Type expressions

3.5 Type expressions

`typexpr`	::=	`type-ord`
	\|	`type-rec`
`type-ord`	::=	`'` `ident`
	\|	`(` `type-ord` `)`
	\|	`type-tuple`
	\|	`type-tuple` `->` `type-tuple`
	\|	`full-typeconstr-name`
	\|	`type-ord` `full-typeconstr-name`
	\|	`(` `type-ord` { `,` `type-ord` } `)` `full-typeconstr-name`
`type-tuple`	::=	`<` `>`
	\|	`<` `type-ord` { `*` `type-ord` } `>`
`typrec`	::=	`type-ord` `where` `type-defs`
`type-defs`	::=	`'` `ident` `=` `typtop` { `and` `'` `ident` `=` `typtop` }

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

Operator	Associativity
Type constructor application	--
`*`	right
`<`	--

Type expressions denote types in compilation unit interfaces. They occur in the type declaration of values.

Type variables

The type expression ' ident stands for the type variable named ident . In abstract data type declarations, type variables are names for the data type parameters. In value type declarations, they represent unspecified types that can be instantiated by any type.

Parenthesized types

The type expression ( type-ord ) denotes the same type as type-ord .

Port types

The type expression < type-ord ₁ * type-ord ₂ * ... * type-ord _n > denotes the type of an asynchronous port name carrying n arguments of type type-ord ₁, type-ord ₂,...type-ord _n.

The type expression

< type-ord ₁ * type-ord ₂ * ... * type-ord _n > -> < type-ord _n+1 * type-ord _n+2 * ... * type-ord _n+m >

denotes the type of an synchronous port name carrying n arguments of types type-ord ₁, type-ord ₂,...type-ord _n, and giving back m results of types type-ord _n+1, type-ord _n+2,...type-ord _n+m.

Constructed types

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

The type expression type-ord typeconstr , where full-typeconstr-name is a type constructor with one parameter, denotes the application of the unary type constructor full-typeconstr-name to the type type-ord .

The type expression ( type-ord ₁ ,... , type-ord _n ) full-typeconstr-name , where full-typeconstr-name is a type constructor with n parameters, denotes the application of the n-ary type constructor full-typeconstr-name to the types type-ord ₁ through type-ord _n. Parenthesis are optional when n equals one.

Recursive types

The type expression type-ord where ' ident ₁ = typtop ₁ and ... and ' ident _n = typtop _n denotes the same type as type-ord , and also binds the type variables ident ₁, ..., ident _n to the types typexpr ₁, ...typexpr _n, both in type-ord and in typexpr ₁, ...typexpr _n. When one of the type variables ident _i actually occurs inside one of the type expressions typexpr _j, a recursive type is created.