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# Types and Function Specifications

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## The Erlang Type Language

Erlang is a dynamically typed language. Still, it comes with a notation for declaring sets of Erlang terms to form a particular type. This effectively forms specific subtypes of the set of all Erlang terms.

Subsequently, these types can be used to specify types of record fields and also the argument and return types of functions.

Type information can be used for the following:

- To document function interfaces
- To provide more information for bug detection tools, such as Dialyzer
- To be leveraged by documentation tools, such as ExDoc or EDoc, for generating documentation

It is expected that the type language described in this section supersedes and replaces the purely comment-based `@type` and `@spec` declarations used by EDoc.

## Types and their Syntax

Types describe sets of Erlang terms. Types consist of, and are built from, a set of predefined types, for example, `integer/0`, `atom/0`, and `pid/0`. Predefined types represent a typically infinite set of Erlang terms that belong to this type. For example, the type `atom/0` denotes the set of all Erlang atoms.

For integers and atoms, it is allowed for singleton types; for example, the integers `-1` and `42`, or the atoms `'foo'` and `'bar'`. All other types are built using unions of either predefined types or singleton types. In a type union between a type and one of its subtypes, the subtype is absorbed by the supertype. Thus, the union is then treated as if the subtype was not a constituent of the union. For example, the type union:

    atom() | 'bar' | integer() | 42

describes the same set of terms as the type union:

    atom() | integer()

Because of subtype relations that exist between types, all types, except `dynamic/0`, form a lattice where the top-most element, `any/0`, denotes the set of all Erlang terms and the bottom-most element, `none/0`, denotes the empty set of terms.

To facilitate gradual typing of Erlang, the type `dynamic/0` is provided. The type `dynamic/0` represents a statically unknown type. It is similar to Any in Python, any in TypeScript and dynamic in Hack. `any/0` and `dynamic/0` interact with success typing the same way, so Dialyzer doesn't distinguish between them.

The set of predefined types and the syntax for types follows:

    Type :: any()                 %% The top type, the set of all Erlang terms
          | none()                %% The bottom type, contains no terms
          | dynamic()
          | pid()
          | port()
          | reference()
          | []                    %% nil
          | Atom
          | Bitstring
          | float()
          | Fun
          | Integer
          | List
          | Map
          | Tuple
          | Union
          | UserDefined           %% described in Type Declarations of User-Defined Types

    Atom :: atom()
          | Erlang_Atom           %% 'foo', 'bar', ...

    Bitstring :: <<>>
               | <<_:M>>          %% M is an Integer_Value that evaluates to a positive integer
               | <<_:_*N>>        %% N is an Integer_Value that evaluates to a positive integer
               | <<_:M, _:_*N>>

    Fun :: fun()                  %% any function
         | fun((...) -> Type)     %% any arity, returning Type
         | fun(() -> Type)
         | fun((TList) -> Type)

    Integer :: integer()
             | Integer_Value
             | Integer_Value..Integer_Value      %% specifies an integer range

    Integer_Value :: Erlang_Integer              %% ..., -1, 0, 1, ... 42 ...
                   | Erlang_Character            %% $a, $b ...
                   | Integer_Value BinaryOp Integer_Value
                   | UnaryOp Integer_Value

    BinaryOp :: '*' | 'div' | 'rem' | 'band' | '+' | '-' | 'bor' | 'bxor' | 'bsl' | 'bsr'

    UnaryOp :: '+' | '-' | 'bnot'

    List :: list(Type)                           %% Proper list ([]-terminated)
          | maybe_improper_list(Type1, Type2)    %% Type1=contents, Type2=termination
          | nonempty_improper_list(Type1, Type2) %% Type1 and Type2 as above
          | nonempty_list(Type)                  %% Proper non-empty list

    Map :: #{}                                   %% denotes the empty map
         | #{AssociationList}

    Tuple :: tuple()                             %% denotes a tuple of any size
           | {}
           | {TList}

    AssociationList :: Association
                     | Association, AssociationList

    Association :: Type := Type                  %% denotes a mandatory association
                 | Type => Type                  %% denotes an optional association

    TList :: Type
           | Type, TList

    Union :: Type1 | Type2

Integer values are either integer or character literals or expressions consisting of possibly nested unary or binary operations that evaluate to an integer. Such expressions can also be used in bit strings and ranges.

The general form of bit strings is `<<_:M, _:_*N>>`, where `M` and `N` must evaluate to positive integers. It denotes a bit string that is `M + (k*N)` bits long (that is, a bit string that starts with `M` bits and continues with `k` segments of `N` bits each, where `k` is also a positive integer). The notations `<<_:_*N>>`, `<<_:M>>`, and `<<>>` are convenient shorthands for the cases that `M` or `N`, or both, are zero.

Because lists are commonly used, they have shorthand type notations. The types `list(T)` and `nonempty_list(T)` have the shorthands `[T]` and `[T,...]`, respectively. The only difference between the two shorthands is that `[T]` can be an empty list but `[T,...]` cannot.

Notice that the shorthand for `list/0`, that is, the list of elements of unknown type, is `[_]` (or `[any()]`), not `[]`. The notation `[]` specifies the singleton type for the empty list.

The general form of map types is `#{AssociationList}`. The key types in `AssociationList` are allowed to overlap, and if they do, the leftmost association takes precedence. A map association has a key in `AssociationList` if it belongs to this type. `AssociationList` can contain both mandatory `(:=)` and optional `(=>)` association types. If an association type is mandatory, an association with that type needs to be present. In the case of an optional association type it is not required for the key type to be present.

The notation `#{}` specifies the singleton type for the empty map. Note that this notation is not a shorthand for the `map/0` type.

For convenience, the following types are also built-in. They can be thought as predefined aliases for the type unions also shown in the table.

Built-in type | Defined as
--- | ---
`term/0` | `any/0`
`binary/0` | `<<_:_*8>>`
`nonempty_binary/0` | `<<_:8, _:_*8>>`
`bitstring/0` | `<<_:_*1>>`
`nonempty_bitstring/0` | `<<_:1, _:_*1>>`
`boolean/0` | `'false'` | `'true'`
`byte/0` | `0..255`
`char/0` | `0..16#10ffff`
`nil/0` | `[]`
`number/0` | `integer/0` | `float/0`
`list/0` | `[any()]`
`maybe_improper_list/0` | `maybe_improper_list(any(), any())`
`nonempty_list/0` | `nonempty_list(any())`
`string/0` | `[char()]`
`nonempty_string/0` | `[char(),...]`
`iodata/0` | `iolist()` | `binary()`
`iolist/0` | `maybe_improper_list(byte()` | `binary()` | `iolist(), binary()` | `[])`
`map/0` | `#{any() => any()}`
`function/0` | `fun()`
`module/0` | `atom/0`
`mfa/0` | `{module(),atom(),arity()}`
`arity/0` | `0..255`
`identifier/0` | `pid()` | `port()` | `reference()`
`node/0` | `atom/0`
`timeout/0` | `'infinity'` | `non_neg_integer()`
`no_return/0` | `none/0`

Table: Built-in types, predefined aliases

In addition, the following three built-in types exist and can be thought as defined below, though strictly their "type definition" is not valid syntax according to the type language defined above.

Built-in type | Can be thought defined by the syntax
--- | ---
`non_neg_integer/0` | `0..`
`pos_integer/0` | `1..`
`neg_integer/0` | `..-1`

Table: Additional built-in types

#### Note

The following built-in list types also exist, but they are expected to be rarely used. Hence, they have long names:

    nonempty_maybe_improper_list() :: nonempty_maybe_improper_list(any(), any())
    nonempty_improper_list(Type1, Type2)
    nonempty_maybe_improper_list(Type1, Type2)

where the last two types define the set of Erlang terms one would expect.

Also for convenience, record notation is allowed to be used. Records are shorthands for the corresponding tuples:

    Record :: #Erlang_Atom{}
            | #Erlang_Atom{Fields}

Records are extended to possibly contain type information. This is described in Type Information in Record Declarations.

### Redefining built-in types

#### Change

Starting from Erlang/OTP 26, it is permitted to define a type having the same name as a built-in type.

It is recommended to avoid deliberately reusing built-in names because it can be confusing. However, when an Erlang/OTP release introduces a new type, code that happened to define its own type having the same name will continue to work.

As an example, imagine that the Erlang/OTP 42 release introduces a new type `gadget()` defined like this:

    -type gadget() :: {'gadget', reference()}.

Further imagine that some code has its own (different) definition of `gadget()`, for example:

    -type gadget() :: #{}.

Since redefinitions are allowed, the code will still compile (but with a warning), and Dialyzer will not emit any additional warnings.

## Type Declarations of User-Defined Types

As seen, the basic syntax of a type is an atom followed by closed parentheses. New types are declared using `-type`, `-opaque`, and `-nominal` attributes as in the following example:

    -type my_struct_type() :: Type.
    -opaque my_opaq_type() :: Type.
    -nominal my_nominal_type() :: Type.

The type name is the atom `my_struct_type`, followed by parentheses. `Type` is a type as defined in the previous section. A current restriction is that `Type` can contain only predefined types, or user-defined types which are either of the following:

- Module-local type, that is, with a definition that is present in the code of the module
- Remote type, that is, type defined in, and exported by, other modules; more about this soon.

For module-local types, the restriction that their definition exists in the module is enforced by the compiler and results in a compilation error. (A similar restriction currently exists for records.)

Type declarations can also be parameterized by including type variables between the parentheses. The syntax of type variables is the same as Erlang variables, that is, starts with an upper-case letter. These variables is to appear on the RHS of the definition. A concrete example follows:

    -type orddict(Key, Val) :: [{Key, Val}].

A module can export some types to declare that other modules are allowed to refer to them as remote types. This declaration has the following form:

    -export_type([T1/A1, ..., Tk/Ak]).

Here the `Ti`s are atoms (the name of the type) and the `Ai`s are their arguments.

Example:

    -export_type([my_struct_type/0, orddict/2]).

Assuming that these types are exported from module `'mod'`, you can refer to them from other modules using remote type expressions like the following:

    mod:my_struct_type()
    mod:orddict(atom(), term())

It is not allowed to refer to types that are not declared as exported.

Types declared as `opaque` represent sets of terms whose structure is not supposed to be visible from outside of their defining module. That is, only the module defining them is allowed to depend on their term structure. Consequently, such types do not make much sense as module local - module local types are not accessible by other modules anyway - and is always to be exported.

#### Change

Nominal types were introduced in Erlang/OTP 28.

Types declared as `nominal` are type-checked according to the user-defined names instead of their structure. That is, `-nominal feet() :: integer()` and `-nominal meter() :: integer()` are not the same type, while if `-type` is used it would be.

Read more on Opaques and Nominals

## Type Information in Record Declarations

The types of record fields can be specified in the declaration of the record. The syntax for this is as follows:

    -record(rec, {field1 :: Type1, field2, field3 :: Type3}).

For fields without type annotations, their type defaults to `any()`. That is, the previous example is a shorthand for the following:

    -record(rec, {field1 :: Type1, field2 :: any(), field3 :: Type3}).

In the presence of initial values for fields, the type must be declared after the initialization, as follows:

    -record(rec, {field1 = [] :: Type1, field2, field3 = 42 :: Type3}).

The initial values for fields are to be compatible with (that is, a member of) the corresponding types. This is checked by the compiler and results in a compilation error if a violation is detected.

#### Change

Before Erlang/OTP 19, for fields without initial values, the singleton type `'undefined'` was added to all declared types. In other words, the following two record declarations had identical effects:

    -record(rec, {f1 = 42 :: integer(),
                 f2      :: float(),
                 f3      :: 'a' | 'b'}).

    -record(rec, {f1 = 42 :: integer(),
                  f2      :: 'undefined' | float(),
                  f3      :: 'undefined' | 'a' | 'b'}).

This is no longer the case. If you require `'undefined'` in your record field type, you must explicitly add it to the typespec, as in the 2nd example.

Any record, containing type information or not, once defined, can be used as a type using the following syntax:

    #rec{}

In addition, the record fields can be further specified when using a record type by adding type information about the field as follows:

    #rec{some_field :: Type}

Any unspecified fields are assumed to have the type in the original record declaration.

#### Note

When records are used to create patterns for ETS and Mnesia match functions, Dialyzer may need some help not to emit bad warnings. For example:

    -type height() :: pos_integer().
    -record(person, {name :: string(), height :: height()}).

    lookup(Name, Tab) ->
        ets:match_object(Tab, #person{name = Name, _ = '_'}).

Dialyzer will emit a warning since `'_'` is not in the type of record field `height`.

The recommended way of dealing with this is to declare the smallest record field types to accommodate all your needs, and then create refinements as needed. The modified example:

    -record(person, {name :: string(), height :: height() | '_'}).

    -type person() :: #person{height :: height()}.

In specifications and type declarations the type `person()` is to be preferred before `#person{}`.

## Specifications for Functions

A specification (or contract) for a function is given using the `-spec` attribute. The general format is as follows:

    -spec Function(ArgType1, ..., ArgTypeN) -> ReturnType.

An implementation of the function with the same name `Function` must exist in the current module, and the arity of the function must match the number of arguments, otherwise the compilation fails.

The following longer format with module name is also valid as long as `Module` is the name of the current module. This can be useful for documentation purposes.

    -spec Module:Function(ArgType1, ..., ArgTypeN) -> ReturnType.

Also, for documentation purposes, argument names can be given:

    -spec Function(ArgName1 :: Type1, ..., ArgNameN :: TypeN) -> RT.

A function specification can be overloaded. That is, it can have several types, separated by a semicolon (`;`). For example:

    -spec foo(T1, T2) -> T3;
             (T4, T5) -> T6.

A current restriction, which currently results in a warning by Dialyzer, is that the domains of the argument types cannot overlap. For example, the following specification results in a warning:

    -spec foo(pos_integer()) -> pos_integer();
             (integer()) -> integer().

Type variables can be used in specifications to specify relations for the input and output arguments of a function. For example, the following specification defines the type of a polymorphic identity function:

    -spec id(X) -> X.

Notice that the above specification does not restrict the input and output type in any way. These types can be constrained by guard-like subtype constraints and provide bounded quantification:

    -spec id(X) -> X when X :: tuple().

Currently, the `::` constraint (read as "is a subtype of") is the only guard constraint that can be used in the `when` part of a `-spec` attribute.

#### Note

The above function specification uses multiple occurrences of the same type variable. That provides more type information than the following function specification, where the type variables are missing:

    -spec id(tuple()) -> tuple().

The latter specification says that the function takes some tuple and returns some tuple. The specification with the `X` type variable specifies that the function takes a tuple and returns the same tuple.

However, it is up to the tools that process the specifications to choose whether to take this extra information into account or not.

The scope of a `::` constraint is the `(...) -> RetType` specification after which it appears. To avoid confusion, it is suggested that different variables are used in different constituents of an overloaded contract, as shown in the following example:

    -spec foo({X, integer()}) -> X when X :: atom();
             ([Y]) -> Y when Y :: number().

Some functions in Erlang are not meant to return; either because they define servers or because they are used to throw exceptions, as in the following function:

    my_error(Err) -> throw({error, Err}).

For such functions, it is recommended to use the special `no_return/0` type for their "return", through a contract of the following form:

    -spec my_error(term()) -> no_return().

#### Note

Erlang uses the shorthand version `_` as an anonymous type variable equivalent to `term/0` or `any/0`. For example, the following function

    -spec Function(string(), _) -> string().

is equivalent to:

    -spec Function(string(), any()) -> string().

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