The Fortress Language Specification - CiteSeerX

The More Specific Rule for Functional Methods: Suppose that f (P) and f (Q) are two functional method declarations
occurring in trait or object declarations such that neither P nor Q is a subtype of the other and P and Q are
not incompatible with one another. Let f (P) and f (Q) have self parameters at i and j respectively. Also, let S be the
set of types that P defines coercions from and T be the set of types that Q defines coercions from. f (P) and f (Q) are
valid overloadings if all of the following hold:
• i = j
• either P ♦ Q or if there exists a trait or object C that provides both f (P) and f (Q) then P ≠ Q and there is a
declaration f (P ∩ Q) provide by C, and
• either P ⊳ Q or Q ⊳ P or for all P ′ ∈ S and Q ′ ∈ T one of the two conditions holds:
– P ′ ♦ Q ′ , or
– there is a declaration f (P ′ ∩ Q ′ ) provided by C.
Verifying the More Specific Rule for functional methods can be thought of as a two step process. First there must be no
ambiguity caused by the position of the self parameter. To guarantee this, overloaded declarations with different self
parameter positions must be incompatible with one another. Second, functional method declarations that create the
potential for ambiguity because neither is more specific than the other must be accompanied by a third disambiguating
declaration that is more specific than both. Notice that the second step is similar to the overloading requirements
placed on dotted methods.
33.5 Coercion and Overloading Resolution
The restrictions on overloaded declarations given in this chapter are sufficient to prove the following two facts:
1. If no declaration is applicable to a static call but there is a declaration that is applicable with coercion then there
exists a single most specific declaration that is applicable with coercion to the static call.
2. If any declaration is applicable to a static call then there exists a single most specific declaration that is applicable
to the static call and a single most specific declaration that is applicable to the corresponding dynamic call.
Moreover, we can prove that the most specific declaration that is applicable to a dynamic call is more specific than the
most specific declaration that is applicable to the corresponding static call.
Appendix B formally proves that the restrictions discussed in the previous sections guarantee the static resolution
of coercion (described in Section 17.5) is well defined for functions (the case for methods is analogous). Also in
Appendix B is a proof that the restrictions placed on overloaded function declarations are sufficient to guarantee no
undefined nor ambiguous calls at run time (again, the case for methods is analogous).
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