/* This function allows you to replace, for example:
*
* Bpl.BoundVariable iVar = new Bpl.BoundVariable(e.tok, new Bpl.TypedIdent(e.tok, "$i", Bpl.Type.Int));
* Bpl.IdentifierExpr i = new Bpl.IdentifierExpr(e.tok, iVar);
*
* with:
*
* Bpl.Expr i; var iVar = BplBoundVar("$i", Bpl.Type.Int, out i);
*/
static Bpl.BoundVariable BplBoundVar(string name, Bpl.Type ty, out Bpl.Expr e)
{
Contract.Requires(ty != null);
var v = new Bpl.BoundVariable(ty.tok, new Bpl.TypedIdent(ty.tok, name, ty));
e = new Bpl.IdentifierExpr(ty.tok, name, ty);
return(v);
}
public void CachedHashCodeIdentifierExpr()
{
var id = new IdentifierExpr(Token.NoToken, "foo", BasicType.Bool, /*immutable=*/true);
Assert.AreEqual(id.ComputeHashCode(), id.GetHashCode());
var variable = new BoundVariable(Token.NoToken, new TypedIdent(Token.NoToken, "foo2", BasicType.Int));
var id2 = new IdentifierExpr(Token.NoToken, variable, /*immutable=*/true);
Assert.AreEqual(id2.ComputeHashCode(), id2.GetHashCode());
}
public void CachedHashCodeForAllExpr()
{
var x = new BoundVariable(Token.NoToken, new TypedIdent(Token.NoToken, "x", BasicType.Int));
var y = new BoundVariable(Token.NoToken, new TypedIdent(Token.NoToken, "x", BasicType.Int));
var body = Expr.Gt (new IdentifierExpr (Token.NoToken, x, /*immutable=*/true),
new IdentifierExpr(Token.NoToken, y, /*immutable=*/true));
var forAll = new ForallExpr(Token.NoToken, new List<Variable> () {x, y }, body, /*immutable=*/ true);
Assert.AreEqual(forAll.ComputeHashCode(), forAll.GetHashCode());
}
public override Expr VisitIdentifierExpr(IdentifierExpr node)
{
if (node.Decl == null || !(node.Decl is LocalVariable || node.Decl is Formal || node.Decl is GlobalVariable))
{
return node;
}
else
{
BoundVariable boundVar;
if (!Substitutions.TryGetValue(node.Decl, out boundVar))
{
boundVar = new BoundVariable(Token.NoToken, new TypedIdent(Token.NoToken, node.Name, node.Type));
Substitutions[node.Decl] = boundVar;
}
return new IdentifierExpr(node.tok, boundVar);
}
}
public override BoundVariable VisitBoundVariable(BoundVariable node)
{
Contract.Ensures(Contract.Result<BoundVariable>() == node);
return (BoundVariable)this.VisitVariable(node);
}
public virtual BoundVariable VisitBoundVariable(BoundVariable node) {
Contract.Requires(node != null);
Contract.Ensures(Contract.Result<BoundVariable>() != null);
node = (BoundVariable)this.VisitVariable(node);
return node;
}
public override Absy Visit(Absy node)
{
//Contract.Requires(node != null);
Contract.Ensures(Contract.Result<Absy>() != null);
node = base.Visit(node);
LambdaExpr lambda = node as LambdaExpr;
if (lambda != null) {
IToken/*!*/ tok = lambda.tok;
Contract.Assert(tok != null);
Set freeVars = new Set();
lambda.ComputeFreeVariables(freeVars);
// this is ugly, the output will depend on hashing order
Dictionary<Variable, Expr> subst = new Dictionary<Variable, Expr>();
List<Variable> formals = new List<Variable>();
List<Expr> callArgs = new List<Expr>();
List<Expr> axCallArgs = new List<Expr>();
List<Variable> dummies = new List<Variable>(lambda.Dummies);
List<TypeVariable> freeTypeVars = new List<TypeVariable>();
List<Type/*!*/> fnTypeVarActuals = new List<Type/*!*/>();
List<TypeVariable> freshTypeVars = new List<TypeVariable>(); // these are only used in the lambda@n function's definition
foreach (object o in freeVars) {
// 'o' is either a Variable or a TypeVariable. Since the lambda desugaring happens only
// at the outermost level of a program (where there are no mutable variables) and, for
// procedure bodies, after the statements have been passified (when mutable variables have
// been replaced by immutable incarnations), we are interested only in BoundVar's and
// TypeVariable's.
BoundVariable v = o as BoundVariable;
if (v != null) {
TypedIdent ti = new TypedIdent(v.TypedIdent.tok, v.TypedIdent.Name, v.TypedIdent.Type);
Formal f = new Formal(v.tok, ti, true);
formals.Add(f);
BoundVariable b = new BoundVariable(v.tok, ti);
dummies.Add(b);
callArgs.Add(new IdentifierExpr(v.tok, v));
Expr/*!*/ id = new IdentifierExpr(f.tok, b);
Contract.Assert(id != null);
subst.Add(v, id);
axCallArgs.Add(id);
} else if (o is TypeVariable) {
TypeVariable tv = (TypeVariable)o;
freeTypeVars.Add(tv);
fnTypeVarActuals.Add(tv);
freshTypeVars.Add(new TypeVariable(tv.tok, tv.Name));
}
}
Formal res = new Formal(tok, new TypedIdent(tok, TypedIdent.NoName, cce.NonNull(lambda.Type)), false);
Function fn = new Function(tok, "lambda@" + lambdaid++, freshTypeVars, formals, res, "auto-generated lambda function", lambda.Attributes);
lambdaFunctions.Add(fn);
FunctionCall fcall = new FunctionCall(new IdentifierExpr(tok, fn.Name));
fcall.Func = fn; // resolve here
List<Expr/*!*/> selectArgs = new List<Expr/*!*/>();
foreach (Variable/*!*/ v in lambda.Dummies) {
Contract.Assert(v != null);
selectArgs.Add(new IdentifierExpr(v.tok, v));
}
NAryExpr axcall = new NAryExpr(tok, fcall, axCallArgs);
axcall.Type = res.TypedIdent.Type;
axcall.TypeParameters = SimpleTypeParamInstantiation.From(freeTypeVars, fnTypeVarActuals);
NAryExpr select = Expr.Select(axcall, selectArgs);
select.Type = lambda.Body.Type;
List<Type/*!*/> selectTypeParamActuals = new List<Type/*!*/>();
List<TypeVariable> forallTypeVariables = new List<TypeVariable>();
foreach (TypeVariable/*!*/ tp in lambda.TypeParameters) {
Contract.Assert(tp != null);
selectTypeParamActuals.Add(tp);
forallTypeVariables.Add(tp);
}
forallTypeVariables.AddRange(freeTypeVars);
select.TypeParameters = SimpleTypeParamInstantiation.From(lambda.TypeParameters, selectTypeParamActuals);
Expr bb = Substituter.Apply(Substituter.SubstitutionFromHashtable(subst), lambda.Body);
NAryExpr body = Expr.Eq(select, bb);
body.Type = Type.Bool;
body.TypeParameters = SimpleTypeParamInstantiation.EMPTY;
Trigger trig = new Trigger(select.tok, true, new List<Expr> { select });
lambdaAxioms.Add(new ForallExpr(tok, forallTypeVariables, dummies, lambda.Attributes, trig, body));
NAryExpr call = new NAryExpr(tok, fcall, callArgs);
call.Type = res.TypedIdent.Type;
call.TypeParameters = SimpleTypeParamInstantiation.From(freeTypeVars, fnTypeVarActuals);
return call;
}
return node;
}
public void CachedHashCodeLambdaExpr()
{
var x = new BoundVariable(Token.NoToken, new TypedIdent(Token.NoToken, "x", BasicType.Int));
var y = new BoundVariable(Token.NoToken, new TypedIdent(Token.NoToken, "x", BasicType.Int));
var body = Expr.Gt (new IdentifierExpr (Token.NoToken, x, /*immutable=*/true),
new IdentifierExpr(Token.NoToken, y, /*immutable=*/true));
var lambda = new LambdaExpr(Token.NoToken, new List<TypeVariable>(), new List<Variable>() { x, y},
null, body, /*immutable=*/true);
Assert.AreEqual(lambda.ComputeHashCode(), lambda.GetHashCode());
}
public void ProtectedForAllExprBody()
{
var x = new BoundVariable(Token.NoToken, new TypedIdent(Token.NoToken, "x", BasicType.Int));
var y = new BoundVariable(Token.NoToken, new TypedIdent(Token.NoToken, "x", BasicType.Int));
var xId = new IdentifierExpr(Token.NoToken, x, /*immutable=*/true);
var yId = new IdentifierExpr(Token.NoToken, y, /*immutable=*/true);
var body = Expr.Gt(xId, yId);
var forAll = new ForallExpr(Token.NoToken, new List<Variable> () { x, y }, body, /*immutable=*/true);
forAll.Body = Expr.Lt(xId, yId); // Changing the body of an immutable ForAllExpr should fail
}
public Expr Compute()
{
Search(second.thatAction.Blocks[0], false);
Dictionary<Variable, Expr> map = new Dictionary<Variable, Expr>();
List<Variable> boundVars = new List<Variable>();
if (first != null)
{
foreach (Variable v in first.thisAction.LocVars)
{
BoundVariable bv = new BoundVariable(Token.NoToken, new TypedIdent(Token.NoToken, v.Name, v.TypedIdent.Type));
map[v] = new IdentifierExpr(Token.NoToken, bv);
boundVars.Add(bv);
}
}
foreach (Variable v in second.thatAction.LocVars)
{
BoundVariable bv = new BoundVariable(Token.NoToken, new TypedIdent(Token.NoToken, v.Name, v.TypedIdent.Type));
map[v] = new IdentifierExpr(Token.NoToken, bv);
boundVars.Add(bv);
}
Substitution subst = Substituter.SubstitutionFromHashtable(map);
if (boundVars.Count > 0)
return new ExistsExpr(Token.NoToken, boundVars, Substituter.Apply(subst, transitionRelation));
else
return transitionRelation;
}
private void CreateFailurePreservationChecker(Program program, ActionInfo first, ActionInfo second)
{
Tuple<ActionInfo, ActionInfo> actionPair = new Tuple<ActionInfo, ActionInfo>(first, second);
if (failurePreservationCheckerCache.Contains(actionPair))
return;
failurePreservationCheckerCache.Add(actionPair);
List<Variable> inputs = new List<Variable>();
inputs.AddRange(first.thisInParams);
inputs.AddRange(second.thatInParams);
Expr transitionRelation = (new TransitionRelationComputation(program, second)).Compute();
Expr expr = Expr.True;
foreach (AssertCmd assertCmd in first.thisGate)
{
expr = Expr.And(assertCmd.Expr, expr);
}
List<Requires> requires = DisjointnessRequires(program, first, second);
requires.Add(new Requires(false, Expr.Not(expr)));
foreach (AssertCmd assertCmd in second.thatGate)
{
requires.Add(new Requires(false, assertCmd.Expr));
}
Dictionary<Variable, Expr> map = new Dictionary<Variable, Expr>();
Dictionary<Variable, Expr> oldMap = new Dictionary<Variable, Expr>();
List<Variable> boundVars = new List<Variable>();
foreach (Variable v in program.GlobalVariables())
{
BoundVariable bv = new BoundVariable(Token.NoToken, new TypedIdent(Token.NoToken, "post_" + v.Name, v.TypedIdent.Type));
boundVars.Add(bv);
map[v] = new IdentifierExpr(Token.NoToken, bv);
}
foreach (Variable v in second.thatOutParams)
{
{
BoundVariable bv = new BoundVariable(Token.NoToken, new TypedIdent(Token.NoToken, "post_" + v.Name, v.TypedIdent.Type));
boundVars.Add(bv);
map[v] = new IdentifierExpr(Token.NoToken, bv);
}
{
BoundVariable bv = new BoundVariable(Token.NoToken, new TypedIdent(Token.NoToken, "pre_" + v.Name, v.TypedIdent.Type));
boundVars.Add(bv);
oldMap[v] = new IdentifierExpr(Token.NoToken, bv);
}
}
foreach (Variable v in second.thatAction.LocVars)
{
BoundVariable bv = new BoundVariable(Token.NoToken, new TypedIdent(Token.NoToken, "pre_" + v.Name, v.TypedIdent.Type));
boundVars.Add(bv);
oldMap[v] = new IdentifierExpr(Token.NoToken, bv);
}
Expr ensuresExpr = Expr.And(transitionRelation, Expr.Not(expr));
if (boundVars.Count > 0)
{
Substitution subst = Substituter.SubstitutionFromHashtable(map);
Substitution oldSubst = Substituter.SubstitutionFromHashtable(oldMap);
ensuresExpr = new ExistsExpr(Token.NoToken, boundVars, (Expr)new MySubstituter(subst, oldSubst).Visit(ensuresExpr));
}
List<Ensures> ensures = new List<Ensures>();
ensures.Add(new Ensures(false, ensuresExpr));
List<Block> blocks = new List<Block>();
blocks.Add(new Block(Token.NoToken, "L", new List<Cmd>(), new ReturnCmd(Token.NoToken)));
string checkerName = string.Format("FailurePreservationChecker_{0}_{1}", first.proc.Name, second.proc.Name);
List<IdentifierExpr> globalVars = new List<IdentifierExpr>();
program.GlobalVariables().Iter(x => globalVars.Add(new IdentifierExpr(Token.NoToken, x)));
Procedure proc = new Procedure(Token.NoToken, checkerName, new List<TypeVariable>(), inputs, new List<Variable>(), requires, globalVars, ensures);
Implementation impl = new Implementation(Token.NoToken, checkerName, new List<TypeVariable>(), inputs, new List<Variable>(), new List<Variable>(), blocks);
impl.Proc = proc;
this.decls.Add(impl);
this.decls.Add(proc);
}
public override Expr VisitLambdaExpr(LambdaExpr lambda) {
var baseResult = base.VisitLambdaExpr(lambda);
lambda = baseResult as LambdaExpr;
if (lambda == null) {
return baseResult; // apparently, the base visitor already turned the lambda into something else
}
// We start by getting rid of any use of "old" inside the lambda. This is done as follows.
// For each variable "g" occurring inside lambda as "old(... g ...)", create a new name "og".
// Replace each old occurrence of "g" with "og", removing the enclosing "old" wrappers.
var oldFinder = new OldFinder();
oldFinder.Visit(lambda);
var oldSubst = new Dictionary<Variable, Expr>(); // g -> g0
var callOldMapping = new Dictionary<Variable, Expr>(); // g0 -> old(g)
foreach (var v in oldFinder.FreeOldVars) {
var g = v as GlobalVariable;
if (g != null) {
var g0 = new GlobalVariable(g.tok, new TypedIdent(g.tok, g.TypedIdent.Name + "@old", g.TypedIdent.Type));
oldSubst.Add(g, new IdentifierExpr(g0.tok, g0));
callOldMapping.Add(g0, new OldExpr(g0.tok, new IdentifierExpr(g.tok, g)));
}
}
var lambdaBody = Substituter.ApplyReplacingOldExprs(
Substituter.SubstitutionFromHashtable(new Dictionary<Variable,Expr>()),
Substituter.SubstitutionFromHashtable(oldSubst),
lambda.Body);
var lambdaAttrs = Substituter.ApplyReplacingOldExprs(
Substituter.SubstitutionFromHashtable(new Dictionary<Variable, Expr>()),
Substituter.SubstitutionFromHashtable(oldSubst),
lambda.Attributes);
if (0 < CommandLineOptions.Clo.VerifySnapshots && QKeyValue.FindStringAttribute(lambdaAttrs, "checksum") == null)
{
// Attach a dummy checksum to avoid issues in the dependency analysis.
var checksumAttr = new QKeyValue(lambda.tok, "checksum", new List<object> { "lambda expression" }, null);
if (lambdaAttrs == null)
{
lambdaAttrs = checksumAttr;
}
else
{
lambdaAttrs.AddLast(checksumAttr);
}
}
// this is ugly, the output will depend on hashing order
var subst = new Dictionary<Variable, Expr>();
var substFnAttrs = new Dictionary<Variable, Expr>();
var formals = new List<Variable>();
var callArgs = new List<Expr>();
var axCallArgs = new List<Expr>();
var dummies = new List<Variable>(lambda.Dummies);
var freeTypeVars = new List<TypeVariable>();
var fnTypeVarActuals = new List<Type/*!*/>();
var freshTypeVars = new List<TypeVariable>(); // these are only used in the lambda@n function's definition
// compute the free variables of the lambda expression, but with lambdaBody instead of lambda.Body
Set freeVars = new Set();
BinderExpr.ComputeBinderFreeVariables(lambda.TypeParameters, lambda.Dummies, lambdaBody, lambdaAttrs, freeVars);
foreach (object o in freeVars) {
// 'o' is either a Variable or a TypeVariable.
if (o is Variable) {
var v = o as Variable;
var ti = new TypedIdent(v.TypedIdent.tok, v.TypedIdent.Name, v.TypedIdent.Type);
var f = new Formal(v.tok, ti, true);
formals.Add(f);
substFnAttrs.Add(v, new IdentifierExpr(f.tok, f));
var b = new BoundVariable(v.tok, ti);
dummies.Add(b);
if (callOldMapping.ContainsKey(v)) {
callArgs.Add(callOldMapping[v]);
} else {
callArgs.Add(new IdentifierExpr(v.tok, v));
}
Expr id = new IdentifierExpr(b.tok, b);
subst.Add(v, id);
axCallArgs.Add(id);
} else {
var tv = (TypeVariable)o;
freeTypeVars.Add(tv);
fnTypeVarActuals.Add(tv);
freshTypeVars.Add(new TypeVariable(tv.tok, tv.Name));
}
}
var sw = new System.IO.StringWriter();
var wr = new TokenTextWriter(sw, true);
lambda.Emit(wr);
string lam_str = sw.ToString();
FunctionCall fcall;
IToken tok = lambda.tok;
Formal res = new Formal(tok, new TypedIdent(tok, TypedIdent.NoName, cce.NonNull(lambda.Type)), false);
if (liftedLambdas.TryGetValue(lambda, out fcall)) {
if (CommandLineOptions.Clo.TraceVerify) {
Console.WriteLine("Old lambda: {0}", lam_str);
}
} else {
if (CommandLineOptions.Clo.TraceVerify) {
Console.WriteLine("New lambda: {0}", lam_str);
}
Function fn = new Function(tok, FreshLambdaFunctionName(), freshTypeVars, formals, res, "auto-generated lambda function",
Substituter.Apply(Substituter.SubstitutionFromHashtable(substFnAttrs), lambdaAttrs));
fn.OriginalLambdaExprAsString = lam_str;
fcall = new FunctionCall(new IdentifierExpr(tok, fn.Name));
fcall.Func = fn; // resolve here
liftedLambdas[lambda] = fcall;
List<Expr/*!*/> selectArgs = new List<Expr/*!*/>();
foreach (Variable/*!*/ v in lambda.Dummies) {
Contract.Assert(v != null);
selectArgs.Add(new IdentifierExpr(v.tok, v));
}
NAryExpr axcall = new NAryExpr(tok, fcall, axCallArgs);
axcall.Type = res.TypedIdent.Type;
axcall.TypeParameters = SimpleTypeParamInstantiation.From(freeTypeVars, fnTypeVarActuals);
NAryExpr select = Expr.Select(axcall, selectArgs);
select.Type = lambdaBody.Type;
List<Type/*!*/> selectTypeParamActuals = new List<Type/*!*/>();
List<TypeVariable> forallTypeVariables = new List<TypeVariable>();
foreach (TypeVariable/*!*/ tp in lambda.TypeParameters) {
Contract.Assert(tp != null);
selectTypeParamActuals.Add(tp);
forallTypeVariables.Add(tp);
}
forallTypeVariables.AddRange(freeTypeVars);
select.TypeParameters = SimpleTypeParamInstantiation.From(lambda.TypeParameters, selectTypeParamActuals);
Expr bb = Substituter.Apply(Substituter.SubstitutionFromHashtable(subst), lambdaBody);
NAryExpr body = Expr.Eq(select, bb);
body.Type = Type.Bool;
body.TypeParameters = SimpleTypeParamInstantiation.EMPTY;
Trigger trig = new Trigger(select.tok, true, new List<Expr> { select });
lambdaFunctions.Add(fn);
lambdaAxioms.Add(new ForallExpr(tok, forallTypeVariables, dummies,
Substituter.Apply(Substituter.SubstitutionFromHashtable(subst), lambdaAttrs),
trig, body));
}
NAryExpr call = new NAryExpr(tok, fcall, callArgs);
call.Type = res.TypedIdent.Type;
call.TypeParameters = SimpleTypeParamInstantiation.From(freeTypeVars, fnTypeVarActuals);
return call;
}
public void SimpleLambda() {
var boundVar = new BoundVariable(Token.NoToken, new TypedIdent(Token.NoToken,"foo",Microsoft.Boogie.Type.Bool));
var id = new IdentifierExpr(Token.NoToken, boundVar);
// This is basically an Identity Map
var lambdaExpr = new LambdaExpr(Token.NoToken, new List<TypeVariable>() , new List<Variable>() { boundVar }, null, id);
var id2 = new IdentifierExpr(Token.NoToken, boundVar);
var lambdaExpr2 = new LambdaExpr(Token.NoToken, new List<TypeVariable>() , new List<Variable>() { boundVar }, null, id2);
Assert.AreNotSame(lambdaExpr, lambdaExpr2); // These are different references
Assert.IsTrue(lambdaExpr.Equals(lambdaExpr2)); // These are "structurally equal"
Assert.AreEqual(lambdaExpr.GetHashCode(), lambdaExpr2.GetHashCode()); // If the .Equals() is true then hash codes must be the same
}
public void SimpleExists() {
var boundVar = new BoundVariable(Token.NoToken, new TypedIdent(Token.NoToken,"foo",Microsoft.Boogie.Type.Bool));
var id = new IdentifierExpr(Token.NoToken, boundVar);
var exists = new ExistsExpr(Token.NoToken, new List<Variable>() { boundVar }, id);
var id2 = new IdentifierExpr(Token.NoToken, boundVar);
var exists2 = new ExistsExpr(Token.NoToken, new List<Variable>() { boundVar }, id2);
Assert.AreNotSame(exists, exists2); // These are different references
Assert.IsTrue(exists.Equals(exists2)); // These are "structurally equal"
Assert.AreEqual(exists.GetHashCode(), exists2.GetHashCode()); // If the .Equals() is true then hash codes must be the same
}
public Expr DisjointnessExpr(string domainName, HashSet<Variable> scope)
{
LinearDomain domain = linearDomains[domainName];
BoundVariable partition = new BoundVariable(Token.NoToken, new TypedIdent(Token.NoToken, string.Format("partition_{0}", domainName), new MapType(Token.NoToken, new List<TypeVariable>(), new List<Type> { domain.elementType }, Microsoft.Boogie.Type.Int)));
return SubsetExprs(domain, scope, partition, 0, Expr.True);
}
public LinearDomain(Program program, string domainName, Dictionary<Type, Function> collectors)
{
this.axioms = new List<Axiom>();
this.collectors = collectors;
MapType setType = (MapType)collectors.First().Value.OutParams[0].TypedIdent.Type;
this.elementType = setType.Arguments[0];
MapType mapTypeBool = new MapType(Token.NoToken, new List<TypeVariable>(), new List<Type> { this.elementType }, Type.Bool);
MapType mapTypeInt = new MapType(Token.NoToken, new List<TypeVariable>(), new List<Type> { this.elementType }, Type.Int);
this.mapOrBool = new Function(Token.NoToken, "linear_" + domainName + "_MapOr",
new List<Variable> { new Formal(Token.NoToken, new TypedIdent(Token.NoToken, "a", mapTypeBool), true),
new Formal(Token.NoToken, new TypedIdent(Token.NoToken, "b", mapTypeBool), true) },
new Formal(Token.NoToken, new TypedIdent(Token.NoToken, "c", mapTypeBool), false));
if (CommandLineOptions.Clo.UseArrayTheory)
{
this.mapOrBool.AddAttribute("builtin", "MapOr");
}
else
{
BoundVariable a = new BoundVariable(Token.NoToken, new TypedIdent(Token.NoToken, "a", mapTypeBool));
IdentifierExpr aie = Expr.Ident(a);
BoundVariable b = new BoundVariable(Token.NoToken, new TypedIdent(Token.NoToken, "b", mapTypeBool));
IdentifierExpr bie = Expr.Ident(b);
BoundVariable x = new BoundVariable(Token.NoToken, new TypedIdent(Token.NoToken, "x", elementType));
IdentifierExpr xie = Expr.Ident(x);
var mapApplTerm = new NAryExpr(Token.NoToken, new FunctionCall(mapOrBool), new List<Expr> { aie, bie } );
var lhsTerm = new NAryExpr(Token.NoToken, new MapSelect(Token.NoToken, 1), new List<Expr> { mapApplTerm, xie } );
var rhsTerm = Expr.Or(new NAryExpr(Token.NoToken, new MapSelect(Token.NoToken, 1), new List<Expr> { aie, xie } ),
new NAryExpr(Token.NoToken, new MapSelect(Token.NoToken, 1), new List<Expr> { bie, xie} ));
var axiomExpr = new ForallExpr(Token.NoToken, new List<TypeVariable>(), new List<Variable> { a, b }, null,
new Trigger(Token.NoToken, true, new List<Expr> { mapApplTerm }),
new ForallExpr(Token.NoToken, new List<Variable> { x }, Expr.Binary(BinaryOperator.Opcode.Eq, lhsTerm, rhsTerm)));
axiomExpr.Typecheck(new TypecheckingContext(null));
axioms.Add(new Axiom(Token.NoToken, axiomExpr));
}
this.mapImpBool = new Function(Token.NoToken, "linear_" + domainName + "_MapImp",
new List<Variable> { new Formal(Token.NoToken, new TypedIdent(Token.NoToken, "a", mapTypeBool), true),
new Formal(Token.NoToken, new TypedIdent(Token.NoToken, "b", mapTypeBool), true) },
new Formal(Token.NoToken, new TypedIdent(Token.NoToken, "c", mapTypeBool), false));
if (CommandLineOptions.Clo.UseArrayTheory)
{
this.mapImpBool.AddAttribute("builtin", "MapImp");
}
else
{
BoundVariable a = new BoundVariable(Token.NoToken, new TypedIdent(Token.NoToken, "a", mapTypeBool));
IdentifierExpr aie = Expr.Ident(a);
BoundVariable b = new BoundVariable(Token.NoToken, new TypedIdent(Token.NoToken, "b", mapTypeBool));
IdentifierExpr bie = Expr.Ident(b);
BoundVariable x = new BoundVariable(Token.NoToken, new TypedIdent(Token.NoToken, "x", elementType));
IdentifierExpr xie = Expr.Ident(x);
var mapApplTerm = new NAryExpr(Token.NoToken, new FunctionCall(mapImpBool), new List<Expr> { aie, bie });
var lhsTerm = new NAryExpr(Token.NoToken, new MapSelect(Token.NoToken, 1), new List<Expr> { mapApplTerm, xie });
var rhsTerm = Expr.Imp(new NAryExpr(Token.NoToken, new MapSelect(Token.NoToken, 1), new List<Expr> { aie, xie }),
new NAryExpr(Token.NoToken, new MapSelect(Token.NoToken, 1), new List<Expr> { bie, xie }));
var axiomExpr = new ForallExpr(Token.NoToken, new List<TypeVariable>(), new List<Variable> { a, b }, null,
new Trigger(Token.NoToken, true, new List<Expr> { mapApplTerm }),
new ForallExpr(Token.NoToken, new List<Variable> { x }, Expr.Binary(BinaryOperator.Opcode.Eq, lhsTerm, rhsTerm)));
axiomExpr.Typecheck(new TypecheckingContext(null));
axioms.Add(new Axiom(Token.NoToken, axiomExpr));
}
this.mapConstBool = new Function(Token.NoToken, "linear_" + domainName + "_MapConstBool",
new List<Variable> { new Formal(Token.NoToken, new TypedIdent(Token.NoToken, "b", Type.Bool), true) },
new Formal(Token.NoToken, new TypedIdent(Token.NoToken, "c", mapTypeBool), false));
if (CommandLineOptions.Clo.UseArrayTheory)
{
this.mapConstBool.AddAttribute("builtin", "MapConst");
}
else
{
BoundVariable x = new BoundVariable(Token.NoToken, new TypedIdent(Token.NoToken, "x", elementType));
IdentifierExpr xie = Expr.Ident(x);
var trueTerm = new NAryExpr(Token.NoToken, new MapSelect(Token.NoToken, 1),
new List<Expr> { new NAryExpr(Token.NoToken, new FunctionCall(mapConstBool), new List<Expr> { Expr.True }), xie });
var trueAxiomExpr = new ForallExpr(Token.NoToken, new List<Variable> { x }, trueTerm);
trueAxiomExpr.Typecheck(new TypecheckingContext(null));
axioms.Add(new Axiom(Token.NoToken, trueAxiomExpr));
var falseTerm = new NAryExpr(Token.NoToken, new MapSelect(Token.NoToken, 1),
new List<Expr> { new NAryExpr(Token.NoToken, new FunctionCall(mapConstBool), new List<Expr> { Expr.False }), xie });
var falseAxiomExpr = new ForallExpr(Token.NoToken, new List<Variable> { x }, Expr.Unary(Token.NoToken, UnaryOperator.Opcode.Not, falseTerm));
falseAxiomExpr.Typecheck(new TypecheckingContext(null));
axioms.Add(new Axiom(Token.NoToken, falseAxiomExpr));
}
this.mapEqInt = new Function(Token.NoToken, "linear_" + domainName + "_MapEq",
new List<Variable> { new Formal(Token.NoToken, new TypedIdent(Token.NoToken, "a", mapTypeInt), true),
new Formal(Token.NoToken, new TypedIdent(Token.NoToken, "b", mapTypeInt), true) },
new Formal(Token.NoToken, new TypedIdent(Token.NoToken, "c", mapTypeBool), false));
if (CommandLineOptions.Clo.UseArrayTheory)
{
this.mapEqInt.AddAttribute("builtin", "MapEq");
}
else
{
BoundVariable a = new BoundVariable(Token.NoToken, new TypedIdent(Token.NoToken, "a", mapTypeInt));
IdentifierExpr aie = Expr.Ident(a);
BoundVariable b = new BoundVariable(Token.NoToken, new TypedIdent(Token.NoToken, "b", mapTypeInt));
IdentifierExpr bie = Expr.Ident(b);
BoundVariable x = new BoundVariable(Token.NoToken, new TypedIdent(Token.NoToken, "x", elementType));
IdentifierExpr xie = Expr.Ident(x);
var mapApplTerm = new NAryExpr(Token.NoToken, new FunctionCall(mapEqInt), new List<Expr> { aie, bie });
var lhsTerm = new NAryExpr(Token.NoToken, new MapSelect(Token.NoToken, 1), new List<Expr> { mapApplTerm, xie });
var rhsTerm = Expr.Eq(new NAryExpr(Token.NoToken, new MapSelect(Token.NoToken, 1), new List<Expr> { aie, xie }),
new NAryExpr(Token.NoToken, new MapSelect(Token.NoToken, 1), new List<Expr> { bie, xie }));
var axiomExpr = new ForallExpr(Token.NoToken, new List<TypeVariable>(), new List<Variable> { a, b }, null,
new Trigger(Token.NoToken, true, new List<Expr> { mapApplTerm }),
new ForallExpr(Token.NoToken, new List<Variable> { x }, Expr.Binary(BinaryOperator.Opcode.Eq, lhsTerm, rhsTerm)));
axiomExpr.Typecheck(new TypecheckingContext(null));
axioms.Add(new Axiom(Token.NoToken, axiomExpr));
}
this.mapConstInt = new Function(Token.NoToken, "linear_" + domainName + "_MapConstInt",
new List<Variable> { new Formal(Token.NoToken, new TypedIdent(Token.NoToken, "b", Type.Int), true) },
new Formal(Token.NoToken, new TypedIdent(Token.NoToken, "c", mapTypeInt), false));
if (CommandLineOptions.Clo.UseArrayTheory)
{
this.mapConstInt.AddAttribute("builtin", "MapConst");
}
else
{
BoundVariable a = new BoundVariable(Token.NoToken, new TypedIdent(Token.NoToken, "a", Type.Int));
IdentifierExpr aie = Expr.Ident(a);
BoundVariable x = new BoundVariable(Token.NoToken, new TypedIdent(Token.NoToken, "x", elementType));
IdentifierExpr xie = Expr.Ident(x);
var lhsTerm = new NAryExpr(Token.NoToken, new MapSelect(Token.NoToken, 1), new List<Expr> { new NAryExpr(Token.NoToken, new FunctionCall(mapConstInt), new List<Expr> { aie }), xie });
var axiomExpr = new ForallExpr(Token.NoToken, new List<Variable> { a, x }, Expr.Binary(BinaryOperator.Opcode.Eq, lhsTerm, aie));
axiomExpr.Typecheck(new TypecheckingContext(null));
axioms.Add(new Axiom(Token.NoToken, axiomExpr));
}
foreach (var axiom in axioms)
{
axiom.Expr.Resolve(new ResolutionContext(null));
axiom.Expr.Typecheck(new TypecheckingContext(null));
}
}
// We have to give the type explicitly, because the type of the formal "likeThisOne" can contain type variables
protected Variable CreateTemporaryVariable(List<Variable> tempVars, Variable likeThisOne, Type ty, TempVarKind kind)
{
Contract.Requires(ty != null);
Contract.Requires(likeThisOne != null);
Contract.Requires(tempVars != null);
Contract.Ensures(Contract.Result<Variable>() != null);
string/*!*/ tempNamePrefix;
switch (kind) {
case TempVarKind.Formal:
tempNamePrefix = "formal@";
break;
case TempVarKind.Old:
tempNamePrefix = "old@";
break;
case TempVarKind.Bound:
tempNamePrefix = "forall@";
break;
default: {
Contract.Assert(false);
throw new cce.UnreachableException();
} // unexpected kind
}
TypedIdent ti = likeThisOne.TypedIdent;
TypedIdent newTi = new TypedIdent(ti.tok, "call" + UniqueId + tempNamePrefix + ti.Name, ty);
Variable/*!*/ v;
if (kind == TempVarKind.Bound) {
v = new BoundVariable(likeThisOne.tok, newTi);
} else {
v = new LocalVariable(likeThisOne.tok, newTi);
tempVars.Add(v);
}
return v;
}
public void ProtectedLambdaExprBody()
{
var x = new BoundVariable(Token.NoToken, new TypedIdent(Token.NoToken, "x", BasicType.Int));
var y = new BoundVariable(Token.NoToken, new TypedIdent(Token.NoToken, "x", BasicType.Int));
var xId = new IdentifierExpr(Token.NoToken, x, /*immutable=*/true);
var yId = new IdentifierExpr(Token.NoToken, y, /*immutable=*/true);
var body = Expr.Gt(xId, yId);
var lambda = new LambdaExpr(Token.NoToken, new List<TypeVariable>(), new List<Variable>() { x, y},
null, body, /*immutable=*/true);
lambda.Body = Expr.Lt(xId, yId); // Changing the body of an immutable ExistsExpr should fail
}
private void PopulateExistsVars(Variable v)
{
if (existsVars.ContainsKey(v)) return;
existsVars[v] = new BoundVariable(Token.NoToken, new TypedIdent(Token.NoToken, "#tmp_" + existsVars.Count, v.TypedIdent.Type));
}
public Expr DisjointnessExpr(string domainName, HashSet<Variable> scope)
{
LinearDomain domain = linearDomains[domainName];
BoundVariable partition = new BoundVariable(Token.NoToken, new TypedIdent(Token.NoToken, string.Format("partition_{0}", domainName), new MapType(Token.NoToken, new List<TypeVariable>(), new List<Type> { domain.elementType }, Microsoft.Boogie.Type.Int)));
Expr disjointExpr = Expr.True;
int count = 0;
foreach (Variable v in scope)
{
IdentifierExpr ie = new IdentifierExpr(Token.NoToken, v);
Expr e = new NAryExpr(Token.NoToken, new FunctionCall(domain.mapConstInt), new List<Expr>{ new LiteralExpr(Token.NoToken, Microsoft.Basetypes.BigNum.FromInt(count++)) } );
e = new NAryExpr(Token.NoToken, new FunctionCall(domain.mapEqInt), new List<Expr> { new IdentifierExpr(Token.NoToken, partition), e } );
e = new NAryExpr(Token.NoToken, new FunctionCall(domain.mapImpBool), new List<Expr> { v.TypedIdent.Type is MapType ? ie : Singleton(ie, domainName), e } );
e = Expr.Binary(BinaryOperator.Opcode.Eq, e, new NAryExpr(Token.NoToken, new FunctionCall(domain.mapConstBool), new List<Expr> { Expr.True }));
disjointExpr = Expr.Binary(BinaryOperator.Opcode.And, e, disjointExpr);
}
var expr = new ExistsExpr(Token.NoToken, new List<Variable> { partition }, disjointExpr);
expr.Resolve(new ResolutionContext(null));
expr.Typecheck(new TypecheckingContext(null));
return expr;
}
private Expr DisjointnessExpr(string domainName, Variable inputVar, HashSet<Variable> scope)
{
if (scope.Count == 0)
{
return Expr.True;
}
LinearDomain domain = linearDomains[domainName];
BoundVariable partition = new BoundVariable(Token.NoToken, new TypedIdent(Token.NoToken, string.Format("partition_{0}", domainName), new MapType(Token.NoToken, new List<TypeVariable>(), new List<Type> { domain.elementType }, Microsoft.Boogie.Type.Int)));
return SubsetExprs(domain, scope, partition, 1, SubsetExpr(domain, Expr.Ident(inputVar), partition, 0));
}
public override BoundVariable VisitBoundVariable(BoundVariable node) {
//Contract.Requires(node != null);
Contract.Ensures(Contract.Result<BoundVariable>() != null);
return base.VisitBoundVariable((BoundVariable)node.Clone());
}
private void AddPath()
{
HashSet<Variable> existsVars = new HashSet<Variable>();
Dictionary<Variable, Expr> varToExpr = new Dictionary<Variable, Expr>();
foreach (Variable v in frame)
{
varToExpr[v] = Expr.Ident(v);
}
if (first != null)
{
foreach (Variable v in first.thatOutParams)
{
varToExpr[v] = Expr.Ident(v);
}
}
foreach (Variable v in second.thisOutParams)
{
varToExpr[v] = Expr.Ident(v);
}
List<Expr> pathExprs = new List<Expr>();
int boundVariableCount = 0;
foreach (Cmd cmd in cmdStack)
{
if (cmd is AssumeCmd)
{
AssumeCmd assumeCmd = cmd as AssumeCmd;
FlattenAnd(assumeCmd.Expr, pathExprs);
}
else if (cmd is AssignCmd)
{
AssignCmd assignCmd = (cmd as AssignCmd).AsSimpleAssignCmd;
Dictionary<Variable, Expr> map = new Dictionary<Variable, Expr>();
for (int k = 0; k < assignCmd.Lhss.Count; k++)
{
map[assignCmd.Lhss[k].DeepAssignedVariable] = assignCmd.Rhss[k];
}
Substitute(map, ref pathExprs, ref varToExpr);
}
else if (cmd is HavocCmd)
{
HavocCmd havocCmd = cmd as HavocCmd;
Dictionary<Variable, Expr> map = new Dictionary<Variable, Expr>();
foreach (IdentifierExpr ie in havocCmd.Vars)
{
BoundVariable bv = new BoundVariable(Token.NoToken, new TypedIdent(Token.NoToken, "#tmp_" + boundVariableCount++, ie.Decl.TypedIdent.Type));
map[ie.Decl] = Expr.Ident(bv);
existsVars.Add(bv);
}
Substitute(map, ref pathExprs, ref varToExpr);
}
else
{
Debug.Assert(false);
}
}
paths.Add(new PathInfo(existsVars, varToExpr, pathExprs));
}
