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A lazy approach to partial algebras

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Recent Trends in Data Type Specification (ADT 1994, COMPASS 1994)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 906))

Abstract

Starting from the analysis of which features are required by an algebraic formalism to describe at least the more common data types used in imperative and functional programming, a framework is proposed, collecting many techniques and ideas from the algebraic community, with the capability for an immediate representation of partiality and error-recovery. This formalism, of so called lazy algebras, inherits mainly from two parents: partial and label algebras; from the former especially on a technical side and from the later from a philosophical point of view. But, as all children, it has its own individuality and in particular an original mechanism to represent lazy evaluation in an algebraic framework has been introduced.

This work has been partially supported by ESPRIT BRA WG n. 6112 COMPASS, HCM-Medicis and MURST 40% Modelli della computazione e dei linguaggi di programmazione.

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References

  1. E. Astesiano and M. Cerioli. Non-strict don't care algebras and specifications. In S. Abramsky and T.S.E. Maibaum, editors, Proceedings of TAPSOFT'91, number 493 in Lecture Notes in Computer Science, pages 121–142, Berlin, 1992. Springer Verlag.

    Google Scholar 

  2. E. Astesiano and M. Cerioli. Free objects and equational deduction for partial conditional specifications. Theoretical Computer Science, 1995. To appear.

    Google Scholar 

  3. E. Astesiano and M. Cerioli. Relationships between logical frames. In Recent Trends in Data Type Specification, number 655 in Lecture Notes in Computer Science, pages 126–143, Berlin, 1993. Springer Verlag.

    Google Scholar 

  4. E. Astesiano and M. Cerioli. Multiparadigm specification languages: a first attempt at foundations. In D.J. Andrews, J.F. Groote, and C.A. Middelburg, editors, Semantics of Specification Languages (SoSL'93), Workshops in Computing, pages 168–185. Springer Verlag, 1994.

    Google Scholar 

  5. J.A. Bergstra and J.V. Tucker. The inescapable stack: an exercize in algebraic specification with total functions. Technical Report P8804, University of Amsterdam; Programming Research Group, 1988.

    Google Scholar 

  6. G. Bernot and P. Le Gall. Label algebras: a systematic use of terms. In Recent Trends in Data Type Specification, number 655 in Lecture Notes in Computer Science, pages 144–163, Berlin, 1993. Springer Verlag.

    Google Scholar 

  7. P. Burmeister. A Model Theoretic Oriented Approach to Partial Algebras. Akademie Verlag, Berlin, 1986.

    Google Scholar 

  8. M. Cerioli. Relationships between Logical Formalisms. PhD thesis, Universities of Geneva, Pisa and Udine, 1993. Available as internal report of Pisa University, TD-4/93.

    Google Scholar 

  9. R. Diaconescu. The logic of Horn clauses is equational. Submitted for publication, 1992.

    Google Scholar 

  10. J.A. Goguen and R. Diaconescu. A survey of order sorted algebra. Draft, 1992.

    Google Scholar 

  11. V. Manca, A. Salibra, and G. Scollo. Equational type logic. Theoretical Computer Science, 77:131–159, 1990. Special Issue dedicated to AMAST'89.

    Article  Google Scholar 

  12. A. Mégrelis. Algèbre galactique — Un procédé de calcul formel, relatif aux semi-functions, à l'inclusion et à légalité. PhD thesis, University of Nancy I, 1990.

    Google Scholar 

  13. P. Mosses. Unified algebras and institutions. In Proceedings of 4th Annual IEEE Symposium on Logic in Computer Science, pages 304–312, 1989.

    Google Scholar 

  14. P. Mosses. The use of sorts in algebraic specifications. In Recent Trends in Data Type Specification, number 655 in Lecture Notes in Computer Science, pages 66–92, Berlin, 1993. Springer Verlag.

    Google Scholar 

  15. A. Poigné. Partial algebras, subsorting, and dependent types: Prerequisites of error handling in algebraic specifications. In Recent Trends in Data Type Specification, number 332 in Lecture Notes in Computer Science, pages 208–234, Berlin, 1987. Springer Verlag.

    Google Scholar 

  16. H. Reichel. Initial Computability, Algebraic Specifications, and Partial Algebras. Akademie Verlag, 1986.

    Google Scholar 

  17. A. Salibra and G. Scollo. A soft stairway to institutions. In Recent Trends in Data Type Specification, number 655 in Lecture Notes in Computer Science, pages 310–329, Berlin, 1992. Springer Verlag.

    Google Scholar 

  18. D. Sannella and A. Tarlecki. Specifications in an arbitrary institution. Information and Computation, 76:165–210, 1988.

    Article  Google Scholar 

  19. M. Wirsing. Algebraic specification. In Handbook of Theoretical Computer Science. North Holland, 1990.

    Google Scholar 

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Authors and Affiliations

  1. DISI-Dipartimento di Informatica e Scienze dell'Informazione, Università di Genova, Viale Benedetto XV, 3-16132, Genova, Italy

    M. Cerioli

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  1. M. Cerioli
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Egidio Astesiano Gianna Reggio Andrzej Tarlecki

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© 1995 Springer-Verlag Berlin Heidelberg

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Cerioli, M. (1995). A lazy approach to partial algebras. In: Astesiano, E., Reggio, G., Tarlecki, A. (eds) Recent Trends in Data Type Specification. ADT COMPASS 1994 1994. Lecture Notes in Computer Science, vol 906. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0014428

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  • DOI: https://doi.org/10.1007/BFb0014428

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-59132-0

  • Online ISBN: 978-3-540-49198-9

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