# Algebraic Specification

**Algebraic specification**^{[1]}^{[2]}^{[3]} is a formal process of refining specifications to systematically develop more efficient programs.The purpose of an algebraic specification is to:

1. represent mathematical structures and functions over those

2. while abstracting from implementation details such as the size of representations (in memory) and the efficiency of obtaining outcome of computations

3. as such formalizing computations on data

4. allowing for automation due to a limited set of rules

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:

1. constructor functions: these are introduced to create elements of the sort or to construct complex
elements from simpler ones.

2. 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.

It is directly applicable to computer science.

References:

## See also

## Notes

- ↑ 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.