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Pattern Matching

pattern-matching.livemd

Pattern Matching

Introduction

The = operator is used for pattern maching:

v = 42

This binds the variables on the left-hand side to elements of the structure of the right-hand side. After this, the variable v can be referenced:

IO.puts(v)

Underscore will match anything (but not bind a name to it):

_ = 42

Binding values is only part of the purpose of pattern matching. It is also used to verify structure (this is also the case for tuples, lists, maps …):

42 = 42

A particular match is either successful (and all bindings are established) or it fails:

42 = 56

Sometimes, however, it can be convenient to match and not bind. For that we use the pin operator ^:

a = 2
{a, ^a} = {1, 2}

Matching Tuples

Variables names can be bound to the individual elements of a tuple:

{x, y} = {1, 2}

Since no name is being bound by underscores, each underscore can match something different:

{_, _} = {1, 2}

The number of elements has to be matched:

{x, y} = {1, 2, 3}

If you don’t care about the last element you can either match it with an underscore or bind a variable that i prefixed by an underscore to it:

{x, y, _z} = {1, 2, 3}

Matching Lists

A lists head and tail can be pattern matched:

[a | b] = [1, 2, 3, 4]
{a, b}

Patterns can (in general) be nested:

[a | [b | c]] = [1, 2, 3, 4]
{a, b, c}

Keyword Lists

Since keyword lists are lists, the same rules apply:

[a | b] = [a: 1, b: 2, c: 3, d: 4]
{a, b}

This, however, is counter to how we normally think of keyword lists and this not very useful.

Instead, we have specific syntax for matching keyword lists:

[r: r, g: g, b: b] = [r: 127, g: 255, b: 0]
{r, g, b}

This does, however, require you to specify all keys in correct order, and is thus rarely used.

Matching Maps

Matching of any type of keys:

%{"r" => r, "g" => g, "b" => b} = %{"r" => 127, "g" => 255, "b" => 0}
{r, g, b}

Shorthand for when keys are atoms:

%{r: r, g: g, b: b} = %{r: 127, g: 255, b: 0}
{r, g, b}

Any subset can be matched:

%{g: g} = %{r: 127, g: 255, b: 0}
g

Note that the result of a pattern match is the right-hand side:

%{g: g} = %{r: 127, g: 255, b: 0}

So we could perform two pattern matches:

%{b: b} = %{g: g} = %{r: 127, g: 255, b: 0}
{b, g}

This is the case for any pattern match, and that becomes especially interesting when dealing with function parameters. See Function Declarations for details.

Matching Strings

While pattern matching on strings (or binaries) is both possible and extremely convening when implementing network protocols, it is a bit more tricky. For now, we will skip it.

Matching Nested Structures

Patterns may be combined:

book = %{
  authors: [
    %{first: "Donald", last: "Knuth", born: 1938}
  ],
  title: "Art of Computer Programming, Volume 1: Fundamental Algorithms",
  isbn: "9780201896831",
  pagecount: 672
}

%{authors: [%{last: lastname} | _], title: title} = book
"#{lastname}: #{title}"

Function Declarations

Anonymous Functions

An anonymous function essentially has a built-in case construction that can take any number of patterns. First match stops the search:

luminance = fn
  %{r: r, g: g, b: b} -> 0.2126 * r + 0.7152 * g + 0.0722 * b
  g = _greyness -> g
end

{
  luminance.(%{r: 127, g: 255, b: 0}),
  luminance.(137)
}

Module Functions

In modules, you simply declare one function per pattern. Again, they are search in order until a match is found:

defmodule Color do
  def luminance(%{r: r, g: g, b: b}) do
    0.2126 * r + 0.7152 * g + 0.0722 * b
  end

  def luminance(greyness) do
    greyness
  end
end

{
  Color.luminance(%{r: 127, g: 255, b: 0}),
  Color.luminance(137)
}

Guards

Patterns used outside of simple the match operator may be guarded. A guard is a codition over one or more of the bound variables that must hold for the match to succeed.

For instance:

data = [
  {1, 2},
  {2, 2},
  {2, 1}
]

data
|> Enum.map(fn datum ->
  case datum do
    {a, b} when a > b -> "a is greater than b"
    {a, b} when a < b -> "a is less than b"
    {_a, _b} -> "a and b are equal"
  end
end)

One can also check the types:

data = [
  true,
  :ok,
  1,
  1.2,
  "The got the mustard out!",
  {1, 2},
  [1, 2],
  %{a: 1, b: 2},
  self(),
  nil
]

data
|> Enum.map(fn datum ->
  case datum do
    t when is_boolean(t) -> "boolean"
    t when is_atom(t) -> "atom"
    t when is_integer(t) -> "integer"
    t when is_float(t) -> "float"
    t when is_binary(t) -> "binary"
    t when is_tuple(t) -> "tuple"
    t when is_list(t) -> "list"
    t when is_map(t) -> "map"
    t when is_pid(t) -> "pid"
    t when is_nil(t) -> "nil"
    _ -> "something else"
  end
end)

Note: As booleans are atoms as well the order of the two first guards determine how true and false are categorized.

In Anonymous Functions

Guards can be used in anonymous functions:

stringify = fn
  v when is_integer(v) -> "#{v}.0"
  v when is_float(v) -> "#{v}"
end
{
  stringify.(42),
  stringify.(3.14)
}

Note: This function is not defined for parameters of other types than integers and floats:

stringify.(true)

In Module Functions

Guards for module functions look like this:

defmodule Stringify do
  def process(v) when is_integer(v) do
    "#{v}.0"
  end

  def process(v) when is_float(v) do
    "#{v}"
  end
end
{
  Stringify.process(42),
  Stringify.process(3.14)
}

Complex Guards

Guards are expressions (of limited expressability though) that supports logical and, or and not operations:

combine = fn
  a, b when is_integer(a) and is_integer(b) ->
    a + b

  a, b when is_binary(a) and is_binary(b) ->
    a <> b
end
{
  combine.(1, 2),
  combine.("1", "2")
}