Scala: Applicative with scalaz example

I’ve talked on Functor previously, will repeat myself that construction is very useful in the Scala's world. We covered Comonad as well, it is extending Functor and adds functionality for the extraction value or the wrapping of already wrapped.

This post is related to Applicative. Applicative is coupled with Functor, even has an alternative name: Applicative Functor. At first let look into class hierarchy for Applicative in scalaz library:

Scala: Comonad (scalaz example)

When we were talking on Functor - we described it as a construction that can apply function to incapsulated value and return a new instance of the same container with function result value inside. Quite useful construction, it is even implemented by scala library's classes: like Option, List and others. To be honest Scala's standart library classes mixing Functor and Monad, but lets do not concentrate on this now.

Scala: Functor (scalaz example)

Function programming got a proven handy in structuring the code, from where we have common structures/classes presented in many functional languages. All this magic comes from mathematic and in the most parts aren't so easy to get for regular developers with imperative experience. I've been googling a lot to get essence and still getting a lot of "news". Looks like the best way to review FP types in Scala is using examples from scalaz library. Let try to start from the Functor.

Functor 

Functor is a something you can map over, it has only one method map (called fmap scalaz). Class diagram is very simple:

Rework: Monads in Scala - 4

Monadic Zero

Do U remember second state of Response - Marvelous?
If we represent Marvelous via Answer with null inside - it's not enough, than we can translate Marvelous into Answer - ignoring it's Essentials - that is error:

    val box = new Answer[Any](null)
    val func:(Any)=>Int = (in) => 5
    val res = box map func // Produces Answer(5)

Expected behavior, that is described via The First Zero Law: Identity

     mzero map/flatMap f = mzero

Rework: Monads in Scala - 3

Today we will speak more about flatMap, Monadic Zero and other steps.

Let's start from the Business. Should I use Monads?

Its good to start with Scala's Option class, but while we are still don't understand the theory, lets reinvent the wheel to drive into details. Additionally we will try to follow Function and Object Oriented best practices and won't do optimizations etc, while we are not implementing library.

Rework: Monads in Scala - 2

During previous session we captured in mind 3 transformations/conversions. While moving out from mathematical pressure we just got 3 simple formulas:


a) (A => B ) => (M[A] => M[B]) // Monad
b) (A => M[B] ) => (M[A] => M[B]) //Functor
c) (M [A => B]) => (M[A] => M[B]) //Applicative


As an implementation we've chosen functional way:

a) Func(A => B) : M[A] => M[B] // Monad
b) Func(A => Box[B]) : Box[A] => Box[B] //Functor
c) Func(Box[A => B]) : Box[A] => Box[B] //Applicative

Rework: Monads in Scala - 1

I have to spend more time than other (smart guys) trying to get simple topics. As a profit - getting clean description for myself - using simple (clean for non math geek) vision. I've read hundred of articles/examples/... + done few presentations on the same topic. Just want to finalize it and forget:)

As a conclusion generalization of my previous self-study experience I would kindly ask James Iry:

Usually articles that start with words like "monad" and "functor" quickly devolve into soup of Greek letters. That's because both are abstract concepts in a branch of mathematics called category theory and explaining them completely is a mathematical exercise.

JAMES IRY

But there must be possibility to avoid complexity, to allow understanding the topic while reading in the bus or 3 minutes before falling asleep. U r welcome to the world of Monads in Scala.