The Fortress Language Specification - CiteSeerX

Appendix A
Fortress Calculi
A.1 Basic Core Fortress
In this section, we define a basic core calculus for Fortress. We call this calculus Basic Core Fortress. Following the
precedent set by prior core calculi such as Featherweight Generic Java [12], we have abided by the restriction that all
valid Basic Core Fortress programs are valid Fortress programs.
A.1.1
Syntax
A syntax for Basic Core Fortress is provided in Figure A.1. We use the following notational conventions:
• For brevity, we omit separators such as , and ; from Basic Core Fortress.
• −→ τ is a shorthand for a (possibly empty) sequence τ 1 , · · · , τ n .
• Similarly, we abbreviate a sequence of relations α 1 extends N 1 , · · · , α n extends N n to −−−−−−−−−→ αextends N
• We use τ i to denote the ith element of −→ τ .
• For simplicity, we assume that every name (type variables, field names, and parameters) is different and every
trait/object declaration declares unique name.
• We prohibit cycles in type hierarchies.
The syntax of Basic Core Fortress allows only a small subset of the Fortress language to be formalized. Basic Core
Fortress includes trait and object definitions, method and field invocations, and self expressions. The types of
Basic Core Fortress include type variables, instantiated traits, instantiated objects, and the distinguished trait Object.
Note that we syntactically prohibit extending objects. Among other features, Basic Core Fortress does not include
top-level variable and function definitions, overloading, excludes clauses, bounds clauses, where clauses, object
expressions, and function expressions. Basic Core Fortress will be extended to formalize a larger set of Fortress
programs in the future.
A.1.2
Dynamic Semantics
A dynamic semantics for Basic Core Fortress is provided in Figure A.2. This semantics has been mechanized via
the PLT Redex tool [15]. It therefore follows the style of explicit evaluation contexts and redexes. The Basic Core
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