Algebraic Specification
Algebraic specification [1][2][3] is a specific approach to the formal specification, prototyping, and general development of computer programs.
Overview
As an area of applied mathematics and computer science, algebraic specification addresses these concerns[1]:
- design of algebraic specification formalisms;
- application of algebraic specification techniques to the definition programming languages;
- generation of testable or executable prototypes from specifications.
Although there is also a branch of this topic which is more concentrated on theoretical computer than applications, the latter are the focus of this article.
Implementation
An algebraic specification achieves these goals by means of defining a number of sorts (data types) together
with a collection of functions on them. These functions can usually be divided into two classes:
- constructor functions: these are introduced to create elements of the sort or to construct complex elements from simpler ones.
- additional functions: these are functions defined in terms of the constructor functions.
If one considers an algebraic specification of the Booleans the constructors can be true and false. In that
case all other connectives, such as ^ and _, may be considered to be additional functions. Alternatively,
also the combination of false and ¬ can be considered constructors. In that case true may be considered
an additional function.
In the context of the description of state and state change one may think of the sort as the set of possible
states (not necessarily all of them can occur in practice) and one may think of the functions as being useful
for describing the state changes that may occur.
Researchers
See also
Notes
- ↑ 1.0 1.1 Bergstra, J. A.; B. Mahr (1989). Algebraic Specification. Academic Press. ISBN 0-201-41635-2.
- ↑ Ehrig, E.; J. Heering, J. Klint (1985). Algebraic Specification. EATCS Monographs on Theoretical Computer Science. 6. Springer-Vrlag.
- ↑ Wirsing, M. (1990). J. van Leeuwen (ed.). ed. Algebraic Specification. Handbook of Theoretical Computer Science. B. Elsevier. pp. 675–788.
