private BasicMapWrite(
MapType mapType,
ITypeTuple indexTypes,
IType sourceType,
IType resultType,
ITypeTuple mapTypeArguments
)
{
Debug.Assert(mapType != null);
Debug.Assert(mapTypeArguments != null);
Debug.Assert(indexTypes != null);
Debug.Assert(sourceType != null);
Debug.Assert(resultType != null);
Debug.Assert(indexTypes.Count() == mapType.domain.Count());
Debug.Assert(mapTypeArguments.Count() == mapType.typeParameters.Length);
this.mapType = mapType;
mapIndexTypes = indexTypes;
this.sourceType = sourceType;
this.resultType = resultType;
this.mapTypeArguments = TypeTuple.make(mapTypeArguments);
Debug.Assert(this.mapTypeArguments != null);
this.typeArguments = TypeTuple.make(new IType[1] {
mapType
}.Concat(mapTypeArguments));
this.argumentTypes = TypeTuple.make(new [] { mapType }.Concat(mapIndexTypes).Concat(new[] { sourceType }));
this.freeTypeVariables =
new HashSet <TypeVariable>(resultType.freeTypeVariables.
Union(mapType.freeTypeVariables).
Union(sourceType.freeTypeVariables).
Union(from it in mapIndexTypes from fv in it.freeTypeVariables select fv)
);
}
////////////////////////////////////////////
////////////////////////////////////////////
public override Expression substitute(ExpressionSubstitution s)
{
string ss = makeSubstitutionString(s);
if (substitutionCache.ContainsKey(ss))
{
return(substitutionCache[ss]);
}
bool needSubstitution = false;
foreach (var fv in freeVariables)
{
if (s.lookup(fv.name) != null)
{
needSubstitution = true;
}
}
foreach (var ftv in freeTypeVariables)
{
if (s.typeSubstitution.map(ftv) != null)
{
needSubstitution = true;
}
}
Expression result = this;
if (needSubstitution)
{
ExpressionList sArgs = arguments.substitute(s);
if (function.name == "==<>")
{
Debug.Assert(sArgs.count == 2);
if (sArgs[0].type.ToStringN() == sArgs[1].type.ToStringN())
{
result =
new BasicFAE(
BFunctionTemplate.eq.getInstance(TypeTuple.make(new[] { sArgs[0].type })), sArgs);
}
else if (sArgs.freeTypeVariables.Count > 0)
{
result =
new BasicFAE(
BFunctionTemplate.eqG.getInstance(TypeTuple.make(from a in sArgs select a.type)), sArgs);
}
else
{
result = new BasicLiteralExpression(BooleanValue.makeBooleanValue(false));
}
//equality of different types
}
else
{
result = new BasicFAE(function.substitute(s.typeSubstitution), sArgs);
}
}
substitutionCache[ss] = result;
return(result);
}
public static Function eq(IType t)
{
if (t is BooleanType)
{
return(equivalence);
}
return(BFunctionTemplate.eq.getInstance(TypeTuple.make(new [] { t })));
}
protected Operator(string name, string nameN, IEnumerable <IType> argumentTypes)
{
Debug.Assert(name != null);
Debug.Assert(!name.Contains('!'));
this.name = name;
this.nameN = nameN;
this.argumentTypes = TypeTuple.make(argumentTypes);
}
public ITypeTuple makeTypes(IList <Type> boogieTypes, Context context)
{
var types = new IType[boogieTypes.Count];
for (int i = 0; i < boogieTypes.Count; i++)
{
types[i] = makeTypeI(boogieTypes[i], context);
}
return(TypeTuple.make(types));
}
public IFormula visit(ExistentialFormula f)
{
var fvs = (from fv in f.f.ffreeVariables where fv != f.var select fv).ToArray();
var fvts = TypeTuple.make(from fv in fvs select fv.type);
var newF = srs.getFreshFunction("@sk", fvts, f.var.type);
var fvTerms = (from fv in fvs select new Variable(fv)).ToArray <ITerm>();
return(f.f.substitute(new Substitution(f.var, new FunctionApplicationFormula(newF, fvTerms))).visit(this));
}
public BasicFunctionSignature(IType resultType, IEnumerable <IType> arguments)
{
Debug.Assert(resultType != null);
Debug.Assert(arguments != null);
foreach (var a in arguments)
{
Debug.Assert(a != null);
}
this.resultType = resultType;
argumentTypes = TypeTuple.make(arguments);
}
public static BasicMapRead mapRead(MapType mapType, ITypeTuple typeArguments)
{
Debug.Assert(mapType != null);
Debug.Assert(typeArguments != null);
Debug.Assert(mapType.typeParameters.Length == typeArguments.Count());
var s = new TypeParameterInstantiation(mapType.typeParameters, typeArguments);
var argumentTypes = TypeTuple.make(new [] { mapType }.Concat(from a in mapType.domain select a.substitute(s)));
var resultType = mapType.range.substitute(s);
return(mapRead(typeArguments, argumentTypes, resultType));
}
public static Function eq(IType t1, IType t2)
{
//urij: special treatment for equality with type quantification
Debug.Assert(!t1.isGround || !t2.isGround);
if (t1.ToStringN() == t2.ToStringN())
{
return(BFunctionTemplate.eq.getInstance(TypeTuple.make(new [] { t1 })));
}
else
{
return(BFunctionTemplate.eqG.getInstance(TypeTuple.make(new[] { t1, t2 })));
}
}
public BasicFunctionTemplateInstance(
FunctionTemplate template,
IEnumerable <IType> typeArguments
)
: base(
template.name,
template.signature.resultType.substitute(new TypeParameterInstantiation(template.typeParameters,
typeArguments)),
(from at in template.signature.argumentTypes
select at.substitute(new TypeParameterInstantiation(template.typeParameters, typeArguments))).ToArray()
)
{
this.template = template;
pTypeArguments = TypeTuple.make(typeArguments);
}
protected TermTupleC(IEnumerable <T> ts)
: base(ts)
{
this.orderedFreeVariables = new List <LVar>();
foreach (var t in ts)
{
foreach (var fv in t.orderedFreeVariables)
{
if (!orderedFreeVariables.Contains(fv))
{
orderedFreeVariables.Add(fv);
}
}
}
this.dataTypes = TypeTuple.make(from t in ts select t.type);
}
private BoogieBitVectorConcatenationFunction(BvConcatExpr bce, int w0, int w1)
: base(
"++",//bce."++",//FunctionSymbol.ToString(),
BitVectorType.makeBitVectorType(w0 + w1),
new IType[2]
{
BitVectorType.makeBitVectorType(w0),
BitVectorType.makeBitVectorType(w1)
}
)
{
boogieExpression = bce;
this.w0 = w0;
this.w1 = w1;
typeArguments = TypeTuple.make();
}
private BoogieBitVectorExtractorFunction(BvExtractExpr bee, int w, int from, int to)
: base(
"BV[]",//bee.FunctionSymbol.ToString(),
BitVectorType.makeBitVectorType(to - from),
new IType[1]
{
BitVectorType.makeBitVectorType(w)
}
)
{
boogieExpression = bee;
this.w = w;
this.from = from;
this.to = to;
typeArguments = TypeTuple.make();
}
private Expression makeMapWriteMap(FAE fae)
{
Debug.Assert(fae.function is MapWrite);
Debug.Assert(fae.arguments[0].type is MapType);
var mu = fae.function as MapWrite;
Expression result;
if (!versionMap.TryGetValue(fae.ToString(), out result))
{
var ot = fae.arguments[0].type as MapType;
Debug.Assert(ot != null);
var s = new TypeParameterInstantiation(ot.typeParameters, mu.typeArguments.Skip(1).ToArray());
// var ots = new MapType(new TypeVariable[0], (from m in ot.domain select m.substitute(s)).ToArray(), ot.range.substitute(s));
Expression m = fae.arguments[0];
Expression[] i = fae.arguments.Take(fae.arguments.count - 1).Skip(1).ToArray();
if (fae.freeVariables.Count > 0)
{
//m(fv)[i(fv):=x(fv)] ==> v(fv) (assume v(fv)[i]==x, assume forall fv : forall j : j!=i(fv) ==> v(fv)[j] == m(fv)[j]
var fvt = TypeTuple.make(from fv in fae.freeVariables select fv.type);
string fn = getFreshMUName("mu");
var ft = new BFunctionTemplate(fn, "", new TypeVariable[0], new BasicFunctionSignature(ot, fvt),
null);
Function f = ft.getInstance();
IEnumerable <BasicBoundVariableExpression> fve = from fv in fae.freeVariables
select new BasicBoundVariableExpression(fv);
result = new BasicFAE(f, new ExpressionList(fve));
}
else
{
//m[i:=x] ==> v (assume v[i]==x, assume forall j : j!=i ==> v[j] == m[j]
string nvn = getFreshMUName("mu");
var nv = new ProgramVariable(nvn, ot, false, false, false, false);
procedure.addVariable(nv);
result = new BasicProgramVariableExpression(nv);
}
Expression[] j =
(from e in i select new BasicBoundVariableExpression(makeBoundVariable(e.type))).ToArray();
//forall j : j!=i ==> v[j]==m[j]
addConditionalMapEqualityAxiom(i, result, m, mu.typeArguments);
//v[i]==x;
Expression x = fae.arguments.Last();
addEqualityAxiom(ml(result, i, mu.typeArguments.Skip(1).ToArray(), x.type), fae.arguments.Last());
}
return(result);
}
private Literal makeDefinition(ISet <Clause> d, Clause c)
{
Debug.Assert(!c.isFalse);
Debug.Assert(!c.isTrue);
Debug.Assert(c.literals.Count > 0);
if (c.literals.Count == 1)
{
return(c.literals.First());
}
var fvs = c.freeVariables.ToArray();
var dts = TypeTuple.make(from fv in fvs select fv.type);
var N = srs.getFreshPredicate(CSRS.NPPrefix, dts);
// Console.WriteLine("\t\t Defining {0} as {1}", c.ToString(), N.name);
{
var nc = new List <Literal>();
var vs = srs.getFreshVariables(fvs);
var vts = (from v in vs select new Variable(v)).ToArray();
nc.Add(new Literal(new PredicateApplication(N, vts), false));
var s = new Substitution(fvs, vts);
foreach (var a in c.literals)
{
nc.Add(a.substitute(s));
}
d.Add(new Clause(nc));
// Console.WriteLine("\t\t\t Adding {0}", nc.ToString());
}
foreach (var a in c.literals)
{
var nc = new List <Literal>();
var vs = srs.getFreshVariables(fvs);
var vts = (from v in vs select new Variable(v)).ToArray();
var s = new Substitution(fvs, vts);
nc.Add(new Literal(new PredicateApplication(N, vts), true));
nc.Add(a.substitute(s).negate());
d.Add(new Clause(nc));
// Console.WriteLine("\t\t\t Adding {0}", nc.ToString());
}
var ovts = (from v in fvs select new Variable(v)).ToArray();
return(new Literal(new PredicateApplication(N, ovts), true));
}
public BFunction(
string name,
IType resultType,
IEnumerable <IType> argumentTypes
)
{
Debug.Assert(name != null);
Debug.Assert(resultType != null);
Debug.Assert(argumentTypes != null);
foreach (var at in argumentTypes)
{
Debug.Assert(at != null);
}
// Debug.Assert(name != "true" && name != "True" && name != "false" && name != "False");
this.name = name;
this.argumentTypes = TypeTuple.make(argumentTypes);
this.resultType = resultType;
}
public static BasicMapRead mapRead(IEnumerable <IType> typeArguments, IEnumerable <IType> argumentTypes, IType resultType)
{
Debug.Assert(typeArguments != null);
Debug.Assert(argumentTypes != null);
Debug.Assert(argumentTypes.Count() > 0);
var mapType = argumentTypes.First() as MapType;
Debug.Assert(mapType != null);
Debug.Assert(typeArguments.Count() == mapType.typeParameters.Length);
Debug.Assert(mapType.domain.Count() == argumentTypes.Count() - 1);
var substitution = new TypeParameterInstantiation(mapType.typeParameters, typeArguments);
IType sresultType = mapType.range.substitute(substitution);
Debug.Assert(resultType.ToStringN() == sresultType.ToStringN());
Debug.Assert(argumentTypes.Skip(1).Zip(mapType.domain, (at, mtD) => at.isEquivalent(mtD.substitute(substitution))).All(x => x));
string indexString = makeIndexString(TypeTuple.make(typeArguments), TypeTuple.make(argumentTypes));
BasicMapRead result = null;
bool foundInstance = instances.TryGetValue(indexString, out result);
if (result != null)
{
if (!ReferenceEquals(resultType, result.resultType))
{
foundInstance = false;
}
else
if (argumentTypes.Zip(result.argumentTypes, (x, y) => x.isEquivalent(y)).Any(x => !x))
{
foundInstance = false;
}
}
if (!foundInstance)
{
var indexTypes = argumentTypes.Skip(1);
result = new BasicMapRead(mapType, typeArguments, indexTypes, resultType);
instances[indexString] = result;
}
return(result);
}
public Expression visit(FAE e)
{
var ml = e.function as MapRead;
if (ml != null)
{
Dictionary <string, ITypeTuple> entry;
if (!srs.mapReads.TryGetValue(ml.mapType.ToStringN(), out entry))
{
srs.mapReads[ml.mapType.ToStringN()] = entry = new Dictionary <string, ITypeTuple>();
}
var dts = TypeTuple.make(ml.mapTypeArguments);
entry[dts.ToString()] = dts;
}
foreach (var a in e.arguments)
{
a.visit(this);
}
return(e);
}
private Predicate makeDefinition(SortedSet <Clause> d, IEnumerable <Clause> cs)
{
// N :: forall ci in cs :: [ N \/ \/_i !Nci ] /\ /\_i [!N \/ Nci]
var defs = from c in cs select makeDefinition(d, c);
var fvs = freeVariables(cs).ToArray();
var dts = TypeTuple.make(from fv in fvs select fv.type);
var N = srs.getFreshPredicate(CSRS.NPPrefix, dts);
// Console.WriteLine("\t Defining {0} as {1}", cs.ToString(), N.name);
foreach (var def in defs)
{
var c = new List <Literal>();
var vs = srs.getFreshVariables(fvs);
var vts = (from v in vs select new Variable(v)).ToArray();
c.Add(new Literal(new PredicateApplication(N, vts), false));
var s = new Substitution(fvs, vts);
c.Add(def.substitute(s));
d.Add(new Clause(c));
// Console.WriteLine("\t\t Adding {0}", c.ToString());
}
{
var c = new List <Literal>();
var vs = srs.getFreshVariables(fvs);
var vts = (from v in vs select new Variable(v)).ToArray();
var s = new Substitution(fvs, vts);
c.Add(new Literal(new PredicateApplication(N, vts), true));
foreach (var def in defs)
{
c.Add(def.substitute(s).negate());
}
d.Add(new Clause(c));
// Console.WriteLine("\t\t Adding {0}", c.ToString());
}
// definitionMap[cs.ToString()] = N;
return(N);
}
private BasicMapRead(MapType mapType, IEnumerable <IType> mapTypeArguments, IEnumerable <IType> indexTypes, IType resultType)
{
Debug.Assert(mapType != null);
Debug.Assert(indexTypes != null);
Debug.Assert(resultType != null);
Debug.Assert(mapType.domain.Count() == indexTypes.Count());
Debug.Assert(mapTypeArguments != null);
Debug.Assert(mapType.typeParameters.Length == mapTypeArguments.Count());
var substitution = new TypeParameterInstantiation(mapType.typeParameters, mapTypeArguments);
Debug.Assert(resultType.ToStringN() == mapType.range.substitute(substitution).ToStringN());
Debug.Assert(mapType.domain.Zip(indexTypes, (x, y) => x.substitute(substitution).isEquivalent(y)).All(x => x));
/* for (int i = 0; i < indexTypes.Count(); i++)
* Debug.Assert(indexTypes[i].ToStringExpanded() ==
* mapType.domain[i].substitute(substitution).ToStringExpanded());
*/
this.mapType = mapType;
mapIndexTypes = TypeTuple.make(indexTypes);
this.resultType = resultType;
this.mapTypeArguments = TypeTuple.make(mapTypeArguments);
}
public CFG <BasicBlock, BasicEdge> getCFGFromDAG(Implementation imp, Program program)
{
// Console.WriteLine("getCFGFromDAG");
cfg = new CFG <BasicBlock, BasicEdge>();
entry = cfg.addNode("$start");
exit = cfg.addNode("$exit");
labelIndex = 0;
// Console.WriteLine("\t\t\tDeclarations");
foreach (var tld in program.TopLevelDeclarations)
{
var a = tld as Axiom;
if (a != null)
{
// Console.WriteLine("\t\tAdding axiom {0}",a.Expr.ToString());
var assume = new Assume(procedure.expressionFactory.makeExpression(a.Expr));
entry.appendStatement(assume);
}
else
{
var bf = tld as Function;
if (bf != null && bf.Body != null)
{
var ft = scope.findFunctionTemplate(bf.Name);
var b = ft.body;
Debug.Assert(b != null);
var eqF = BFunctionTemplate.eq.getInstance(TypeTuple.make(new[] { ft.signature.resultType }));
var lhs = new BasicFAE(ft.getInstance(TypeTuple.make(from tv in ft.typeParameters select new VariableType(tv))), new ExpressionList(from bv in b.arguments select new BasicBoundVariableExpression(bv)));
var eqe = new BasicFAE(eqF, new ExpressionList(lhs, b.expression));
var axiom = procedure.expressionFactory.makeSentence(eqe);
var assume = new Assume(axiom);
entry.appendStatement(assume);
}
}
}
// Console.WriteLine("\t\t\tBlocks");
// var topoSortedBlocks
foreach (var b in topoSort(imp.Blocks, imp.Blocks[0]))
{
addBlock(b);
}
BasicBlock start = cfg.lookupOrAddNode(imp.Blocks[0].Label);
entry.setControlStatement(new UnconditionalBranch(entry, start));
exit.setControlStatement(new Programs.Statements.Block(exit));
cfg.setStartNode("$start");
cfg.setEndNode("$exit");
foreach (var bb in cfg.nodes)
{
if (!ReferenceEquals(bb, exit) && bb.successors.Count == 0)
{
bb.setControlStatement(new UnconditionalBranch(bb, exit));
}
}
foreach (var bb in cfg.nodes)
{
if (!ReferenceEquals(bb, entry) && bb.predecessors.Count == 0)
{
Console.WriteLine("Warning - removing orphan - {0}", bb.label);
bb.setControlStatement(new Programs.Statements.Block(bb));
bb.delete();
}
}
return(cfg);
}
////////////////////////////////////////////////////////////////////////////////////
private Expression makeExpression(NAryExpr fae, bool old)
{
if (fae.Fun is TypeCoercion)
{
return(makeExpression(fae.Args[0], old));
}
var arguments = new ExpressionList((from Expr e in fae.Args select makeExpression(e, old)).ToArray());
Function function;
if (fae.Fun is MapSelect)
{
var typeArguments = new IType[fae.TypeParameters.FormalTypeParams.Count];
for (int i = 0; i < fae.TypeParameters.FormalTypeParams.Count; i++)
{
typeArguments[i] = makeType(fae.TypeParameters[fae.TypeParameters.FormalTypeParams[i]]);
}
var argumentTypes = TypeTuple.make(from a in arguments select a.type);
function = BasicMapRead.mapRead(
typeArguments,
argumentTypes,
makeType(fae.Type)
);
}
else if (fae.Fun is MapStore)
{
var typeArguments = new IType[fae.TypeParameters.FormalTypeParams.Count];
for (int i = 0; i < fae.TypeParameters.FormalTypeParams.Count; i++)
{
typeArguments[i] = makeType(fae.TypeParameters[fae.TypeParameters.FormalTypeParams[i]]);
}
function = BasicMapWrite.makeMapWrite(typeArguments, (from a in arguments select a.type).ToArray(),
makeType(fae.ShallowType));
}
else if (fae.Fun.FunctionName == "==" || fae.Fun.FunctionName == "!=")
{
if (arguments[0].type.isEquivalent(arguments[1].type))
{
function = BFunction.eq(arguments[0].type);
}
else
{
Debug.Assert(!arguments[0].type.isGround || !arguments[1].type.isGround);
function = BFunction.eq(arguments[0].type, arguments[1].type);
}
if (fae.Fun.FunctionName == "!=")
{
arguments = new ExpressionList(
new BasicFAE(
function,
arguments
)
);
function = scope.getFunction("!", TypeTuple.make());
}
}
else if (fae.Fun.FunctionName == "<:")
{
function = scope.getFunction(fae.Fun.FunctionName, TypeTuple.make(new[] { arguments[0].type }));
}
else if (fae.Fun.FunctionName == BFunctionTemplate.iteName)
{
function = scope.getFunction(fae.Fun.FunctionName, TypeTuple.make(new[] { arguments[1].type }));
}
else if (fae.Fun.FunctionName == @"-" && fae.Fun.ArgumentCount == 1)
{
arguments = new ExpressionList(new[] { new BasicLiteralExpression(IntegerValue.make(0)), arguments[0] });
function = scope.getFunction(@"-", TypeTuple.make());
}
else
{
var typeArguments = TypeTuple.make((fae.TypeParameters == null)
? new IType[0]
: (from ftp in fae.TypeParameters.FormalTypeParams
select scope.typeFactory.makeTypeI(fae.TypeParameters[ftp], context)));
function = scope.getFunction(fae.Fun.FunctionName, typeArguments);
}
var result = new BoogieFunctionApplicationExpression(fae, function, arguments);
Debug.Assert(result.type.ToStringN() ==
makeType(fae.Type == null ? fae.ShallowType : fae.Type).ToStringN());
Debug.Assert(result != null);
foreach (var fv in result.freeVariables)
{
Debug.Assert(context.lookupVariableByOwnName(fv.name) == fv);
}
foreach (var ftv in result.freeTypeVariables)
{
Debug.Assert(ReferenceEquals(context.lookupTypeVariable(ftv.name), ftv));
}
return(result);
}
private LTPredicate() : base(StateSpace.Functions.Basic.BFunctionTemplate.lt.name, TypeTuple.make(new[] { IntegerType.integerType, IntegerType.integerType }))
{
}
public Function getInstance()
{
return(getInstance(TypeTuple.make()));
}
public static MapRead mu2ml(MapWrite mu)
{
var mlArgTypes = TypeTuple.make(mu.argumentTypes.Take(mu.argumentTypes.Count() - 1));
return(BasicMapRead.mapRead(mu.typeArguments.Skip(1).ToArray(), mlArgTypes, mu.argumentTypes.Last()));
}
public MapRead mapRead(IEnumerable <IType> mapTypeArgs)
{
Debug.Assert(mapTypeArgs.Count() == mapType.typeParameters.Length);
return(BasicMapRead.mapRead(mapType, TypeTuple.make(mapTypeArgs)));
}
private FalsePredicate()
: base("false", TypeTuple.make())
{
}
private TruePredicate()
: base("true", TypeTuple.make())
{
}
public static BasicMapWrite makeMapWrite(
IEnumerable <IType> mapTypeArgumentsA,
IEnumerable <IType> argumentTypesA,
IType resultType)
{
var mapTypeArguments = TypeTuple.make(mapTypeArgumentsA);
var argumentTypes = TypeTuple.make(argumentTypesA);
Debug.Assert(mapTypeArguments != null);
Debug.Assert(argumentTypes != null);
Debug.Assert(argumentTypes.Count() > 1);
var mapType = argumentTypes[0] as MapType;
var sourceType = argumentTypes.Last();
Debug.Assert(mapType != null);
Debug.Assert(mapType.domain.Count() == argumentTypes.Count() - 2);
Debug.Assert(mapType.typeParameters.Count() == mapTypeArguments.Count());
var indexString = "";
foreach (var a in argumentTypes)
{
indexString += (indexString == "" ? "" : ",") + a.ToString();
}
var indexTypes = TypeTuple.make(argumentTypes.Skip(1).Take(argumentTypes.Count() - 2));
BasicMapWrite result = null;
bool foundInstance = instances.TryGetValue(indexString, out result);
if (result != null)
{
if (!ReferenceEquals(resultType, result.resultType))
{
foundInstance = false;
}
else
{
for (int i = 0; i < argumentTypes.Count(); i++)
{
if (!ReferenceEquals(argumentTypes[i], result.argumentTypes[i]))
{
foundInstance = false;
break;
}
}
}
}
if (!foundInstance)
{
result = new BasicMapWrite(mapType, indexTypes, sourceType, resultType, mapTypeArguments);
Debug.Assert(indexString != null);
Debug.Assert(instances != null);
Debug.Assert(result != null);
// instances.Add(indexString,result);
instances[indexString] = result;
}
return(result);
}
