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Admissibility of fixed-point induction in first-order logic of typed theories

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International Symposium on Theoretical Programming

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 5))

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References

  1. Gentzen, G., Untersuchungen über das logische Schließen, Mathemtische Zeitschrift, 39 (1934–5).

    Google Scholar 

  2. Igarashi, S., An axiomatic approach to the equivalence problems of algorithms with applications, Reports of Computer Centre, University of Tokyo, 1, No. 1 (1968).

    Google Scholar 

  3. Igarashi, S., Semantic of Algol-like statements, Symposium on Semantics of Algorithmic Languages, Engeler, E. (ed.), Lecture Notes in Mathematics, 188, Springer-Verlag (1971).

    Google Scholar 

  4. McCarthy, J., On adding quantifiers to LCF, private communication, Stanford (1972).

    Google Scholar 

  5. McCarthy, J., & Painter, J., Correctness of a compiler for arithmetic expressions, Proceedings of a Symposium in Applied Mathematics, 19, Schwartz, J.T. (ed.), American Mathematical Society, (1967).

    Google Scholar 

  6. Milner, R., Implementation and applications of Scott's logic for computable functions, Proceedings of a Conference on Proving Assertions about Programs, New Mexico State University, SIGPLAN Notices 7 (1972).

    Google Scholar 

  7. Milner, R., Private Communication, Stanford (1972).

    Google Scholar 

  8. Milner, R. and Weyhrauch, R., Proving compiler correctness in a mechanized logic, Machine Intelligence 7, Michie, D. (ed.) Edinburgh University Press (1972, to appear).

    Google Scholar 

  9. Park, D., Fixpoint induction and proofs of program properties, Machine Intelligence 5, Meltzer, B. and Michie, D. (eds.), Edinburgh University Press (1970).

    Google Scholar 

  10. Scott, D., Private Communication, Oxford (1969).

    Google Scholar 

  11. Shoenfield, J.R., Mathematical Logic, Addison-Wesley Publ. Co. (1967).

    Google Scholar 

  12. Wang, H., Logic of many-sorted theories, Journal of Symbolic Logic, 17, No. 2 (1952).

    Google Scholar 

  13. Weyhrauch, R. and Milner, R., Program semantics and correctness in a mechanized logic, Proceedings of USA-Japan Computer Conference, Tokyo, (1972, to appear).

    Google Scholar 

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Andrei Ershov Valery A. Nepomniaschy

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© 1974 Springer-Verlag Berlin Heidelberg

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Igarashi, S. (1974). Admissibility of fixed-point induction in first-order logic of typed theories. In: Ershov, A., Nepomniaschy, V. (eds) International Symposium on Theoretical Programming. Lecture Notes in Computer Science, vol 5. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-06720-5_22

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  • DOI: https://doi.org/10.1007/3-540-06720-5_22

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-06720-7

  • Online ISBN: 978-3-540-38012-2

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