Enumerable protocol

Enumerable protocol used by Enum and Stream modules.

When you invoke a function in the Enum module, the first argument is usually a collection that must implement this protocol. For example, the expression:

Enum.map([1, 2, 3], &(&1 * 2))

invokes Enumerable.reduce/3 to perform the reducing operation that builds a mapped list by calling the mapping function &(&1 * 2) on every element in the collection and consuming the element with an accumulated list.

Internally, Enum.map/2 is implemented as follows:

def map(enumerable, fun) do
  reducer = fn x, acc -> {:cont, [fun.(x) | acc]} end
  Enumerable.reduce(enumerable, {:cont, []}, reducer) |> elem(1) |> :lists.reverse()
end

Notice the user-supplied function is wrapped into a reducer/0 function. The reducer/0 function must return a tagged tuple after each step, as described in the acc/0 type. At the end, Enumerable.reduce/3 returns result/0.

This protocol uses tagged tuples to exchange information between the reducer function and the data type that implements the protocol. This allows enumeration of resources, such as files, to be done efficiently while also guaranteeing the resource will be closed at the end of the enumeration. This protocol also allows suspension of the enumeration, which is useful when interleaving between many enumerables is required (as in zip).

This protocol requires four functions to be implemented, reduce/3, count/1, member?/2, and slice/1. The core of the protocol is the reduce/3 function. All other functions exist as optimizations paths for data structures that can implement certain properties in better than linear time.

Summary

Types

acc()

The accumulator value for each step

continuation()

A partially applied reduce function

reducer()

The reducer function

result()

The result of the reduce operation

slicing_fun()

A slicing function that receives the initial position and the number of elements in the slice

t()

Functions

count(enumerable)

Retrieves the number of elements in the enumerable

member?(enumerable, element)

Checks if an element exists within the enumerable

reduce(enumerable, acc, fun)

Reduces the enumerable into an element

slice(enumerable)

Returns a function that slices the data structure contiguously

Types

acc()

acc() :: {:cont, term()} | {:halt, term()} | {:suspend, term()}

The accumulator value for each step.

It must be a tagged tuple with one of the following “tags”:

• :cont - the enumeration should continue
• :halt - the enumeration should halt immediately
• :suspend - the enumeration should be suspended immediately

Depending on the accumulator value, the result returned by Enumerable.reduce/3 will change. Please check the result/0 type documentation for more information.

In case a reducer/0 function returns a :suspend accumulator, it must be explicitly handled by the caller and never leak.

continuation()

continuation() :: (acc() -> result())

A partially applied reduce function.

The continuation is the closure returned as a result when the enumeration is suspended. When invoked, it expects a new accumulator and it returns the result.

A continuation can be trivially implemented as long as the reduce function is defined in a tail recursive fashion. If the function is tail recursive, all the state is passed as arguments, so the continuation is the reducing function partially applied.

reducer()

reducer() :: (term(), term() -> acc())

The reducer function.

Should be called with the enumerable element and the accumulator contents.

Returns the accumulator for the next enumeration step.

result()

result() ::
  {:done, term()} | {:halted, term()} | {:suspended, term(), continuation()}

The result of the reduce operation.

It may be done when the enumeration is finished by reaching its end, or halted/suspended when the enumeration was halted or suspended by the reducer/0 function.

In case a reducer/0 function returns the :suspend accumulator, the :suspended tuple must be explicitly handled by the caller and never leak. In practice, this means regular enumeration functions just need to be concerned about :done and :halted results.

Furthermore, a :suspend call must always be followed by another call, eventually halting or continuing until the end.

slicing_fun()

slicing_fun() ::
  (start :: non_neg_integer(), length :: pos_integer() -> [term()])

A slicing function that receives the initial position and the number of elements in the slice.

The start position is a number >= 0 and guaranteed to exist in the enumerable. The length is a number >= 1 in a way that start + length <= count, where count is the maximum amount of elements in the enumerable.

The function should return a non empty list where the amount of elements is equal to length.

t()

t() :: term()

Functions

count(enumerable)

count(t()) :: {:ok, non_neg_integer()} | {:error, module()}

Retrieves the number of elements in the enumerable.

It should return {:ok, count} if you can count the number of elements in the enumerable.

Otherwise it should return {:error, __MODULE__} and a default algorithm built on top of reduce/3 that runs in linear time will be used.

member?(enumerable, element)

member?(t(), term()) :: {:ok, boolean()} | {:error, module()}

Checks if an element exists within the enumerable.

It should return {:ok, boolean} if you can check the membership of a given element in the enumerable with === without traversing the whole enumerable.

Otherwise it should return {:error, __MODULE__} and a default algorithm built on top of reduce/3 that runs in linear time will be used.

reduce(enumerable, acc, fun)

reduce(t(), acc(), reducer()) :: result()

Reduces the enumerable into an element.

Most of the operations in Enum are implemented in terms of reduce. This function should apply the given reducer/0 function to each item in the enumerable and proceed as expected by the returned accumulator.

See the documentation of the types result/0 and acc/0 for more information.

Examples

As an example, here is the implementation of reduce for lists:

def reduce(_,       {:halt, acc}, _fun),   do: {:halted, acc}
def reduce(list,    {:suspend, acc}, fun), do: {:suspended, acc, &reduce(list, &1, fun)}
def reduce([],      {:cont, acc}, _fun),   do: {:done, acc}
def reduce([h | t], {:cont, acc}, fun),    do: reduce(t, fun.(h, acc), fun)

slice(enumerable)

slice(t()) ::
  {:ok, size :: non_neg_integer(), slicing_fun()} | {:error, module()}

Returns a function that slices the data structure contiguously.

It should return {:ok, size, slicing_fun} if the enumerable has a known bound and can access a position in the enumerable without traversing all previous elements.

Otherwise it should return {:error, __MODULE__} and a default algorithm built on top of reduce/3 that runs in linear time will be used.

Differences to count/1

The size value returned by this function is used for boundary checks, therefore it is extremely important that this function only returns :ok if retrieving the size of the enumerable is cheap, fast and takes constant time. Otherwise the simplest of operations, such as Enum.at(enumerable, 0), will become too expensive.

On the other hand, the count/1 function in this protocol should be implemented whenever you can count the number of elements in the collection.