internal static bool WantsAutoTriggers(QuantifierExpr quantifier)
{
Contract.Requires(quantifier.SplitQuantifier == null); // Don't call this on a quantifier with a Split clause: it's not a real quantifier
bool wantsAutoTriggers = true;
return(!Attributes.ContainsBool(quantifier.Attributes, "autotriggers", ref wantsAutoTriggers) || wantsAutoTriggers);
}
// need to push bound type variables
public override QuantifierExpr VisitQuantifierExpr(QuantifierExpr node)
{
if (!(node is ForallExpr || node is ExistsExpr))
{
throw new ProofGenUnexpectedStateException(GetType(), "can only handle forall and exists quantifiers");
}
//Quantifers with multiple bound variables are desugared into multiple quantifiers expressions with single variables
foreach (var boundTyVar in node.TypeParameters)
{
tyVarTranslation.AddBoundVariable(boundTyVar);
}
var numTyVarBefore = tyVarTranslation.NumBoundVariables();
Visit(node.Body);
if (numTyVarBefore != tyVarTranslation.NumBoundVariables())
{
throw new ProofGenUnexpectedStateException(GetType(),
"quantifier levels not the same before and after");
}
for (var i = node.TypeParameters.Count - 1; i >= 0; i--)
{
tyVarTranslation.DropLastBoundVariable();
}
return(node);
}
private static bool ShallowEq(QuantifierExpr expr1, QuantifierExpr expr2)
{
if (!TriggerUtils.SameNullity(expr1.SplitQuantifier, expr2.SplitQuantifier))
{
return(false);
}
if (expr1.SplitQuantifier != null && expr2.SplitQuantifier != null)
{
return(ShallowEq_Top(expr1.SplitQuantifierExpression, expr2.SplitQuantifierExpression));
}
if (expr1.TypeArgs.Count != expr2.TypeArgs.Count ||
!TriggerUtils.SameNullity(expr1.Range, expr2.Range))
{
return(false);
}
if (expr1 is ExistsExpr && expr2 is ExistsExpr)
{
return(ShallowEq((ExistsExpr)expr1, (ExistsExpr)expr2));
}
else if (expr1 is ForallExpr && expr2 is ForallExpr)
{
return(ShallowEq((ForallExpr)expr1, (ForallExpr)expr2));
}
else
{
return(false);
}
}
private static bool AllowsSplitting(QuantifierExpr quantifier)
{
// allow split if attributes doesn't contains "split" or it is "split: true" and it is not an empty QuantifierExpr (boundvar.count>0)
bool splitAttr = true;
return((!Attributes.ContainsBool(quantifier.Attributes, "split", ref splitAttr) || splitAttr) && (quantifier.BoundVars.Count > 0));
}
internal IEnumerable <TriggerMatch> LoopingSubterms(QuantifierExpr quantifier)
{
Contract.Requires(quantifier.SplitQuantifier == null); // Don't call this on a quantifier with a Split clause: it's not a real quantifier
var matchingSubterms = this.MatchingSubterms(quantifier);
var boundVars = new HashSet <BoundVar>(quantifier.BoundVars);
return(matchingSubterms.Where(tm => tm.CouldCauseLoops(Terms, boundVars)));
}
private bool IsForall(QuantifierExpr quantifierExpr)
{
if (quantifierExpr is ForallExpr)
{
return(true);
}
if (quantifierExpr is ExistsExpr)
{
return(false);
}
throw new ProofGenUnexpectedStateException(GetType(), "Unexpected quantifier");
}
// This is necessary because the root of the Tree might be a QuantifierExpr
public override QuantifierExpr VisitQuantifierExpr(QuantifierExpr node)
{
bool goDeeper = CountExpr(node);
if (goDeeper)
{
return(base.VisitQuantifierExpr(node));
}
else
{
return(node);
}
}
public override QuantifierExpr VisitQuantifierExpr(QuantifierExpr node)
{
if (node.TypeParameters.Count > 0)
{
_result = true;
_hasTypeQuantification = true;
}
_withinNumQuantifier++;
Visit(node._Body);
_withinNumQuantifier--;
return(node);
}
public override QuantifierExpr VisitQuantifierExpr(QuantifierExpr node)
{
var oldE = existentialExpr;
if (node is ExistsExpr)
{
existentialExpr = (node as ExistsExpr);
}
node = base.VisitQuantifierExpr(node);
existentialExpr = oldE;
return(node);
}
internal static IEnumerable <Expression> SplitQuantifier(QuantifierExpr quantifier)
{
var body = quantifier.Term;
var binary = body as BinaryExpr;
if (quantifier is ForallExpr)
{
IEnumerable <Expression> stream;
if (binary != null && (binary.Op == BinaryExpr.Opcode.Imp || binary.Op == BinaryExpr.Opcode.Or))
{
stream = SplitAndStich(binary, BinaryExpr.Opcode.And);
}
else
{
stream = SplitExpr(body, BinaryExpr.Opcode.And);
}
foreach (var e in stream)
{
var tok = new NestedToken(quantifier.tok, e.tok);
yield return(new ForallExpr(tok, quantifier.TypeArgs, quantifier.BoundVars, quantifier.Range, e, CopyAttributes(quantifier.Attributes))
{
Type = quantifier.Type
});
}
}
else if (quantifier is ExistsExpr)
{
IEnumerable <Expression> stream;
if (binary != null && binary.Op == BinaryExpr.Opcode.And)
{
stream = SplitAndStich(binary, BinaryExpr.Opcode.Or);
}
else
{
stream = SplitExpr(body, BinaryExpr.Opcode.Or);
}
foreach (var e in stream)
{
var tok = new NestedToken(quantifier.tok, e.tok);
yield return(new ExistsExpr(tok, quantifier.TypeArgs, quantifier.BoundVars, quantifier.Range, e, CopyAttributes(quantifier.Attributes))
{
Type = quantifier.Type
});
}
}
else
{
yield return(quantifier);
}
}
// Do not dualise quantified variables
public override QuantifierExpr VisitQuantifierExpr(QuantifierExpr node)
{
List <Variable> vs = node.Dummies;
foreach (Variable dummy in vs)
{
quantifiedVars.Add(dummy);
}
base.VisitQuantifierExpr(node);
foreach (Variable dummy in vs)
{
quantifiedVars.Remove(dummy);
}
return(node);
}
public override QuantifierExpr VisitQuantifierExpr(QuantifierExpr node)
{
if (!(node is ForallExpr || node is ExistsExpr))
{
throw new ProofGenUnexpectedStateException(GetType(), "can only handle forall and exists quantifiers");
}
var isForall = IsForall(node);
//Quantifers with multiple bound variables are desugared into multiple quantifiers expressions with single variables
foreach (var boundVar in node.Dummies)
{
boogieVarTranslation.VarTranslation.AddBoundVariable(boundVar);
}
foreach (var boundTyVar in node.TypeParameters)
{
boogieVarTranslation.TypeVarTranslation.AddBoundVariable(boundTyVar);
}
var numValVarBefore = boogieVarTranslation.VarTranslation.NumBoundVariables();
var numTyVarBefore = boogieVarTranslation.TypeVarTranslation.NumBoundVariables();
var result = Translate(node.Body);
if (numValVarBefore != boogieVarTranslation.VarTranslation.NumBoundVariables() ||
numTyVarBefore != boogieVarTranslation.TypeVarTranslation.NumBoundVariables())
{
throw new ProofGenUnexpectedStateException(GetType(),
"quantifier levels not the same before and after");
}
for (var i = node.Dummies.Count - 1; i >= 0; i--)
{
boogieVarTranslation.VarTranslation.DropLastBoundVariable();
var boundVar = node.Dummies[i];
var boundVarType = typeIsaVisitor.Translate(boundVar.TypedIdent.Type);
result = IsaBoogieTerm.Quantifier(isForall, boundVarType, result);
}
for (var i = node.TypeParameters.Count - 1; i >= 0; i--)
{
boogieVarTranslation.TypeVarTranslation.DropLastBoundVariable();
result = IsaBoogieTerm.TypeQuantifier(isForall, result);
}
ReturnResult(result);
return(node);
}
////////////////////////////////////////////////////////////////////////////////////
//TODO:Check if we get functions here
private Term makeExpression(QuantifierExpr qe, bool old)
{
Term e = null;
{
List <Logic.Variable> quantifiedVariables = new List <Logic.Variable>();
foreach (Microsoft.Boogie.Variable bv in qe.Dummies)
{
quantifiedVariables.Add(new Logic.Basic.Variable(bv.TypedIdent.Name));
}
foreach (var v in quantifiedVariables)
{
boundVariables.Add(v.name, v);
}
e = makeExpression(qe.Body, old);
foreach (var v in quantifiedVariables)
{
boundVariables.Remove(v.name);
}
}
{
Logic.Quantifier q = makeQuantifier(qe.Kind);
for (int i = qe.Dummies.Length - 1; i >= 0; i--)
{
Microsoft.Boogie.Variable v = qe.Dummies[i];
Logic.Sort ls = new Logic.Boogie.BoogieSort(v.TypedIdent.Type);
Logic.Variable lv = new Logic.Boogie.BoogieVariable(v);
e = new Boogie.QuantifiedExpression(qe, q, lv, ls, e);
}
}
{
Logic.TypeQuantifier tq = makeTypeQuantifier(qe.Kind);
for (int i = qe.TypeParameters.Length - 1; i >= 0; i--)
{
Microsoft.Boogie.TypeVariable btv = qe.TypeParameters[i];
Logic.TypeVariable tv = new Logic.Boogie.TypeVariable(btv);
e = new Boogie.QuantifiedTypeExpression(qe, tq, tv, e);
}
}
return(e);
}
///////////////////////////////////////////////////////////
public BoogieQuantifiedTypeExpression(
QuantifierExpr boogieExpression,
TypeQuantifier quantifier,
TypeVariable variable,
Expression expression,
List <Expression> triggers,
string attributes
)
:
base(
quantifier,
variable,
expression,
triggers,
attributes
)
{
Debug.Assert(boogieExpression != null);
boogieQTExpression = boogieExpression;
}
///////////////////////////////////////////////////////////
public BoogieQuantifiedExpression(
Scope s,
QuantifierExpr boogieExpression,
Quantifier quantifier,
BoundVariable variable,
Expression expression,
IEnumerable <IEnumerable <Expression> > triggers,
string attributes
)
: base(
s,
quantifier,
variable,
expression,
triggers,
attributes
)
{
Debug.Assert(boogieExpression != null);
boogieQExpression = boogieExpression;
}
bool RewriteMatchingLoop()
{
if (expr is QuantifierExpr && TriggerUtils.WantsMatchingLoopRewrite((QuantifierExpr)expr))
{
QuantifierExpr quantifier = (QuantifierExpr)expr;
var l = new List <QuantifierWithTriggers>();
// only split quantifier expr now.
List <Expression> splits = new List <Expression>();
foreach (var q in quantifiers)
{
var matchingLoopRewriter = new MatchingLoopRewriter();
var qq = matchingLoopRewriter.RewriteMatchingLoops(q);
splits.Add(qq);
l.Add(new QuantifierWithTriggers(qq));
}
quantifier.SplitQuantifier = splits;
quantifiers = l;
return(true);
}
return(false);
}
bool RewriteMatchingLoop()
{
if (expr is QuantifierExpr)
{
QuantifierExpr quantifier = (QuantifierExpr)expr;
var l = new List <QuantifierWithTriggers>();
List <Expression> splits = new List <Expression>();
bool rewritten = false;
foreach (var q in quantifiers)
{
if (TriggerUtils.NeedsAutoTriggers(q.quantifier) && TriggerUtils.WantsMatchingLoopRewrite(q.quantifier))
{
var matchingLoopRewriter = new MatchingLoopRewriter();
var qq = matchingLoopRewriter.RewriteMatchingLoops(q);
splits.Add(qq);
l.Add(new QuantifierWithTriggers(qq));
rewritten = true;
}
else
{
// don't rewrite the quantifier if we are not auto generate triggers.
// This is because rewriting introduces new boundvars and will cause
// user provided triggers not mention all boundvars
splits.Add(q.quantifier);
l.Add(q);
}
}
if (rewritten)
{
quantifier.SplitQuantifier = splits;
quantifiers = l;
return(true);
}
}
return(false);
}
internal static IEnumerable <TriggerMatch> SubexpressionsMatchingTrigger(this QuantifierExpr quantifier, Expression trigger)
{
return(quantifier.AllSubExpressions(true, true)
.Select(e => TriggerUtils.PrepareExprForInclusionInTrigger(e).MatchAgainst(trigger, quantifier.BoundVars, e))
.Where(e => e.HasValue).Select(e => e.Value));
}
List <Expression> GenerateAutoReqs(Expression expr, Function parent)
{
List <Expression> reqs = new List <Expression>();
Func <Expression, List <Expression> > generateAutoReqs = e => GenerateAutoReqs(e, parent);
if (expr is LiteralExpr)
{
}
else if (expr is ThisExpr)
{
}
else if (expr is IdentifierExpr)
{
}
else if (expr is SeqDisplayExpr)
{
SeqDisplayExpr e = (SeqDisplayExpr)expr;
foreach (var elt in e.Elements)
{
reqs.AddRange(generateAutoReqs(elt));
}
}
else if (expr is FieldSelectExpr)
{
FieldSelectExpr e = (FieldSelectExpr)expr;
reqs.AddRange(generateAutoReqs(e.Obj));
}
else if (expr is SeqSelectExpr)
{
SeqSelectExpr e = (SeqSelectExpr)expr;
reqs.AddRange(generateAutoReqs(e.Seq));
if (e.E0 != null)
{
reqs.AddRange(generateAutoReqs(e.E0));
}
if (e.E1 != null)
{
reqs.AddRange(generateAutoReqs(e.E1));
}
}
else if (expr is SeqUpdateExpr)
{
SeqUpdateExpr e = (SeqUpdateExpr)expr;
reqs.AddRange(generateAutoReqs(e.Seq));
reqs.AddRange(generateAutoReqs(e.Index));
reqs.AddRange(generateAutoReqs(e.Value));
}
else if (expr is FunctionCallExpr)
{
FunctionCallExpr e = (FunctionCallExpr)expr;
foreach (var arg in e.Args)
{
reqs.AddRange(generateAutoReqs(arg));
}
if (parent == null || parent.Name != e.name)
{
ReqFunction(e.Function);
reqs.AddRange(GatherReqs(e.Function, e.Args));
}
}
else if (expr is DatatypeValue)
{
DatatypeValue dtv = (DatatypeValue)expr;
for (int i = 0; i < dtv.Arguments.Count; i++)
{
Expression arg = dtv.Arguments[i];
reqs.AddRange(generateAutoReqs(arg));
}
}
else if (expr is OldExpr)
{
}
else if (expr is MatchExpr)
{
MatchExpr e = (MatchExpr)expr;
reqs.AddRange(generateAutoReqs(e.Source));
List <MatchCaseExpr> newMatches = new List <MatchCaseExpr>();
foreach (MatchCaseExpr caseExpr in e.Cases)
{
MatchCaseExpr c = new MatchCaseExpr(caseExpr.name, caseExpr.Arguments, Andify(generateAutoReqs(caseExpr.Body)));
newMatches.Add(c);
}
reqs.Add(new MatchExpr(e.Source, newMatches));
}
else if (expr is FreshExpr)
{
}
else if (expr is UnaryExpr)
{
UnaryExpr e = (UnaryExpr)expr;
Expression arg = e.E;
reqs.AddRange(generateAutoReqs(arg));
}
else if (expr is BinaryExpr)
{
BinaryExpr e = (BinaryExpr)expr;
switch (e.Op)
{
case BinaryExpr.Opcode.Imp:
case BinaryExpr.Opcode.And:
reqs.AddRange(generateAutoReqs(e.E0));
foreach (var req in generateAutoReqs(e.E1))
{
reqs.Add(new BinaryExpr(Token.NoToken, BinaryExpr.Opcode.Imp, e.E0, req));
}
break;
case BinaryExpr.Opcode.Or:
reqs.AddRange(generateAutoReqs(e.E0));
foreach (var req in generateAutoReqs(e.E1))
{
reqs.Add(new BinaryExpr(Token.NoToken, BinaryExpr.Opcode.Imp,
new UnaryExpr(Token.NoToken, UnaryExpr.Opcode.Not, e.E0), req));
}
break;
default:
reqs.AddRange(generateAutoReqs(e.E0));
reqs.AddRange(generateAutoReqs(e.E1));
break;
}
}
else if (expr is LetExpr)
{
var e = (LetExpr)expr;
if (e.Exact)
{
foreach (var rhs in e.RHSs)
{
reqs.AddRange(generateAutoReqs(rhs));
}
var new_reqs = generateAutoReqs(e.Body);
if (new_reqs.Count > 0)
{
reqs.Add(new LetExpr(e.Exact, e.LHSs, e.RHSs, Andify(new_reqs)));
}
}
}
else if (expr is QuantifierExpr)
{
QuantifierExpr e = (QuantifierExpr)expr;
var auto_reqs = generateAutoReqs(e.Term);
if (auto_reqs.Count > 0)
{
Expression allReqsSatisfied = Andify(auto_reqs);
Expression allReqsSatisfiedAndTerm = new BinaryExpr(Token.NoToken, BinaryExpr.Opcode.And, allReqsSatisfied, e.Term);
e.Term = allReqsSatisfiedAndTerm;
}
}
else if (expr is StmtExpr)
{
var e = (StmtExpr)expr;
reqs.AddRange(generateAutoReqs(e.E));
}
else if (expr is ITEExpr)
{
ITEExpr e = (ITEExpr)expr;
reqs.AddRange(generateAutoReqs(e.Test));
reqs.Add(new ITEExpr(e.Test, Andify(generateAutoReqs(e.Thn)), Andify(generateAutoReqs(e.Els))));
}
return(reqs);
}
private TriggerAnnotation AnnotateQuantifier(QuantifierExpr expr)
{
return(AnnotateQuantifierOrLetExpr(expr, expr.BoundVars));
}
private Expr PrintQuantifierExpr(QuantifierExpr QE)
{
if (QE is ExistsExpr)
{
TW.Write("(exists");
}
else if (QE is ForallExpr)
{
TW.Write("(forall");
}
else
{
throw new NotSupportedException("Unsupported quantifier expr");
}
PushIndent();
PrintSeperator();
TW.Write("(");
PushIndent();
PrintSeperator();
foreach (var boundVar in QE.Dummies)
{
PrintSeperator();
TW.Write("(" + boundVar.Name + " " + GetSMTLIBType(boundVar.TypedIdent.Type) + ")");
}
PopIndent();
PrintSeperator();
TW.Write(")");
PrintSeperator();
// Handle Triggers
if (QE.Triggers == null || !PrintTriggers)
{
PrintExpr(QE.Body);
}
else
{
TW.Write("(!");
PushIndent();
PrintSeperator();
PrintExpr(QE.Body);
PrintSeperator();
// fixme: pos!
// Print triggers
var trigger = QE.Triggers;
if (trigger.Pos)
{
while (trigger != null)
{
// list of expressions
TW.Write(":pattern (");
PushIndent();
PrintSeperator();
foreach (var triggerExpr in trigger.Tr)
{
PrintExpr(triggerExpr);
PrintSeperator();
}
PopIndent();
TW.Write(")");
trigger = trigger.Next;
}
}
else
{
if (trigger.Tr.Count != 1)
{
throw new InvalidDataException("Negative trigger is malformed");
}
// no-pattern takes an expression rather than a list of expressions
TW.Write(":no-pattern");
PushIndent();
PrintSeperator();
PrintExpr(trigger.Tr[0]);
PopIndent();
}
PopIndent();
PrintSeperator();
TW.Write(")");
}
PopIndent();
PrintSeperator();
TW.Write(")");
return(QE);
}
internal QuantifierWithTriggers(QuantifierExpr quantifier)
{
this.quantifier = quantifier;
this.RejectedCandidates = new List <TriggerCandidate>();
}
public override QuantifierExpr VisitQuantifierExpr(QuantifierExpr node)
{
add(node);
return(base.VisitQuantifierExpr(node));
}
public override QuantifierExpr VisitQuantifierExpr(QuantifierExpr node)
{
FindInstantiationSources(node, "skolem_add_to_pool");
return(base.VisitQuantifierExpr(node));
}
public override QuantifierExpr VisitQuantifierExpr(QuantifierExpr node)
{
return(base.VisitQuantifierExpr((QuantifierExpr)node.Clone()));
}
public override QuantifierExpr VisitQuantifierExpr(QuantifierExpr node)
{
node = base.VisitQuantifierExpr(node);
quantifiersExist = true;
return(node);
}
public RtlExp GhostExpressionRec(Expression exp, bool inRecSpec = false, bool inRequiresOrOld = false)
{
Util.Assert(!isPrinting);
exp = GetExp(exp);
StmtExpr stmtExpr = exp as StmtExpr;
IdentifierExpr idExp = exp as IdentifierExpr;
LiteralExpr literal = exp as LiteralExpr;
BinaryExpr binary = exp as BinaryExpr;
UnaryExpr unary = exp as UnaryExpr;
ITEExpr ite = exp as ITEExpr;
ExistsExpr existsExp = exp as ExistsExpr;
ForallExpr forallExp = exp as ForallExpr;
LetExpr letExp = exp as LetExpr;
MatchExpr matchExp = exp as MatchExpr;
OldExpr oldExp = exp as OldExpr;
FreshExpr freshExp = exp as FreshExpr;
FunctionCallExpr funCall = exp as FunctionCallExpr;
DatatypeValue dataVal = exp as DatatypeValue;
FieldSelectExpr fieldSelect = exp as FieldSelectExpr;
SeqSelectExpr seqSelect = exp as SeqSelectExpr;
SeqUpdateExpr seqUpdate = exp as SeqUpdateExpr;
SeqDisplayExpr seqDisplay = exp as SeqDisplayExpr;
Func <Expression, RtlExp> G = e => GhostExpression(e, inRecSpec, inRequiresOrOld);
if (stmtExpr != null)
{
if (stmtExprEnabled)
{
if (ignoreStmtExpr == 0)
{
AddGhostStatement(stmtExpr.S);
}
return(G(stmtExpr.E));
}
else
{
throw new Exception("not implemented: cannot handle statement expression here");
}
}
else if (idExp != null)
{
return(AsVar(idExp));
}
else if (literal != null && literal.Value is BigInteger)
{
return(new RtlInt((BigInteger)(literal.Value)));
}
else if (literal != null && literal.Value is bool)
{
return(new RtlLiteral((bool)(literal.Value) ? "true" : "false"));
}
else if (literal != null && literal.Value == null)
{
return(new RtlLiteral("ArrayOfInt(0 - 1, NO_ABS)"));
}
else if (literal != null && literal.Value is Microsoft.Basetypes.BigDec)
{
return(new RtlLiteral(((Microsoft.Basetypes.BigDec)literal.Value).ToDecimalString()));
}
else if (binary != null)
{
string op = null;
string internalOp = null;
CompileFunction compileFunction = this as CompileFunction;
string thisFuncName = (compileFunction == null) ? null : compileFunction.function.Name;
switch (binary.ResolvedOp)
{
case BinaryExpr.ResolvedOpcode.SeqEq:
return(new RtlApply(dafnySpec.GetSeqOperationName(AppType(binary.E0.Type), "Seq_Equal"),
new RtlExp[] { G(binary.E0), G(binary.E1) }));
case BinaryExpr.ResolvedOpcode.SeqNeq:
return(new RtlLiteral("(!" +
new RtlApply(dafnySpec.GetSeqOperationName(AppType(binary.E0.Type), "Seq_Equal"),
new RtlExp[] { G(binary.E0), G(binary.E1) }) + ")"));
case BinaryExpr.ResolvedOpcode.Concat:
return(new RtlApply(dafnySpec.GetSeqOperationName(AppType(binary.Type), "Seq_Append"),
new RtlExp[] { G(binary.E0), G(binary.E1) }));
}
if (binary.Op == BinaryExpr.Opcode.Exp)
{
binary = new BinaryExpr(binary.tok, BinaryExpr.Opcode.Imp, binary.E0, binary.E1);
}
switch (binary.Op)
{
case BinaryExpr.Opcode.Disjoint:
case BinaryExpr.Opcode.In:
case BinaryExpr.Opcode.NotIn:
throw new Exception("not implemented: binary operator '" + BinaryExpr.OpcodeString(binary.Op) + "'");
}
if (AppType(binary.E0.Type) is IntType && AppType(binary.E1.Type) is IntType)
{
switch (binary.Op)
{
case BinaryExpr.Opcode.Le: internalOp = "INTERNAL_le_boogie"; break;
case BinaryExpr.Opcode.Lt: internalOp = "INTERNAL_lt_boogie"; break;
case BinaryExpr.Opcode.Ge: internalOp = "INTERNAL_ge_boogie"; break;
case BinaryExpr.Opcode.Gt: internalOp = "INTERNAL_gt_boogie"; break;
case BinaryExpr.Opcode.Add: internalOp = "INTERNAL_add_boogie"; break;
case BinaryExpr.Opcode.Sub: internalOp = "INTERNAL_sub_boogie"; break;
case BinaryExpr.Opcode.Mul:
op = "*";
if (thisFuncName != "INTERNAL_mul")
{
internalOp = FunName("INTERNAL__mul");
}
break;
case BinaryExpr.Opcode.Div:
op = "div";
if (thisFuncName != "INTERNAL_div")
{
internalOp = FunName("INTERNAL__div");
}
break;
case BinaryExpr.Opcode.Mod:
op = "mod";
if (thisFuncName != "INTERNAL_mod")
{
internalOp = FunName("INTERNAL__mod");
}
break;
default:
op = BinaryExpr.OpcodeString(binary.Op);
break;
}
}
else
{
op = BinaryExpr.OpcodeString(binary.Op);
}
if (internalOp == null)
{
return(new RtlBinary(op, G(binary.E0), G(binary.E1)));
}
else
{
return(new RtlApply(internalOp, new RtlExp[]
{ G(binary.E0), G(binary.E1) }));
}
}
else if (unary != null && unary.Op == UnaryExpr.Opcode.Not)
{
return(new RtlLiteral("(!(" + G(unary.E) + "))"));
}
else if (unary != null && unary.Op == UnaryExpr.Opcode.SeqLength)
{
return(new RtlApply(dafnySpec.GetSeqOperationName(AppType(unary.E.Type), "Seq_Length"),
new RtlExp[] { G(unary.E) }));
}
else if (ite != null)
{
return(GhostIfThenElse(G(ite.Test), () => G(ite.Thn), () => G(ite.Els)));
}
else if (funCall != null)
{
switch (funCall.Function.Name)
{
case "left":
case "right":
case "relation":
case "public":
Util.Assert(funCall.Args.Count == 1);
return(new RtlApply(funCall.Function.Name, new RtlExp[] { G(funCall.Args[0]) }));
case "sizeof":
Util.Assert(funCall.Args.Count == 1);
return(new RtlApply(funCall.Function.Name + "##" + TypeString(AppType(funCall.Args[0].Type)),
new RtlExp[] { G(funCall.Args[0]) }));
case "INTERNAL_add_raw":
Util.Assert(funCall.Args.Count == 2);
return(new RtlBinary("+", G(funCall.Args[0]), G(funCall.Args[1])));
case "INTERNAL_sub_raw":
Util.Assert(funCall.Args.Count == 2);
return(new RtlBinary("-", G(funCall.Args[0]), G(funCall.Args[1])));
case "IntToReal":
Util.Assert(funCall.Args.Count == 1);
return(new RtlApply("real", new RtlExp[] { G(funCall.Args[0]) }));
case "RealToInt":
Util.Assert(funCall.Args.Count == 1);
return(new RtlApply("int", new RtlExp[] { G(funCall.Args[0]) }));
}
TypeApply app = dafnySpec.Compile_Function(funCall.Function,
funCall.TypeArgumentSubstitutions.ToDictionary(p => p.Key, p => AppType(p.Value)));
string name = FunName(SimpleName(app.AppName()));
string fullName = FunName(SimpleName(app.AppFullName()));
List <RtlExp> rtlArgs = funCall.Args.Select(G).ToList();
List <RtlExp> rtlReads = funCall.Function.Reads.Where(e => e.Field != null).ToList()
.ConvertAll(e => (RtlExp) new RtlVar(
GhostVar(e.FieldName), e.Field.IsGhost, AppType(e.Field.Type)));
rtlArgs = rtlReads.Concat(rtlArgs).ToList();
if (name.EndsWith("__INTERNAL__HEAP"))
{
name = name.Substring(0, name.Length - "__INTERNAL__HEAP".Length);
}
else if (DafnySpec.IsHeapFunction(funCall.Function))
{
rtlArgs.Insert(0, new RtlLiteral(inRequiresOrOld ? "$absMem_old" : "$absMem"));
}
if (Attributes.Contains(funCall.Function.Attributes, "opaque") &&
funCall.Function.Formals.Count + rtlReads.Count == 0)
{
rtlArgs.Insert(0, new RtlLiteral("true"));
}
if (fullName == recFunName)
{
name = fullName;
}
if (name == recFunName)
{
recCalls.Add(new List <RtlExp>(rtlArgs));
rtlArgs.Insert(0, new RtlApply("decreases_" + name, new List <RtlExp>(rtlArgs)));
rtlArgs.Insert(1, new RtlLiteral(inRecSpec ? "__unroll" : "__unroll + 1"));
name = "rec_" + name;
}
return(new RtlApply(name, rtlArgs));
}
else if (dataVal != null)
{
bool isSeq = dataVal.Type.TypeName(null).StartsWith("Seq<");
return(new RtlApply((isSeq ? "_" : "") + dafnySpec.Compile_Constructor(
dataVal.Type, dataVal.Ctor.Name, dataVal.InferredTypeArgs, typeApply.typeArgs).AppName(),
dataVal.Arguments.Select(G)));
}
else if (existsExp != null || forallExp != null)
{
QuantifierExpr qExp = (QuantifierExpr)exp;
bool isForall = forallExp != null;
var varTuples = qExp.BoundVars.Select(v => Tuple.Create(GhostVar(v.Name), v.IsGhost, v.Type));
var oldRenamer = PushRename(qExp.BoundVars.Select(v => v.Name));
var oldStmtExprEnabled = stmtExprEnabled;
stmtExprEnabled = false;
RtlExp rExp = new RtlLiteral((isForall ? "(forall " : "(exists ")
+ string.Join(", ", qExp.BoundVars.Select(v => GhostVar(v.Name) + ":" + TypeString(AppType(v.Type))))
+ " :: " + Triggers(qExp.Attributes, G) + " "
+ GetTypeWellFormedExp(varTuples.ToList(), isForall ? "==>" : "&&", G(qExp.Term)) + ")");
stmtExprEnabled = oldStmtExprEnabled;
PopRename(oldRenamer);
return(rExp);
}
else if (letExp != null)
{
List <RtlExp> rhss;
if (letExp.Exact)
{
rhss = letExp.RHSs.ConvertAll(e => G(e));
}
else if (letExp.LHSs.Count == 1 && LiteralExpr.IsTrue(letExp.RHSs[0]) && AppType(letExp.LHSs[0].Var.Type) is IntType)
{
rhss = new List <RtlExp> {
new RtlLiteral("0")
};
}
else
{
throw new Exception("not implemented: LetExpr: " + letExp);
}
return(GhostLet(exp.tok, letExp.LHSs.ConvertAll(lhs => lhs.Var), rhss, () => G(letExp.Body)));
}
else if (matchExp != null)
{
if (matchExp.MissingCases.Count != 0)
{
throw new Exception("not implemented: MatchExpr with missing cases: " + matchExp);
}
//- match src case c1(ps1) => e1 ... cn(psn) => en
//- -->
//- let x := src in
//- if x is c1 then let ps1 := ...x.f1... in e1 else
//- if x is c2 then let ps2 := ...x.f2... in e2 else
//- let ps3 := ...x.f3... in e3
var src = G(matchExp.Source);
var cases = matchExp.Cases;
string x = TempName();
Func <RtlExp> body = null;
for (int i = cases.Count; i > 0;)
{
i--;
MatchCaseExpr c = cases[i];
Func <List <RtlExp> > cRhss = () => c.Ctor.Formals.ConvertAll(f => (RtlExp) new RtlLiteral("("
+ f.Name + "#" + c.Ctor.Name + "(" + GhostVar(x) + "))"));
Func <RtlExp> ec = () => GhostLet(exp.tok, c.Arguments, cRhss(), () => G(c.Body));
if (body == null)
{
body = ec;
}
else
{
var prevBody = body;
body = () => GhostIfThenElse(new RtlLiteral("(" + GhostVar(x) + " is " + c.Ctor.Name + ")"),
ec, prevBody);
}
}
return(GhostLet(exp.tok, new List <BoundVar> {
new BoundVar(exp.tok, x, matchExp.Source.Type)
},
new List <RtlExp> {
src
}, body));
}
else if (oldExp != null)
{
return(new RtlLiteral("old(" + GhostExpression(oldExp.E, inRecSpec, true) + ")"));
}
else if (freshExp != null)
{
Util.Assert(DafnySpec.IsArrayType(freshExp.E.Type));
string abs = G(freshExp.E) + ".arrAbs";
return(new RtlLiteral("(heap_old.absData[" + abs + "] is AbsNone)"));
}
else if (fieldSelect != null && fieldSelect.FieldName.EndsWith("?"))
{
string constructor = fieldSelect.FieldName.Substring(0, fieldSelect.FieldName.Length - 1);
constructor = dafnySpec.Compile_Constructor(fieldSelect.Obj.Type, constructor, null, typeApply.typeArgs).AppName();
bool isSeq = fieldSelect.Obj.Type.TypeName(null).StartsWith("Seq<");
return(isSeq
? new RtlLiteral("is_" + constructor + "(" + G(fieldSelect.Obj) + ")")
: new RtlLiteral("((" + G(fieldSelect.Obj) + ") is " + constructor + ")"));
}
else if (fieldSelect != null && !fieldSelect.Field.IsStatic && AppType(fieldSelect.Obj.Type) is UserDefinedType &&
fieldSelect.Field is DatatypeDestructor)
{
DatatypeDestructor field = (DatatypeDestructor)fieldSelect.Field;
string constructor = dafnySpec.Compile_Constructor(fieldSelect.Obj.Type,
field.EnclosingCtor.Name, null, typeApply.typeArgs).AppName();
bool isSeq = fieldSelect.Obj.Type.TypeName(null).StartsWith("Seq<");
return(new RtlLiteral("(" + fieldSelect.FieldName + (isSeq ? "_" : "#") + constructor
+ "(" + G(fieldSelect.Obj) + "))"));
}
else if (fieldSelect != null && DafnySpec.IsArrayType(AppType(fieldSelect.Obj.Type)) &&
fieldSelect.FieldName == "Length")
{
return(new RtlLiteral("(Arr_Length(" + G(fieldSelect.Obj) + "))"));
}
else if (fieldSelect != null && fieldSelect.Obj is ImplicitThisExpr)
{
//- we don't support objects yet, so interpret this as a global variable
return(new RtlVar(GhostVar(fieldSelect.FieldName), true, fieldSelect.Type));
}
else if (seqSelect != null)
{
if (seqSelect.SelectOne && DafnySpec.IsArrayType(AppType(seqSelect.Seq.Type)))
{
return(new RtlExpComputed(e => "fun_INTERNAL__array__elems__index("
+ (inRequiresOrOld ? "$absMem_old" : "$absMem") + "[" + e.args[0] + ".arrAbs], ("
+ e.args[1] + "))", new RtlExp[] { G(seqSelect.Seq), G(seqSelect.E0) }));
}
else if (seqSelect.SelectOne)
{
return(new RtlApply(dafnySpec.GetSeqOperationName(AppType(seqSelect.Seq.Type), "Seq_Index"),
new RtlExp[] { G(seqSelect.Seq), G(seqSelect.E0) }));
}
else
{
RtlExp seq = G(seqSelect.Seq);
if (DafnySpec.IsArrayType(AppType(seqSelect.Seq.Type)))
{
seq = new RtlApply(FunName("Seq__FromArray"), new RtlExp[] {
new RtlLiteral(inRequiresOrOld ? "$absMem_old" : "$absMem"), seq
});
}
if (seqSelect.E1 != null)
{
seq = new RtlApply(dafnySpec.GetSeqOperationName(AppType(seqSelect.Type), "Seq_Take"),
new RtlExp[] { seq, G(seqSelect.E1) });
}
if (seqSelect.E0 != null)
{
seq = new RtlApply(dafnySpec.GetSeqOperationName(AppType(seqSelect.Type), "Seq_Drop"),
new RtlExp[] { seq, G(seqSelect.E0) });
}
return(seq);
}
}
else if (seqUpdate != null)
{
if (seqUpdate.ResolvedUpdateExpr != null)
{
return(GhostExpressionRec(seqUpdate.ResolvedUpdateExpr, inRecSpec, inRequiresOrOld));
}
return(new RtlApply(dafnySpec.GetSeqOperationName(AppType(seqUpdate.Seq.Type), "Seq_Update"),
new RtlExp[] { G(seqUpdate.Seq), G(seqUpdate.Index), G(seqUpdate.Value) }));
}
else if (seqDisplay != null)
{
RtlExp seq = new RtlApply(dafnySpec.GetSeqOperationName(AppType(seqDisplay.Type), "Seq_Empty"), new RtlExp[0]);
foreach (Expression ei in seqDisplay.Elements)
{
seq = new RtlApply(dafnySpec.GetSeqOperationName(AppType(seqDisplay.Type), "Seq_Build"),
new RtlExp[] { seq, G(ei) });
}
return(seq);
}
else
{
throw new Exception("not implemented: " + exp);
}
}
internal static bool NeedsAutoTriggers(QuantifierExpr quantifier)
{
Contract.Requires(quantifier.SplitQuantifier == null); // Don't call this on a quantifier with a Split clause: it's not a real quantifier
return(!Attributes.Contains(quantifier.Attributes, "trigger") && WantsAutoTriggers(quantifier));
}
public Expression TreeToExpression()
{
Contract.Ensures(Contract.Result <Expression>() != null);
if (IsLeaf())
{
return(Data);
}
if (Data is TacnyBinaryExpr)
{
TacnyBinaryExpr bexp = (TacnyBinaryExpr)Data;
Expression E0 = LChild.TreeToExpression();
Expression E1 = RChild?.TreeToExpression();
return(new TacnyBinaryExpr(bexp.tok, bexp.Op, E0, E1));
}
if (Data is BinaryExpr)
{
BinaryExpr bexp = (BinaryExpr)Data;
Expression E0 = LChild.TreeToExpression();
Expression E1 = RChild?.TreeToExpression();
return(new BinaryExpr(bexp.tok, bexp.Op, E0, E1));
}
if (Data is ChainingExpression)
{
List <Expression> operands = null;
ChainingExpression ce = (ChainingExpression)Data;
operands = GetLeafData();
operands.RemoveAt(1); // hack to remove the duplicate name statement
List <BinaryExpr.Opcode> operators = new List <BinaryExpr.Opcode>();
BinaryExpr expr = (BinaryExpr)LChild.TreeToExpression();
operators.Add(((BinaryExpr)expr.E0).Op);
operators.Add(((BinaryExpr)expr.E1).Op);
return(new ChainingExpression(ce.tok, operands, operators, ce.PrefixLimits, expr));
}
if (Data is ParensExpression)
{
return(new ParensExpression(Data.tok, LChild.TreeToExpression()));
}
if (Data is QuantifierExpr)
{
QuantifierExpr qexp = (QuantifierExpr)Data;
if (Data is ForallExpr)
{
return(new ForallExpr(qexp.tok, qexp.BoundVars, qexp.Range, LChild.TreeToExpression(), qexp.Attributes));
}
if (Data is ExistsExpr)
{
return(new ExistsExpr(qexp.tok, qexp.BoundVars, qexp.Range, LChild.TreeToExpression(), qexp.Attributes));
}
}
else if (Data is NegationExpression)
{
return(new NegationExpression(Data.tok, LChild.TreeToExpression()));
}
else if (Data is SeqSelectExpr)
{
var e = (SeqSelectExpr)Data;
return(new SeqSelectExpr(e.tok, e.SelectOne, e.Seq, LChild.TreeToExpression(), RChild?.TreeToExpression()));
}
return(Data);
}
internal static bool AllowsMatchingLoops(QuantifierExpr quantifier)
{
Contract.Requires(quantifier.SplitQuantifier == null); // Don't call this on a quantifier with a Split clause: it's not a real quantifier
// This is different from nowarn: it won't remove loops at all, even if another trigger is available.
return(Attributes.Contains(quantifier.Attributes, "matchingloop"));
}