The Fortress Language Specification - CiteSeerX

• Left-associate the remaining elements of the juxtaposition.
(Note that this process requires type analysis of newly created chunks along the way.)
Here is an (admittedly contrived) example: reduce(f)(a)(x + 1)sqrt(x + 2) . Suppose that reduce is a curried function
that accepts a function f and returns a function that can be applied to an array a (the idea is to use the function
f , which ought to take two arguments, to combine the elements of the array to produce an accumulated result).
The leftmost function is reduce , and the following element (f ) is parenthesized, so the two elements are replaced with
one: (reduce(f))(a)(x + 1)sqrt(x + 2) . Now type analysis determines that the element (reduce(f)) is a function.
The leftmost function is (reduce(f)) , and the following element (a) is parenthesized, so the two elements are replaced
with one: ((reduce(f))(a))(x + 1)sqrt(x + 2) . Now type analysis determines that the element ((reduce(f))(a))
is not a function.
The leftmost function is (sqrt) , and the following element (x + 2) is parenthesized, so the two elements are replaced
with one: ((reduce(f))(a))(x + 1)(sqrt(x + 2)) . Now type analysis determines that the element (sqrt(x + 2)) is
not a function.
There are no functions remaining in the juxtaposition, so the remaining elements are left-associated:
(((reduce(f))(a))(x + 1))(sqrt(x + 2))
Now the original juxtaposition has been reduced to binary juxtaposition expressions.
16.8 Overview of Operators in the Fortress Standard Libraries
This section provides a high-level overview of the operators in the Fortress standard libraries. See Appendix F for the
detailed rules for the operators provided by the Fortress standard libraries.
16.8.1 Prefix Operators
For all standard numeric types, the prefix operator + simply returns its argument and the prefix operator − returns
the negative of its argument.
The operator ¬ is the logical NOT operator on boolean values and boolean intervals.
The operator ¬ computes the bitwise NOT of an integer.
Big operators such as ∑ begin a reduction expression (Section 13.18). The big operators include ∑ (summation)
and ∏ (product), along with ⋂ , ⋃ , ∧ , ∨ , ∨ , ⊕ , ⊗ , ⊎ , ⊞ , ⊠ , MAX , MIN , and so on.
16.8.2 Postfix Operators
The operator ! computes factorial; the operator !! computes double factorials. They may be applied to a value of any
integral type and produces a result of the same type.
When applied to a floating-point value x , x! computes Γ(1 + x) , where Γ is the Euler gamma function.
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