Class Refinement as Semantics of Correct Object Substitutability

Abstract

Abstract. Subtype polymorphism, based on syntactic conformance of objects' methods and used for substituting subtype objects for supertype objects, is a characteristic feature of the object-oriented programming style. While certainly very useful, typechecking of syntactic conformance of subtype objects to supertype objects is insufficient to guarantee correctness of object substitutability. In addition, the behaviour of subtype objects must be constrained to achieve correctness. In class-based systems classes specify the behaviour of the objects they instantiate. In this paper we define the class refinement relation which captures the semantic constraints that must be imposed on classes to guarantee correctness of substitutability in all clients of the objects these classes instantiate. Clients of class instances are modelled as programs making an iterative choice over invocation of class methods, and we formally prove that when a class C ′ refines a class C , substituting instances of C ′ for instances of C is refinement for the clients.

Stepwise refinement of heap-manipulating code in Chalice

“…For example, Mikhajlova et al [MS97,BMvW00] consider data refinement in an object-oriented language, but their coupling invariants only relate the fields in a class and a subclass, not any other objects in the heap accessible via those fields. Similarly, Grandy et al use the KIV tool to do refinement for Java programs, but the concrete programs contain all new classes, not instances of previously defined classes [GSR07].…”

Integrating Theories and Techniques for Program Modelling, Design and Verification

“…The calculus relates the classic notions of refinement and data refinement [3,16,27] in imperative languages to refactoring and object-oriented design patterns for responsibility assignments [9,19] This takes the initial attempts in formalisation of refactoring in [29,32] a step forward by providing a formal semantic justification of the soundness of the refactoring rules, and advance the theories in [4,5,6,30] on object-oriented refinement to deal with large scale object-oriented program refinement with refactoring, functionality delegation, data encapsulation and class decomposition. Within the calculus, we have already proved the soundness of several design patterns, including Expert pattern, Low Coupling pattern, and High Cohesion pattern [12].…”

REFINEMENT PROPAGATION - Towards Automated Construction of Visual Specifications

“…In our work, we were inspired by the ideas presented by Mikhajlova and Sekerinski (1997), Back et al (2000), and Michajlova (1998). In these works, refinement calculus is used for the formalization of object-oriented program development.…”

“…Börger and Stärk (2003) introduce the Abstract State Machine method of abstract refinable system specifications. Refinement formalization for object-oriented programs using refinement calculus is presented by Mikhajlova and Sekerinski (1997), Back et al (2000), and Michajlova (1998). Back(2005) proposes a method of incremental software construction using refinement diagrams.…”