Hi Siddhartha,
Thank you for the elaborate reply and sorry for not
coming back to you right away.
I had to spend some time trying to wrap my head around it. It appears
the source of my confusion was mixing the the inheritance within the
types; say Animal and Dog, and the variance over the inheritance; which
provides a subtyping relationship between the parameterized types; say
List[Animal] and List[Dog].
I lost you at “increasing and decreasing functions (more precisely order
preserving and order reversing)”. I understood “increasing” as from the
top down the hierarchy and “decreasing” as from the bottom up the
hierarchy of the types. Correct me if this is not what you were trying
to say.
Assuming this hierarchy:
class LivingBeing
class Animal extends LivingBeing
class Dog extends Animal
The following is what I could collect:
| Variance | Notation | Description | T = Animal |
|---|---|---|---|
Covariance |
+T |
"+" is inclusive of the subtypes |
List[Dog] is a subtype of List[Animal] |
Contrvariance |
-T |
"-" is exclusive of the subtypes |
List[LivingBeing] is a subtype of List[Animal] |
Invariance |
T |
"+" is neither inclusive nor exclusive of the subtypes |
List[Animal] is only and only List[Animal] |