Algebraic Specification: Difference between revisions
No edit summary |
No edit summary |
||
| Line 14: | Line 14: | ||
with a collection of functions on them. These functions can usually be divided into two classes:<br /> | with a collection of functions on them. These functions can usually be divided into two classes:<br /> | ||
#. constructor functions: these are introduced to create elements of the sort or to construct complex | #. constructor functions: these are introduced to create elements of the sort or to construct complex elements from simpler ones. | ||
elements from simpler ones. | |||
#. additional functions: these are functions defined in terms of the constructor functions. | #. 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 | 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, | 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 | also the combination of false and ¬ can be considered constructors. In that case true may be considered | ||
an additional function.<br /> | an additional function.<br /> | ||
In the context of the description of state and state change one may think of the sort as the set of possible | 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 | 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.<br /> | for describing the state changes that may occur.<br /> | ||
== Researchers == | == Researchers == | ||
Revision as of 10:57, 21 July 2009
Algebraic specification [1][2] [3] is a specific approach to formal specification of computer programs.
Goals
The purpose of an algebraic specification is to:
- represent mathematical structures and functions over those
- while abstracting from implementation details such as the size of representations (in memory) and the efficiency of obtaining outcome of computations
- as such formalizing computations on data
- . 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:
- . 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
- ↑ 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.
