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Algebraic specification of data types: A synthetic approach

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Abstract

A mathematical interpretation is given to the notion of a data type, which allows procedural data types and circularly defined data types. This interpretation seems to provide a good model for what most computer scientists would call data types, data structures, types, modes, clusters or classes. The spirit of this paper is that of McCarthy [43] and Hoare [18]. The mathematical treatment is the conjunction of the ideas of Scott on the solution of domain equations [34], [35], and [36] and the initiality property noticed by the ADJ group (ADJ [2] and [3]). The present work adds operations to the data types proposed by Scott and proposes an alternative to the equational specifications proposed by Guttag [14], Guttag and Horning [15] and ADJ [2]. The advantages of such a mathematical interpretation are the following: 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.

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Authors and Affiliations

  1. Mathematics Institute Hebrew University, Jerusalem, Israel

    Daniel J. Lehmann

  2. Department of Computer Studies, The University of Leeds, LS2 9JT, Leeds, U.K.

    Michael B. Smyth

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  1. Daniel J. Lehmann
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  2. Michael B. Smyth
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Additional information

This research was conducted at the University of Warwick while both authors were supported by the Science Research Council grant B/RG 31948 to D. Park and M. Paterson. During the final redaction of the paper the first author was partially supported by the National Science Foundation grant MCS78-07461.

EDITOR'S NOTE: This paper is one of several invited for submission to this journal to present different approaches to the subject of the semantics of programming languages.

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Lehmann, D.J., Smyth, M.B. Algebraic specification of data types: A synthetic approach. Math. Systems Theory 14, 97–139 (1981). https://doi.org/10.1007/BF01752392

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