9 Recursion

{% include toc.html %}

9.1 Loops through recursion

Due to immutability, loops in Elixir (and in any functional programming language) are written differently from imperative languages. For example, in an imperative language (like C in the following example), one would write:

for(i = 0; i < array.length; i++) {
  array[i] = array[i] * 2

In the example above, we are mutating both the array and the variable i. Mutating is not possible in Elixir. Instead, functional languages rely on recursion: a function is called recursively until a condition is reached that stops the recursive action from continuing. No data is mutated in this process. Consider the example below that prints a string an arbitrary amount of times:

defmodule Recursion do
  def print_multiple_times(msg, n) when n <= 1 do
    IO.puts msg

  def print_multiple_times(msg, n) do
    IO.puts msg
    print_multiple_times(msg, n - 1)

Recursion.print_multiple_times("Hello!", 3)
# Hello!
# Hello!
# Hello!

Similar to case, a function may have many clauses. A particular clause is executed when the arguments passed to the function match the clause’s argument patterns and its guard evaluates to true.

When print_multiple_times/2 is initially called in the example above, the argument n is equal to 3.

The first clause has a guard which says “use this definition if and only if n is less than or equal to 1”. Since this is not the case, Elixir proceeds to the next clause’s definition.

The second definition matches the pattern and has no guard so it will be executed. It first prints our msg and then calls itself passing n - 1 (2) as the second argument.

Our msg is printed and print_multiple_times/2 is called again this time with the second argument set to 1. Because n is now set to 1, the guard in our first definition of print_multiple_times/2 evaluates to true, and we execute this particular definition. The msg is printed, and there is nothing left to execute.

We defined print_multiple_times/2 so that no matter what number is passed as the second argument it either triggers our first definition (known as a “base case”) or it triggers our second definition which will ensure that we get exactly one step closer to our base case.

9.2 “Reduce” and “map” algorithms

Let’s now see how we can use the power of recursion to sum a list of numbers:

defmodule Math do
  def sum_list([head|tail], accumulator) do
    sum_list(tail, head + accumulator)

  def sum_list([], accumulator) do

Math.sum_list([1, 2, 3], 0) #=> 6

We invoke sum_list with the list [1, 2, 3] and the initial value 0 as arguments. We will try each clause until we find one that matches according to the pattern matching rules. In this case, the list [1, 2, 3] matches against [head|tail] which bounds head to 1 and tail to [2, 3]; accumulator is set to 0.

Then, we add the head of the list to the accumulator head + accumulator and call sum_list again, recursively, passing the tail of the list as its first argument. The tail will once again match [head|tail] until the list is empty, as seen below:

sum_list [1, 2, 3], 0
sum_list [2, 3], 1
sum_list [3], 3
sum_list [], 6

When the list is empty, it will match the final clause which returns the final result of 6.

The process of taking a list and “reducing” it down to one value is known as a “reduce” algorithm and is central to functional programming.

What if we instead want to double all of the values in our list?

defmodule Math do
  def double_each([head|tail]) do
    [head * 2|double_each(tail)]

  def double_each([]) do

Math.double_each([1, 2, 3]) #=> [2, 4, 6]

Here we have used recursion to traverse a list doubling each element and returning a new list. The process of taking a list and “mapping” over it is known as a “map” algorithm.

Recursion and tail call optimization are an important part of Elixir and are commonly used to create loops. However, when programming in Elixir you will rarely use recursion as above to manipulate lists.

The `Enum module </docs/stable/elixir/Enum.html>`__, which we’re going to see in the next chapter, already provides many conveniences for working with lists. For instance, the examples above could be written as:

iex> Enum.reduce([1, 2, 3], 0, fn(x, acc) -> x + acc end)
iex> Enum.map([1, 2, 3], fn(x) -> x * 2 end)
[2, 4, 6]

Or, using the capture syntax:

iex> Enum.reduce([1, 2, 3], 0, &+/2)
iex> Enum.map([1, 2, 3], &(&1 * 2))
[2, 4, 6]

Let’s take a deeper look at Enumerables and, while we’re at it, their lazy counterpart, Streams.