internal ArraySort(Context ctx, Sort domain, Sort range)
: base(ctx, Native.Z3_mk_array_sort(ctx.nCtx, domain.NativeObject, range.NativeObject))
{
Contract.Requires(ctx != null);
Contract.Requires(domain != null);
Contract.Requires(range != null);
}
/// <summary>
/// Z3 expr to C# pretty printer
/// </summary>
public CSPrettyPrinter(Context z3)
{
this.charSort = z3.MkBitVecSort(16);
this.tt = z3.MkBool(true);
this.ff = z3.MkBool(false);
this.encoding = 16;
}
public Automaton<Expr> getAutomata(Z3Provider z3p, Expr universe, Expr var, Sort sort)
{ //Sort for pairs (input theory, BV)
var bv = z3p.Z3.MkBitVecSort(BVConst.BVSIZE);
var pairSort = z3p.MkTupleSort(sort, bv);
var dfapair = this.Normalize().PushQuantifiers().getAutomata(z3p, new List<string>(), universe, var, sort);
//Compute the new moves by dropping the last bit of every element in the phiMoves
var newMoves = Automaton<Expr>.Empty.GetMoves().ToList();
foreach (var oldMove in dfapair.GetMoves())
{
var oldCond = oldMove.Label;
//Compute the new condition as ()
Expr newCond = oldCond;
//Update the new set of moves
newMoves.Add(new Move<Expr>(oldMove.SourceState, oldMove.TargetState, newCond));
}
//Build the new dfa with the new moves
var automaton = Automaton<Expr>.Create(dfapair.InitialState, dfapair.GetFinalStates(), newMoves);
return automaton.Determinize(z3p).Minimize(z3p);
}
internal TupleSort(Context ctx, Symbol name, uint numFields, Symbol[] fieldNames, Sort[] fieldSorts)
: base(ctx)
{
Contract.Requires(ctx != null);
Contract.Requires(name != null);
IntPtr t = IntPtr.Zero;
NativeObject = Native.Z3_mk_tuple_sort(ctx.nCtx, name.NativeObject, numFields,
Symbol.ArrayToNative(fieldNames), AST.ArrayToNative(fieldSorts),
ref t, new IntPtr[numFields]);
}
/// <summary>
/// Create axiom: function f is injective in the i-th argument.
/// </summary>
/// <remarks>
/// The following axiom is produced:
/// <c>
/// forall (x_0, ..., x_n) finv(f(x_0, ..., x_i, ..., x_{n-1})) = x_i
/// </c>
/// Where, <code>finv</code>is a fresh function declaration.
/// </summary>
public static BoolExpr InjAxiom(Context ctx, FuncDecl f, int i)
{
Sort[] domain = f.Domain;
uint sz = f.DomainSize;
if (i >= sz)
{
Console.WriteLine("failed to create inj axiom");
return null;
}
/* declare the i-th inverse of f: finv */
Sort finv_domain = f.Range;
Sort finv_range = domain[i];
FuncDecl finv = ctx.MkFuncDecl("f_fresh", finv_domain, finv_range);
/* allocate temporary arrays */
Expr[] xs = new Expr[sz];
Symbol[] names = new Symbol[sz];
Sort[] types = new Sort[sz];
/* fill types, names and xs */
for (uint j = 0; j < sz; j++)
{
types[j] = domain[j];
names[j] = ctx.MkSymbol(String.Format("x_{0}", j));
xs[j] = ctx.MkBound(j, types[j]);
}
Expr x_i = xs[i];
/* create f(x_0, ..., x_i, ..., x_{n-1}) */
Expr fxs = f[xs];
/* create f_inv(f(x_0, ..., x_i, ..., x_{n-1})) */
Expr finv_fxs = finv[fxs];
/* create finv(f(x_0, ..., x_i, ..., x_{n-1})) = x_i */
Expr eq = ctx.MkEq(finv_fxs, x_i);
/* use f(x_0, ..., x_i, ..., x_{n-1}) as the pattern for the quantifier */
Pattern p = ctx.MkPattern(new Expr[] { fxs });
/* create & assert quantifier */
BoolExpr q = ctx.MkForall(
types, /* types of quantified variables */
names, /* names of quantified variables */
eq,
1,
new Pattern[] { p } /* patterns */);
return q;
}
/// <summary>
/// Returns the Z3 term corresponding to the MSF rational number.
/// </summary>
/// <param name="rational">The MSF rational</param>
/// <returns>The Z3 term</returns>
public static ArithExpr GetNumeral(Context context, Rational rational, Sort sort = null)
{
try
{
sort = rational.IsInteger() ? ((Sort)context.IntSort) : (sort == null ? (Sort)context.RealSort : sort);
return (ArithExpr)context.MkNumeral(rational.ToString(), sort);
}
catch (Z3Exception e)
{
Console.Error.WriteLine("Conversion of {0} failed:\n {1}", rational, e);
throw new NotSupportedException();
}
}
internal ListSort(Context ctx, Symbol name, Sort elemSort)
: base(ctx)
{
Contract.Requires(ctx != null);
Contract.Requires(name != null);
Contract.Requires(elemSort != null);
IntPtr inil = IntPtr.Zero, iisnil = IntPtr.Zero,
icons = IntPtr.Zero, iiscons = IntPtr.Zero,
ihead = IntPtr.Zero, itail = IntPtr.Zero;
NativeObject = Native.Z3_mk_list_sort(ctx.nCtx, name.NativeObject, elemSort.NativeObject,
ref inil, ref iisnil, ref icons, ref iiscons, ref ihead, ref itail);
}
internal Quantifier(Context ctx, bool isForall, Sort[] sorts, Symbol[] names, Expr body,
uint weight = 1, Pattern[] patterns = null, Expr[] noPatterns = null,
Symbol quantifierID = null, Symbol skolemID = null
)
: base(ctx)
{
Contract.Requires(ctx != null);
Contract.Requires(sorts != null);
Contract.Requires(names != null);
Contract.Requires(body != null);
Contract.Requires(sorts.Length == names.Length);
Contract.Requires(Contract.ForAll(sorts, s => s != null));
Contract.Requires(Contract.ForAll(names, n => n != null));
Contract.Requires(patterns == null || Contract.ForAll(patterns, p => p != null));
Contract.Requires(noPatterns == null || Contract.ForAll(noPatterns, np => np != null));
Context.CheckContextMatch(patterns);
Context.CheckContextMatch(noPatterns);
Context.CheckContextMatch(sorts);
Context.CheckContextMatch(names);
Context.CheckContextMatch(body);
if (sorts.Length != names.Length)
throw new Z3Exception("Number of sorts does not match number of names");
IntPtr[] _patterns = AST.ArrayToNative(patterns);
if (noPatterns == null && quantifierID == null && skolemID == null)
{
NativeObject = Native.Z3_mk_quantifier(ctx.nCtx, (isForall) ? 1 : 0, weight,
AST.ArrayLength(patterns), AST.ArrayToNative(patterns),
AST.ArrayLength(sorts), AST.ArrayToNative(sorts),
Symbol.ArrayToNative(names),
body.NativeObject);
}
else
{
NativeObject = Native.Z3_mk_quantifier_ex(ctx.nCtx, (isForall) ? 1 : 0, weight,
AST.GetNativeObject(quantifierID), AST.GetNativeObject(skolemID),
AST.ArrayLength(patterns), AST.ArrayToNative(patterns),
AST.ArrayLength(noPatterns), AST.ArrayToNative(noPatterns),
AST.ArrayLength(sorts), AST.ArrayToNative(sorts),
Symbol.ArrayToNative(names),
body.NativeObject);
}
}
internal RankedAlphabet(
TreeTheory tt,
string[] symbols,
Dictionary<string, int> idMap,
Sort alphabetSort,
Sort nodeSort,
int[] ranks,
FuncDecl[] constructors,
FuncDecl[][] accessors,
FuncDecl[] testers,
FuncDecl acceptor,
Expr[] vars
)
{
this.tt = tt;
this.symbols = new List<string>(symbols).AsReadOnly();
this.idMap = idMap;
this.alphabetSort = alphabetSort;
this.nodeSort = nodeSort;
this.ranks = ranks;
this.constructors = constructors;
this.accessors = accessors;
this.testers = testers;
this.acceptor = acceptor;
this.vars = vars;
this.trans = tt.GetTrans(alphabetSort, alphabetSort);
this.emptyAcceptor = TreeTransducer.MkEmpty(this);
this.fullAcceptor = TreeTransducer.MkFull(this);
this.idAut = TreeTransducer.MkId(this);
this.symbolsOfRank = new Dictionary<int, List<FuncDecl>>();
for (int i = 0; i < ranks.Length; i++)
{
var r = ranks[i];
if (!symbolsOfRank.ContainsKey(r))
symbolsOfRank[r] = new List<FuncDecl>();
symbolsOfRank[r].Add(constructors[i]);
}
var attrDomain = tt.Z.MkFreshFuncDecl("_", new Sort[] { nodeSort }, tt.Z.BoolSort);
this.attrExpr = tt.Z.MkApp(attrDomain, vars[0]);
tt.Z.AssertAxiom(this.attrExpr, tt.Z.True, vars[0]);
}
public UnrankedTreeInfo(Sort treeListSort, FuncDecl getNodeValue, FuncDecl getSubtrees, FuncDecl mkNode,
FuncDecl mkLeaf, FuncDecl getLeafValue, FuncDecl isNode, FuncDecl isLeaf,
Expr empty, FuncDecl first, FuncDecl rest,
FuncDecl cons, FuncDecl isEmpty, FuncDecl isCons)
{
this.TreeListSort = treeListSort;
this.GetNodeLabel = getNodeValue;
this.GetNodeSubtrees = getSubtrees;
this.MkNode = mkNode;
this.EmptyTreeList = empty;
this.GetFirst = first;
this.GetRest = rest;
this.MkCons = cons;
this.IsEmpty = isEmpty;
this.IsCons = isCons;
this.MkLeaf = mkLeaf;
this.GetLeafValue = getLeafValue;
this.IsNode = isNode;
this.IsLeaf = isLeaf;
}
public Const(ConstDef def, FastTransducerInstance fti, Z3Provider z3p)
{
this.z3p = z3p;
this.name = def.id.text;
switch (def.sort.kind)
{
case (FastSortKind.Real):
{
sort = z3p.RealSort;
break;
}
case (FastSortKind.Bool):
{
sort = z3p.BoolSort;
break;
}
case (FastSortKind.Int):
{
sort = z3p.IntSort;
break;
}
case (FastSortKind.String):
{
sort = z3p.MkListSort(z3p.CharSort);
break;
}
case (FastSortKind.Tree):
{
foreach (var enumSort in fti.enums)
{
if (enumSort.name == def.sort.name.text)
{
sort = enumSort.sort;
break;
}
}
break;
}
}
this.value = GenerateZ3ExprFromExpr(def.expr, fti).Simplify();
}
internal override Automaton<Expr> getAutomata(Z3Provider z3p, List<string> variables, Expr universe, Expr var, Sort sort)
{
//var bit1 = z3p.Z3.MkInt2Bv(1,
// z3p.MkInt(1));
var bit1 = z3p.Z3.MkInt2BV(BVConst.BVSIZE, (IntExpr)z3p.MkInt(1));
//Sort for pairs (input theory, BV)
var bv = z3p.Z3.MkBitVecSort(BVConst.BVSIZE);
var pairSort = z3p.MkTupleSort(sort, bv);
//Add the representation of the existential variable to the list of variables
var newVariables = variables.ToArray().ToList();
newVariables.Insert(0, variable);
//Compute the DFA for the formula phi
var phiDfa = phi.getAutomata(z3p, newVariables, universe, var, sort);
//Compute the new moves by dropping the last bit of every element in the phiMoves
var newMoves = Automaton<Expr>.Empty.GetMoves().ToList();
foreach (var oldMove in phiDfa.GetMoves())
{
var oldCond = oldMove.Label;
var t = z3p.MkProj(1,var);
//Compute the new conditions
var newCond0 = z3p.ApplySubstitution(oldCond, t,
z3p.Z3.MkBVSHL((BitVecExpr)t, (BitVecExpr)bit1));
var newCond1 = z3p.ApplySubstitution(oldCond, t,
z3p.MkBvAdd(
z3p.Z3.MkBVSHL((BitVecExpr)t, (BitVecExpr)bit1),
bit1));
//Update the new set of moves
newMoves.Add(new Move<Expr>(oldMove.SourceState, oldMove.TargetState, z3p.MkOr(z3p.Simplify(newCond0),z3p.Simplify(newCond1))));
}
//Build the new dfa with the new moves
return Automaton<Expr>.Create(phiDfa.InitialState, phiDfa.GetFinalStates(), newMoves);
//.Determinize(z3p).MinimizeClassical(z3p, int.MaxValue,false);
}
internal Constructor(Context ctx, Symbol name, Symbol recognizer, Symbol[] fieldNames,
Sort[] sorts, uint[] sortRefs)
: base(ctx)
{
Contract.Requires(ctx != null);
Contract.Requires(name != null);
Contract.Requires(recognizer != null);
n = AST.ArrayLength(fieldNames);
if (n != AST.ArrayLength(sorts))
throw new Z3Exception("Number of field names does not match number of sorts");
if (sortRefs != null && sortRefs.Length != n)
throw new Z3Exception("Number of field names does not match number of sort refs");
if (sortRefs == null) sortRefs = new uint[n];
NativeObject = Native.Z3_mk_constructor(ctx.nCtx, name.NativeObject, recognizer.NativeObject,
n,
Symbol.ArrayToNative(fieldNames),
Sort.ArrayToNative(sorts),
sortRefs);
}
/// <summary>
/// Create a new list sort.
/// </summary>
public ListSort MkListSort(string name, Sort elemSort)
{
Contract.Requires(elemSort != null);
Contract.Ensures(Contract.Result<ListSort>() != null);
CheckContextMatch(elemSort);
return new ListSort(this, MkSymbol(name), elemSort);
}
/// <summary>
/// Creates a new function declaration.
/// </summary>
public FuncDecl MkFuncDecl(string name, Sort domain, Sort range)
{
Contract.Requires(range != null);
Contract.Requires(domain != null);
Contract.Ensures(Contract.Result<FuncDecl>() != null);
CheckContextMatch(domain);
CheckContextMatch(range);
Sort[] q = new Sort[] { domain };
return new FuncDecl(this, MkSymbol(name), q, range);
}
/// <summary>
/// Creates a new function declaration.
/// </summary>
public FuncDecl MkFuncDecl(string name, Sort[] domain, Sort range)
{
Contract.Requires(range != null);
Contract.Requires(Contract.ForAll(domain, d => d != null));
Contract.Ensures(Contract.Result<FuncDecl>() != null);
CheckContextMatch(domain);
CheckContextMatch(range);
return new FuncDecl(this, MkSymbol(name), domain, range);
}
/// <summary>
/// Create the full set.
/// </summary>
public Expr MkFullSet(Sort domain)
{
Contract.Requires(domain != null);
Contract.Ensures(Contract.Result<Expr>() != null);
CheckContextMatch(domain);
return Expr.Create(this, Native.Z3_mk_full_set(nCtx, domain.NativeObject));
}
/// <summary>
/// Creates a fresh constant function declaration with a name prefixed with <paramref name="prefix"/>.
/// </summary>
/// <seealso cref="MkFuncDecl(string,Sort,Sort)"/>
/// <seealso cref="MkFuncDecl(string,Sort[],Sort)"/>
public FuncDecl MkFreshConstDecl(string prefix, Sort range)
{
Contract.Requires(range != null);
Contract.Ensures(Contract.Result<FuncDecl>() != null);
CheckContextMatch(range);
return new FuncDecl(this, prefix, null, range);
}
internal FuncDecl(Context ctx, string prefix, Sort[] domain, Sort range)
: base(ctx, Native.Z3_mk_fresh_func_decl(ctx.nCtx, prefix, AST.ArrayLength(domain), AST.ArrayToNative(domain), range.NativeObject))
{
Contract.Requires(ctx != null);
Contract.Requires(range != null);
}
/// <summary>
/// Creates a new bound variable.
/// </summary>
/// <param name="index">The de-Bruijn index of the variable</param>
/// <param name="ty">The sort of the variable</param>
public Expr MkBound(uint index, Sort ty)
{
Contract.Requires(ty != null);
Contract.Ensures(Contract.Result<Expr>() != null);
return Expr.Create(this, Native.Z3_mk_bound(nCtx, index, ty.NativeObject));
}
/// <summary>
/// Create a set type.
/// </summary>
public SetSort MkSetSort(Sort ty)
{
Contract.Requires(ty != null);
Contract.Ensures(Contract.Result<SetSort>() != null);
CheckContextMatch(ty);
return new SetSort(this, ty);
}
/// <summary>
/// Create a Term of a given sort. This function can be use to create numerals that fit in a machine integer.
/// It is slightly faster than <c>MakeNumeral</c> since it is not necessary to parse a string.
/// </summary>
/// <param name="v">Value of the numeral</param>
/// <param name="ty">Sort of the numeral</param>
/// <returns>A Term with value <paramref name="v"/> and type <paramref name="ty"/></returns>
public Expr MkNumeral(ulong v, Sort ty)
{
Contract.Requires(ty != null);
Contract.Ensures(Contract.Result<Expr>() != null);
CheckContextMatch(ty);
return Expr.Create(this, Native.Z3_mk_unsigned_int64(nCtx, v, ty.NativeObject));
}
/// <summary>
/// Create a Quantifier.
/// </summary>
public Quantifier MkQuantifier(bool universal, Sort[] sorts, Symbol[] names, Expr body, uint weight = 1, Pattern[] patterns = null, Expr[] noPatterns = null, Symbol quantifierID = null, Symbol skolemID = null)
{
Contract.Requires(body != null);
Contract.Requires(names != null);
Contract.Requires(sorts != null);
Contract.Requires(sorts.Length == names.Length);
Contract.Requires(Contract.ForAll(sorts, s => s != null));
Contract.Requires(Contract.ForAll(names, n => n != null));
Contract.Requires(patterns == null || Contract.ForAll(patterns, p => p != null));
Contract.Requires(noPatterns == null || Contract.ForAll(noPatterns, np => np != null));
Contract.Ensures(Contract.Result<Quantifier>() != null);
if (universal)
return MkForall(sorts, names, body, weight, patterns, noPatterns, quantifierID, skolemID);
else
return MkExists(sorts, names, body, weight, patterns, noPatterns, quantifierID, skolemID);
}
/// <summary>
/// Parse the given string using the SMT-LIB2 parser.
/// </summary>
/// <seealso cref="ParseSMTLIBString"/>
/// <returns>A conjunction of assertions in the scope (up to push/pop) at the end of the string.</returns>
public BoolExpr ParseSMTLIB2String(string str, Symbol[] sortNames = null, Sort[] sorts = null, Symbol[] declNames = null, FuncDecl[] decls = null)
{
Contract.Ensures(Contract.Result<BoolExpr>() != null);
uint csn = Symbol.ArrayLength(sortNames);
uint cs = Sort.ArrayLength(sorts);
uint cdn = Symbol.ArrayLength(declNames);
uint cd = AST.ArrayLength(decls);
if (csn != cs || cdn != cd)
throw new Z3Exception("Argument size mismatch");
return (BoolExpr)Expr.Create(this, Native.Z3_parse_smtlib2_string(nCtx, str,
AST.ArrayLength(sorts), Symbol.ArrayToNative(sortNames), AST.ArrayToNative(sorts),
AST.ArrayLength(decls), Symbol.ArrayToNative(declNames), AST.ArrayToNative(decls)));
}
/// <summary>
/// Create a new tuple sort.
/// </summary>
public TupleSort MkTupleSort(Symbol name, Symbol[] fieldNames, Sort[] fieldSorts)
{
Contract.Requires(name != null);
Contract.Requires(fieldNames != null);
Contract.Requires(Contract.ForAll(fieldNames, fn => fn != null));
Contract.Requires(fieldSorts == null || Contract.ForAll(fieldSorts, fs => fs != null));
Contract.Ensures(Contract.Result<TupleSort>() != null);
CheckContextMatch(name);
CheckContextMatch(fieldNames);
CheckContextMatch(fieldSorts);
return new TupleSort(this, name, (uint)fieldNames.Length, fieldNames, fieldSorts);
}
/// <summary>
/// Create an array constant.
/// </summary>
public ArrayExpr MkArrayConst(string name, Sort domain, Sort range)
{
Contract.Requires(domain != null);
Contract.Requires(range != null);
Contract.Ensures(Contract.Result<ArrayExpr>() != null);
return (ArrayExpr)MkConst(MkSymbol(name), MkArraySort(domain, range));
}
/// <summary>
/// Parse the given string using the SMT-LIB parser.
/// </summary>
/// <remarks>
/// The symbol table of the parser can be initialized using the given sorts and declarations.
/// The symbols in the arrays <paramref name="sortNames"/> and <paramref name="declNames"/>
/// don't need to match the names of the sorts and declarations in the arrays <paramref name="sorts"/>
/// and <paramref name="decls"/>. This is a useful feature since we can use arbitrary names to
/// reference sorts and declarations.
/// </remarks>
public void ParseSMTLIBString(string str, Symbol[] sortNames = null, Sort[] sorts = null, Symbol[] declNames = null, FuncDecl[] decls = null)
{
uint csn = Symbol.ArrayLength(sortNames);
uint cs = Sort.ArrayLength(sorts);
uint cdn = Symbol.ArrayLength(declNames);
uint cd = AST.ArrayLength(decls);
if (csn != cs || cdn != cd)
throw new Z3Exception("Argument size mismatch");
Native.Z3_parse_smtlib_string(nCtx, str,
AST.ArrayLength(sorts), Symbol.ArrayToNative(sortNames), AST.ArrayToNative(sorts),
AST.ArrayLength(decls), Symbol.ArrayToNative(declNames), AST.ArrayToNative(decls));
}
/// <summary>
/// Create a datatype constructor.
/// </summary>
/// <param name="name"></param>
/// <param name="recognizer"></param>
/// <param name="fieldNames"></param>
/// <param name="sorts"></param>
/// <param name="sortRefs"></param>
/// <returns></returns>
public Constructor MkConstructor(string name, string recognizer, string[] fieldNames = null, Sort[] sorts = null, uint[] sortRefs = null)
{
Contract.Ensures(Contract.Result<Constructor>() != null);
return new Constructor(this, MkSymbol(name), MkSymbol(recognizer), MkSymbols(fieldNames), sorts, sortRefs);
}
/// <summary>
/// Create a new array sort.
/// </summary>
public ArraySort MkArraySort(Sort domain, Sort range)
{
Contract.Requires(domain != null);
Contract.Requires(range != null);
Contract.Ensures(Contract.Result<ArraySort>() != null);
CheckContextMatch(domain);
CheckContextMatch(range);
return new ArraySort(this, domain, range);
}
/// <summary>
/// Creates a fresh Constant of sort <paramref name="range"/> and a
/// name prefixed with <paramref name="prefix"/>.
/// </summary>
public Expr MkFreshConst(string prefix, Sort range)
{
Contract.Requires(range != null);
Contract.Ensures(Contract.Result<Expr>() != null);
CheckContextMatch(range);
return Expr.Create(this, Native.Z3_mk_fresh_const(nCtx, prefix, range.NativeObject));
}
/// <summary>
/// The finite set of distinct values that represent the interpretation for sort <paramref name="s"/>.
/// </summary>
/// <seealso cref="Sorts"/>
/// <param name="s">An uninterpreted sort</param>
/// <returns>An array of expressions, where each is an element of the universe of <paramref name="s"/></returns>
public Expr[] SortUniverse(Sort s)
{
Contract.Requires(s != null);
Contract.Ensures(Contract.Result<Expr[]>() != null);
ASTVector nUniv = new ASTVector(Context, Native.Z3_model_get_sort_universe(Context.nCtx, NativeObject, s.NativeObject));
uint n = nUniv.Size;
Expr[] res = new Expr[n];
for (uint i = 0; i < n; i++)
res[i] = Expr.Create(Context, nUniv[i].NativeObject);
return res;
}
internal Parameter(Z3_parameter_kind k, Sort s)
{
this.kind = k;
this.srt = s;
}
