The Fortress Language Specification - CiteSeerX

An implicit range may be used only in certain contexts, such as array subscripts, that can supply implicit information.
Suppose an implicit range is used as a subscript for an axis of array for which the lower bound is l and the upper bound
is u.
• The implicit range : is treated as l : u .
• The implicit range : : c is treated as l : u :c.
• The implicit range : b is treated as l : b .
• The implicit range : b : c is treated as l : b : c .
• The implicit range a : is treated as a :u.
• The implicit range a : : c is treated as a :u:c.
One may test whether an integer is in a range by using the operator ∈:
if j ∈ a :b then print “win” end
Ranges may be compared as if they were sets of integers by using ⊂ ( SUBSET ) and ⊆ ( SUBSETEQ ) and = and
⊇ ( SUPSETEQ ) and ⊃ ( SUPSET ).
Nonstrided ranges may be intersected using the operator ∩ ( INTERSECTION ).
The size of a range (the number of integers in the set) may be found by using the set-cardinality operator |. . .| . For
example, the value of |3 : 7| is 5 and the value of |1 : 100 :2| is 50 .
Note that a range is very different from an interval with integer endpoints. The range 3 :5 contains only the values 3,
4, and 5, whereas the interval [3, 5] contains all real numbers x such that 3 ≤ x ≤ 5 .
13.17 Generators
Syntax:
GeneratorList ::= Generator ( , Generator) ∗
Generator ::= Id ← Expr
| ( Id , IdList ) ← Expr
| Expr
IdList ::= Id ( , Id) ∗
Fortress makes extensive use of comma-separated generator lists to express parallel iteration. Generator lists occur in
generated expressions (described in Section 13.11.1), for loops (described in Section 13.15), sums and big operators
(described in Section 13.18), and comprehensions (described in Section 13.29). We refer to these collectively as
expressions with generators. Every expression with generators contains a body expression (for an assignment this
expression is the assignment itself) which is evaluated for each combination of values bound in the generator list.
An element of a generator list is either a generator binding or a boolean expression. A generator binding consists of
one or more comma-separated identifiers followed by the token ← , followed by a subexpression (called the generator
expression). A generator expression evaluates to an object whose type is Generator. For each iteration, a generator
object produces a value or a tuple of values. These values are bound to the identifiers to the left of the arrow, which
are in scope of subsequent generator list elements and of the body of the construct containing the generator list.
A boolean expression in a generator list is interpreted as a filter. An iteration is performed only if the result of the filter
expression is true. If the filter is false, subsequent expressions in the generator list will not be evaluated. However, other
than this restriction, there is no implied order of evaluation of the generator expressions or the boolean expressions in
a generator list. Thus, for example, if a boolean expression in the middle of the list evaluates to true , then generator
expressions to its right in the list may be evaluated before generator expressions to its left.
102