Abstract Data Types (ADT) are used when creating software systems, in the systems design. Usually we use algebraic specification to specify the operations in a data type. The use of data types is a methodology or style of working which yields improved design when followed. In this paper we study the addition of input-output operations to the algebraic specification of operations over a data type. The motivation is that input-output operations are used in actual implementations. A specification with input-output is more complete than one without it. We need input-output operations in our programs. This justifies the addition of such operations to the specification. We consider the definition of input-output operations in functional programming in particular in Haskell. Our input-output specifications are not exactly equal to Haskell programs although some of them are likely. We specify input-output operations in a form likely to the specification of the other operations. The result is the algebraic specification of the input-output operations for many frequently used data types. The language considered is sufficiently expressive to model all these operations. The technique is illustrated by means of a variety of examples. We started from sequences, continued with sets and finish with dictionaries. The specifications we present in this paper can be used as specifications of methods of ADT definitions in object oriented programing.
| Published in | Mathematics and Computer Science (Volume 6, Issue 2) |
| DOI | 10.11648/j.mcs.20210602.11 |
| Page(s) | 30-37 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2024. Published by Science Publishing Group |
Abstract Data Types, Algebraic Specification, Input-Output
| [1] | Dahl, O.-J., SIMULA an Algol-Based Simulation Language. Communications of the ACM, Vol 9, Number 9, September 1966. |
| [2] | Dijkstra, E. W.. Notes on structured programming. In Structured Programming, Academic Press, New York, 1972. |
| [3] | Hoare, C. A. R., Proof of correctness of data representations. Acta Informatica 1 (1972), 271-281. |
| [4] | Parnas D. L., A Technique for Software Module Specification with Examples. Communications of the ACM, Vol 15, Number 5, May 1972. |
| [5] | Hoare, C. A. R., and Wirth, N. An Axiomatic definition of the programming language Pascal, Acta Informatica 2 (1973) 335-355. |
| [6] | Liskov B., Zilles S., Programming with Abstract Data Types, Proceedings of the ACM Sigplan Symopsium on very high level languages, pag 50-59, 1974. |
| [7] | Parnas D. L. A., The influence of Software Structure on Reliability, ACM Sigplan Notices, Vol 10, Issue 6, April 1975. |
| [8] | J. V. Guttag, E. Horowitz, D. R. Musser, The Design of Data Type Specifications, Proceedings of the 2nd International Conference on Software Engineering, pp 414-420, San Francisco, California, USA, 1976. |
| [9] | J. V. Guttag, E. Horowitz, D. R. Musser, Abstract Data Types and Software Validation, Information Sciences Institute, University of Southern California, August 1976, ARPA ORDER No 2223. |
| [10] | J. Guttag, Abstract Data Types and the Development of Data Structures, Communications of the ACM, June 1977, Vol. 20, Number 6. |
| [11] | J. A. Goguen, J. W. Thatcher, E. G. Wagner, J. B. Wright, Initial Algebra Semantics and Continuous Algebras, ACM, 1977. |
| [12] | J. A. Bergstra and J. V. Tucker, The Completeness of the Algebraic Specification Methods for Computable Data Types, Information and Control 54, 186-200 (1982). |
| [13] | Cardelli, L., Wegner, P., On Understanding Types, Data Abstraction, and Polymorphism, Computing Surveys, Vol. 17, No 4, December 1985. |
| [14] | Dahl, O.-J., The Birth of Object Orientation, The Simula Languages, Software Pioneers, Springer 2002. |
| [15] | J. Guttag, Abstract Data Types, Then and Now, M Broy, E. Denert (Eds): Software Pionners, Springer-Verlag Berlin Heidelberg, 2002. |
| [16] | Hal Daume III, Yet Another Haskell Tutorial, Copyright (c) Hal Daume III, 2002-2006. |
| [17] | Haskell/Print version from Wikibooks, the open-content textbooks collection. June 2018. |
| [18] | Reading 10: Abstract Data Types, course 6.031 Software Construction, MIT, Spring 2018, http://web.mit.edu/6.031/www/sp18/classes/10-abstract-data-types/ |
APA Style
Patricia Peratto. (2021). Algebraic Specification for Input-Output in Abstract Data Types. Mathematics and Computer Science, 6(2), 30-37. https://doi.org/10.11648/j.mcs.20210602.11
ACS Style
Patricia Peratto. Algebraic Specification for Input-Output in Abstract Data Types. Math. Comput. Sci. 2021, 6(2), 30-37. doi: 10.11648/j.mcs.20210602.11
AMA Style
Patricia Peratto. Algebraic Specification for Input-Output in Abstract Data Types. Math Comput Sci. 2021;6(2):30-37. doi: 10.11648/j.mcs.20210602.11
Share This Article
Twitter
Linked In
Facebook
Copy
Download@article{10.11648/j.mcs.20210602.11,
author = {Patricia Peratto},
title = {Algebraic Specification for Input-Output in Abstract Data Types},
journal = {Mathematics and Computer Science},
volume = {6},
number = {2},
pages = {30-37},
doi = {10.11648/j.mcs.20210602.11},
url = {https://doi.org/10.11648/j.mcs.20210602.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mcs.20210602.11},
abstract = {Abstract Data Types (ADT) are used when creating software systems, in the systems design. Usually we use algebraic specification to specify the operations in a data type. The use of data types is a methodology or style of working which yields improved design when followed. In this paper we study the addition of input-output operations to the algebraic specification of operations over a data type. The motivation is that input-output operations are used in actual implementations. A specification with input-output is more complete than one without it. We need input-output operations in our programs. This justifies the addition of such operations to the specification. We consider the definition of input-output operations in functional programming in particular in Haskell. Our input-output specifications are not exactly equal to Haskell programs although some of them are likely. We specify input-output operations in a form likely to the specification of the other operations. The result is the algebraic specification of the input-output operations for many frequently used data types. The language considered is sufficiently expressive to model all these operations. The technique is illustrated by means of a variety of examples. We started from sequences, continued with sets and finish with dictionaries. The specifications we present in this paper can be used as specifications of methods of ADT definitions in object oriented programing.},
year = {2021}
}
TY - JOUR T1 - Algebraic Specification for Input-Output in Abstract Data Types AU - Patricia Peratto Y1 - 2021/04/29 PY - 2021 N1 - https://doi.org/10.11648/j.mcs.20210602.11 DO - 10.11648/j.mcs.20210602.11 T2 - Mathematics and Computer Science JF - Mathematics and Computer Science JO - Mathematics and Computer Science SP - 30 EP - 37 PB - Science Publishing Group SN - 2575-6028 UR - https://doi.org/10.11648/j.mcs.20210602.11 AB - Abstract Data Types (ADT) are used when creating software systems, in the systems design. Usually we use algebraic specification to specify the operations in a data type. The use of data types is a methodology or style of working which yields improved design when followed. In this paper we study the addition of input-output operations to the algebraic specification of operations over a data type. The motivation is that input-output operations are used in actual implementations. A specification with input-output is more complete than one without it. We need input-output operations in our programs. This justifies the addition of such operations to the specification. We consider the definition of input-output operations in functional programming in particular in Haskell. Our input-output specifications are not exactly equal to Haskell programs although some of them are likely. We specify input-output operations in a form likely to the specification of the other operations. The result is the algebraic specification of the input-output operations for many frequently used data types. The language considered is sufficiently expressive to model all these operations. The technique is illustrated by means of a variety of examples. We started from sequences, continued with sets and finish with dictionaries. The specifications we present in this paper can be used as specifications of methods of ADT definitions in object oriented programing. VL - 6 IS - 2 ER -
Email: