Introducing Reference Semantics via Refinement

Abstract

Abstract. Two types of semantics have been given to object-oriented formal specification languages. Value semantics denote a class by a set of values representing its objects. Reference semantics denote a class by a set of references, or pointers, to values representing its objects. While adopting the former facilitates formal reasoning, adopting the latter facilitates transformation to object-oriented code. In this paper, we propose a combined approach using value semantics for abstract specification and reasoning, and then refining to a reference semantics before transforming specification to code.

Compositional Verification for Object-Z

“…However, referring to work by Smith [Smi02], we argue that a system specification on an abstract level given in a value semantics can be refined to a more concrete specification in a reference semantics. Compositional verification, as suggested in this paper, is to be applied on the abstract level focusing on properties of a system's functionality, rather than details of its object-oriented design.…”

“…Therefore, our approach focuses on Object-Z specifications with fixed object hierarchies and with value semantics [Smi92] rather than reference semantics. As shown recently by Smith [Smi02], Object-Z specifications with value semantics can be refined to those with reference semantics. Hence, our approach does not limit the potential for transformation of specifications to object-oriented code.…”

Integrating BON and Object-Z.

“…Void is then introduced as a global constant of type None. An alternative approach, which is also taken in [18], would be to introduce an attribute Void : B in each class; the INIT schema would then contain clauses initializing each attribute. We prefer the former approach since it directly expresses the semantics of BON classes.…”

From Object-Z Specification to Groovy Implementation

“…For example, there are 18 papers on animating formal speci cations; 11 papers used Object-Z [8][9][10][11][12][13][14][15][16][17][18]; seven used VDM and VDM++ [19][20][21][22][23][24][25] as the source speci cation languages. In addition, there are at least 32 works focusing on re nement of formal speci cations from which 10 approaches re ned Object-Z speci cations [26][27][28][29][30][31][32][33][34][35], 5 methods applied VDM++ [36][37][38][39][40], and 17 papers were published for B, Event-B, and UML-B [41][42][43][44][45][46][47][48][49][50][51][52][53][54][55]…”