Set-theoretic types cheatsheet

Indivisible types

binary()
empty_list()
integer()
float()
pid()
port()
reference()

Atoms

All atoms

atom()

Individual atoms

:ok
:error
SomeModule

Functions

All functions

function()

n-arity functions

(-> :ok)
(integer() -> boolean())
(binary(), binary() -> binary())

Multiple clauses

(integer() -> binary()) and (binary() -> atom())

Maps

All maps

map()

Empty map

empty_map()

Maps with atom keys

# Only has the keys name and age
%{name: binary(), age: integer()}

# Has the name key and age is optional
%{name: binary(), age: if_set(integer())}

# Has the keys name and age and may have other keys (open map)
%{..., name: binary(), age: integer()}

# Has the key name, may have other keys, but age is not set
%{..., name: binary(), age: not_set()}

Maps with domain keys (domain keys are always treated as optional)

# Has atom and binary keys
%{atom() => binary(), binary() => binary()}

# Has atom and binary keys and may have other keys (open map)
%{..., atom() => binary(), binary() => binary()}

Maps with mixed keys

# Has atom keys with binary values but a `:root` key of type integer
%{atom() => binary(), root: integer()}

# Has atom keys with binary values but a `:root` key of type integer, and may have other keys
%{..., atom() => binary(), root: integer()}

Domain keys are atom(), binary(), integer(), float(), fun(), list(), map(), pid(), port(), reference(), tuple()

Non-empty lists

Proper lists

non_empty_list(elem_type)

Improper lists (as long as tail_type does not include lists)

non_empty_list(elem_type, tail_type)

Tuples

All tuples

tuple()

n-element tuples

{:ok, binary()}
{:error, binary(), term()}
{pid(), reference()}

At least n-element tuples

{binary(), binary(), ...}