Scala, as a functional language, treats functions as first class citizens. Of course it’s also object oriented language. Those two paradigms can be seen as conflicting with each other. In this post I’d like to show you some different ways of creating a functions in Scala to show that these two worlds can coexist.

# Foreword

## Function

Let us start by defining what a function is. Wikipedia supplies us with this:

A function f from X to Y is a subset of the Cartesian product X × Y subject to the following condition: every element of X is the first component of one and only one ordered pair in the subset.

This is of course mathematical definition of a function. It says that given two sets `X` and `Y` we define `f` as some kind of mapping from `X` to `Y`. Also we have to define such mapping for all elements from `X`, and each element from `X` have only one mapping to any element from `Y`.

So let’s get back to the programming world. We have functions here, but our functions are not quite like the definition says. We can make the function be non-deterministic which means that it can basically return different values when called with the same inputs twice. Those functions have some kind of side effect. Reading data from network with `receive` function is a good example. We always call it with the same arguments, yet it always returns different data.

But as it turns out - if we create a function that operates only on its arguments it’s impossible to make it return different values for the same arguments.

Functions that operate only on their arguments are called pure functions. We all should always use pure functions, because they are easy to reason about. Unfortunately sometimes we have to interact with outside world and this is mostly done through side effects.

## Partial function

Partial function is a function that is defined only for some elements of `X`. This means that there are some elements of `X` that cannot be supplied as an argument to our function - it would give us an error.

``````def partial(input: Int) = match {
case 1 => "One"
}``````

This example function will work only for one argument: `1`. Any other value would cause an error.

## Higher order function

One last thing we should know before going further is: what is higher order function? Well it’s just a function that operates on other functions. It can receive a function as an argument or it can create a function and return it as a value.

``def apply(f: Int => String, arg: Int) = f(arg)``

This simple higher order function just takes two parameters - a function and a number. Then it applies the `f` function to the number.

# Define a function in Scala

To define a function or method in Scala we normally write:

``def greet(name: String): String = s"Hello \$name"``

Then we can use this function as a parameter to other function:

``Seq("Bob", "Ben").map(greet)``

Here `map` is a higher order function which translates each `Seq` element to new element using the function that was supplied as its argument. Result will be: `Seq("Hello Bob", "Hello Ben")`.

In Scala there is a special method that we can implement in our class or object that gives it function-like invocation:

``````object Greeter {
def apply(name: String) = s"Hello \$name"
}

Greeter("Ben") // will return "Hello Ben"``````

So the `apply` method gives us some syntactic sugar in Scala - nice! But if we can use it as a function, can we pass it to the higher order function like `map`?

``Seq("Bob", "Ben").map(Greeter)``

This will unfortunately throw an error at compile time saying that it wanted a function ```String => String``` and got `Greeter`.

The good news is that we can fix this! We must tell the compiler that our object is also a function by extending it’s type signature:

``````object Greeter extends (String => String) {
def apply(name: String) = s"Hello \$name"
}``````

Now we can pass our `Greeter` object to `map` and everything works fine!

As you can see Scala merges the world of object oriented programming and the world of functional programming by allowing objects and classes to act like functions.

# Sequences and Maps

As I mentioned above - functions are mappings. This means that we could define a new function just by defining a mapping between two sets of data. This is why Scala’s `Map[A, B]` extends the `A => B` type signature. It basically allows us to use any `Map` as a function from type `A` to type `B`:

``````val numbers = Map(1 -> "one", 2 -> "two", 3 -> "three")
val result = Seq(3, 2, 1).map(numbers)``````

This will give the `result` a value of `Seq("three", "two", "one")` so map acts exactly as partial function. It’s partial because it’s defined only for values 1, 2, and 3.

And what about other collections? Well, a sequence maps index to a value, doesn’t it?

``````val letters = Seq("e", "h", "l", "o")
val result = Seq(1, 0, 2, 2, 3).map(letters).mkString``````

The `result` value will be “hello”.

# Function composition

Mapping over some sequence is fine to show that lists and maps are functions but you may say that it doesn’t really give us much because after all we can write it like this:

``Seq(1, 0, 2, 2, 3).map(num => letters(num))``

The true fun begins when you want to operate on some functions. For example we would like to compose two functions. This means that we apply the first function to the argument and then apply the second to the value returned by the first: `f(g(x))`.

This can be also done with maps and sequences:

``````val englishToInteger = Map("zero" -> 0, "one" -> 1, "two" -> 2, "three" -> 3)
val integerToGerman = Seq("null", "eins", "zwei", "drei")
val englishToGerman = englishToInteger andThen integerToGerman

val zwei = englishToGerman("two")``````

Of course value of `zwei` will be a string “zwei”. The `andThen` is a method of Function1 class and it composes two functions. Here we create the function `englishToGerman` by composing `englishToInteger` with `integerToGerman`. The argument flow is quite straightforward here - “one” is passed to the `englishToInteger` function (which is a Map!). This gives us an integer representing the number: `1`. Then this integer is passed to `integerToGerman` sequence which maps indexes to German numbers.

# Summary

Even though I’ve been using Scala for some time now I’ve discovered that maps and lists act as functions very recently. What is great here is that knowing that gives me a new perspective on those data structures. I hope that for you this is as much fun as it is for me.