The Fortress Language Specification - CiteSeerX

trait B extends A end
trait C extends B
coercion (a :A) = . . .
end
17.7 Coercions for Tuple and Arrow Types
Unlike other types, tuple types (described in Section 8.4) and arrow types (described in Section 8.5) are not defined
explicitly. Therefore coercions to these types are also not defined explicitly. Instead, the following rules describe when
these coercions are implicitly defined.
There is a coercion from a tuple type X to a tuple type Y if all the following conditions hold:
1. X is not a subtype of Y ;
2. for every plain type T in Y , there is a corresponding plain type in X whose type is substitutable for T ;
3. if neither X nor Y has a varargs type, then they have the same number of plain types;
4. if X has a varargs type, then Y has a varargs type, the type S of the varargs type S... in X is substitutable for
the type T of the varargs type T... in Y , and X and Y have the same number of plain types;
5. if X has no varargs type and Y has a varargs type T..., then every plain type in X that has no corresponding
plain type in Y is substitutable for T ; and
6. the correspondence between keyword-type pairs in X and Y is bijective, and the type of each such pair in X is
substitutable for the type in the corresponding pair in Y .
Tuple type coercions are invoked by distributing the coercion elementwise. However, if an element type of the tuple
type being coerced from is a subtype of the corresponding element type of the tuple type being coerced to, the coercion
is ignored. For example, the following coercions:
(A, B). coercion (x, y)
(kwd = A). coercion (kwd = x)
are rewritten to:
(A. coercion (x), B. coercion (y))
(kwd = A. coercion (x))
However, if the type of y were a subtype of B then the first coercion would instead be rewritten to:
(A. coercion (x), y)
Coercions to varargs types such as the following:
(A . . .). coercion (x, y)
are invoked by applying the coercion to the type in the varargs type, A in this example, to each of the elements of the
tuple. Additionally, there is a coercion from any type T to a tuple type solely with varargs type (T . . .) .
There is a coercion from arrow type “ A → B throws C ” to arrow type “D → E throws F ” if all of the following
conditions hold:
1. “ A → B throws C ” is not a subtype of “ D → E throws F ”;
2. D is substitutable for A;
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