The Fortress Language Specification - CiteSeerX

13.27.2 Static Expressions and Values
Static parameters are static expressions. A nat parameter denotes a value that has type NaturalStatic (which extends
IntegerStatic). An int parameter denotes a value that has type IntegerStatic. A bool parameter denotes a value
that has type BooleanStatic.
Boolean static expressions may be combined using the operators ∧ , ∨ , ⊕ , ≡ , ↔ , NAND , NOR , = , ≠ , and →
(See Appendix F for a discussion of Fortress operators.) to produce other static expressions denoting boolean static
expressions. If both operands are boolean constant expressions, then the result is also a boolean constant expression.
Character static expressions may be compared using the operators < , ≤ , ≥ , > , = , and ≠ to produce boolean static
expressions. If both operands are character constant expressions, then the result is a boolean constant expression.
Numeric static expressions may be compared using the operators < , ≤ , ≥ , > , = , and ≠ to produce boolean static
expressions. If both operands are numeric constant expressions, then the result is a boolean constant expression.
Numeric static expressions may be combined using the operators and functions + , − , × , · , / , ! , MIN , MAX ,
√ , floor , ceiling , hyperfloor , hyperceiling , gcd , lcm, sin , cos , tan , arcsin , arccos , and arctan to produce
new numeric static expressions. If the result is indeed a numeric static expression, and both operands are numeric
constant expressions, then the result is also a numeric constant expression (except under certain circumstances—for
example, sqrt 5 denotes a numeric constant expression, and so does (1 + sqrt 5)/2 , but sqrt((1 + sqrt 5)/2) does
not, because it is too complicated).
Where things get too complicated, a static expression evaluation backs off, widest-need processing steps in at a later
stage and chooses an appropriate precision of floating-point arithmetic.
13.28 Aggregate Expressions
Syntax:
Value ::= Aggregate
Aggregate expressions evaluate to values that are themselves homogeneous collections of values. Evaluation of the
subexpressions of an aggregate expression is performed in parallel. Evaluation steps of the subexpressions can be
interleaved and even reordered to form an evaluation of the aggregates expression. See Section 4.4 for a discussion of
parallel evaluation.
Syntax for aggregate expressions are provided in the Fortress standard libraries for sets, maps, lists, tuples, matrices,
vectors, and arrays.
Set Expressions:
Syntax:
Aggregate ::= { [ExprList] }
ExprList ::= Expr ( , Expr) ∗
Set element expressions are enclosed in braces and separated by commas. The type of a set expression is SetT ,
where T is the union type of the types of all element expressions of the set expression.
Set containment is checked with the operator ∈ and the subset relationship is checked with the operator ⊆ . For
example:
evaluates to true and
3 ∈ {0, 1, 2, 3, 4, 5}
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