Raising the abstraction level with HKTs and type classes

I suppose it's an objective of every developer writing reusable code. Statically typed FP and higher-kinded types lets you raise the abstraction level enormously with respect to OOP and, more generally, languages which don't have HKTs and type classes.

In this talk you'll see how to take advantage of HKTs to implement a very reusable function. I'll start by implementing it using a quick & dirty approach and then trying to make it more abstract and reusable thanks to more or less known type classes, actually making sense of them so you can see they are not just confined to theory and useless in practice.

Transcript

1. A monad is just monoid in
   the category of
   endofunctors.
   What's the problem with this sentence?
   Alessandro Lacava, @lambdista | Scala Italy 2017 | Rome
   

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2. At least two problems
   → It's scary if you're not a math junkie
   → It's true!
   Alessandro Lacava, @lambdista | Scala Italy 2017 | Rome
   

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3. The real question is: why should I care
   about monads?
   Alessandro Lacava, @lambdista | Scala Italy 2017 | Rome
   

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4. Very common answers
   Effects. Huh?
   Sequencing.
   ...
   Alessandro Lacava, @lambdista | Scala Italy 2017 | Rome
   

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5. They help you raise the abstraction level
   Talk is cheap. Show me the code.
   — Linus Torvalds
   Alessandro Lacava, @lambdista | Scala Italy 2017 | Rome
   

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6. Advertising service
   Very small and simplified subset of the model
   sealed trait KeywordMatchType
   case object Broad extends KeywordMatchType
   case object Exact extends KeywordMatchType
   case object Phrase extends KeywordMatchType
   final case class Keyword(text: String, matchType: KeywordMatchType)
   Alessandro Lacava, @lambdista | Scala Italy 2017 | Rome
   

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7. Some type aliases
   type Keywords = List[Keyword]
   type Result[+A] = Either[String, A]
   Alessandro Lacava, @lambdista | Scala Italy 2017 | Rome
   

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8. Keyword Expander
   Keywords => Future[Keywords]
   Alessandro Lacava, @lambdista | Scala Italy 2017 | Rome
   

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9. Write a function that reduces an expander
   list
   def foldFutureKeywords(fs: List[Keywords => Future[Keywords]])
   (init: Keywords): Future[Keywords] = ???
   What will you use to reduce a List?
   Alessandro Lacava, @lambdista | Scala Italy 2017 | Rome
   

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10. First quick & dirty attempt
    def foldFutureKeywords(fs: List[Keywords => Future[Keywords]])
    (init: Keywords): Future[Keywords] =
    fs.foldLeft(Future.successful(init)) { (acc, f) =>
    acc.flatMap(f)
    }
    Alessandro Lacava, @lambdista | Scala Italy 2017 | Rome
    

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11. Usage
    val keywordExpanders: List[Keywords => Future[Keywords]] = ???
    val expand: Keywords => Future[Keywords] =
    foldFutureKeywords(keywordExpanders)
    → What's the problem?
    Alessandro Lacava, @lambdista | Scala Italy 2017 | Rome
    

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12. Improved version
    def foldFuture[A](fs: List[A => Future[A]])
    (init: A): Future[A] =
    fs.foldLeft(Future.successful(init)) { (acc, f) =>
    acc.flatMap(f)
    }
    Alessandro Lacava, @lambdista | Scala Italy 2017 | Rome
    

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13. Keyword Validator
    Keywords => Result[Keywords]
    Alessandro Lacava, @lambdista | Scala Italy 2017 | Rome
    

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14. Write a function that reduces a validator
    list
    def foldEither[A](fs: List[A => Result[A]])
    (init: A): Result[A] =
    fs.foldLeft(Right(init): Result[A]) { (acc, f) =>
    acc.flatMap(f)
    }
    Alessandro Lacava, @lambdista | Scala Italy 2017 | Rome
    

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15. Usage
    val keywordValidators: List[Keywords => Result[Keywords]] = ???
    val validate: Keywords => Result[Keywords] =
    foldEither(keywordValidators)
    → What's the problem?
    Alessandro Lacava, @lambdista | Scala Italy 2017 | Rome
    

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16. DRY (Don't Repeat Yourself)
    Alessandro Lacava, @lambdista | Scala Italy 2017 | Rome
    

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17. Repetions
    def **foldFuture**[A](fs: List[A => **Future**[A]])
    (init: A): **Future**[A] =
    fs.foldLeft(**Future.successful(init)**) { (acc, f) =>
    acc.flatMap(f)
    }
    def **foldEither**[A](fs: List[A => **Result**[A]])
    (init: A): **Result**[A] =
    fs.foldLeft(**Right(init): Result[A]**) { (acc, f) =>
    acc.flatMap(f)
    }
    Alessandro Lacava, @lambdista | Scala Italy 2017 | Rome
    

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18. Higher-kinded types
    Symbol Kind Examples
    * Simple type Int, String, Double
    * -> * Unary type constructor List[_], Option[_], Future[_]
    * -> * -> * Binary type constructor Either[_, _], Function1[_,
    _], Map[_, _]
    (* -> *) -> * Higher-order type
    operator, higher-kinded
    type for friends
    Foo[F[_]], Bar[G[_]],
    Functor[F[_]], Monad[M[_]]
    Alessandro Lacava, @lambdista | Scala Italy 2017 | Rome
    

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19. Monad for developers
    trait Monad[M[_]] extends Applicative[M] {
    def pure[A](a: A): M[A]
    def flatMap[A, B](ma: M[A])(f: A => M[B]): M[B]
    // ...
    }
    → It's a type class that is polymorphic over a unary type constructor
    (M[_])
    → It has two abstract methods
    → Its instances must respect some laws
    Alessandro Lacava, @lambdista | Scala Italy 2017 | Rome
    

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20. Back to our repeated code
    def **foldFuture**[A](fs: List[A => **Future**[A]])
    (init: A): **Future**[A] =
    fs.foldLeft(**Future.successful(init)**) { (acc, f) =>
    acc.flatMap(f)
    }
    def **foldEither**[A](fs: List[A => **Result**[A]])
    (init: A): **Result**[A] =
    fs.foldLeft(**Right(init): Result[A]**) { (acc, f) =>
    acc.flatMap(f)
    }
    Alessandro Lacava, @lambdista | Scala Italy 2017 | Rome
    

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21. Factored out
    def foldList[M[_], A](fs: List[A => M[A]])
    (init: A)
    (implicit M: Monad[M]): M[A] =
    fs.foldLeft(M.pure(init)) { (acc, f) =>
    M.flatMap(acc)(f)
    }
    → Let's give it a spin!
    Alessandro Lacava, @lambdista | Scala Italy 2017 | Rome
    

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22. val keywordExpanders: List[Keywords => Future[Keywords]] = ???
    val keywordValidators: List[Keywords => Result[Keywords]] = ???
    val expand: Keywords => Future[Keywords] = foldList(keywordExpanders)
    val validate: Keywords => Result[Keywords] = foldList(keywordValidators)
    → !
    Alessandro Lacava, @lambdista | Scala Italy 2017 | Rome
    

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23. Can we do
    better?
    Alessandro Lacava, @lambdista | Scala Italy 2017 | Rome
    

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24. Sure
    Let's try to abstract over this List sh*t
    def foldList[M[_], A](fs: List[A => M[A]])
    (init: A)
    (implicit M: Monad[M]): M[A] =
    fs.foldLeft(M.pure(init)) { (acc, f) =>
    M.flatMap(acc)(f)
    }
    Alessandro Lacava, @lambdista | Scala Italy 2017 | Rome
    

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25. def foldTraversable[M[_], A](fs: GenTraversableOnce[A => M[A]])
    (init: A)
    (implicit M: Monad[M]): M[A] =
    fs.foldLeft(M.pure(init)) { (acc, f) =>
    M.flatMap(acc)(f)
    }
    Alessandro Lacava, @lambdista | Scala Italy 2017 | Rome
    

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26. Can we do even better?
    → Yes. Before I said that version worked for all
    subclasses of GenTraversableOnce.
    → I made a mistake. I opted for subtype polymorphism
    instead of parametric and ad hoc one.
    → Is there a type class which represent the foldable
    concept?
    → Yep, Foldable!
    Alessandro Lacava, @lambdista | Scala Italy 2017 | Rome
    

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27. Final version
    def fold[M[_], F[_], A](fs: F[A => M[A]])
    (init: A)
    (implicit
    M: Monad[M],
    F: Foldable[F]
    ): M[A] =
    F.foldLeft(fs, M.pure(init)) { (fa, f) =>
    M.flatMap(fa)(f)
    }
    → How beautiful and simple that is!
    Alessandro Lacava, @lambdista | Scala Italy 2017 | Rome
    

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28. Simple != Easy
    Simplicity is the ultimate sofistication
    — Leonardo Da Vinci
    Alessandro Lacava, @lambdista | Scala Italy 2017 | Rome
    

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29. Takeaways
    → Monads & co. are practically useful
    → Don't let the buzzwords scare you
    → Always follow the types
    Alessandro Lacava, @lambdista | Scala Italy 2017 | Rome
    

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30. Questions?
    → twitter: @lambdista
    → blog: http://www.lambdista.com
    → github: https://github.com/lambdista
    Alessandro Lacava, @lambdista | Scala Italy 2017 | Rome
    

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