Exemple #1
0
    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);
        }
    }