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A system for reasoning within and about algebraic specifications

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International Symposium on Programming (Programming 1982)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 137))

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Abstract

A machine-implemented system to support the reasoning about algebraic specifications is presented. The PAT-system is an attempt to ease design, analysis, and implementation of partial abstract data types. More precisely, the PAT-system

  • allows to write "axiomatic abstract types", i.e. parameterised hierarchical algebraic specifications, as well as "domain types", i.e. abstract types defined by domain equations,

  • introduces automatically the semantic conventions for the theory of partial abstract types including axioms for strictness (of partial functions) and for the validity of data type induction,

  • facilitates proofs of derived properties: PAT provides (semiautomatic) strategies for using derived rules of inference as well as for simplifying conditional equations. It allows to use a metalanguage — Edinburgh-ML /LCF 79/ — for generating and performing proofs interactively;

  • makes first attempts for analysing algebraic specifications by checking sufficient conditions for the existence of initial algebras (of hierachical specifications and/or parameterised specifications — for nonhierarchical and nonparameterised specifications initial algebras always exist) and for the existence of weakly terminal algebras,

  • supports development and proof of correctness of implementations; in particular it is possible to verify implementations of "axiomatic types" by "domain types".

The PAT-system is implemented in Edinburgh-ML being part of an interactive verification system, Edinburgh-LCF, which seems particularly appropriate to support proofs with algebraic specifications.

The system PAT tries to use as much as possible the facilities and properties of the underlying Edinburgh-LCF system. Only necessary changes — such as "smash" product instead of "cartesian" product — and extensions — such as the introduction of certain induction schemata — are made.

A short characterisation of LCF and a description of the PAT-system is given. The PAT-system is shortly compared with other systems manipulating algebraic specifications. Finally, as an example for the reasoning with and about algebraic specifications priority queues over linearly ordered data types are described as a parameterised abstract type, PQ.

This research was partially sponsored by the Sonderforschungsbereich 49, Programmiertechnik, Munich

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Author information

Authors and Affiliations

  1. Institute of Computer Science, Polish Academy of Sciences, P.O. BOX 22, 00-901, Warszawa, PKiN, Poland

    Jaoek Leszczylowski

  2. Institut für Informatik, Technische Universität München, Arcisstrasse 21, D-8000, München 2, FRG

    Martin Wirsing

Authors
  1. Jaoek Leszczylowski
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  2. Martin Wirsing
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Mariangiola Dezani-Ciancaglini Ugo Montanari

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© 1982 Springer-Verlag Berlin Heidelberg

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Leszczylowski, J., Wirsing, M. (1982). A system for reasoning within and about algebraic specifications. In: Dezani-Ciancaglini, M., Montanari, U. (eds) International Symposium on Programming. Programming 1982. Lecture Notes in Computer Science, vol 137. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-11494-7_18

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  • DOI: https://doi.org/10.1007/3-540-11494-7_18

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  • Online ISBN: 978-3-540-39184-5

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