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Expressing program developments in a design calculus

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Logic of Programming and Calculi of Discrete Design

Part of the book series: NATO ASI Series ((NATO ASI F,volume 36))

Abstract

The present paper describes a step in the study of means to express software developments. This study is also related to approaches where programs are extracted from proofs, and it is influenced by the spirit and the techniques of constructive logic.

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References

  • Abrial, J.R., Programming as a mathematical exercise, in: C.A.R. Hoare and J.C. Shepherdson (eds.), Mathematical Logic and Programming languages, Prentice-Hall, 1985.

    Google Scholar 

  • Bauer, F., et al., The Munich Project CIP, Vol I, LNCS183, Springer, 1985.

    Book  MATH  Google Scholar 

  • Bourbaki, N., Théorie des Ensembles, Hermann, Paris, 1970.

    MATH  Google Scholar 

  • Burstall, R.M., and J.A. Darlington, A transformation system for developing recursive programs, J ACM 24, 1(1977)44–67.

    Article  MathSciNet  MATH  Google Scholar 

  • Burstall, R.M., and B. Lampson, A kernel language for abstract datatypes and modules, Proc. Symp. on Semantics of Data Types, LNCS173, Springer, 1984.

    Google Scholar 

  • Cardelli, L., A polymorphic λ-calculus with type: type, RIO, Digital Systems Research Center, Palo Alto CA, 1986.

    Google Scholar 

  • Coquand, Th., and G. Huet, Constructions: a higher order proof system, EURO-CAL85, LNCS203, Springer, 1985.

    Google Scholar 

  • Constable, R.L., and al., Implementing Mathematics with the Nuprl Proof Development System, Prentice Hall, 1986.

    Google Scholar 

  • Curry, H.B., and R. Feys, Combinatory Logic Vol I, North-Holland, 1958.

    Google Scholar 

  • de Bruijn, N.G., Lambda-calculus notation with nameless dummies, Indag. Math. 84, 5(1972),381–392.

    Google Scholar 

  • de Bruijn, N.G., A survey of the project Automath, in: J.P. Seldin and J.R. Hindley (eds.), To H.B.Curry: Essays in Combinatory Logic, Lambda Calculus and Formalism, Academic Press, 1980.

    Google Scholar 

  • de Groote, Ph., Peirce-like formalization of intuitionistic propositional logic, RR86–12, Unité d’Informatique, University of Louvain, 1986.

    Google Scholar 

  • de Groote, Ph., Fatima A. Hussain, R. Jacquart, S. Jähnichen, T.T. Nguyen, M. Sintzoff, and M. Weber, Requirements and feasibility studies for a development language, Esprit510(ToolUse)-T32, RR86–06, Unité d’Informatique, University of Louvain, 1986.

    Google Scholar 

  • Delsarte, Ph., D. Snyers and A. Thayse, Preuves de théorèmes basées sur des propositions de la logique de Boole, C.R. 5ème Congrès Reconnaissance des Formes et Intelligence Artiûcielle, AFCET, Paris, 1985, 869–879.

    Google Scholar 

  • Ehrich, H.D., On the theory of specification, implementation, and parametrization of abstract data types, JACM 29, 1(1982), 206–227.

    Article  MathSciNet  MATH  Google Scholar 

  • Goad, Ch.A., Computational uses of the manipulation of formal proofs, Ph.D. thesis, Computer Sci. Dept, Stanford University, 1980.

    Google Scholar 

  • Gries, D., The Science of Programming, Springer, 1981.

    MATH  Google Scholar 

  • Hanna, F.K., and N. Daeche, Purely functional implementation of a logic, Proc. 8th Intern. Conf. on Automated Deduction, Springer LNCS 230, 1986, 598–607.

    Google Scholar 

  • Hermes, H., Introduction to Mathematical Logic, Springer, 1973.

    MATH  Google Scholar 

  • Hindley, J.R., and J.P. Seldin, Introduction to Combinators and λ-Calculus, Cambridge University Press, 1986.

    Google Scholar 

  • Jähnichen S., Fatima A. Hussain, and M. Weber, Program development using a design calculus, Proc. ESPRIT Technical Week 86, North-Holland, 1986.

    Google Scholar 

  • Jones, C.B., Systematic Software development using VDM, Prentice-Hall, 1986.

    MATH  Google Scholar 

  • Kleene, S.C., Introduction to Metamathematics, North-Holland, 1952.

    MATH  Google Scholar 

  • Manna, Z., and R. Waldinger, Special relations in automated deduction, JACM 33,1 (1986), 1–59.

    Article  MathSciNet  MATH  Google Scholar 

  • Martin-Löf, P., Amendment and addition to the intuitionistic theory of types, Lecture, University of Louvain, April 1986.

    Google Scholar 

  • Miller, D., and A. Felty, An integration of resolution and natural deduction theorem proving, Proc. 5th Natl Conf. on Artif. Intelligence AAAI86, Morgan Kaufmann, Los Altos CA, 1986, 198–202.

    Google Scholar 

  • Milner, R., The use of machines to assist in rigorous proof, in: C.A.R. Hoare and J.C. Shepherdson (eds.), Mathematical Logic and Programming languages, Prentice-Hall, 1985.

    Google Scholar 

  • Mitchell, J.C., Representation independence and data abstraction, Proc. 13th Conf. on Principles of Progr. Languages, ACM, 1986.

    Google Scholar 

  • Murray, N., Completely non-clausal theorem proving, J. Artif. Intelligence 18(1982), 67–85.

    Article  MATH  Google Scholar 

  • Nait Abdallah, M.A., Procedures in Horn-clause programming, 3rd Intern. Conf. on Logic Programming, Springer LNCS225, 1986, 433–447.

    Google Scholar 

  • Nguyen, T.T., Divide and conquer strategy, RR85–11, Unité d’Informatique, University of Louvain, 1985.

    Google Scholar 

  • Nguyen, T.T., Development of iterative programs, RR86–10, Unité d’Informatique, University of Louvain, 1986.

    Google Scholar 

  • Nordström, B., Programming in constructive set theory: some examples, Proc. Conf. on Functional Programming Languages and Computer Architecture, ACM, 1981.

    Google Scholar 

  • Novikov, P.S., Konstruktivnaya Matematicheskaya Logika s Tochki Zreniya Klassicheskoi, Nauka, 1977.

    Google Scholar 

  • Peirce, Ch.S., Existential Graphs, in: Ch. Hartshorne and P. Weiss (eds.), Collected Papers of Charles Saunders Peirce, Vol. IV, Harvard University Press, 4th ed., 1974.

    Google Scholar 

  • Pepper, P., A simple calculus for program transformations, Institut für Informatik, Technical University of Munich, 1984.

    Google Scholar 

  • Schütte, K., Proof Theory, Springer, 1977.

    Book  MATH  Google Scholar 

  • Sintzoff, M., Suggestions for composing and specifying program design decisions, Proc. 4th Symp. on Programming, LNCS70, Springer, 1980.

    Google Scholar 

  • Sintzoff, M., Proof-oriented and applicative valuations in definitions of algorithms, Proc. Conf. on Functional Languages and Computer Architecture, ACM, 1981.

    Google Scholar 

  • Sintzoff, M., Understanding and expressing software construction, in: P. Pepper (ed.), Program Transformation and Programming Environments, Springer, 1984.

    Google Scholar 

  • Sintzoff, M., Exploratory proposals for a calculus of software development, RR84–2, Unité d’Informatique, University of Louvain; Workshop on Combining Specification Methods, Denmark, 1984.

    Google Scholar 

  • Sintzoff, M., Desiderata for a design calculus, RR85–13, Unité d’Informatique, University of Louvain; Workshop on Specification and Derivation of Programs, Sweden, 1985.

    Google Scholar 

  • Smith, D.R., Top-down synthesis of divide-and-conquer algorithms, J. Artif, Intelligence 27, 1 (1985).

    Article  MATH  Google Scholar 

  • Sowa, J.F., Conceptual Structures, Addison Wesley, 1984.

    MATH  Google Scholar 

  • Traugott, J., Nested resolution, Proc. 8th Intern, Conf. Automated Deduction, Springer LNCS 230, 1986, 394–402.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Unité d’Informatique, Université Catholique de Louvain, place Sainte-Barbe 2, B-1348, Louvain-la-Neuve, Belgium

    Michel Sintzoff

Authors
  1. Michel Sintzoff
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Editor information

Editors and Affiliations

  1. Fakultät für Mathematik und Informatik, Universität Passau, Postfach 2540, 8390, Passau, Federal Republic of Germany

    Manfred Broy

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© 1987 Springer-Verlag Berlin Heidelberg

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Sintzoff, M. (1987). Expressing program developments in a design calculus. In: Broy, M. (eds) Logic of Programming and Calculi of Discrete Design. NATO ASI Series, vol 36. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-87374-4_13

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  • DOI: https://doi.org/10.1007/978-3-642-87374-4_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-87376-8

  • Online ISBN: 978-3-642-87374-4

  • eBook Packages: Springer Book Archive

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