Let p be a prime number. In this article we present a theorem, suggested by Peter Scholze, which states that Gal(Qp/Qp) is the étale fundamental group of a certain object Z which is defined over an algebraically closed field. This object is the quotient of the “punctured perfectoid open disk” by an action of the group Qp . The proof of this fact combines two themes: the tilting equivalence for ...

This paper describes the translation of Object-Z speciications of container classes to C++ test oracle classes. It presents a three-stage translation process and describes how the derived test oracles are integrated into the ClassBench testing framework. The method caters for object-oriented features such as inheritance and aggregation. Translation issues and limitations of the method are discu...

This paper presents a method of reasoning about Object-Z speciications. The approach utilises the mod-ularity inherent in Object-Z speciications to simplify proofs. Properties proved for a class in isolation can be used when that class is either inherited by another class or instantiated as part of a system of interacting objects. Proofs using structural induction and the notion of object integ...

This paper presents a logic for Object-Z which extends W, the logic for Z adopted as the basis of the deductive system in the Z Base Standard. The logic provides a basis on which tool support for reasoning about Object-Z speciications can be developed. It also formalises the intended meaning of Object-Z constructs and hence provides an abstract, axiomatic semantics of the language.

Object-Z is an object-oriented specification language which extends the Z with classes, objects, inheritance and polymorphism that can be used to represent of a complex system as collections objects. There are number existing works mapped C++ Java programming languages. Since Python share many similarities, both paradigm, support set theory predicate calculus moreover, functional naturally clos...

In this paper, we present a case study for using formal object-oriented speciication languages, such as Object-Z, to specify the semantics of object-oriented programming languages. The key idea in this case study is to model language constructs, such as expressions, statements, methods and classes, as objects and to specify the semantics of each language construct using an Object-Z class. This ...

In this paper‎, ‎we consider a general integral operator $G_n(z).$ The main object of the present paper is to study some properties of this integral operator on the classes $mathcal{S}^{*}(alpha),$ $mathcal{K}(alpha),$ $mathcal{M}(beta),$ $mathcal{N}(beta)$ and $mathcal{KD}(mu,beta).$‎

This paper presents a framework for compositional verification of Object-Z specifications. Its key feature is a proof rule based on decomposition of hierarchical Object-Z models. For each component in the hierarchy local properties are proven in a single proof step. However, we do not consider components in isolation. Instead, components are envisaged in the context of the referencing super-com...

Software systems have become increasingly distributed, dynamic and mobile. The complex state and dynamic interfaces of software components and their concurrent interactions provide challenging research issues in system specification and design. An effective combination of structured state-based formalism and dynamic action-based calculus may be a good solution for modeling complex distributed m...