Mind the gap! Abstract versus concrete models of specifications

Donald Sannella, Andrzej Tarlecki

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract / Description of output

In the theory of algebraic specifications, many-sorted algebras are used to model programs: the representation of data is arbitrary and operations are modelled as ordinary functions. The theory that underlies the formal development of programs from specifications takes advantage of the many useful properties that these models enjoy.

The models that underlie the semantics of programming languages are different. For example, the semantics of Standard ML uses rather concrete models, where data values are represented as closed constructor terms and functions are represented as “closures”. The properties of these models are quite different from those of many-sorted algebras.

This discrepancy brings into question the applicability of the theory of specification and formal program development in the context of a concrete programming language, as has been attempted in the Extended ML framework for the formal development of Standard ML programs. This paper is a preliminary study of the difference between abstract and concrete models of specifications, inspired by the kind of concrete models used in the semantics of Standard ML, in an attempt to determine the consequences of the discrepancy.
Original languageEnglish
Title of host publicationMathematical Foundations of Computer Science 1996
Subtitle of host publication21st International Symposium, MFCS'96 Cracow, Poland, September 2–6, 1996 Proceedings
EditorsWojciech Penczek, Andrzej Szalas
PublisherSpringer-Verlag GmbH
Number of pages21
ISBN (Electronic)978-3-540-70597-0
ISBN (Print)978-3-540-61550-7
Publication statusPublished - 1996

Publication series

NameLecture Notes in Computer Science
PublisherSpringer Berlin / Heidelberg
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


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