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An overview of compositional translations

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Compositionality: The Significant Difference (COMPOS 1997)

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Abstract

Translations from one language to another arise in many fields of science: in computer science (compilers, data base views), logic (embeddings), natural language (translation), and philosophy (Montague grammar). In all these fields one can find the same method: compositional translation, or in mathematical formulation, algebraic translation. In some fields it is a standard method, in other fields a rare approach. The aim of this paper is to give an overview of compositional translations. Special attention will be given to the notion ‘correct translation’ (which can be formalized by commutativity of a diagram). Furthermore, the first steps will be will be made towards a mathematical theory of translating.

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References

  1. F. Bancilhon and N. Spyratos. Update semantics of relational views. ACM Transactions on data bases, 6:557–575, 1981.

    Article  MATH  Google Scholar 

  2. R.M. Burstall and P.J. Landin. Programs and their proofs: an algebraic approach. In B. Meltzer and D. Michie, editors, Machine Intelligence, volume 5, chapter 2, pages 17–43. American Elsevier, New York, 1969.

    Google Scholar 

  3. L.M. Chirica. Contributions to compiler correctness. PhD thesis, Dept. of Computer Science, University of California, Los Angeles, 1976. report UCLA-ENG-7697.

    Google Scholar 

  4. D. van Dalen. Intuitionistic logic. In D. Gabbay and F. Guenthner, editors, Handbook of philosphical logic. Vol III. Alternatives to classical logic, number 166 in Synthese Library, chapter 4, pages 225–339. Reidel. Dodrecht, 1986.

    Google Scholar 

  5. D. Davidson and G. Harman, editors. Semantics of natural language. Number 40 in Synthese library. Reidel, Dordrecht, 1972.

    Google Scholar 

  6. P. Dybjer. Using domain algebras to prove the correctness of a compiler. In K. Mehlhorn, editor, STACS 85, 2nd annual symposium on theoretical aspects of computer science, Saarbrücken, 1985, number 182 in Lecture notes in computer science, pages 98–108, Berlin, 1985. Springer.

    Google Scholar 

  7. P. van Emde Boas and T.M.V. Janssen. The impact of Frege’s principle of compositionality for the semantics of programming and natural language. In “Begriffsschrift”. Jenaer Frege-Conferenz 1979, pages 110–129, Jena, 1979. Friedrich-Schiller Universität.

    Google Scholar 

  8. R.L. Epstein. The semantic foundation of logic. vol 1. Propositional logic. Number 35 in Nijhoff international philosophy series. Nijhoff/Kluwer, Dordrecht, 1990. Second edition published by Oxford University Press, Oxford.

    Google Scholar 

  9. J. Goguen and R. Burstall. Institutions: abstract model theory for specification and programming. Journal of the Association for Computing Machinery, 39(1):95–146, 1992.

    MATH  MathSciNet  Google Scholar 

  10. J.A. Goguen and G. Malcolm. Algebraic semantics of imperative programs. Foundations of computing. The MIT Press, Cambridge, Mass., 1996.

    Google Scholar 

  11. J. Groenendijk and M. Stokhof. Semantic analysis of wh-complements. Linguistics and Philosophy, 5:175–233, 1982.

    Google Scholar 

  12. H.-K. Hung and J. I. Zucker. Semantics of pointers, referencing and dereferencing with intensional logic. In Proc. 6th annual IEEE symposium on Logic in Computer Science, pages 127–136, Los Almolitos, California, 1991. IEEE Computer Society Press.

    Chapter  Google Scholar 

  13. T.M.V. Janssen. Foundations and Applications of Montague Grammar: part 1, Philosophy, Framework, Computer Science. Number 19 in CWI tract. Centre for Mathematics and Computer Science, Amsterdam, 1986.

    Google Scholar 

  14. T.M.V. Janssen. Compositionality (with an appendix by B. Partee). In J. van Benthem and A. ter Meulen, editors, Handbook of logic and language, chapter 7, pages 417–473. Elsevier, Amsterdam and The MIT Press, Cambridge, Mass., 1997.

    Chapter  Google Scholar 

  15. T.M.V. Janssen. Algebraic translations, correctness and algebraic compiler construction. Journal of theoretical computer science, 1998. to appear.

    Google Scholar 

  16. T.M.V. Janssen and P. van Emde Boas. The expressive power of intensional logic in the semantics of programming languages. In J. Gruska, editor, Mathematical foundations of computer science 1977 (Proc. 6th. symp. Tatranska Lomnica), number 53 in Lecture notes in computer science, pages 303–311, Berlin, 1977. Springer.

    Google Scholar 

  17. T.M.V. Janssen and P. van Emde Boas. On the proper treatment of referencing, dereferencing and assignment. In A. Salomaa and M. Steinby, editors, Automata, languages and programming (Proc. 4th. coll. Turku), number 52 in Lecture notes in computer science, pages 282–300, Berlin, 1977. Springer.

    Google Scholar 

  18. D. Lewis. General semantics. Synthese, 22:18–67, 1970. Reprinted in [5, pp. 169/2-248] and in [31, pp. 1/2-50].

    Article  MATH  Google Scholar 

  19. A. Mazurkiewicz. Parallel recursive program schemes. In J. Becvar, editor, Mathematical foundations of computer science (4 th. coll., Marianske Lazne), number 32 in Lecture notes in computer science, pages 75–87, Berlin, 1975. Springer.

    Google Scholar 

  20. E. Meijer. Calculating compilers. PhD thesis, Katholieke University Nijmegen, Nijmegen, 1992. ISBN 90-9004673-9.

    Google Scholar 

  21. H. J. Milner. Processes: a mathematical model of computing agents. In Rose H.E and J.C. Shepherdson (eds.), editors, Logic colloquium’ 73 (Bristol), number 80 in Studies in logic and the foundations of mathematics, pages 157–173, Amsterdam, 1975. North Holland.

    Google Scholar 

  22. R. Milner and R. Weyrauch. Proving compiler correctness in a mechanized logic. In B. Meltzer and D. Michie, editors, Machine Intelligence, volume 7, chapter 3, pages 51–70. American Elsevier, New York, 1972.

    Google Scholar 

  23. R. Montague. Universal grammar. Theoria, 36:373–398, 1970. Reprinted in [41, pp. 222/2-246].

    Article  MathSciNet  Google Scholar 

  24. R. Montague. The proper treatment of quantification in ordinary English. In K.J.J. Hintikka, J.M.E. Moravcsik, and P. Suppes, editors, Approaches to natural language, Synthese Library 49, pages 221–242. Reidel, Dordrecht, 1973. Reprinted in [41, pp. 247/2-270].

    Google Scholar 

  25. F.L. Morris. Advice on structuring compilers and proving them correct. In Proceedings ACM Symposium on principles of programming languages, Boston, 1973, pages 144–152. Association for Computing Machinery, 1973.

    Google Scholar 

  26. Y. Moscowitz and E. Shapiro. On the structural simplicity of machines and languages. Technical Report CS93-04, Weizman institute, dept. of appl. math. and comp. sc., Rehovot, Israel, 1993. to appear in ‘Annals of mathematics and artificial intelligence’.

    Google Scholar 

  27. P. Mosses. A constructive approach to compiler correctness. In N.D. Jones, editor, Semantics-directed compiler generation (Proc. Workshop, Aarhus), number 94 in Lecture notes in computer science, pages 189–210. Springer, Berlin, 1980.

    Google Scholar 

  28. P. Mosses. A constructive approach to compiler correctness. In J. de Bakker and J. van Leeuwen, editors, Automata, languages and programming (seventh colloquium, Noordwijkerhout), number 85 in Lecture notes in computer science, pages 449–469. Springer, Berlin, 1980.

    Google Scholar 

  29. M. Müller-Olm. Modular Compiler verification. Number 1283 in Lecture notes in computer science. Springer, Berlin, 1997.

    Google Scholar 

  30. E.J. Neuholt, editor. Formal description of programming language concepts, Proc, IFIP working conference on formal description of programming concepts St. Andrews, Canada 1977, Amsterdam, 1978.

    Google Scholar 

  31. B. Partee, editor. Montague grammar. Academic Press, New York, 1976.

    Google Scholar 

  32. B. Partee, A. ter Meulen, and R.E. Wall. Mathematical Methods in Linguistics. Number 30 in Studies in Linguistics and Philosophy. Kluwer, Dordrecht, 1990.

    MATH  Google Scholar 

  33. W. Polak. Compiler specification and verification. Number 124 in Lecture notes in computer science. Springer, Berlin, 1981.

    MATH  Google Scholar 

  34. M.T. Rosetta. Compositional Translation. The Kluwer International Series in Engineering and Computer Science 230. Kluwer, Dordrecht, 1994. (M.T. Rosetta = L. Appelo, T. Janssen, F. de Jong, J. Landsbergen (eds.)).

    MATH  Google Scholar 

  35. V. Royer. Transformations of denotational semantics in semantics directed compiler generation. In Proceedings of the SIGPLAN’ 86 symposium on compiler construction, SIGPLAN notices Vol. 21, Nr. 7, pages 68–73. Association for Computing Machinery, 1986.

    Article  Google Scholar 

  36. T. Rus. Algebraic construction of compilers. Theoretical Computer Science, 90:271–308, 1991.

    MATH  MathSciNet  Google Scholar 

  37. T. Rus. Algebraic processing of programming languages. In A. Nijholt, G. Scollo, and R. Steetskamp, editors, Algebraic methods in language processing AMILP’95, number 10 in Twente workshop In language technology, pages 1–41, Enschede, 1995. Universiteit Twente.

    Google Scholar 

  38. E. Shapiro. Separating concurrent languages with categories of language embeddings. In Proceedings of the 23 annual symposium on theory of computing (STOC’91, New Orleans), pages 198–208. ACM, 1991.

    Google Scholar 

  39. E. Shapiro. Embeddings among concurrent programming languages. In W. R Cleaveland, editor, Proc. third international conference on concurrency theory, Stony Brook 92, Springer lecture notes in computer science, pages 486–503, Berlin, 1992. Springer.

    Google Scholar 

  40. J.W. Thatcher, E.G. Wagner, and J.B. Wright. More on advice on structuring compilers and proving them correct. In H.A. Maurer, editor, Automata, languages and programming. (Proc. 6th. coll. Graz), number 71 in Lecture notes in computer science, Berlin, 1979. Springer.

    Google Scholar 

  41. R.H. Thomason. Formal Philosophy. Selected Papers of Richard Montague. Yale University Press, New Haven, 1974.

    Google Scholar 

  42. M. Tofte. Compiler generators. What they can do, what they might do, and what they will probably never do. Number 19 in EATCS monographs on theoretical computer science. Springer, Berlin, 1990.

    MATH  Google Scholar 

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Authors and Affiliations

  1. Computer Science, University of Amsterdam Plantage Muidergracht 24, 1018TV, Amsterdam, The Netherlands

    Theo M. V. Janssen

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  1. Theo M. V. Janssen
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Editors and Affiliations

  1. Department of Informatics and Applied Mathematics, Christian Albrechts University at Kiel, Preußerstr. 1-9, D-24105, Kiel, Germany

    Willem-Paul de Roever  & Hans Langmaack  & 

  2. Department of Applied Mathematics and Computer Science, Weizmann Institute of Science, P.O. Box 26, Rehovot, 76100, Israel

    Amir Pnueli

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Janssen, T.M.V. (1998). An overview of compositional translations. In: de Roever, WP., Langmaack, H., Pnueli, A. (eds) Compositionality: The Significant Difference. COMPOS 1997. Lecture Notes in Computer Science, vol 1536. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49213-5_12

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  • DOI: https://doi.org/10.1007/3-540-49213-5_12

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  • Print ISBN: 978-3-540-65493-3

  • Online ISBN: 978-3-540-49213-9

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