The Fortress Language Specification - CiteSeerX

left context whitespace operator fixity whitespace right context
yes
infix
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primary
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primary
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, ; right encloser
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operator
error (left encloser) yes
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operator
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operator error (nofix) , ; right encloser
operator error (nofix) line break
, ; left encloser left encloser primary
, ; left encloser left encloser operator
, ; left encloser nofix , ; right encloser
, ; left encloser error (left encloser) line break
Figure 16.2: Operator Fixity (II)
16.4 Chained and Multifix Operators
Certain infix mathematical operators that are traditionally regarded as relational operators, delivering boolean results,
may be chained. For example, an expression such as A ⊆ B ⊂ C ⊆ D is treated as being equivalent to
(A ⊆ B) ∧ (B ⊂ C) ∧ (C ⊆ D) except that the expressions B and C are evaluated only once (which matters only if
they have side effects such as writes or input/output actions). Fortress restricts such chaining to operators of the same
kind and having the same sense of monotonicity; for example, neither A ⊆ B ≤ C nor A ⊆ B ⊃ C is permitted.
Equivalence operators may be mixed into a chain; for example, one may write A ⊆ B = C ⊆ D . This transformation
is done before type checking. In particular, it is done even though these operators do not return boolean values, and
the resulting expression is checked for type correctness. (See Section F.4 for a detailed description of which operators
may be chained.)
Any infix operator that does not chain may be treated as multifix. If n − 1 occurrences of the same operator separate
n operands where n ≥ 3, then the compiler first checks to see whether there is a definition for that operator that will
accept n arguments. If so, that definition is used; if not, then the operator is treated as left-associative and the compiler
looks for a two-argument definition for the operator to use for each occurrence. As an example, the cartesian product
S 1 × S 2 × · · · × S n of n sets may usefully be defined as a multifix operator, but ordinary addition p + q + r + s is
normally treated as ((p + q) + r) + s .
16.5 Enclosing Operators
These operators are always used in pairs as enclosing operators:
(/ /) (\ \)
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