The Fortress Language Specification - CiteSeerX

• element types of a tuple type can be separated by the token × instead of by commas, with enclosing parentheses
elided and
• element types of a tuple type that have the same type can be abbreviated using superscripts.
Here are some examples:
R64 × R64 → R64
N → N × N throws IOException
(N, N) → N × N
Z 3 → Z
Parameter types are contravariant but return types are covariant; arrow type “A → B throws C ” is a subtype of
arrow type “D → E throws F ” if and only if:
• D is a subtype of A and
• B is a subtype of E and
• for all X in C, there exists Y in F such that X is a subtype of Y .
Coercion between arrow types are described in Section 17.7.
An arrow type excludes any nonarrow type other than Object. However, arrow types do not exclude other arrow types
because of overloading as described in Chapter 33.
8.6 Bottom Type
Syntax:
TypeRef ::= BottomType
Fortress provides a special bottom type, BottomType, which is an uninhabited type. No value in Fortress has the
bottom type; throw and exit expressions have the bottom type. The bottom type is a subtype of every type.
Intersection of any exclusive types is the bottom type.
8.7 Types in the Fortress Standard Libraries
The Fortress standard libraries define simple standard types for literals such as BooleanLiteralb , () (pronounced
“void”), Character, String, and Numeraln, m, r, v for appropriate values of b , n , m , r , and v (See Section 13.1
for a discussion of Fortress literals). Moreover, there are several simple standard numeric types. These types are
mutually exclusive; no value has more than one of them. Values of these types are immutable.
The numeric types share the common supertype Number. Fortress includes types for arbitrary-precision integers (of
type Z), their unsigned equivalents (of type N), rational numbers (of type Q), fixed-size representations for integers
including the types Z8, Z16, Z32, Z64, Z128, their unsigned equivalents N8, N16, N32, N64, N128, floating-point
numbers (described below), intervals (of type IntervalX , abbreviated as 〈|X|〉 , where X can be instantiated with
any number type), and imaginary and complex numbers of fixed size (in rectangular form with types Cn for n =
16, 32, 64, 128, 256 and polar form with type PolarX where X can be instantiated with any real number type).
For floating-point numbers, Fortress supports types R32 and R64 to be 32 and 64-bit IEEE 754 floating-point numbers
respectively, and defines two functions on types: DoubleF is a floating-point type twice the size of the floatingpoint
type F , and ExtendedF is a floating-point type sufficiently larger than the floating-point type F to perform
summations of “reasonable” size. 1
1 This formulation of floating-point types follows a proposal under consideration by the IEEE 754 committee.
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