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Lehmann, Daniel, 1946- and Smyth, M. B. (Michael B.) (1977) Data types. University of Warwick. Department of Computer Science. (Theory of Computation Report). (Unpublished)
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Abstract
A Mathematical interpretation is given to the notion of a data type. The main novelty is in the generality of the mathematical treatment which allows procedural data types and circularly defined data types. What is meant by data type is pretty close to what any computer scientist would understand by this term or by data structure, type, mode, cluster, class. The mathematical treatment is the conjunction of the ideas of D. Scott on the solution of domain equations (Scott (71), (72) and (76)) and the initiality property noticed by the ADJ group (ADJ (75), ADJ (77)). The present work adds operations to the data types proposed by Scott and generalizes the data types of ADJ to procedural types and arbitrary circular type definitions. The advantages of a mathematical interpretation of data types are those of mathematical semantics in general : throwing light on some ill-understood constructs in high-level programming languages, easing the task of writing correct programs and making possible proofs of correctness for programs or implementations".
| Item Type: | Report |
|---|---|
| Subjects: | Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software |
| Divisions: | Faculty of Science > Computer Science |
| Library of Congress Subject Headings (LCSH): | Data structures (Computer science) -- Mathematical models |
| Series Name: | Theory of Computation Report |
| Publisher: | University of Warwick. Department of Computer Science |
| Date: | May 1977 |
| Number: | Number 19 |
| Number of Pages: | 68 |
| Identification Number: | CS-RR-019 |
| Institution: | University of Warwick |
| Theses Department: | Department of Computer Science |
| Status: | Not Peer Reviewed |
| Publication Status: | Unpublished |
| Access rights to Published version: | Open Access |
| Funder: | Science Research Council (Great Britain) (SRC) |
| Grant number: | B/RG 31948 |
| Version or Related Resource: | Lehmann, D.J. and Smyth, M.B. (1977). Data types. 18th Annual Symposium on Foundations of Computer Science, Providence, RI, IEEE, New York, pp. 7-12. |
| URI: | http://wrap.warwick.ac.uk/id/eprint/46317 |
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