Quantitative And Qualitative Evaluation Of Metrics On Object Graphs Extracted By Abstract Interpretation

syntax. A portion of the abstract syntax for Ownership Domains is presented (Figure 2.2), focusing on class declarations, field declarations, expressions e.g., method invocations, field reads and field writes. The meta-variable C ranges over class names; T ranges over types; f ranges over fields; v ranges over values; d ranges over domain names; and p ranges over formal domain parameters, actual domains, or domain SHARED. An overbar over the meta-variable represents a sequence. 7 cdef ::= class C<α, β> extends C <α> { dom; T f ; md} dom ::= [public] domain d; md ::= TR m(T x) Tthis {ret = eR; return eR; } e ::= x = new C(e) | x = r.m(e) | x = y.f | x.f = y . . . n ::= x | v | r | y p ::= α | n.d | SHARED T ::= C v, l ∈ locations Figure 2.2: Portions of the Ownership Domains abstract syntax [3]. A class is parameterized by a list of domain parameters, and extends another class that has a subsequence of its domain parameters. A type T is a class name and a set of actual domain parameters C. The first domain parameter of a class is its owning domain followed by other domain parameters. Data types. The internal representation of an OOG is an OGraph. The OGraph has two types of nodes: the OObjects referred to by the meta-variable O and the ODomains referred to by the meta-variable D. Two OObjects may be connected by OEdges referred to by the meta-variable E and can represent points-to, or dataflow relations. An OObject is represented using the tuple 〈A,D1, D2〉. The tuple represents an abstract object of type A whose owning domain is D1; D2 is a domain that the object has access to, i.e., it references objects from that domain. By having abstract objects of the form 〈C,D1, D2〉, the OOG distinguishes different abstract objects of the same type C that are in different owning domains or that have the same owning domain but different other domains that the object has access to. The ODomain represents an abstraction of a runtime domain, one domain declaration D in a type C can correspond to multiple ODomains Di in the OGraph. The static analysis computes an abstract object of type C in some domain D based on mapping the formal domain parameters in the code to domains that may be declared by other types Ci.