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 (Unpublished)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".

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