = t;
done:
memo.Add(t, res);
return res;
}
private bool EvalToFalse(RPFP rpfp, RPFP.Node root, Term expr,StratifiedInliningInfo info)
{
Term res = rpfp.Eval(root.Outgoing,expr);
return res.Equals(ctx.MkTrue());
}
public Term Letify(Term t)
{
var thing = new Letifier(this);
return(thing.Letify(t));
}
private bool IsVariable(Term t)
{
// TODO: is this right?
// return t.IsFunctionApp() && t.GetAppArgs().Length == 0;
return t is VCExprVar && !(t is VCExprConstant);
}
private Term CollectParamsRec(TermDict<Term> memo, Term t, List<FuncDecl> parms, List<RPFP.Node> nodes, Dictionary<Term, Term> done)
{
Term res;
if (memo.TryGetValue(t, out res))
return res;
if (t.GetKind() == TermKind.App)
{
var f = t.GetAppDecl();
Node node;
if (relationToNode.TryGetValue(f, out node))
{
if (done.ContainsKey(t))
res = done[t];
else
{
f = SuffixFuncDecl(t, parms.Count);
parms.Add(f);
nodes.Add(node);
done.Add(t,res); // don't count same expression twice!
}
}
var args = t.GetAppArgs();
args = args.Select(x => CollectParamsRec(memo, x, parms, nodes, done)).ToArray();
res = ctx.CloneApp(t, args);
} // TODO: handle quantifiers
else
res = t;
memo.Add(t, res);
return res;
}
public void AddAxiom(Term ax)
{
axioms.Add(ax);
}
public static bool IsFalse(this Term t)
{
return(t == VCExpressionGenerator.False);
}
public static bool IsFunctionApp(this Term t)
{
return(t.GetKind() == TermKind.App && t.GetAppDecl().GetKind() == DeclKind.Uninterpreted);
}
public static Sort GetSort(this Term t)
{
return(t.Type);
}
public static string LabelName(this Term t)
{
return((GetAppDecl(t) as VCExprLabelOp).label);
}
public static FuncDecl GetAppDecl(this Term t)
{
Microsoft.Boogie.VCExprAST.VCExprNAry tn = t as Microsoft.Boogie.VCExprAST.VCExprNAry;
return(tn.Op);
}
public static Term[] GetAppArgs(this Term t)
{
Microsoft.Boogie.VCExprAST.VCExprNAry tn = t as Microsoft.Boogie.VCExprAST.VCExprNAry;
return(tn.ToArray());
}
/** Convert an array of clauses to an RPFP.
*/
public void FromClauses(Term[] clauses)
{
FuncDecl failName = ctx.MkFuncDecl("@Fail", ctx.MkBoolSort());
foreach(var clause in clauses){
Node foo = GetNodeFromClause(clause,failName);
if(foo != null)
nodes.Add(foo);
}
foreach (var clause in clauses)
edges.Add(GetEdgeFromClause(clause,failName));
}
/** Sets the value in the counterexample of a symbol occuring in the transformer formula of
* a given edge. */
public void SetValue(Edge e, Term variable, Term value)
{
if (e.valuation == null)
e.valuation = new TermDict< Term>();
e.valuation.Add(variable, value);
}
public void RemoveAxiom(Term ax)
{
axioms.Remove(ax);
}
private Edge GetEdgeFromClause(Term t, FuncDecl failName)
{
Term[] args = t.GetAppArgs();
Term body = args[0];
Term head = args[1];
Term[] _IndParams;
FuncDecl Name;
if (head.IsFalse())
{
Name = failName;
_IndParams = new Term[0];
}
else
{
_IndParams = head.GetAppArgs();
Name = head.GetAppDecl();
}
for(int i = 0; i < _IndParams.Length; i++)
if (!IsVariable(_IndParams[i]))
{
Term v = ctx.MkConst("@a" + i.ToString(), _IndParams[i].GetSort());
body = ctx.MkAnd(body, ctx.MkEq(v, _IndParams[i]));
_IndParams[i] = v;
}
var relParams = new List<FuncDecl>();
var nodeParams = new List<RPFP.Node>();
var memo = new TermDict< Term>();
var done = new Dictionary<Term, Term>(); // note this hashes on equality, not reference!
body = CollectParamsRec(memo, body, relParams, nodeParams,done);
Transformer F = CreateTransformer(relParams.ToArray(), _IndParams, body);
Node parent = relationToNode[Name];
return CreateEdge(parent, F, nodeParams.ToArray());
}
public Term MkApp(FuncDecl f, Term arg)
{
return(Function(f, arg));
}
private Term SubstPredsRec(TermDict< Term> memo, Dictionary<FuncDecl,FuncDecl> subst, Term t)
{
Term res;
if (memo.TryGetValue(t, out res))
return res;
if (t.GetKind() == TermKind.App)
{
var args = t.GetAppArgs();
args = args.Select(x => SubstPredsRec(memo,subst,x)).ToArray();
FuncDecl nf = null;
var f = t.GetAppDecl();
if (subst.TryGetValue(f, out nf))
{
res = ctx.MkApp(nf, args);
}
else
{
res = ctx.CloneApp(t, args);
}
} // TODO: handle quantifiers
else
res = t;
memo.Add(t, res);
return res;
}
public Term MkAnd(Term arg1, Term arg2)
{
return(And(arg1, arg2));
}
private Term CollectGoalsRec(TermDict< Term> memo, Term t, List<Term> goals, List<Term> cruft)
{
Term res;
if (memo.TryGetValue(t, out res))
return res;
var kind = t.GetKind();
if (kind == TermKind.App)
{
var f = t.GetAppDecl();
if (f.GetKind() == DeclKind.Implies)
{
CollectGoalsRec(memo, t.GetAppArgs()[1], goals, cruft);
goto done;
}
else if (f.GetKind() == DeclKind.And)
{
foreach (var arg in t.GetAppArgs())
{
CollectGoalsRec(memo, arg, goals, cruft);
}
goto done;
}
else if (f.GetKind() == DeclKind.Label)
{
var arg = t.GetAppArgs()[0];
var r = arg.GetAppDecl();
if (r.GetKind() == DeclKind.Uninterpreted)
{
if (memo.TryGetValue(arg, out res))
goto done;
if (!annotationInfo.ContainsKey(r.GetDeclName()) && !arg.GetAppDecl().GetDeclName().StartsWith("_solve_"))
goto done;
goals.Add(arg);
memo.Add(arg, arg);
goto done;
}
else
return CollectGoalsRec(memo, arg, goals, cruft);
}
else if (f.GetKind() == DeclKind.Uninterpreted)
{
string name = f.GetDeclName();
if (name.StartsWith("_solve_"))
{
if (memo.TryGetValue(t, out res))
goto done;
goals.Add(t);
memo.Add(t, t);
return t;
}
}
}
// else the goal must be cruft
cruft.Add(t);
done:
res = t; // just to return something
memo.Add(t, res);
return res;
}
public Term MkNot(Term arg1)
{
return(Not(arg1));
}
private void ExtractSmallerVCs(Term t, List<Term> small)
{
TermDict< Term> memo = new TermDict< Term>();
Term top = ExtractSmallerVCsRec(memo, t, small);
small.Add(top);
}
public Term MkImplies(Term arg1, Term arg2)
{
return(Implies(arg1, arg2));
}
private void FactorVCs(Term t, List<Term> vcs)
{
List<Term> small = new List<Term>();
ExtractSmallerVCs(t, small);
foreach (var smm in small)
{
List<Term> goals = new List<Term>();
List<Term> cruft = new List<Term>();
var sm = largeblock ? MergeGoals(smm) : smm;
CollectGoals(sm, goals,cruft);
foreach (var goal in goals)
{
TermDict< Term> memo = new TermDict< Term>();
foreach (var othergoal in goals)
memo.Add(othergoal, othergoal.Equals(goal) ? ctx.MkFalse() : ctx.MkTrue());
foreach (var thing in cruft)
memo.Add(thing, ctx.MkTrue());
var vc = SubstRecGoals(memo, sm);
vc = ctx.MkImplies(ctx.MkNot(vc), goal);
vcs.Add(vc);
}
{
TermDict< Term> memo = new TermDict< Term>();
foreach (var othergoal in goals)
memo.Add(othergoal, ctx.MkTrue());
var vc = SubstRecGoals(memo, sm);
if (vc != ctx.MkTrue())
{
vc = ctx.MkImplies(ctx.MkNot(vc), ctx.MkFalse());
vcs.Add(vc);
}
}
}
}
public Term MkEq(Term arg1, Term arg2)
{
return(Eq(arg1, arg2));
}
/** Create a node in the graph. The input is a term R(v_1...v_n)
* where R is an arbitrary relational symbol and v_1...v_n are
* arbitary distinct variables. The names are only of mnemonic value,
* however, the number and type of arguments determine the type
* of the relation at this node. */
public Node CreateNode(Term t)
{
Node n = new Node();
// Microsoft.Boogie.VCExprAST.VCExprNAry tn = t as Microsoft.Boogie.VCExprAST.VCExprNAry;
// Term[] _IndParams = tn.ToArray();
Term[] _IndParams = t.GetAppArgs();
FuncDecl Name = t.GetAppDecl();
n.Annotation = CreateRelation(_IndParams,ctx.MkTrue());
n.Bound = CreateRelation(_IndParams, ctx.MkTrue());
n.owner = this;
n.number = ++nodeCount;
n.Name = Name; // just to have a unique name
n.Incoming = new List<Edge>();
return n;
}
private Term MergeGoals(Term t)
{
TermDict< Term> memo = new TermDict< Term>();
return MergeGoalsRec(memo, t);
}
/** Determines the value in the counterexample of a symbol occuring in the transformer formula of
* a given edge. */
public Term Eval(Edge e, Term t)
{
if (e.valuation == null)
e.valuation = new TermDict< Term>();
if (e.valuation.ContainsKey(t))
return e.valuation[t];
return null; // TODO
}
private Term MergeGoalsRec(TermDict< Term> memo, Term t)
{
Term res;
if (memo.TryGetValue(t, out res))
return res;
var kind = t.GetKind();
if (kind == TermKind.App)
{
var f = t.GetAppDecl();
var args = t.GetAppArgs();
if (f.GetKind() == DeclKind.Implies)
{
res = ctx.MkImplies(args[0], MergeGoalsRec(memo, args[1]));
goto done;
}
else if (f.GetKind() == DeclKind.And)
{
args = args.Select(x => MergeGoalsRec(memo, x)).ToArray();
res = ctx.MkApp(f, args);
goto done;
}
else if (f.GetKind() == DeclKind.Label)
{
var arg = t.GetAppArgs()[0];
var r = arg.GetAppDecl();
if (r.GetKind() == DeclKind.Uninterpreted)
{
res = NormalizeGoal(arg, f);
goto done;
}
}
}
res = t;
done:
memo.Add(t, res);
return res;
}
/** Do not call this. */
public void RemoveAxiom(Term t)
{
ctx.RemoveAxiom(t);
}
private Term NormalizeGoal(Term goal, FuncDecl label)
{
var f = goal.GetAppDecl();
var args = goal.GetAppArgs();
int number;
if (!goalNumbering.TryGetValue(f, out number))
{
number = goalNumbering.Count;
goalNumbering.Add(f, number);
}
Term[] tvars = new Term[args.Length];
Term[] eqns = new Term[args.Length];
AnnotationInfo info = null;
annotationInfo.TryGetValue(f.GetDeclName(), out info);
for (int i = 0; i < args.Length; i++)
{
string pname = (info == null) ? i.ToString() : info.argnames[i];
tvars[i] = ctx.MkConst("@a" + number.ToString() + "_" + pname, args[i].GetSort());
eqns[i] = ctx.MkEq(tvars[i], args[i]);
}
return ctx.MkImplies(ctx.MkAnd(eqns), ctx.MkApp(label, ctx.MkApp(f, tvars)));
}
private Term BindVariables(Term t, bool universal = true)
{
TermDict< bool> memo = new TermDict<bool>();
List<Term> vars = new List<Term>();
CollectVariables(memo,t,vars);
return universal ? ctx.MkForall(vars.ToArray(), t) : ctx.MkExists(vars.ToArray(), t);
}
private Term SubstRec(TermDict< Term> memo, Term t)
{
Term res;
if (memo.TryGetValue(t, out res))
return res;
var kind = t.GetKind();
if (kind == TermKind.App)
{
// var f = t.GetAppDecl();
var args = t.GetAppArgs().Select(x => SubstRec(memo, x)).ToArray();
res = ctx.CloneApp(t, args);
}
else res = t;
memo.Add(t, res);
return res;
}
private void CollectVariables(TermDict< bool> memo, Term t, List<Term> vars)
{
if (memo.ContainsKey(t))
return;
if (IsVariable(t))
vars.Add(t);
if (t.GetKind() == TermKind.App)
{
foreach (var s in t.GetAppArgs())
CollectVariables(memo, s, vars);
}
memo.Add(t, true);
}
private Term SubstRecGoals(TermDict< Term> memo, Term t)
{
Term res;
if (memo.TryGetValue(t, out res))
return res;
var kind = t.GetKind();
if (kind == TermKind.App)
{
var f = t.GetAppDecl();
var args = t.GetAppArgs();
if (f.GetKind() == DeclKind.Implies){
res = SubstRecGoals(memo, args[1]);
if (res != ctx.MkTrue())
res = ctx.MkImplies(args[0],res);
goto done;
}
else if (f.GetKind() == DeclKind.And)
{
args = args.Select(x => SubstRecGoals(memo, x)).ToArray();
args = args.Where(x => x != ctx.MkTrue()).ToArray();
res = ctx.MkAnd(args);
goto done;
}
else if (f.GetKind() == DeclKind.Label)
{
var arg = t.GetAppArgs()[0];
var r = arg.GetAppDecl();
if (r.GetKind() == DeclKind.Uninterpreted)
{
if (memo.TryGetValue(arg, out res))
{
if(res != ctx.MkTrue())
res = ctx.MkApp(f, res);
goto done;
}
}
else
{
res = ctx.MkApp(f, SubstRecGoals(memo, arg));
goto done;
}
}
// what's left could be cruft!
if (memo.TryGetValue(t, out res))
{
goto done;
}
}
res = t;
done:
memo.Add(t, res);
return res;
}
private Node GetNodeFromClause(Term t, FuncDecl failName)
{
Term[] args = t.GetAppArgs();
Term body = args[0];
Term head = args[1];
FuncDecl Name;
Term[] _IndParams;
bool is_query = false;
if (head.Equals(ctx.MkFalse()))
{
Name = failName;
is_query = true;
_IndParams = new Term[0];
}
else
{
Name = head.GetAppDecl();
_IndParams = head.GetAppArgs();
}
if (relationToNode.ContainsKey(Name))
return null;
for (int i = 0; i < _IndParams.Length; i++)
if (!IsVariable(_IndParams[i]))
{
Term v = ctx.MkConst("@a" + i.ToString(), _IndParams[i].GetSort());
_IndParams[i] = v;
}
Term foo = ctx.MkApp(Name, _IndParams);
Node node = CreateNode(foo);
relationToNode[Name] = node;
if (is_query)
node.Bound = CreateRelation(new Term[0], ctx.MkFalse());
return node;
}
// TODO: this is a bit cheesy. Rather than finding the argument position
// of a relational term in a transformer by linear search, better to index this
// somewhere, but where?
private int TransformerArgPosition(RPFP rpfp, RPFP.Node root, Term expr)
{
FuncDecl rel = expr.GetAppDecl();
string relname = rel.GetDeclName();
var rps = root.Outgoing.F.RelParams;
for (int i = 0; i < rps.Length; i++)
{
string thisname = rps[i].GetDeclName();
if (thisname == relname)
return i;
}
return -1;
}
private Term SubstPreds(Dictionary<FuncDecl, FuncDecl> subst, Term t)
{
TermDict< Term> memo = new TermDict< Term>();
return SubstPredsRec(memo, subst, t);
}
public void FindLabelsRec(HashSet<Term> memo, Term t, Dictionary<string, Term> res)
{
if (memo.Contains(t))
return;
if (t.IsLabel())
{
string l = t.LabelName();
if (!res.ContainsKey(l))
res.Add(l, t.GetAppArgs()[0]);
}
if (t.GetKind() == TermKind.App)
{
var args = t.GetAppArgs();
foreach (var a in args)
FindLabelsRec(memo, a, res);
} // TODO: handle quantifiers
memo.Add(t);
}
// This returns a new FuncDel with same sort as top-level function
// of term t, but with numeric suffix appended to name.
private FuncDecl SuffixFuncDecl(Term t, int n)
{
var name = t.GetAppDecl().GetDeclName() + "_" + n.ToString();
return ctx.MkFuncDecl(name, t.GetAppDecl());
}
private void CollectGoals(Term t, List<Term> goals, List<Term> cruft)
{
TermDict< Term> memo = new TermDict< Term>();
CollectGoalsRec(memo, t.GetAppArgs()[1], goals, cruft);
}
