Invariant Functors Unlocked
We tend to forget this quite often. An invariant functor or an exponential functor is, given
A => B and
B => A , it converts type
A to type
B in the same context
F[_]. We call this
That’s the famous
Functor ! Covariant functor implements
xmap by discarding the function
B => A .
As expected, it discards
f: A => B and makes use of
contramap to implement
Example for Contravariant Functor
Example for covariant Functor
As expected, it is
DecodeJson, where the type parameter in the type class comes at covariant position (method result)
If type parameters are at covariant position, that means the method return contains the type.
If type parameters are at contravariant position, that means the method parameters contain the type.
When is invariant functor?
We may have types at covariant (output) or contravariant (input) position. However, we may sometime deal with both covariance and contravariance in the same type class.
Let’s bring in EncodeJson and DecodeJson into one type class.
EncodeJson and DecodeJson
Functor but invariant
So an individual
contramap to upcast (or downcast) an A to B in the context of
F[_] is not possible if
F has types both in covariant and contravariant positions. It means,
F has to have an invariant functor for it!
Apply, Applicative to Divide, Divisible
We saw the contra-variant version of functor. We will see the contra-variant version of
Apply , which is called
Divide and how that can be more powerful if
EncodeJson had an instance of
Divide in the next blog. Along with it, we will discuss more on
Applicative and how
Divisible form the hierarchy!
Originally published at gist.github.com.