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Formal Modelling in VDM

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The Vienna Development Method

The Vienna Development Method (VDM) is one of the longest established model-oriented formal methods for the development of computer-based systems and software. It consists of a group of mathematically well-founded languages and tools for expressing and analyzing system models during early design stages, before expensive implementation commitments are made. The construction and analysis of the model help to identify areas of incompleteness or ambiguity in informal system specifications, and provide some level of confidence that a valid implementation will have key properties, especially those of safety or security. VDM has a strong record of industrial application, in many cases by practitioners who are not specialists in the underlying formalism or logic. Experience with the method suggests that the effort expended on formal modeling and analysis can be recovered in reduced rework costs arising from design errors.


VDM models are expressed in a specification language (VDM-SL) that supports the description of data and functionality. Data are defined by means of types built using constructors that define structured data and collections such as sets, sequences and mappings from basic values such as Booleans and numbers. These types are very abstract, allowing the user to add any relevant constraints as data type invariants. Functionality is defined in terms of operations over these data types. Operations can be defined implicitly by preconditions and postconditions that characterize their behavior, or explicitly by means of specific algorithms. An extension of VDM-SL, called VDM++, supports object-oriented structuring of models and permits direct modeling of concurrency.

Since the modeling language has a formal mathematical semantics, a wide range of analyses can be performed on models, both to check internal consistency and to confirm that models have emergent properties. Analyses may be performed by inspection, static analysis, testing or mathematical proof. To assist in this process, there is extensive tool support for building models in collaboration with other modeling tools, to execute and test models, to carry out different forms of static analysis and to generate executable code in a high-level programming language.


The use of VDM involves the development and analysis of models to help understand systems and predict their properties. Good models exhibit abstraction and rigor. Abstraction is the suppression of detail that is not relevant to the purpose for which a model is constructed. The decision about what to include and what to omit from an abstract model requires good engineering judgment. A guiding principle in VDM is that only elements relevant to the model’s purpose should be included; it follows that the model’s purpose should be clearly understood and described. Rigor is the capacity to perform a mathematical analysis of the model’s properties in order to gain confidence that an accurate implementation of the modeled system will have certain key characteristics. In computing systems development, modeling and design notations with a strong mathematical basis are termed formal. VDM is based on a formal specification language VDM-SL, the semantics of which are given mathematically in an ISO Standard [6]. VDM models, although often expressed in an executable subset, are developed primarily for analysis rather than serving as final implementations.

Model Structure

In VDM, models consist of representations of the data on which a system operates and the functionality that is to be performed. Data includes the externally visible input/output and internal state data. Functionality includes the operations that may be invoked at the system interface as well as auxiliary functions that exist purely to assist in the definition of the operations. In the ISO Standard [6] there is an informative appendix providing a modular framework for flat VDM-SL models. This modular framework includes traditional import and export features as well as parameterized modules and instantiations of these.

The VDM++ language extends flat VDM-SL with facilities for specification of object-oriented systems, and structures models into class definitions, each of which has similar elements to a single VDM-SL specification, with the state variables taking the role of instance variables and the operations playing the part of methods. The remainder of this section will restrict consideration to VDM-SL, with VDM++ considered at a later stage.

Modeling data

Data models in VDM are founded on basic abstract data types together with a set of type constructors. A full account of VDM-SL data types and type constructors is provided in current texts [5]. Basic types include numbers (natural, integer, rational and real) and characters. Note that, in accordance with VDM’s abstraction principle, there are no predetermined maximum representable numbers or real number precisions. If a user wishes to specify these limits because they are relevant to the problem being modeled, it is possible to do so explicitly by means of invariants. Invariants are logical expressions (predicates) that represent conditions to be respected by all elements of the data type to which they are attached.