The Fortress Language Specification - CiteSeerX

Traits defining a method: defining p (f, N) = { −→ N }
defining p (f,Object) = ∅
⎧
⋃
defining p (f, [ −→ τ / −→ α ]N i )
⎪⎨
defining p (f, C −→ τ ) =
N i ∈{ −→ N }
⋃
if C α −→
−→ extends { N } ∈ p and f ∉ definedp (C)
defining p (f, [ −→ τ / −→ α ]N i ) ∪ {C −→ τ }
⎪⎩
N i ∈{ −→ N }
if
C −→ α extends {
−→ N } ∈ p and f ∈ definedp (C)
Auxiliary functions for methods: defined p / inherited p / visible p (C) = { −→ f }
defined p (C) = { −−−−−−−→ Fname(fd)} where C −→ fd ∈ p
inherited p (C) = ⊎ N i ∈{ −→ N } {f i | f i ∈ visible p (N i ), f i ∉ defined p (C)} where C extends { −→ N } ∈ p
visible p (C) = defined p (C) ⊎ inherited p (C)
Figure A.12: Static Semantics of Core Fortress with Where Clauses (IV)
A.3 Core Fortress with Overloading
In this section, we define a Fortress core calculus with overloading for dotted methods and first-order functions. We
call this calculus Core Fortress with Overloading. Core Fortress with Overloading is an extension of Basic Core
Fortress with overloading.
A.3.1
Syntax
The syntax for Core Fortress with Overloading is provided in Figure A.13.
A.3.2
Dynamic Semantics
A dynamic semantics for Core Fortress with Overloading is provided in Figure A.14.
A.3.3
Static Semantics
A static semantics for Core Fortress with Overloading is provided in Figures A.15, A.16, A.17, and A.18.
We proved the type soundness of Core Fortress with Overloading using the standard technique of proving a progress
theorem and a subject reduction theorem.
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