NDLI: Algebra and models

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Volume 18, Issue 5, Dec. 1993

Algebra and models

Using style to understand descriptions of software architecture

Mechanisms for generic process support

Fine-grained revision control for collaborative software development

Direct update of data flow representations for a meaning-preserving program restructuring tool

Towards increased productivity of algorithm implementation

A practical approach to software engineering using Z and the refinement calculus

Deriving modular designs from formal specifications

Targeting safety-related errors during software requirements analysis

Does every inspection need a meeting?

Enhancing compositional reachability analysis with context constraints

A framework for programming and formalizing concurrent objects

A logical approach to data structures

Test case generation by means of learning techniques

Software measure specification

Partition testing, stratified sampling, and cluster analysis

Signature matching

Scalable software libraries

Volume 18, Issue 4, Oct. 1993

Volume 18, Issue 3, July 1993

Volume 18, Issue 2, April 1993

Volume 18, Issue 1, Jan. 1993

Algebra and models

Content Provider	ACM Digital Library
Author	Hoare, C. A. R.
Abstract	Science makes progress by constructing mathematical models, deducing their observable consequences, and testing them by experiment. Successful theoretical models are later taken as the basis for engineering methods and codes of practice for design of reliable and useful products. Models can play a similar central role in the progress and practical application of Computing Science.A model of a computational paradigm starts with choice of a carrier set of potential direct or indirect observations that can be made of a computational process. A particular process is modelled as the subset of observations to which it can give rise. Process composition is modelled by relating observations of a composite process to those of its components. Indirect observations play an essential role in such compositions. Algebraic properties of the composition operators are derived with the aid of the simple theory of sets and relations. Feasibility is checked by a mapping from a more operational model.A model constructed as a family of sets is easily adapted as a calculus of design for total correctness. A specification is given by an arbitrary set containing all observations permitted in the required product. It should be expressed as clearly as possible with the aid of the full power of mathematics and logic. A product meets a specification if its potential observations form a subset of its permitted observations. This principle requires that all envisaged failure modes of a product are modelled as indirect observations, so that their avoidance can be proved. Specifications of components can be composed mathematically by the same operators as the components themselves. This permits top-down proof of correctness of designs even before their implementation begins. Algebraic properties and reasoning are helpful throughout development. Non-determinism is seen as no problem, but rather as a part of the solution.
Starting Page	1
Ending Page	8
Page Count	8
File Format	PDF
ISSN	01635948
DOI	10.1145/167049.167053
Journal	ACM SIGSOFT Software Engineering Notes (SOEN)
Volume Number	18
Issue Number	5
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	1979-04-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Content Type	Text
Resource Type	Article

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