Type expressions

typexpr:
      ' ident
   |  ( typexpr )
   |  typexpr -> typexpr
   |  typexpr {* typexpr}+
   |  typeconstr
   |  typexpr typeconstr
   |  ( typexpr {, typexpr} ) typeconstr
   |  typexpr as ' ident
   |  < [..] >
   |  < method-type {; method-type} [; ..] >
   |  # class-path
   |  typexpr # class-path
   |  ( typexpr {, typexpr}) # class-path

method-type:
      method-name : typexpr

The table below shows the relative precedences and associativity of operators and non-closed type constructions. The constructions with higher precedences come first.

Operator	Associativity
Type constructor application	--
*	--
->	right
as	--

Type expressions denote types in definitions of data types as well as in type constraints over patterns and expressions.

Type variables

The type expression ' ident stands for the type variable named ident. In data type definitions, type variables are names for the data type parameters. In type constraints, they represent unspecified types that can be instantiated by any type to satisfy the type constraint.

Parenthesized types

The type expression ( typexpr ) denotes the same type as typexpr.

Function types

The type expression typexpr₁ -> typexpr₂ denotes the type of functions mapping arguments of type typexpr₁ to results of type typexpr₂.

Tuple types

The type expression typexpr₁ *...* typexpr_n denotes the type of tuples whose elements belong to types typexpr₁,...typexpr_n respectively.

Constructed types

Type constructors with no parameter, as in typeconstr, are type expressions.

The type expression typexpr typeconstr, where typeconstr is a type constructor with one parameter, denotes the application of the unary type constructor typeconstr to the type typexpr.

The type expression (typexpr₁,...,typexpr_n) typeconstr, where typeconstr is a type constructor with n parameters, denotes the application of the n-ary type constructor typeconstr to the types typexpr₁ through typexpr_n.

Recursive types

The type expression typexpr as ' ident denotes the same type as typexpr, and also binds the type variable ident to type typexpr both in typexpr and in the remaining part of the type. If the type variable ident actually occurs in typexpr, a recursive type is created. Recursive types are only allowed when any recursion crosses an object type.

Object types

An object type < method-type {; method-type} > is a record of method types.

The type < method-type {; method-type} ; .. > is the type of an object with methods and their associated types are described by method-type₁,...,method-type_n, and possibly some other methods represented by the ellipsis. This ellipsis actually is a special kind of type variable, named row variable.

#-types

The type # class-path is a special kind of abbreviation. This abbreviation unifies with the type of any object belonging to a subclass of class class-path. It is handled in a special way as it usually hides a type variable (an ellipsis, representing the methods that may be added in a subclass). In particular, it vanishes when the ellipsis gets instantiated. Each type expression # class-path defines a new type variable, so type # class-path -> # class-path is usually not the same as type # class-path as ' ident -> ' ident.