/// <summary>
        /// Creates a separate callable for each intrinsic specialization,
        /// and replaces the specialization implementations of the original callable with a call to these.
        /// Self adjoint generation directives in intrinsic callables are replaced by a provided implementation.
        /// Type constructors and generic callables or callables that already define a target instruction name are left unchanged.
        /// </summary>
        /// <exception cref="ArgumentException">
        /// An intrinsic callable contains non-intrinsic specializations
        /// or a non-intrinsic callable contains intrinsic specializations,
        /// or the a callable doesn't have a body specialization.
        /// </exception>
        /// <exception cref="InvalidOperationException">
        /// A specialization has explicit type arguments;
        /// Monomorphization needs to run before separating target instructions.
        /// </exception>
        private static QsNamespace LiftIntrinsicSpecializations(QsNamespace ns)
        {
            var elements = ImmutableArray.CreateBuilder <QsNamespaceElement>();

            foreach (var element in ns.Elements)
            {
                if (element is QsNamespaceElement.QsCallable c &&
                    c.Item.Signature.TypeParameters.Length == 0 &&
                    !c.Item.Kind.IsTypeConstructor)
                {
                    if (c.Item.IsIntrinsic)
                    {
                        QsCallable callable = c.Item;
                        if (!callable.Specializations.Any(spec => spec.Kind.IsQsBody))
                        {
                            throw new ArgumentException("missing body specialization");
                        }
                        else if (callable.Specializations.Any(spec => spec.TypeArguments.IsValue))
                        {
                            throw new InvalidOperationException("specialization with type arguments");
                        }
                        else if (callable.Specializations.Length == 1 && callable.Attributes.Any(BuiltIn.DefinesTargetInstruction))
                        {
                            elements.Add(element);
                        }
                        else
                        {
                            QsQualifiedName GeneratedName(QsSpecializationKind kind) =>
                            new QsQualifiedName(callable.FullName.Namespace, $"{callable.FullName.Name}{SpecializationSuffix(kind)}");

                            var specializations = ImmutableArray.CreateRange(callable.Specializations.Select(spec =>
                            {
                                var inferredInfo = spec.Signature.Information.InferredInformation;
                                if (!inferredInfo.IsIntrinsic && !inferredInfo.IsSelfAdjoint)
                                {
                                    throw new ArgumentException("non-intrinsic specialization for intrinsic callable");
                                }

                                // Get the correct argument tuple both for the added intrinsic callable
                                // and the generated provided specialization that replaces the intrinsic one.
                                var argTuple = BuildSpecArgTuple(callable.ArgumentTuple, spec.Kind);

                                // Create a separate callable for that specialization,
                                // unless the specialization is not needed for a self-adjoint callable.

                                var genCallableSignature = new ResolvedSignature(
                                    ImmutableArray <QsLocalSymbol> .Empty,
                                    spec.Signature.ArgumentType,
                                    spec.Signature.ReturnType,
                                    new CallableInformation(
                                        ResolvedCharacteristics.Empty,
                                        new InferredCallableInformation(isIntrinsic: true, isSelfAdjoint: false)));
                                var genCallableName = GeneratedName(
                                    inferredInfo.IsSelfAdjoint && spec.Kind.IsQsAdjoint ? QsSpecializationKind.QsBody :
                                    inferredInfo.IsSelfAdjoint && spec.Kind.IsQsControlledAdjoint ? QsSpecializationKind.QsControlled :
                                    spec.Kind);

                                if (!inferredInfo.IsSelfAdjoint || spec.Kind.IsQsBody || spec.Kind.IsQsControlled)
                                {
                                    var genCallableBody = new QsSpecialization(
                                        QsSpecializationKind.QsBody,
                                        genCallableName,
                                        spec.Attributes,
                                        spec.Source,
                                        QsNullable <QsLocation> .Null,
                                        spec.TypeArguments,
                                        genCallableSignature,
                                        SpecializationImplementation.Intrinsic,
                                        spec.Documentation,
                                        spec.Comments);
                                    var genCallable = new QsCallable(
                                        callable.Kind,
                                        genCallableName,
                                        callable.Attributes,
                                        callable.Access,
                                        spec.Source,
                                        spec.Location,
                                        genCallableSignature,
                                        argTuple,
                                        ImmutableArray.Create(genCallableBody),
                                        ImmutableArray <string> .Empty,
                                        QsComments.Empty);
                                    elements.Add(QsNamespaceElement.NewQsCallable(genCallable));
                                }

                                // Create a specialization that calls into the generated callable,
                                // or the corresponding callable no callable for the specialization
                                // has been added due to hte operation being self-adjoint.

                                var genCallableType =
                                    callable.Kind == QsCallableKind.Operation
                                    ? OperationTypeFromSignature(genCallableSignature)
                                    : TypeKind.NewFunction(genCallableSignature.ArgumentType, genCallableSignature.ReturnType);
                                var call = SyntaxGenerator.CallNonGeneric(
                                    IdentifierForCallable(genCallableName, genCallableType),
                                    SyntaxGenerator.ArgumentTupleAsExpression(argTuple));
                                var statement = new QsStatement(
                                    QsStatementKind.NewQsReturnStatement(call),
                                    LocalDeclarations.Empty,
                                    QsNullable <QsLocation> .Null,
                                    QsComments.Empty);
                                var localDeclarations = new LocalDeclarations(
                                    SyntaxGenerator.ValidDeclarations(SyntaxGenerator.ExtractItems(argTuple)));

                                return(spec.WithImplementation(SpecializationImplementation.NewProvided(
                                                                   argTuple,
                                                                   new QsScope(ImmutableArray.Create(statement), localDeclarations))));
                            }));

                            // Create a callable that contains all specializations that
                            // call into the generated callables for each specialization.

                            var inlineAttribute = AttributeUtils.BuildAttribute(BuiltIn.Inline.FullName, SyntaxGenerator.UnitValue);
                            var signature       = new ResolvedSignature(
                                ImmutableArray <QsLocalSymbol> .Empty,
                                callable.Signature.ArgumentType,
                                callable.Signature.ReturnType,
                                new CallableInformation(
                                    callable.Signature.Information.Characteristics,
                                    new InferredCallableInformation(isSelfAdjoint: callable.IsSelfAdjoint, isIntrinsic: false)));
                            var redirect = new QsCallable(
                                callable.Kind,
                                callable.FullName,
                                ImmutableArray.Create(inlineAttribute),
                                callable.Access,
                                callable.Source,
                                callable.Location,
                                signature,
                                callable.ArgumentTuple,
                                specializations,
                                callable.Documentation,
                                callable.Comments);
                            elements.Add(QsNamespaceElement.NewQsCallable(redirect));
                        }
                    }
                    else if (c.Item.Specializations.Any(spec => spec.Implementation.IsIntrinsic))
                    {
                        throw new ArgumentException("intrinsic specialization for non-intrinsic callable");
                    }
                    else
                    {
                        elements.Add(element);
                    }
                }
        /// <summary>
        /// Replaces self adjoint generation directives in non-intrinsic callables with a provided implementation
        /// that calls the appropriate specialization of the callable.
        /// Intrinsic callables are left unchanged.
        /// </summary>
        private static QsNamespace ReplaceSelfAdjointSpecializations(QsNamespace ns)
        {
            var elements = ImmutableArray.CreateBuilder <QsNamespaceElement>();

            foreach (var element in ns.Elements)
            {
                if (element is QsNamespaceElement.QsCallable c)
                {
                    if (c.Item.IsSelfAdjoint && !c.Item.IsIntrinsic)
                    {
                        var callableId = IdentifierForCallable(
                            c.Item.FullName,
                            OperationTypeFromSignature(c.Item.Signature));

                        var callable = c.Item.WithSpecializations(specs =>
                                                                  ImmutableArray.CreateRange(specs.Select(spec =>
                        {
                            if (spec.Kind.IsQsBody || spec.Kind.IsQsControlled)
                            {
                                return(spec);
                            }
                            else
                            {
                                var argTuple = BuildSpecArgTuple(c.Item.ArgumentTuple, spec.Kind);
                                var callee   = spec.Kind.IsQsControlledAdjoint
                                        ? SyntaxGenerator.AutoGeneratedExpression(
                                    ExpressionKind.NewControlledApplication(callableId),
                                    OperationTypeFromSignature(spec.Signature),
                                    false)
                                        : callableId;

                                var call = SyntaxGenerator.CallNonGeneric(
                                    callee,
                                    SyntaxGenerator.ArgumentTupleAsExpression(argTuple));
                                var statement = new QsStatement(
                                    QsStatementKind.NewQsReturnStatement(call),
                                    LocalDeclarations.Empty,
                                    QsNullable <QsLocation> .Null,
                                    QsComments.Empty);
                                var localDeclarations = new LocalDeclarations(
                                    SyntaxGenerator.ValidDeclarations(SyntaxGenerator.ExtractItems(argTuple)));

                                return(spec.WithImplementation(SpecializationImplementation.NewProvided(
                                                                   argTuple,
                                                                   new QsScope(ImmutableArray.Create(statement), localDeclarations))));
                            }
                        })));
                        elements.Add(QsNamespaceElement.NewQsCallable(callable));
                    }
                    else
                    {
                        elements.Add(element);
                    }
                }
                else
                {
                    elements.Add(element);
                }
            }
            return(new QsNamespace(ns.Name, elements.ToImmutable(), ns.Documentation));
        }