Abstract
A set of operations for constructing algebraic specifications in an arbitrary logical system is presented. This builds on the framework provided by Goguen and Burstall's work on the notion of an institution as a formalisation of the concept of a logical system for writing specifications. We show how to introduce free variables into the sentences of an arbitrary institution and how to add quantifiers which bind them. We use this foundation to define a set of primitive operations for building specifications in an arbitrary institution based loosely on those in the ASL kernel specification language. We examine the set of operations which results when the definitions are instantiated in an institution of first-order logic and compare these with the operations found in existing specification languages. The result of instantiating the operations in an institution of partial first-order logic is also discussed.
On leave from institute of Computer Science, Polish Academy of Sciences, Warsaw.
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8 References
Goguen, J.A., Thatcher, J.W. and Wagner, E.G. An initial algebra approach to the specification, correctness, and implementation of abstract data types. IBM research report RC 6487. Also in: Current Trends in Programming Methodology. Vol. 4: Data Structuring (R. T. Yeh, ed.). Prentice-Hall. pp. 80–149 (1978).
Goguen, J.A., Thatcher, J.W., Wagner, E.G. and Wright, J.B. Initial algebra semantics and continuous algebras. JACM 24, 1 pp. 68–95.
Ehrig, H., Kreowski, H.-J., Thatcher, J.W., Wagner, E.G. and Wright, J.B. Parameterized data types in algebraic specification languages (short version). Proc. 7th ICALP. Noordwijkerhout, Netherlands. Springer LNCS 85.
Arbib, M.A. and Manes, E.G. Arrow, Structures and Functors: the Categorical Imperative. Academic Press.
Barwise, K.J. Axioms for abstract model theory. Annals of Math. Logic 7 pp. 221–265.
Bauer, F.L. et al (the CIP Language Group) Report on a wide spectrum language for program specification and development (tentative version). Report TUM-18104, Technische Univ. München.
Benecke, K. and Reichel, H. Equational partiality. Algebra Universalis 16 pp. 219–232.
Bergstra, J.A. and Meyer, J.J. I/O computable data structures. SIGPLAN Notices 16, 4 pp. 27–32.
Bloom, S.L. and Wagner, E.G. Many-sorted theories and their algebras, with examples from computer science (Working paper). US-French Joint Symp. on the Applications of Algebra to Language Definition and Compilation, Fontainebleau.
Broy, M. and Wirsing, M. Partial abstract types. Acta Informatica 18 pp. 47–64.
Burmeister, P. Partial algebras — survey of a unifying approach towards a two-valued model theory for partial algebras. Algebra Universalis 15 pp. 306–358.
Burstall, R.M. and Goguen, J.A. The semantics of Clear, a specification language. Proc. of Advanced Course on Abstract Software Specifications, Copenhagen. Springer LNCS 86, pp. 292–332.
Burstall, R.M. and Goguen, J.A. An informal introduction to specifications using Clear. In: The Correctness Problem in Computer Science (R.S. Boyer and J.S. Moore eds.), Academic Press. pp. 185–213.
Ehrig, H., Thatcher, J.W., Lucas, P. and Zilles, S.N. Denotational and initial algebra semantics of the algebraic specification language LOOK. Draft report, IBM research.
Ehrig, H., Wagner, E.G. and Thatcher, J.W. Algebraic specifications with generating constraints. Proc. 10th ICALP. Barcelona. Springer LNCS 154, pp. 188–202.
Giarratana, V., Gimona, F. and Montanarl, U. Observability concepts in abstract data type specification. Proc. 5th MFCS, Gdansk. Springer LNCS 45.
Gogolla, M., Drosten, K., Lipeck, U. and Ehrich, H.D. Algebraic and operational semantics of specifications allowing exceptions and errors. Fb. 140, Abteilung Informatik. Univ. of Dortmund.
Goguen, J.A. Abstract errors for abstract data types. Proc. IFIP Working Conf. on the Formal Description of Programming Concepts, New Brunswick, New Jersey.
Goguen, J.A. Order sorted algebras: exceptions and error sorts, coercions and overloaded operators. Semantics and Theory of Computation Report No. 14, Dept. of Computer Science, UCLA.
Goguen, J.A. and Burstall, R.M. Some fundamental algebraic tools for the semantics of computation. Research Report No. 5. Dept. of Artificial Intelligence. Univ. of Edinburgh: to appear in TCS.
Goguen, J.A. and Burstall, R.M. Introducing institutions. Proc. Logics of Programming Workshop (E. Clarke, ed.), CMU.
Goguen, J.A. and Meseguer, J. Universal realization, persistent interconnection and implementation of abstract modules. Proc. 9th ICALP, Aarhus, Denmark. Springer LNCS 140, pp. 265–281.
Goguen, J.A. and Meseguer, J. An initiality primer. Draft report. SRI International.
Kamin, S. Final data types and their specification. TOPLAS 5, 1 pp. 97–121.
Liskov, B.H. and Berzins, V. An appraisal of program specifications. Computation Structures Group memo 141-1, Laboratory for Computer Science, MIT.
MacLane, S. Categories for the Working Mathematician. Springer.
Mahr, B. and Makowsky, J.A. Characterizing specification languages which admit initial semantics. To appear in TCS.
Pepper, P. On the correctness of type transformations. Talk at 2nd Workshop on Theory and Applications of Abstract Data Types, Passau.
Reichel, H. Behavioural equivalence — a unifying concept for initial and final specification methods. Proc. 3rd Hungarian Computer Science Conf., Budapest. pp. 27–39.
Reichel, H. Structural induction on partial algebras. Akademie-Verlag. Berlin.
Sannella, D.T. Behavioural equivalence and algebraic specification (extended abstract). Workshop on Semantics of Programming Languages. Goteborg, pp. 162–166.
Sannella, D.T. and Wirsing, M. A kernel language for algebraic specification and implementation. Long version: Report CSR-131-83. Dept. of Computer Science, Univ. of Edinburgh: Extended abstract in: Proc. Intl. Conf. on Foundations of Computation Theory, Borgholm, Sweden, Springer LNCS 158, pp. 413–427.
Schoett, O. A theory of program modules, their specification and implementation (extended abstract). Report CSR-155-83, Dept. of Computer Science, Univ. of Edinburgh.
Sufrin, B. Formal specification of a display-oriented text editor. Science of Computer Programming 1 pp. 157–202.
Tarlecki, A. Free constructions in algebraic institutions. Long version: Report CSR-149-83, Dept. of Computer Science, Univ. of Edinburgh: Extended abstract in: Proc. MFCS 84. Prague. Springer LNCS (to appear).
Tarlecki, A. Free constructions in abstract algebraic institutions. Draft report, Univ. of Edinburgh.
Wand, M. Final algebra semantics and data type extensions. JCSS 19 pp. 27–44.
Wirsing, M. Structured algebraic specifications. Proc. AFCET Symp. on Mathematics for Computer Science, Paris, pp. 93–107.
Wirsing, M. Structured algebraic specifications: a kernel language. Habilitation thesis. Technische Univ. München.
Zilles, S.N., Lucas, P. and Thatcher, J.W. A look at algebraic specifications. IBM research report RJ 3568.
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Sannella, D., Tarlecki, A. (1984). Building specifications in an arbitrary institution. In: Kahn, G., MacQueen, D.B., Plotkin, G. (eds) Semantics of Data Types. SDT 1984. Lecture Notes in Computer Science, vol 173. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-13346-1_17
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DOI: https://doi.org/10.1007/3-540-13346-1_17
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