## 6.10 Module types (module specifications)

Module types are the module-level equivalent of type expressions: they specify the general shape and type properties of modules.

`module-type` | ::= | `modtype-path`
| ∣ | `sig` { `specification` [`;;`] } `end`
| ∣ | `functor` `(` `module-name` `:` `module-type` `)` `->` `module-type`
| ∣ | `module-type` `with` `mod-constraint` { `and` `mod-constraint` }
| ∣ | `(` `module-type` `)`
`mod-constraint` | ::= | `type` [`type-parameters`] `typeconstr` `=` `typexpr`
| ∣ | `module` `module-path` `=` `extended-module-path`

`specification` | ::= | `val` `value-name` `:` `typexpr`
| ∣ | `external` `value-name` `:` `typexpr` `=` `external-declaration`
| ∣ | `type-definition`
| ∣ | `exception` `constr-decl`
| ∣ | `class-specification`
| ∣ | `classtype-definition`
| ∣ | `module` `module-name` `:` `module-type`
| ∣ | `module` `module-name` { `(` `module-name` `:` `module-type` `)` } `:` `module-type`
| ∣ | `module` `type` `modtype-name`
| ∣ | `module` `type` `modtype-name` `=` `module-type`
| ∣ | `open` `module-path`
| ∣ | `include` `module-type`

### 6.10.1 Simple module types

The expression `modtype-path` is equivalent to the module type bound to the name `modtype-path`. The expression `(` `module-type` `)` denotes the same type as `module-type`.

### 6.10.2 Signatures

Signatures are type specifications for structures. Signatures `sig` … `end` are collections of type specifications for value names, type names, exceptions, module names and module type names. A structure will match a signature if the structure provides definitions (implementations) for all the names specified in the signature (and possibly more), and these definitions meet the type requirements given in the signature.
For compatibility with Caml Light, an optional `;;` is allowed after each specification in a signature. The `;;` has no semantic meaning.

#### Value specifications

A specification of a value component in a signature is written `val` `value-name` `:` `typexpr`, where `value-name` is the name of the value and `typexpr` its expected type.
The form `external` `value-name` `:` `typexpr` `=` `external-declaration` is similar, except that it requires in addition the name to be implemented as the external function specified in `external-declaration` (see chapter 18).

#### Type specifications

A specification of one or several type components in a signature is written `type` `typedef` { `and` `typedef` } and consists of a sequence of mutually recursive definitions of type names.
Each type definition in the signature specifies an optional type equation `=` `typexp` and an optional type representation `=` `constr-decl` … or `=` `{` `label-decl` … `}`. The implementation of the type name in a matching structure must be compatible with the type expression specified in the equation (if given), and have the specified representation (if given). Conversely, users of that signature will be able to rely on the type equation or type representation, if given. More precisely, we have the following four situations:

Abstract type: no equation, no representation.
  Names that are defined as abstract types in a signature can be implemented in a matching structure by any kind of type definition (provided it has the same number of type parameters). The exact implementation of the type will be hidden to the users of the structure. In particular, if the type is implemented as a variant type or record type, the associated constructors and fields will not be accessible to the users; if the type is implemented as an abbreviation, the type equality between the type name and the right-hand side of the abbreviation will be hidden from the users of the structure. Users of the structure consider that type as incompatible with any other type: a fresh type has been generated.
Type abbreviation: an equation `=` `typexp`, no representation.
  The type name must be implemented by a type compatible with `typexp`. All users of the structure know that the type name is compatible with `typexp`.
New variant type or record type: no equation, a representation.
  The type name must be implemented by a variant type or record type with exactly the constructors or fields specified. All users of the structure have access to the constructors or fields, and can use them to create or inspect values of that type. However, users of the structure consider that type as incompatible with any other type: a fresh type has been generated.
Re-exported variant type or record type: an equation, a representation.
  This case combines the previous two: the representation of the type is made visible to all users, and no fresh type is generated.

#### Exception specification

The specification `exception` `constr-decl` in a signature requires the matching structure to provide an exception with the name and arguments specified in the definition, and makes the exception available to all users of the structure.

#### Class specifications

A specification of one or several classes in a signature is written `class` `class-spec` { `and` `class-spec` } and consists of a sequence of mutually recursive definitions of class names.
Class specifications are described more precisely in section 6.9.4.

#### Class type specifications

A specification of one or several classe types in a signature is written `class` `type` `classtype-def` { `and` `classtype-def` } and consists of a sequence of mutually recursive definitions of class type names. Class type specifications are described more precisely in section 6.9.5.

#### Module specifications

A specification of a module component in a signature is written `module` `module-name` `:` `module-type`, where `module-name` is the name of the module component and `module-type` its expected type. Modules can be nested arbitrarily; in particular, functors can appear as components of structures and functor types as components of signatures.
For specifying a module component that is a functor, one may write
`module` `module-name` `(` `name`1 `:` `module-type`1 `)` … `(` `name`n `:` `module-type`n `)` `:` `module-type`
instead of
`module` `module-name` `:` `functor` `(` `name`1 `:` `module-type`1 `)` `->` … `->` `module-type`

#### Module type specifications

A module type component of a signature can be specified either as a manifest module type or as an abstract module type.
An abstract module type specification `module` `type` `modtype-name` allows the name `modtype-name` to be implemented by any module type in a matching signature, but hides the implementation of the module type to all users of the signature.
A manifest module type specification `module` `type` `modtype-name` `=` `module-type` requires the name `modtype-name` to be implemented by the module type `module-type` in a matching signature, but makes the equality between `modtype-name` and `module-type` apparent to all users of the signature.

#### Opening a module path

The expression `open` `module-path` in a signature does not specify any components. It simply affects the parsing of the following items of the signature, allowing components of the module denoted by `module-path` to be referred to by their simple names `name` instead of path accesses `module-path` `.` `name`. The scope of the `open` stops at the end of the signature expression.

#### Including a signature

The expression `include` `module-type` in a signature performs textual inclusion of the components of the signature denoted by `module-type`. It behaves as if the components of the included signature were copied at the location of the `include`. The `module-type` argument must refer to a module type that is a signature, not a functor type.

### 6.10.3 Functor types

The module type expression `functor` `(` `module-name` `:` `module-type`1 `)` `->` `module-type`2 is the type of functors (functions from modules to modules) that take as argument a module of type `module-type`1 and return as result a module of type `module-type`2. The module type `module-type`2 can use the name `module-name` to refer to type components of the actual argument of the functor. No restrictions are placed on the type of the functor argument; in particular, a functor may take another functor as argument (“higher-order” functor).

### 6.10.4 The `with` operator

Assuming `module-type` denotes a signature, the expression `module-type` `with` `mod-constraint` { `and` `mod-constraint` } denotes the same signature where type equations have been added to some of the type specifications, as described by the constraints following the `with` keyword. The constraint `type` [`type-parameters`] `typeconstr` `=` `typexp` adds the type equation `=` `typexp` to the specification of the type component named `typeconstr` of the constrained signature. The constraint `module` `module-path` `=` `extended-module-path` adds type equations to all type components of the sub-structure denoted by `module-path`, making them equivalent to the corresponding type components of the structure denoted by `extended-module-path`.
For instance, if the module type name `S` is bound to the signature

            sig type t module M: (sig type u end) end

then `S with type t=int` denotes the signature

            sig type t=int module M: (sig type u end) end

and `S with module M = N` denotes the signature

            sig type t module M: (sig type u=N.u end) end

A functor taking two arguments of type `S` that share their `t` component is written

            functor (A: S) (B: S with type t = A.t) ...

Constraints are added left to right. After each constraint has been applied, the resulting signature must be a subtype of the signature before the constraint was applied. Thus, the `with` operator can only add information on the type components of a signature, but never remove information.