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generics - Java map with values limited by key's type parameter

Is there a way in Java to have a map where the type parameter of a value is tied to the type parameter of a key? What I want to write is something like the following:

public class Foo {
    // This declaration won't compile - what should it be?
    private static Map<Class<T>, T> defaultValues;

    // These two methods are just fine
    public static <T> void setDefaultValue(Class<T> clazz, T value) {
        defaultValues.put(clazz, value);
    }

    public static <T> T getDefaultValue(Class<T> clazz) {
        return defaultValues.get(clazz);
    }
}

That is, I can store any default value against a Class object, provided the value's type matches that of the Class object. I don't see why this shouldn't be allowed since I can ensure when setting/getting values that the types are correct.

EDIT: Thanks to cletus for his answer. I don't actually need the type parameters on the map itself since I can ensure consistency in the methods which get/set values, even if it means using some slightly ugly casts.

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You're not trying to implement Joshua Bloch's typesafe hetereogeneous container pattern are you? Basically:

public class Favorites {
  private Map<Class<?>, Object> favorites =
    new HashMap<Class<?>, Object>();

  public <T> void setFavorite(Class<T> klass, T thing) {
    favorites.put(klass, thing);
  }

  public <T> T getFavorite(Class<T> klass) {
    return klass.cast(favorites.get(klass));
  }

  public static void main(String[] args) {
    Favorites f = new Favorites();
    f.setFavorite(String.class, "Java");
    f.setFavorite(Integer.class, 0xcafebabe);
    String s = f.getFavorite(String.class);
    int i = f.getFavorite(Integer.class);
  }
}

From Effective Java (2nd edition) and this presentation.


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