# 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 `xmap`

.

# Covariant Functor

That’s the famous `Functor`

! Covariant functor implements `xmap`

by discarding the function `B => A`

.

# Contravariant Functor

As expected, it discards `f: A => B`

and makes use of `contramap`

to implement `xmap`

# Example for Contravariant Functor

# Usage

# Example for covariant Functor

As expected, it is `DecodeJson`

, where the type parameter in the type class comes at covariant position (method result)

# Note

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 `map`

or `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 `Apply`

and `Applicative`

and how `Divide`

and `Divisible`

form the hierarchy!

*Originally published at **gist.github.com**.*