There is significant interest in the use of Z in conjunction with object-orientation. Here we present a new approach to structuring Z specifications in an object-oriented (OO) style. Our structuring is based on views, it uses the schema calculus, and it does not extend Z. The resulting OO Z specifications are comprehensible, modular, and conceptually clear. The modularity of the new approach su...

(In first case we say (F,G2) are an adjoint pair and in the second case we say that (G1, F ) are an adjoint pair.) (2) An object A in a category C is called initial (resp. final) if for every object B in C, HomC(A,B) (resp. HomC(B,A)) is a singleton. Prove that an initial (resp. final) object, if it exists, is unique up to unique isomorphism. Determine if such objects exist in the following cat...

For analytic functions f (z) = z p +a p+1 z p+1 +··· in the open unit disk U and a polynomial Q(z) of degree n > 0, the function F(z) = f (z)[Q(z)] β/n is introduced. The object of the present paper is to determine the radius of p-valently strongly starlikeness of order γ for F(z).

1 The Approximate Solution Curve Tracing (ASCT) Method 1.1 The correct solution space (CSS) Figure 1: The CSS represents the correct solution .space which all of the depth values on the illuminated object are included in. LB is the lower bound of the CSS. All of the depth values on the illuminated object will be not "deeper" than it. UB is the upper boumt of the CSS. All of the depth values on ...

This paper describes an exercise in object-oriented modelling where Formal Concept Analysis is applied to a formal specification case study using Object-Z. In particular, the informal description from the case study is treated as a set of use-cases from which candidate classes and objects are derived. The resulting class structure is contrasted with the existing Object-Z design and the two appr...

The Object-Z notation is a good meta-language that can be used to specify denotational semantics of programming languages. It has been effectively applied to some categories of languages. These include the procedural languages, the object-oriented procedural languages [9] and specification languages [8]. To widen these catergories, this paper applies Object-Z to the specification of the semanti...

Most SVRC technical reports are available via anonymous ftp, from svrc.it.uq.edu.au in the directory /pub/techreports. Abstracts and compressed postscript les are available from Abstract This paper presents a method of formally specifying systems involving continuous variables and real-time constraints using the object-oriented state-based speciication language Object-Z together with the timed ...

Object-oriented architectures for Graphical User Interfaces (GUI’s) model the interface as a composition of interacting objects which each present an internal state to the user and provide operations on that state. Two such architectures are Model-View-Controller (MVC) and Presentation-Abstraction-Control (PAC). We use Object-Z to describe examples of the MVC and PAC architectures. We compare t...

This paper addresses the problem of identity fusion, i.e. the problem of selecting one of several identity hypotheses concerning an observed object. Two problems are considered. Firstly the problem of representing and fusing measurements relating to identity hypotheses is treated. Here it is shown that if the hypotheses are chosen to be concerned with object properties rather than object identi...

As modern complex systems become increasingly large, sophisticated, feature-rich and data-intensive, people have recognized the importance of precisely and unambiguously specifying them with formal methods for a number of years. This paper advocates the use of Object-Z, a formal specification language, in the description of complex systems. Object-Z is an extension to the Z language to facilita...