A reification calculus for model-oriented software specification

This paper presents a transformational approach to the derivation of implementations from model-oriented specifications of abstract data types. The purpose of this research is to reduce the number of formal proofs required in model refinement, which hinder software development. It is shown to be appli- cable to the transformation of models written in Meta-iv (the specification lan- guage of Vdm) towards their refinement into, for example, Pascal or relational DBMSs. The approach includes the automatic synthesis of retrieve functions between models, and data-type invariants. The underlying algebraic semantics is the so-called final semantics “`a la Wand”: a specification “is” a model (heterogeneous algebra) which is the final ob ject (up to isomorphism) in the category of all its implementations. The transformational calculus approached in this paper follows from exploring the properties of finite, recursively defined sets. This work extends the well-known strategy of program transformation to model transformation, adding to previous work on a transformational style for operation- decomposition in META-IV. The model-calculus is also useful for improving model-oriented specifications.(undefined

Sound and Relaxed Behavioural Inheritance

Object-oriented (OO) inheritance establishes taxonomies of OO classes. Behavioural inheritance (BI), a strong version, emphasises substitutability: objects of child classes replace objects of their ascendant classes without any observable effect difference on the system. BI is related to data refinement, but refinement's constrictions rule out many useful OO subclassings. This paper revisits BI at the light of Z and the theory of data refinement. It studies existing solutions to this problem, criticises them, and proposes improved relaxations. The results are applicable to any OO language that supports design-by-contract (DbC). The paper's contributions include three novel BI relaxations supported by a mathematical model with proofs carried out in the Isabelle proof assistant, and an examination of BI in the DbC languages Eiffel, JML and Spec#

Object oriented programming : data preparation and visualization of FEM models

In this paper two object oriented applications are described. The former is intended to generate data associated with the finite element method (FEM) and the later is a three-dimensional visualization tool named 3DMesh. Both are based on the principles of object oriented programming, namely encapsulation, inheritance and polymorphism. To support the preparation of FEM data, a language named 3DO was developed. Its syntax is similar to a subset of the C++ programming language. 3DO is based on object construction and modification by methods that require a small number of arguments. With this tool, mesh generation, definition of properties and loads and mesh refinement can be performed with limited user effort, even when the model is complex. All the generated information can be visualized with the program 3DMesh. This application is based on the OpenGL library and uses the Microsoft Foundation Classes to simplify its integration in the MS-Windows environment. 3DMesh implements an interactive navigation technique that allows the visualization of the model interior, preserving its integrity. Model attributes and the results of the FEM analysis can also be visualized

The Ge(001) (2 × 1) reconstruction: asymmetric dimers and multilayer relaxation observed by grazing incidence X-ray diffraction

Grazing incidence X-ray diffraction has been used to analyze in detail the atomic structure of the (2 × 1) reconstruction of the Ge(001) surface involving far reaching subsurface relaxations. Two kinds of disorder models, a statistical and a dynamical were taken into account for the data analysis, both indicating substantial disorder along the surface normal. This can only be correlated to asymmetric dimers. Considering a statistical disorder model assuming randomly oriented dimers the analysis of 13 symmetrically independent in-plane fractional order reflections and of four fractional order reciprocal lattice rods up to the maximum attainable momentum transfer qz = 3c* (c* = 1.77 × 10−1 Å−1) indicates the formation of asymmetric dimers characterized by R>D = 2.46(5) Å as compared to the bulk bonding length of R = 2.45 Å. The dimer height of Δ Z = 0.74(15) Å corresponds to a dimer buckling angle of 17(4)°. The data refinement using anisotropic thermal parameters leads to a bonding length of RD = 2.44(4) Å and to a large anisotropy of the root mean-square vibration amplitudes of the dimer atoms (u112) 1/2 = 0.25 Å, (u222)1/2 = 0.14 Å, (u332)1/2 = 0.50 Å). We have evidence for lateral and vertical disp tenth layer below the surface

Extension of the Finite Integration Technique including dynamic mesh refinement and its application to self-consistent beam dynamics simulations

An extension of the framework of the Finite Integration Technique (FIT) including dynamic and adaptive mesh refinement is presented. After recalling the standard formulation of the FIT, the proposed mesh adaptation procedure is described. Besides the linear interpolation approach, a novel interpolation technique based on specialized spline functions for approximating the discrete electromagnetic field solution during mesh adaptation is introduced. The standard FIT on a fixed mesh and the new adaptive approach are applied to a simulation test case with known analytical solution. The numerical accuracy of the two methods are shown to be comparable. The dynamic mesh approach is, however, much more efficient. This is also demonstrated for the full scale modeling of the complete RF gun at the Photo Injector Test Facility DESY Zeuthen (PITZ) on a single computer. Results of a detailed design study addressing the effects of individual components of the gun onto the beam emittance using a fully self-consistent approach are presented.Comment: 33 pages, 14 figures, 4 table

Error estimation and adaptive moment hierarchies for goal-oriented approximations of the Boltzmann equation

This paper presents an a-posteriori goal-oriented error analysis for a numerical approximation of the steady Boltzmann equation based on a moment-system approximation in velocity dependence and a discontinuous Galerkin finite-element (DGFE) approximation in position dependence. We derive computable error estimates and bounds for general target functionals of solutions of the steady Boltzmann equation based on the DGFE moment approximation. The a-posteriori error estimates and bounds are used to guide a model adaptive algorithm for optimal approximations of the goal functional in question. We present results for one-dimensional heat transfer and shock structure problems where the moment model order is refined locally in space for optimal approximation of the heat flux.Comment: arXiv admin note: text overlap with arXiv:1602.0131

Modal logics for reasoning about object-based component composition

Component-oriented development of software supports the adaptability and maintainability of large systems, in particular if requirements change over time and parts of a system have to be modified or replaced. The software architecture in such systems can be described by components and their composition. In order to describe larger architectures, the composition concept becomes crucial. We will present a formal framework for component composition for object-based software development. The deployment of modal logics for defining components and component composition will allow us to reason about and prove properties of components and compositions