I've recently struggled trough understanding of the basics of functional programming. All the material, that I've found was either for dummies (very boring) or for people with PhD in lambda calculus. With this article, I'm trying to fill the gap.

Among first thing to learn about functional programming, is that functional code is without IO nor any side-effects and it is immutable. Quite obviously, purely functional program will be absolutely useless, so I wouldn't declare FP the new silver bullet. But it is a good way to implement complex business-logic or core functionality.

There are several libraries like Cats or Scalaz defining some helpful types and functions for FP. I personally prefer Cats, but the same result can be achieved with Scalaz or any other mature FP library.

• Why we choose functional programming?
• Magic
• Pure functions
• Always produce result. No exceptions
• Immutability
• Function - first class citizen
• Types
• Conclusion

Functional programming is a programming paradigm based on and very close to lambda calculus, which is

...formal system in mathematical logic for expressing computation... It is a universal model of computation that can be used to simulate any Turing machine.

Apart from the fact that functional code looks a lot like definition of mathematical model of the problem, there are other major advantages to use FP:

• Functional code is easy reasoning about due to referential transparency: a function is referential transparent if by replacing the function call in code by the result of this call (given that the arguments are known), the behavior of the code will stay the same.

  def add(x: Int, y: Int): Int = x + y	

  Function add is referentially transparent. Every call to this function can be replace by its result.

  It is easier to understand this kind of code. Referentially transparent function is dependent only on it's arguments and it produces only one result, which is returned. No change is introduced to the system by call to this function.

  This also means that no matter the scale, it takes about the same amount of effort to understand the code.

• Fewer bugs due to:

  • code is easier to reason about (see above)
  • since the code is much more like a mathematical model, the compiler can check it more thorough. The compilation will fail in case your model is not converging, or there are illegal (in current model) operations

• It is almost always better to tell what to do instead of how. By telling what to do, you're using higher level of abstractions. Smart people dedicated a lot of time and effort to implement the abstraction in efficient, precise and correct way. In rare cases, when you need something better, you'll dedicate all the resources to make it the best way possible. You will not write your own web server just for home page. But in case you need something special, it will become one of core businesses.

  Functional code tells computer what to do (declarative code), while your regular C-like code is telling the machine how to do what it should do (imperative code).

to top

I felt in love with functional paradigm in Scala because of the ability to build type-independent algorithms on simple cases, and then, with a pinch of magic dust, use totally unexpected types in those algorithms. All of this with static type-safety, compile-time optimizations and other goodies.

I will provide a short example here and i will give a sketchy explanation also. My hopes are, that after reading this article, the reader will be able to understand the example fully (since it is very simple).

Given, with functional library Cats, function all defined as:

import cats.{Monoid, Foldable}
import cats.implicits._
def all[T: Monoid, F[_]: Foldable](lst: F[T]): T = lst.foldLeft(Monoid[T].empty)(_ |+| _)

which allows us to use it as:

all(List(1, 2, 3, 4)) // 10
all(List(Set(1, 2, 3), Set(3, 4), Set(5))) // Set(1, 2, 3, 4, 5)

Then, if we define new type

type G[T] = List[Option[T]]

and add a pinch of magic

implicit val fld: Foldable[G] = Foldable[List].compose[Option]

we can use the all function with this new type:

all[Int, G](List(Option(1), Option(2), None, Option(4))) // 7

For more complete example and thorough explanation see here. Here I'll give brief explanation in hope, that all the reset you will understand after finishing the article.

Let's say we have two functions:

def allInt(lst: List[Int]): Int = lst.foldLeft(0)(_ + _)
def allSet[A](lst: List[Set[A]]): Set[A] = lst.foldLeft(Set.empty[A])(_ union _)

Both of these functions are the same except for the type-specific seed element and a method for combining two elements. In mathematics there is a special name for these pairs (seed - combine) - Groups. In FP they are called Monoid. So let's get them out and pass this data as a parameter the algorithm (to the function all):

trait Monoid[T] {
  def empty: T
  def combine(x: T, y: T): T
}
def all[T](lst: List[T], m: Monoid[T]): T = lst.foldLeft(m.empty)(m.combine)

or with functional library Cats (which contains among other things definition of Monoid) and further optimizations:

import cats.Monoid
import cats.implicits._
def all[T: Monoid](lst: List[T]): T = lst.foldLeft(Monoid[T].empty)(_ |+| _)

Since in the function we need only foldLeft, List[T] can be replaced with further abstraction:

import cats.{Monoid, Foldable}
import cats.implicits._
def all[T: Monoid, F[_]: Foldable](lst: F[T]): T = lst.foldLeft(Monoid[T].empty)(_ |+| _)

Foldable also have this nice feature: it can be composed.

F[_] <=> Foldable[F]
G[_] <=> Foldable[G]
type FG[T] = F[G[T]]
F[G[_]] <=> Foldable[F].compose[G] <=> Foldable[FG]

to top

The concept of pure function is of the most importance in FP. My favorite example of one such function is arithmetic operator +. It produces new instance based on arguments and it does only this. It does not change passed objects (which in itself is very bad habit), nor does it change or use some hidden data to produce results.

When starting writing pure function, write full signature:

def foo[T, R](x: T): R

This will also help you later: since it is pure function, you know that it does nothing to the arguments (you may use them again), and it always returns value of type R. So when you see application of the function in the code, in order to get the idea what is going on here, you just need to see it's signature, without the need to dive into all the nuances of the implementation (referential transparency).

Loops are essentially imperative constructions, which also ties via closure internal mutable(!) variable to the algorithm inside it.

Use iteration and transformation over collection. Both standard library and functional libraries (Cats, Scalaz, etc.) have many specialized functions like map, filter, fold, etc. Among many benefits of using these functions are:

• increased readability of the code - explicit names of the functions
• functional (declarative) way of iterating over elements
• for some types there can be more robust implementation of the same iterative function
• some non-collection types implement the same functions (like map for Option) with the same meaning

Only when you have no other chose left, write recursive function with tail call. This kind of recursions is stack safe, since it is transformed by the compiler to loop (oh irony, but also an example of postponing the effects - another perk of FP). BTW, all the library functions use tail call recursions under the hood.

The function all from example above may be rewritten with @tailrec as follows:

def all[T: Monoid](lst: List[T]): T = {
  val M = Monoid[T]
  @tailrec
  def rec(l: List[T], acc: T): T = {
    if(l.isEmpty) acc 
	else rec(l.tail, M.combine(acc, l.head))
  }
  rec(lst, M.empty)
}

Good explanation of tail recursion can be found here.

Another popular use case is calculations based on previous element(s), in other words state. This is very counterintuitive part of FP: the state of the Finite-State-Machine should be an outside parameter. But it is against the rules to introduce mutable variable inside function since the function becomes non-pure. With mutable state the function has side-effect built-in. The solution is (as almost always) in the type that will be returned. The function will receive state and return result and new state.

Very thorough discussion of the state and it's use in FP can be found here, but in I'll give a gist. Random generator as it is - it is not functional way. Each call produce new result without arguments. Not a pure function. The solution is to define random function as follows:

def random(prev: Long): Long = prev * 6364136223846793005L + 1442695040888963407L

(see Knuth’s 64-bit linear congruential generator for the formula). In this particular case, the state is the same as desired value. But let's say we need to know the total number of calls to random:

final case class Seed(seed: Long, count: Long) 
def random(s: Seed): (Seed, Long) = {
    val n = Seed(s.seed * 6364136223846793005L + 1442695040888963407L, count + 1)
    (n, n.seed)
}

This way random still depends on state while being pure function.

to top

Function should always produce a value. Exception is not thrown. Whenever there is a possibility of non-value result (exception, void, undefined, null, etc.), it should be incorporated in the result type. Such types include but not limited to:

Option[T]
Try[T]
JsResult[T]
Future[T]
//etc.

And of course other such types may be introduced as aliases via type or as case-classes:

type Result[T] = Either[Throwable, T]

Functional approach not only better because it is functional, but also it is more robust in general case and in the edge cases gives more control over error handling to developer.

Whenever exception is thrown, runtime have to rollback the call stack till the closest appropriate catch collecting a lot of data along the way, while, with functional approach, the execution chain just stops whenever any function returns an "error":

def foo: Result[T]
def bar(t: T): Result[T]

foo.flatMap(bar).map(...)

In this example, if foo returns Left, the flatMap is not evaluated (see implementation of Either), and neither is the rest of the chain. If foo returns Right, but bar returns Left, then the map would not run. As simple as that.

Since error is allowed as result, we can work with errors same way as with 'valid' result, e.g. transform to default value, collect all errors from many executions, define retry strategy, etc. without excessive code branching as in case of exception/null/undefined based error-handling.

to top

Another cornerstone of FP is immutability. Functional paradigm does not allow to change values. As I've mentioned earlier, absolutely functional code will be absolutely useless, the same is with immutability. The goal is not to write 100% immutable code (although this is good), but to limit mutable code to some reservations, which should be thoroughly tested. Also, these places are the first suspects for bugs.

BTW: while writing immutable code, you will also write pure functions.

Immutability has it's advantages:

• the same instance can be shared indefinitely. One of the consequences of this fact is that parallel access is trivial - no need to sync since only read is possible

• since each function is (should be) pure function and the result depends only on arguments passed, the order of the calls important only if some function uses results of evaluation of another functions. This also means, that compiler may deduce a call tree and run some evaluations in parallel.

One may argue that always creating new objects adds pressure to the memory (in terms of usage and consumption) and to garbage collector. I will argue with that with the facts that:

• most of these immutable instances are short-lived instances. They are forgotten during the first generation (Gen-1). It is the mutable instances that usually survive to Gen-2. As for immutable long-live instances, most of those are application-level constants or singleton instances that lives through to Gen-3.

• As mentioned above, when using immutable values, sharing them became trivial. No need neither for defensive copy-on-share, nor for synchronization of access. Which is beneficial for code complexity, footprint, memory usage and GC.

• And as a last argument (in this article) in favor for immutability, since immutable object doesn't mutate, GC does not need to take it as root on the next scan, again less work for GC.

More about it here and here. And, from Oracle docs:

The impact of object creation is often overestimated, and can be offset by some of the efficiencies associated with immutable objects. These include decreased overhead due to garbage collection, and the elimination of code needed to protect mutable objects from corruption.

to top

Each function has it's type, which consists of types of the arguments and type of the result:

def foo(i: Int, d: Double): String = ??? // (Int, Double) => String
def bar(b: BigInt): Boolean = ??? // BigInt => Boolean

A function with a proper type can be passed to or returned from another function. Most probably you already have seen/used it. Array.map, Array.sort, etc. in JavaScript, C#, Scala, etc., all these functions in all these languages are accepting transformation/sort/etc. function as one of the parameters. If you've used one of those, you've used function as a first class citizen. Functions like Array.map are called Higher Order Functions, because these functions are dealing with other functions either as arguments, or as result value (or both).

And the next reasonable step is to assign function to a variable:

val foo: (Int, Double) => String = (i, d) => s"$i $d"
val baz: BigInt => Boolean = _.isValidInt

to top

There are two sorts of types in FP: Data Type and Type Class.

Data type is a type to store data. With data type you describe measurement from sensor, payment, event or even some executable code (see Function - is first class citizen). Usually case class is used to define this type. "Methods" for this type are defined either in value class or in universal traits (the trait doesn't have to extend Any but the methods should be pure functions).

Type class defines algebra (set of operations) for particular data type. Type class interface defines some operations available on some data type. Usually it is Higher-Kinded Type (which only means that the trait has type-parameter: Monoid[M]) so that instance of the type class defines operations for one specific data type.

In most cases data type is just a way to pass some meaningful data, while type class holds all the know-how of how to handle this type.

What are the benefits of this separation, one might ask. One obvious advantage is the ability to generalize the algorithms over wider range of type than with mere inheritance (see thorough explanation here). Less obvious benefit arises from the constrains that this approach enforce on the developer. It enforces to think of the data type as chunk of data and nothing more. The algorithms become type-independent - all type-related know-how are encapsulated in the type class. And so, by designing the model in accordance with the types-duality (type class & data type), the code is separated to two distinct areas of what (algorithms) and how (type classes).

To illustrate this, let's define simple payment system:

trait Currency
case object Dollar extends Currency
case object Pound extends Currency
case class Purchase(amount: Double, currency: Currency)

Before we bill the user, it is better to collect all payments per each currency and charge once per currence. It can be achieved by quite simple folding:

def collect(charges: List[Purchase]): Map[Currency, Purchase] = {
  def add(a: Purchase, b: Purchase): Purchase = a.copy(amount = a.amount + b.amount)
  def empty(c: Currency): Purchase = Purchase(0.0, c)    
  charges.foldLeft(Map.empty[Currency, Purchase]){
    (m, p) => m + (p.currency -> add(p, m.getOrElse(p.currency, empty(p.currency)))
  }
}

On the other hand, we will have measurements from different parts of the system:

case class Measurements(unit: String, data: Double)

These measurements may be in completely different units (number of clicks vs. avg time on page) or in different scales - KB/MB. In this case the measurement should be separated by units, but transformed to common scale. The function add for Measurement will be a little different:

def scale(a: Measurement): Measurement = a.unit.splitAt(1) match {
  case ("K", u) => Measurement(u, a.data / 1000)
  case ("M", u) => Measurement(u, a.data / 1000000)
}
def addMeasurement(a: Measurement, b: Measurement): Measurement = {
  val sa = scale(a)
  sa.copy(amount = sa.amount + scale(b).amount)
}

With this additions the collect can be repeated for Measurement. But let's try and not repeat ourselves. First let's define the number of operations needed for collect:

trait Collectable[T, Key] {
  def add(a: T, b: T): T
  def empty(key: Key): T
  def key(a: T): Key
}

With this trait collect can be transformed to:

def collect[T, Key](lst: List[T], C: Collectable[T, Key]): Map[Key, T] = 
  lst.map(x => C.key(x) -> x)
    .foldLeft(Map.empty[Key, T]){
      (m, t) => m + (t._1 -> C.add(t._2, m.getOrElse(t._1, C.empty(t._1))))        
    }

All is left is to define Collectable for both Measurement and Purchase:

val purColl = new Collectable[Purchase, Currency] {
  def add(a: Purchase, b: Purchase): Purchase = a.copy(amount = a.amount + b.amount)
  def empyt(key: Currency): Purchase = Purchase(0.0, key)
  def key(a: Purchase): Currency = a.currency
}
val measColl = new Collectable[Measurement, String] {
  def add(a: Measurement, b: Measurement): Measurement = addMeasurement(a, b)
  def empty(key: String): Measurement = scale(Measurement(key, 0.0))
  def key(m: Measurement): String = m.unit
}

And thus, we have generic algorithm collect, and all type-specific know-hows are encapsulated in the instance of Collectable type class. More on this can be found here.

to top

In order to become able to write functional code, or better yet to start thinking functional, you have to exercise it (as with any other language), otherwise it will stay curios academic tricks not applicable to real-life problems. I hope this article will help you to make the first step (leap of faith) to start writing functional code.

to top