The Fortress Language Specification - CiteSeerX

Fortress also allows coercion between types (see Chapter 17). A coercion from T to U is defined in the declaration of
U. We write T →U if U defines a coercion from T . We say that T can be coerced to U, and write T U, if U defines
a coercion from T or any supertype of T : T U ⇐⇒ ∃T ′ : T ≼ T ′ ∧ T ′ →U.
The Fortress type hierarchy is acyclic with respect to both subtyping and coercion relations except for the following:
• The trait Object is a single root of the type hierarchy and it forms a cycle as described in Chapter 23.
• There exists a bidirectional coercion between two tuple types if and only if they have the same sorted form.
8.2 Trait Types
Syntax:
TypeRef ::= TraitType
Traits are declared by trait declarations (described in Chapter 9). A trait has a trait type of the same name. A significant
portion of Fortress types are trait types.
8.3 Object Trait Types
Named objects are declared by object declarations (described in Chapter 10) and anonymous objects are described
by object expressions (described in Section 13.9). A named object has an object trait type of the same name and an
anonymous object has an anonymous object trait type. An object trait type is a special kind of trait type. An object
trait type extends all of the declared supertraits of the object. No other objects can have the object trait type and no
trait type can extend an object trait type (i.e., an object trait type implicitly has an empty comprises clause).
8.4 Tuple Types
Syntax:
TypeRef ::= TupleType
TupleType ::= (TypeRef (,TypeRef ) + )
| ([TypeRef ( , TypeRef ) ∗ , ] TypeRef ... )
| ([TypeRef ( , TypeRef ) ∗ , ] [TypeRef ... , ] Id = TypeRef ( , Id = TypeRef ) ∗ )
A tuple is an ordered sequence of keyword-value pairs. See Section 13.28 for a discussion of tuple expressions. A
tuple type consists of a parenthesized, comma-separated list of element types where each element type is one of the
following kinds:
• A plain type “T ”
• A varargs type “T . . . ”
• A keyword-type pair “identifier = T ”
The following restrictions apply: No two keyword-type pairs may have the same keyword. No keyword-type pair may
precede a plain type. No varargs type may follow a keyword-type pair or precede a plain type. There must be at least
one element type. If there is exactly one element type, it must be a varargs type or a keyword-type pair (because “(T) ”
is simply a type in parentheses, not a tuple type). Also, there can be at most one element type with varargs type.
An element type in tuple type X corresponds to one in tuple type Y if and only if:
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