public void SimpleForAllWithTrigger()
{
var builder = GetSimpleBuilder();
var freeVarX = GetVariable("x", BasicType.Int);
var xid = new IdentifierExpr(Token.NoToken, freeVarX);
var fb = new FunctionCallBuilder();
var funcCall = fb.CreateUninterpretedFunctionCall("f", BPLType.Int, new List <BPLType>()
{
BPLType.Int
});
var body = builder.Gt(builder.UFC(funcCall, xid), xid);
// Single trigger
var triggers = new Microsoft.Boogie.Trigger(Token.NoToken,
/*positive=*/ true,
new List <Expr>()
{
builder.UFC(funcCall, xid)
}, null);
var result = builder.ForAll(new List <Variable>()
{
freeVarX
}, body, triggers);
Assert.AreEqual("(forall x: int :: { f(x) } f(x) > x)", result.ToString());
CheckIsBoolType(result);
}
// Note: if the trigger is null, makes a forall without any triggers
static Bpl.Expr BplForall(IEnumerable <Bpl.Variable> args_in, Bpl.Trigger trg, Bpl.Expr body)
{
if (trg == null)
{
return(BplForall(args_in, body)); // NO_TRIGGER
}
else
{
var args = new List <Bpl.Variable>(args_in);
if (args.Count == 0)
{
return(body);
}
else
{
return(new Bpl.ForallExpr(body.tok, args, trg, body));
}
}
}
public ExistsExpr(IToken tok, List<Variable> dummies, Trigger triggers, Expr body, bool immutable=false)
: base(tok, new List<TypeVariable>(), dummies, null, triggers, body, immutable) {
Contract.Requires(body != null);
Contract.Requires(dummies != null);
Contract.Requires(tok != null);
Contract.Requires(dummies.Count > 0);
}
public ExistsExpr(IToken/*!*/ tok, List<TypeVariable>/*!*/ typeParams, List<Variable>/*!*/ dummies,
QKeyValue kv, Trigger triggers, Expr/*!*/ body, bool immutable=false)
: base(tok, typeParams, dummies, kv, triggers, body, immutable) {
Contract.Requires(tok != null);
Contract.Requires(typeParams != null);
Contract.Requires(dummies != null);
Contract.Requires(body != null);
Contract.Requires(dummies.Count + typeParams.Count > 0);
}
public void AddLast(Trigger other) {
Trigger current = this;
while (current.Next != null) {
current = current.Next;
}
current.Next = other;
}
public ForallExpr(IToken tok, List<Variable> dummies, Trigger triggers, Expr body)
: base(tok, new List<TypeVariable>(), dummies, null, triggers, body)
{
Contract.Requires(body != null);
Contract.Requires(dummies != null);
Contract.Requires(tok != null);
Contract.Requires(dummies.Count > 0);
}
public override QuantifierExpr VisitQuantifierExpr(QuantifierExpr node)
{
currentTrigger = node.Triggers;
while (currentTrigger != null)
{
foreach (var e in currentTrigger.Tr)
{
VisitExpr(e);
}
currentTrigger = currentTrigger.Next;
}
return base.VisitQuantifierExpr(node);
}
public override Trigger VisitTrigger(Trigger node)
{
Contract.Ensures(Contract.Result<Trigger>() == node);
Trigger origNext = node.Next;
if (origNext != null)
{
this.VisitTrigger(origNext);
}
this.VisitExprSeq(node.Tr.ToList());
return node;
}
void QuantifierBody(IToken/*!*/ q, out List<TypeVariable>/*!*/ typeParams, out List<Variable>/*!*/ ds,
out QKeyValue kv, out Trigger trig, out Expr/*!*/ body) {
Contract.Requires(q != null); Contract.Ensures(Contract.ValueAtReturn(out typeParams) != null); Contract.Ensures(Contract.ValueAtReturn(out ds) != null); Contract.Ensures(Contract.ValueAtReturn(out body) != null);
trig = null; typeParams = new List<TypeVariable> ();
IToken/*!*/ tok;
kv = null;
ds = new List<Variable> ();
if (la.kind == 20) {
TypeParams(out tok, out typeParams);
if (la.kind == 1 || la.kind == 28) {
BoundVars(q, out ds);
}
} else if (la.kind == 1 || la.kind == 28) {
BoundVars(q, out ds);
} else SynErr(129);
QSep();
while (la.kind == 28) {
AttributeOrTrigger(ref kv, ref trig);
}
Expression(out body);
}
static Bpl.Expr BplForall(Bpl.Variable arg, Bpl.Trigger trg, Bpl.Expr body)
{
return(BplForall(Singleton(arg), trg, body));
}
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 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 static void ComputeBinderFreeVariables(List <TypeVariable> typeParameters, List <Variable> dummies, Expr body, Trigger triggers, QKeyValue attributes, Set freeVars)
{
Contract.Requires(dummies != null);
Contract.Requires(body != null);
foreach (var v in dummies)
{
Contract.Assert(v != null);
Contract.Assert(!freeVars[v]);
}
body.ComputeFreeVariables(freeVars);
for (var trig = triggers; trig != null; trig = trig.Next)
{
foreach (var e in trig.Tr)
{
e.ComputeFreeVariables(freeVars);
}
}
for (var a = attributes; a != null; a = a.Next)
{
foreach (var o in a.Params)
{
var e = o as Expr;
if (e != null)
{
e.ComputeFreeVariables(freeVars);
}
}
}
foreach (var v in dummies)
{
freeVars.AddRange(v.TypedIdent.Type.FreeVariables);
}
freeVars.RemoveRange(dummies);
freeVars.RemoveRange(typeParameters);
}
public Trigger(IToken/*!*/ tok, bool pos, List<Expr>/*!*/ tr, Trigger next)
: base(tok)
{
Contract.Requires(tok != null);
Contract.Requires(tr != null);
Contract.Requires(1 <= tr.Count);
Contract.Requires(pos || tr.Count == 1);
this.Pos = pos;
this.Tr = tr;
this.Next = next;
}
public QuantifierExpr(IToken/*!*/ tok, List<TypeVariable>/*!*/ typeParameters,
List<Variable>/*!*/ dummies, QKeyValue kv, Trigger triggers, Expr/*!*/ body, bool immutable)
: base(tok, typeParameters, dummies, kv, body, immutable) {
Contract.Requires(tok != null);
Contract.Requires(typeParameters != null);
Contract.Requires(dummies != null);
Contract.Requires(body != null);
Contract.Requires(dummies.Count + typeParameters.Count > 0);
Contract.Assert((this is ForallExpr) || (this is ExistsExpr));
Triggers = triggers;
SkolemId = GetNextSkolemId();
}
// if the user says ( forall x :: forall y :: ... ) and specifies *no* triggers, we transform it to
// (forall x, y :: ... ) which may help the prover to pick trigger terms
//
// (Note: there used to be a different criterion here, which allowed merging when triggers were specified, which could cause prover errors due to resulting unbound variables in the triggers)
private void MergeAdjecentQuantifier() {
QuantifierExpr qbody = Body as QuantifierExpr;
if (!(qbody != null && (qbody is ForallExpr) == (this is ForallExpr) && Triggers == null)) {
return;
}
qbody.MergeAdjecentQuantifier();
if (this.Triggers != null || qbody.Triggers != null) {
return;
}
Body = qbody.Body;
TypeParameters.AddRange(qbody.TypeParameters);
Dummies.AddRange(qbody.Dummies);
Triggers = qbody.Triggers;
if (qbody.Attributes != null) {
if (Attributes == null) {
Attributes = qbody.Attributes;
} else {
QKeyValue p = Attributes;
while (p.Next != null) {
p = p.Next;
}
p.Next = qbody.Attributes;
}
}
}
static Bpl.Expr BplForall(Bpl.IToken tok, List <Bpl.TypeVariable> typeParams,
List <Bpl.Variable> formals, Bpl.QKeyValue kv, Bpl.Trigger triggers, Bpl.Expr body, bool immutable = false)
{
return((typeParams.Count == 0 && formals.Count == 0) ? body
: new Bpl.ForallExpr(tok, typeParams, formals, kv, triggers, body, immutable));
}
void AttributeOrTrigger(ref QKeyValue kv, ref Trigger trig) {
IToken/*!*/ tok; Expr/*!*/ e; List<Expr>/*!*/ es;
string key;
List<object/*!*/> parameters; object/*!*/ param;
Expect(28);
tok = t;
if (la.kind == 12) {
Get();
Expect(1);
key = t.val; parameters = new List<object/*!*/>();
if (StartOf(16)) {
AttributeParameter(out param);
parameters.Add(param);
while (la.kind == 13) {
Get();
AttributeParameter(out param);
parameters.Add(param);
}
}
if (key == "nopats") {
if (parameters.Count == 1 && parameters[0] is Expr) {
e = (Expr)parameters[0];
if(trig==null){
trig = new Trigger(tok, false, new List<Expr> { e }, null);
} else {
trig.AddLast(new Trigger(tok, false, new List<Expr> { e }, null));
}
} else {
this.SemErr("the 'nopats' quantifier attribute expects a string-literal parameter");
}
} else {
if (kv==null) {
kv = new QKeyValue(tok, key, parameters, null);
} else {
kv.AddLast(new QKeyValue(tok, key, parameters, null));
}
}
} else if (StartOf(9)) {
Expression(out e);
es = new List<Expr> { e };
while (la.kind == 13) {
Get();
Expression(out e);
es.Add(e);
}
if (trig==null) {
trig = new Trigger(tok, true, es, null);
} else {
trig.AddLast(new Trigger(tok, true, es, null));
}
} else SynErr(133);
Expect(29);
}
public virtual Trigger VisitTrigger(Trigger node)
{
Contract.Requires(node != null);
Contract.Ensures(Contract.Result<Trigger>() != null);
Trigger origNext = node.Next;
if (origNext != null) {
Trigger newNext = this.VisitTrigger(origNext);
if (newNext != origNext) {
node = new Trigger(node.tok, node.Pos, node.Tr); // note: this creates sharing between the old and new Tr sequence
node.Next = newNext;
}
}
node.Tr = this.VisitExprSeq(node.Tr);
return node;
}
public virtual Trigger VisitTrigger(Trigger node) {
Contract.Requires(node != null);
Contract.Ensures(Contract.Result<Trigger>() != null);
Trigger origNext = node.Next;
if (origNext != null) {
Trigger newNext = this.VisitTrigger(origNext);
if (newNext != origNext) {
node = new Trigger(node.tok, node.Pos, node.Tr.ToList());
node.Next = newNext;
}
}
node.Tr = this.VisitExprSeq(node.Tr.ToList());
return node;
}
public Trigger(IToken/*!*/ tok, bool pos, IEnumerable<Expr>/*!*/ tr, Trigger next = null)
: base(tok) {
Contract.Requires(tok != null);
Contract.Requires(tr != null);
Contract.Requires(tr.Count() >= 1);
Contract.Requires(pos || tr.Count() == 1);
this.Pos = pos;
this.Tr = new List<Expr>(tr);
this.Next = next;
}
public override Trigger VisitTrigger(Trigger node) {
//Contract.Requires(node != null);
Contract.Ensures(Contract.Result<Trigger>() != null);
return base.VisitTrigger((Trigger)node.Clone());
}
public override Trigger VisitTrigger(Trigger node)
{
//Contract.Requires(node != null);
Contract.Ensures(Contract.Result <Trigger>() != null);
return(base.VisitTrigger((Trigger)node.Clone()));
}