The Fortress Language Specification - CiteSeerX

[ ] [/ /] [* *]
{ } {/ /} {\ \} {* *}
(ASCII encodings are shown here; they all correspond to particular single Unicode characters.) There are other pairs
as well, such as ⌊ ⌋ and ⌈ ⌉. Note that the pairs ( ) and [\ \] (also known as ) are not operators; they play
special roles in the syntax of Fortress, and their behavior cannot be redefined by a library. The bracket pairs that may
be used as enclosing operators are described in Section F.1.
Any number of ‘|’ (vertical line) may also be used in pairs as enclosing operators but there is a trick to it, because on
the face of it you can’t tell whether any given occurrence is a left encloser or a right encloser. Again, context is used
to decide, this time according to Figure 16.2.
This is very similar to Figure 16.1 in Section 16.3; a rough rule of thumb is that if an ordinary operator would be
considered a prefix operator, then one of these will be considered a left encloser; and if an ordinary operator would be
considered a postfix operator, then one of these will be considered a right encloser.
In this manner, one may use |. . .| for absolute values and ||. . .|| for matrix norms.
16.6 Conditional Operators
If a binary operator other than ‘:’ is immediately followed by a ‘:’ then it is conditional: evaluation of the righthand
operand cannot begin until evaluation of the left-hand operand has completed, and whether or not the right-hand
operand is evaluated may depend on the value of the left-hand operand. If the left-hand operand throws an exception,
then the right-hand operand is not evaluated.
The Fortress standard libraries define two conditional operators on boolean values, ∧ : and ∨ : (see Section 16.8.15).
See Section 34.8 for a discussion of how conditional operators are implemented.
16.7 Juxtaposition
Fortress provides several kinds of juxtaposition: juxtaposition may be a function call, a numeral concatenation, or a
special infix operator. See Section 25.1 for an example declaration of a juxtaposition operator.
When two expressions are juxtaposed, the juxtaposition is interpreted as follows: if the left-hand-side expression is a
function, juxtaposition performs function application; if the left-hand-side expression is a number and the right-handside
expression is also a number, juxtaposition performs numeral concatenation; otherwise, juxtaposition performs the
juxtaposition operator application.
The manner in which a juxtaposition of three or more items should be associated requires type information and awareness
of whitespace. (This is an inherent property of customary mathematical notation, which Fortress is designed to
emulate where feasible.) Therefore a Fortress compiler must produce a provisional parse in which such multi-element
juxtapositions are held in abeyance, then perform a type analysis on each element and use that information to rewrite
the n-ary juxtaposition into a tree of binary juxtapositions.
All we need to know is whether the static type of each element of a juxtaposition is an arrow type. There are actually
three legitimate possibilities for each element of a juxtaposition: (a) it has an arrow type, in which case it is considered
to be a function element; (b) it has a type that is not an arrow type, in which case it is considered to be a non-function
element; (c) it is an identifier that has no visible declaration, in which case it is considered to be a function element
(and everything will work out okay if it turns out to be the name of an appropriate functional method).
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