rCOS: A refinement calculus for object systems

This article presents a mathematical characterization of object-oriented concepts by defining an observation-oriented semantics for a relational objectoriented language with a rich variety of features including subtypes, visibility, inheritance, type casting, dynamic binding and polymorphism. The language is expressive enough for the specification of object-oriented designs and programs. We also propose a calculus based on this model to support both structural and behavioral refinement of object-oriented designs. We take the approach of the development of the design calculus based on the standard predicate logic in Hoare and He’s Unifying Theories of Programming (UTP). We also consider object reference in terms of object identity as values and mutually dependent methods

UTP2: Higher-Order Equational Reasoning by Pointing

We describe a prototype theorem prover, UTP2, developed to match the style of hand-written proof work in the Unifying Theories of Programming semantical framework. This is based on alphabetised predicates in a 2nd-order logic, with a strong emphasis on equational reasoning. We present here an overview of the user-interface of this prover, which was developed from the outset using a point-and-click approach. We contrast this with the command-line paradigm that continues to dominate the mainstream theorem provers, and raises the question: can we have the best of both worlds?Comment: In Proceedings UITP 2014, arXiv:1410.785

Computer-Assisted Program Reasoning Based on a Relational Semantics of Programs

We present an approach to program reasoning which inserts between a program and its verification conditions an additional layer, the denotation of the program expressed in a declarative form. The program is first translated into its denotation from which subsequently the verification conditions are generated. However, even before (and independently of) any verification attempt, one may investigate the denotation itself to get insight into the "semantic essence" of the program, in particular to see whether the denotation indeed gives reason to believe that the program has the expected behavior. Errors in the program and in the meta-information may thus be detected and fixed prior to actually performing the formal verification. More concretely, following the relational approach to program semantics, we model the effect of a program as a binary relation on program states. A formal calculus is devised to derive from a program a logic formula that describes this relation and is subject for inspection and manipulation. We have implemented this idea in a comprehensive form in the RISC ProgramExplorer, a new program reasoning environment for educational purposes which encompasses the previously developed RISC ProofNavigator as an interactive proving assistant.Comment: In Proceedings THedu'11, arXiv:1202.453

A robust semantics hides fewer errors

In this paper we explore how formal models are interpreted and to what degree meaning is captured in the formal semantics and to what degree it remains in the informal interpretation of the semantics. By applying a robust approach to the definition of refinement and semantics, favoured by the event-based community, to state-based theory we are able to move some aspects from the informal interpretation into the formal semantics