Static property of type parameter - is this a CLR or C# limitation?

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Here comes a generic class with a static property.
Let's say they are exotic singleton pets.


abstract class Pet {...}

abstract class SharedPet<T>: Pet
where T: SharedPet<T>, new()
{
private static T singleton = new T();
public T Singleton {get {return singleton;}}
}

class KingKong : SharedPet<KingKong> {...}
class Gozilla : SharedPet<Gozilla> {...}


I use pets as a parameter to another generic class:


class PetLover<T>
where T : Pet, new()
{
public virtual T GetAPet
{ return new T(); } //Let it rain cats and dogs...
}

class SharedPetLover<T> : PetLover<T>
where T : SharedPet<T>, new()
{
public override T GetAPet //...but not gozillas
{ return T.Singleton; }
// Compile time error:
// 'T' is a 'type parameter', which is not
// valid in the given context'
}

Unforunately, it seems I can't access a static member
of T, though the constraint ensures it is there.

Is this a restriction of C#, or is it a CLR thing?
Is there a neat way of getting around it, or am I left
with the options of either rewriting the GetAPet
override using reflection, or doing copy-paste
overrides in KingKongLover, GozillaLover,
KermitLover, ReptarLover...?


(In case anyone wonders what the "real beasts"
look like: I'm trying to do a continuation passing
style implementation of a programming language
with a DOM like data model, and the nodes used
to implement continuations etc. must be as slim
as possible, yet compliant with the data model.)


.