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Category Theory and Computer Programming pp 313–333Cite as

A study in the foundations of programming methodology: Specifications, institutions, charters and parchments

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 240))

Abstract

The theory of institutions formalizes the intuitive notion of a "logical system." Institutions were introduced (1) to support as much computer science as possible independently of the underlying logical system, (2) to facilitate the transfer of results (and artifacts such as theorem provers) from one logical system to another, and (3) to permit combining a number of different logical systems. In particular, programming-in-the-large (in the style of the Clear specification language) is available for any specification or "logical" programming language based upon a suitable institution. Available features include generic modules, module hierarchies, "data constraints" (for data abstraction), and "multiplex" institutions (for combining multiple logical systems). The basic components of an institution are: a category of signatures (which generally provide symbols for constructing sentences); a set (or category) of Σ-sentences for each signature Σ; a category (or set) of Σ-models for each Σ; and a Σ-satisfaction relation, between Σ-sentences and Σ-models, for each Σ. The intuition of the basic axiom for institutions is that truth (i.e., satisfaction) is invariant under change of notation. This paper enriches institutions with sentence morphisms to model proofs, and uses this to explicate the notion of a logical programming language.

To ease constructing institutions, and to clarify various notions, this paper introduces two further concepts. A charter consists of an adjunction, a "base" functor, and a "ground" object; we show that "chartering" is a convenient way to "found" institutions. Parchments provide a notion of sentential syntax, and a simple way to "write" charters and thus get institutions. Parchments capture the insight that the syntax of logic is an initial algebra. Everything is illustrated with the many-sorted equational institution. Parchments also explicate the sense of finitude that is appropriate for specifications. Finally, we introduce generalized institutions, which generalize both institutions and Mayoh's "galleries", and we introduce corresponding generalized charters and parchments.

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References

  1. Abrial, J. R., S. A. Schuman and B. Meyer. Specification Language (draft). 1979. Cambridge University.

    Google Scholar 

  2. Barwise, Jon. Axioms for Abstract Model Theory. Annals of Mathematical Logic 7:221–265, 1974.

    Google Scholar 

  3. Beierle, Christoph and Angelika Voss. Implementation Specifications. Technical Report 147/85, Universität Kaiserslautern, 1985.

    Google Scholar 

  4. Bjorner, Dines and Cliff Jones. The Vienna Development Method. Lecture Notes in Computer Science 61, 1978.

    Google Scholar 

  5. Burstall, Rod and Joseph Goguen. Putting Theories together to Make Specifications. Proceedings, Fifth International Joint Conference on Artificial Intelligence 5:1045–1058, 1977.

    Google Scholar 

  6. Burstall, Rod and Joseph Goguen. The Semantics of Clear, a Specification Language. In Lecture Notes in Computer Science. Volume 86: Proceedings of the 1979 Copenhagen Winter School on Abstract Software Specification, pages 292–332. Springer-Verlag, 1980.

    Google Scholar 

  7. Burstall, Rod and Joseph Goguen. An Informal Introduction to Specifications using Clear. In Robert Boyer and J Moore (editors), The Correctness Problem in Computer Science, pages 185–213. Academic Press, 1981. Reprinted in Software Specification Techniques, edited by N. Gehani and A. D. McGettrick, Addison-Wesley, 1985, pages 363–390.

    Google Scholar 

  8. Futatsugi, Kokichi, Joseph Goguen, Jean-Pierre Jouannaud and José Meseguer. Principles of OBJ2. In Proceedings, Symposium on Principles of Programming Languages, pages 52–66. Association for Computing Machinery, 1985.

    Google Scholar 

  9. Goguen, Joseph. Mathematical Representation of Hierarchically Organized Systems. In E. Attinger (editor), Global Systems Dynamics, pages 112–128. S. Karger, 1971.

    Google Scholar 

  10. Goguen, Joseph. Semantics of Computation. In Proceedings, First International Symposium on Category Theory Applied to Computation and Control, pages 234–249. University of Massachusetts at Amherst, 1974. Also published in Lecture Notes in Computer Science, Volume 25, Springer-Verlag, 1975, pages 151–163.

    Google Scholar 

  11. Goguen, Joseph. Reusing and Interconnecting Software Components. IEEE Computer 19(2):16–28, February, 1986.

    Google Scholar 

  12. Goguen, Joseph and Rod Burstall. Some Fundamental Algebraic Tools for the Semantics of Computation, Part 1: Comma Categories, Colimits, Signatures and Theories. Theoretical Computer Science 31(2):175–209, 1984.

    Google Scholar 

  13. Goguen, Joseph and Rod Burstall. Institutions: Abstract Model Theory for Computer Science. Technical Report CSLI-85-30, Center for the Study of Language and Information, Stanford University, 1985. Also submitted for publication; a preliminary version appears in Proceedings, Logics of Programming Workshop, edited by Edward Clarke and Dexter Kozen, volume 164, Springer-Verlag Lecture Notes in Computer Science, pages 221–256, 1984.

    Google Scholar 

  14. Goguen, Joseph and Susanna Ginali. A Categorical Approach to General Systems Theory. In George Klir (editor), Applied General Systems Research, pages 257–270. Plenum, 1978.

    Google Scholar 

  15. Goguen, Joseph and José Meseguer. Completeness of Many-sorted Equational Logic. Houston Journal of Mathematics 11(3):307–334, 1985. Preliminary versions have appeared in: SIGPLAN Notices, July 1981, Volume 16, Number 7, pages 24–37, and January 1982, Volume 17, Number 1, pages 9–17; SRI Technical Report CSL-135, May 1982; and Technical Report CSLI-84-15, Center for the Study of Language and Information, Stanford University, September 1984.

    Google Scholar 

  16. Goguen, Joseph and José Meseguer. Eqlog: Equality, Types, and Generic Modules for Logic Programming. In Douglas DeGroot and Gary Lindstrom (editors), Functional and Logic Programming, pages 295–363. Prentice-Hall, 1986. An earlier version appears in the Journal of Logic Programming, volume 1, number 2, pages 179–210, September 1984.

    Google Scholar 

  17. Goguen, Joseph and José Meseguer. Object-Oriented Programming as Reflective Equational Programming. In preparation. 1986

    Google Scholar 

  18. Goguen, Joseph, James Thatcher, Eric Wagner and Jesse Wright. Initial Algebra Semantics and Continuous Algebras. Journal of the Association for Computing Machinery 24(1), January, 1977.

    Google Scholar 

  19. Lloyd, J. W. Foundations of Logic Programming. Springer-Verlag, 1984.

    Google Scholar 

  20. Lyndon, Roger C. Mathematical Studies. Volume 6: Notes on Logic. Van Nostrand, 1966.

    Google Scholar 

  21. Mac Lane, Saunders. Categories for the Working Mathematician. Springer-Verlag, 1971.

    Google Scholar 

  22. Mayoh, Brian. Galleries and Institutions. Technical Report DAIMI PB-191, Aarhus University, 1985. This contains a number of reports, some of which have been presented at various conferences.

    Google Scholar 

  23. Reichel, Horst. Structural Induction on Partial Algebras. Akademie-Verlag, 1984.

    Google Scholar 

  24. Sanella, Donald and Andrzej Tarlecki. On Observational Equivalence and Algebraic Specification. In Lecture Notes in Computer Science. Volume 185: Mathematical Foundations of Software Development, volume 1: Proceedings of the Colloquium on Trees in Algebra and Programming, pages 308–322. Springer-Verlag, 1985. Also appeared as University of Edinburgh, Department of Computer Science Technical Report CSR-172-84.

    Google Scholar 

  25. Sanella, Donald and Andrzej Tarlecki. Building Specifications in an Arbitrary Institution. In Giles Kahn, David MacQueen and Gordon Plotkin (editor), Lecture Notes in Computer Science. Volume 173: Proceedings, International Symposium on the Semantics of Data Types, pages 337–356. Springer-Verlag, 1985. Also appeared as Internal Report CSR-184-85, University of Edinburgh, Department of Computer Science.

    Google Scholar 

  26. Tarlecki, Andrzej. Free Constructions in Algebraic Institutions. In Lecture Notes in Computer Science. Volume 176: Proceedings, Int. Symp. Math. Foundations of Computer Science, pages 526–534. Springer-Verlag, 1984. Extended version, University of Edinburgh Computer Science Department Report CSR-149-83, and revised version ‘On the existence of Free Models in Abstract Algebraic Institutions', September 1984.

    Google Scholar 

  27. van Emden, Maartin H. and Robert Kowalski. The Semantics of Predicate Logic as a Programming Language. Journal of the Association for Computing Machinery 23(4):733–742, 1976.

    Google Scholar 

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Authors and Affiliations

  1. SRI International, the University of Edinburgh, UK

    Joseph A. Goguen & R. M. Burstall

  2. Center for the the Study of Language and Information at Stanford University, USA

    Joseph A. Goguen & R. M. Burstall

Authors
  1. Joseph A. Goguen
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  2. R. M. Burstall
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David Pitt Samson Abramsky Axel Poigné David Rydeheard

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© 1986 Springer-Verlag Berlin Heidelberg

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Goguen, J.A., Burstall, R.M. (1986). A study in the foundations of programming methodology: Specifications, institutions, charters and parchments. In: Pitt, D., Abramsky, S., Poigné, A., Rydeheard, D. (eds) Category Theory and Computer Programming. Lecture Notes in Computer Science, vol 240. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-17162-2_131

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  • DOI: https://doi.org/10.1007/3-540-17162-2_131

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