## 6.9 Classes

Classes are defined using a small language, similar to the module language.

### 6.9.1 Class types

Class types are the class-level equivalent of type expressions: they specify the general shape and type properties of classes.

`class-type` | ::= | `class-body-type`
| ∣ | [[`?`]`label-name:`] `typexpr` `->` `class-type`
`class-body-type` | ::= | `object` [`(` `typexpr` `)`] {`class-field-spec`} `end`
| ∣ | `class-path`
| ∣ | `[` `typexpr` {`,` `typexpr`} `]` `class-path`
`class-field-spec` | ::= | `inherit` `class-type`
| ∣ | `val` [`mutable`] `inst-var-name` `:` `typexpr`
| ∣ | `method` [`private`] `method-name` `:` `poly-typexpr`
| ∣ | `method` [`private`] `virtual` `method-name` `:` `poly-typexpr`
| ∣ | `constraint` `typexpr` `=` `typexpr`

#### Simple class expressions

The expression `class-path` is equivalent to the class type bound to the name `class-path`. Similarly, the expression `[` `typexpr`1 `,` … `typexpr`n `]` `class-path` is equivalent to the parametric class type bound to the name `class-path`, in which type parameters have been instanciated to respectively `typexpr`1, ...`typexpr`n.

#### Class function type

The class type expression `typexpr` `->` `class-type` is the type of class functions (functions from values to classes) that take as argument a value of type `typexpr` and return as result a class of type `class-type`.

#### Class body type

The class type expression `object` [`(` `typexpr` `)`] {`class-field-spec`} `end` is the type of a class body. It specifies its instance variables and methods. In this type, `typexpr` is matched against the self type, therefore providing a binding for the self type.
A class body will match a class body type if it provides definitions for all the components specified in the class type, and these definitions meet the type requirements given in the class type. Furthermore, all methods either virtual or public present in the class body must also be present in the class type (on the other hand, some instance variables and concrete private methods may be omitted). A virtual method will match a concrete method, which makes it possible to forget its implementation. An immutable instance variable will match a mutable instance variable.

#### Inheritance

The inheritance construct `inherit` `class-type` allows to include methods and instance variables from other classes types. The instance variable and method types from this class type are added into the current class type.

#### Instance variable specification

A specification of an instance variable is written `val` [`mutable`] `inst-var-name` `:` `typexpr`, where `inst-var-name` is the name of the instance variable and `typexpr` its expected type. The flag `mutable` indicates whether this instance variable can be physically modified.
An instance variable specification will hide any previous specification of an instance variable of the same name.

#### Method specification

The specification of a method is written `method` [`private`] `method-name` `:` `poly-typexpr`, where `method-name` is the name of the method and `poly-typexpr` its expected type, possibly polymorphic. The flag `private` indicates that the method cannot be accessed from outside the object.
The polymorphism may be left implicit in public method specifications: any type variable which is not bound to a class parameter and does not appear elsewhere inside the class specification will be assumed to be universal, and made polymorphic in the resulting method type. Writing an explicit polymorphic type will disable this behaviour.
Several specification for the same method must have compatible types. Any non-private specification of a method forces it to be public.

#### Virtual method specification

Virtual method specification is written `method` [`private`] `virtual` `method-name` `:` `poly-typexpr`, where `method-name` is the name of the method and `poly-typexpr` its expected type.

#### Constraints on type parameters

The construct `constraint` `typexpr`1 `=` `typexpr`2 forces the two type expressions to be equals. This is typically used to specify type parameters: they can be that way be bound to a specified type expression.

### 6.9.2 Class expressions

Class expressions are the class-level equivalent of value expressions: they evaluate to classes, thus providing implementations for the specifications expressed in class types.

`class-expr` | ::= | `class-path`
| ∣ | `[` `typexpr` {`,` `typexpr`} `]` `class-path`
| ∣ | `(` `class-expr` `)`
| ∣ | `(` `class-expr` `:` `class-type` `)`
| ∣ | `class-expr` {`argument`}+
| ∣ | `fun` {`parameter`}+ `->` `class-expr`
| ∣ | `let` [`rec`] `let-binding` {`and` `let-binding`} `in` `class-expr`
| ∣ | `object` [`(` `pattern` [`:` `typexpr`] `)`] { `class-field` } `end`

`class-field` | ::= | `inherit` `class-expr` [`as` `value-name`]
| ∣ | `val` [`mutable`] `inst-var-name` [`:` `typexpr`] `=` `expr`
| ∣ | `method` [`private`] `method-name` {`parameter`} [`:` `typexpr`] `=` `expr`
| ∣ | `method` [`private`] `method-name` `:` `poly-typexpr` `=` `expr`
| ∣ | `method` [`private`] `virtual` `method-name` `:` `poly-typexpr`
| ∣ | `constraint` `typexpr` `=` `typexpr`
| ∣ | `initializer` `expr`

#### Simple class expressions

The expression `class-path` evaluates to the class bound to the name `class-path`. Similarly, the expression `[` `typexpr`1 `,` … `typexpr`n `]` `class-path` evaluates to the parametric class bound to the name `class-path`, in which type parameters have been instanciated to respectively `typexpr`1, ...`typexpr`n.
The expression `(` `class-expr` `)` evaluates to the same module as `class-expr`.
The expression `(` `class-expr` `:` `class-type` `)` checks that `class-type` match the type of `class-expr` (that is, that the implementation `class-expr` meets the type specification `class-type`). The whole expression evaluates to the same class as `class-expr`, except that all components not specified in `class-type` are hidden and can no longer be accessed.

#### Class application

Class application is denoted by juxtaposition of (possibly labeled) expressions. Evaluation works as for expression application.

#### Class function

The expression `fun` [[`?`]`label-name:`] `pattern` `->` `class-expr` evaluates to a function from values to classes. When this function is applied to a value v, this value is matched against the pattern `pattern` and the result is the result of the evaluation of `class-expr` in the extended environment.
Conversion from functions with default values to functions with patterns only works identically for class functions as for normal functions.
The expression
`fun` `parameter`1 … `parameter`n `->` `class-expr`
is a short form for
`fun` `parameter`1 `->` … `fun` `parameter`n `->` `expr`

#### Local definitions

The `let` and `let rec` constructs bind value names locally, as for the core language expressions.

#### Class body

The expression `object` `(` `pattern` [`:` `typexpr`] `)` { `class-field` } `end` denotes a class body. This is the prototype for an object : it lists the instance variables and methods of an objet of this class.
A class body is a class value: it is not evaluated at once. Rather, its components are evaluated each time an object is created.
In a class body, the pattern `(` `pattern` [`:` `typexpr`] `)` is matched against self, therefore provinding a binding for self and self type. Self can only be used in method and initializers.
Self type cannot be a closed object type, so that the class remains extensible.

#### Inheritance

The inheritance construct `inherit` `class-expr` allows to reuse methods and instance variables from other classes. The class expression `class-expr` must evaluate to a class body. The instance variables, methods and initializers from this class body are added into the current class. The addition of a method will override any previously defined methods of the same name.
An ancestor can be bound by prepending the construct `as` `value-name` to the inheritance construct above. `value-name` is not a true variable and can only be used to select a method, i.e. in an expression `value-name` `#` `method-name`. This gives access to the method `method-name` as it was defined in the parent class even if it is redefined in the current class. The scope of an ancestor binding is limited to the current class. The ancestor method may be called from a subclass but only indirectly.

#### Instance variable definition

The definition `val` [`mutable`] `inst-var-name` `=` `expr` adds an instance variable `inst-var-name` whose initial value is the value of expression `expr`. Several variables of the same name can be defined in the same class. The flag `mutable` allows physical modification of this variable by methods.
An instance variables can only be used in the following methods and initializers of the class.

#### Method definition

Method definition is written `method` `method-name` `=` `expr`. The definition of a method overrides any previous definition of this method. The method will be public (that is, not private) if any of the definition states so.
A private method, `method` `private` `method-name` `=` `expr`, is a method that can only be invoked on self (from other methods of the same object, defined in this class or one of its subclasses). This invocation is performed using the expression `value-name` `#` `method-name`, where `value-name` is directly bound to self at the beginning of the class definition. Private methods do not appear in object types. A method may have both public and private definitions, but as soon as there is a public one, all subsequent definitions will be made public.
Methods may have an explicitly polymorphic type, allowing them to be used polymorphically in programs (even for the same object). The explicit declaration may be done in one of three ways: (1) by giving an explicit polymorphic type in the method definition, immediately after the method name, i.e. `method` [`private`] `method-name` `:` {`'` `ident`}+ `.` `typexpr` `=` `expr`; (2) by a forward declaration of the explicit polymorphic type through a virtual method definition; (3) by importing such a declaration through inheritance and/or constraining the type of self.
Some special expressions are available in method bodies for manipulating instance variables and duplicating self:

`expr` | ::= | …
| ∣ | `inst-var-name` `<-` `expr`
| ∣ | `{<` [ `inst-var-name` `=` `expr` { `;` `inst-var-name` `=` `expr` } ] `>}`

The expression `inst-var-name` `<-` `expr` modifies in-place the current object by replacing the value associated to `inst-var-name` by the value of `expr`. Of course, this instance variable must have been declared mutable.
The expression `{<` [ `inst-var-name` `=` `expr` { `;` `inst-var-name` `=` `expr` } ] `>}` evaluates to a copy of the current object in which the values of instance variables `inst-var-name`1, …, `inst-var-name`n have been replaced by the values of the corresponding expressions `expr`1, …, `expr`n.

#### Virtual method definition

Method specification is written `method` [`private`] `virtual` `method-name` `:` `poly-typexpr`. It specifies whether the method is public or private, and gives its type. If the method is intended to be polymorphic, the type should be explicit.

#### Constraints on type parameters

The construct `constraint` `typexpr`1 `=` `typexpr`2 forces the two type expressions to be equals. This is typically used to specify type parameters: they can be that way be bound to a specified type expression.

#### Initializers

A class initializer `initializer` `expr` specifies an expression that will be evaluated when an object will be created from the class, once all the instance variables have been initialized.

### 6.9.3 Class definitions

`class-definition` | ::= | `class` `class-binding` { `and` `class-binding` }
`class-binding` | ::= | [`virtual`] [`[` `type-parameters` `]`] `class-name` {`parameter`} [`:` `class-type`] `=` `class-expr`
`type-parameters` | ::= | `'` `ident` { `,` `'` `ident` }

A class definition `class` `class-binding` { `and` `class-binding` } is recursive. Each `class-binding` defines a `class-name` that can be used in the whole expression except for inheritance. It can also be used for inheritance, but only in the definitions that follow its own.
A class binding binds the class name `class-name` to the value of expression `class-expr`. It also binds the class type `class-name` to the type of the class, and defines two type abbreviations : `class-name` and `#` `class-name`. The first one is the type of objects of this class, while the second is more general as it unifies with the type of any object belonging to a subclass (see section 6.4).

#### Virtual class

A class must be flagged virtual if one of its methods is virtual (that is, appears in the class type, but is not actually defined). Objects cannot be created from a virtual class.

#### Type parameters

The class type parameters correspond to the ones of the class type and of the two type abbreviations defined by the class binding. They must be bound to actual types in the class definition using type constraints. So that the abbreviations are well-formed, type variables of the inferred type of the class must either be type parameters or be bound in the constraint clause.

### 6.9.4 Class specification

`class-specification` | ::= | `class` `class-spec` { `and` `class-spec` }
`class-spec` | ::= | [`virtual`] [`[` `type-parameters` `]`] `class-name` `:` `class-type`

This is the counterpart in signatures of class definitions. A class specification matches a class definition if they have the same type parameters and their types match.

### 6.9.5 Class type definitions

`classtype-definition` | ::= | `class` `type` `classtype-def` { `and` `classtype-def` }
`classtype-def` | ::= | [`virtual`] [`[` `type-parameters` `]`] `class-name` `=` `class-body-type`

A class type definition `class` `class-name` `=` `class-body-type` defines an abbreviation `class-name` for the class body type `class-body-type`. As for class definitions, two type abbreviations `class-name` and `#` `class-name` are also defined. The definition can be parameterized by some type parameters. If any method in the class type body is virtual, the definition must be flagged `virtual`.
Two class type definitions match if they have the same type parameters and the types they expand to match.