Abstract data type - Open Access .click

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2008
Fields and division rings are not algebras in the sense of "Universal Algebra", as inverse is not a total function. Mending the inverse by any definition of 0(-1) will not suffice to axiomatize the axiom of inverse x(-1) · x = 1, by an equation. In particular the theory of fields cannot be used for specifying the abstract data type of the rational ...
John V. Tucker, Jan A. Bergstra, Yoram Hirshfeld +2 more
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Abstract Data Types, Then and Now

2002
Data abstraction has come to play an important role in software development. This paper presents one view of what data abstraction is, how it was viewed when it was introduced, and its long-term impact on programming.
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Precise typing of abstract data type specifications

Proceedings of the 10th ACM SIGACT-SIGPLAN symposium on Principles of programming languages - POPL '83, 1983
There are two important notions of data types being used in programming languages today. In the concept called abstract data types, types are algebras; the semantics of programs is described in terms of operations in these algebras. Another notion of type found in most of the "typed" programming languages in actual use regards types as sets of objects;
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Abstract Data Type Sets—II

1990
In chapter 5 we looked at general implementations of the ADT set. As we noticed, not all the set operations could be implemented efficiently using a single data structure. However, many applications using sets require only a limited number of set operations.
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Abstract objects as abstract data types [PDF]