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c# 3.0 - Is it possible to define a generic lambda in C#?

I have some logic in a method that operates on a specified type and I'd like to create a generic lambda that encapsulates the logic. This is the spirit of what I'm trying to do:

public void DoSomething()
{
    // ...

    Func<T> GetTypeName = () => T.GetType().Name;

    GetTypeName<string>();
    GetTypeName<DateTime>();
    GetTypeName<int>();

    // ...
}

I know I can pass the type as a parameter or create a generic method. But I'm interested to know if a lambda can define its own generic parameters. (So I'm not looking for alternatives.) From what I can tell, C# 3.0 doesn't support this.

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While Jared Parson's answer is historically correct (2010!), this question is the first hit in Google if you search for "generic lambda C#". While there is no syntax for lambdas to accept additional generic arguments, you can now use local (generic) functions to achieve the same result. As they capture context, they're pretty much what you're looking for.

public void DoSomething()
{
    // ...

    string GetTypeName<T>() => typeof(T).GetType().Name;

    string nameOfString = GetTypeName<string>();
    string nameOfDT = GetTypeName<DateTime>();
    string nameOfInt = GetTypeName<int>();

    // ...
}

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