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  1. On derived rules of intuitionistic second order arithmetic 1977,Commentariorum
    Mathematicorum Universitatis Sancti Pauli, XXVI, pp.77-103
  2. A note on provable well-orderings in first order systems with infinitary
    inference rules, 1977,Tsukuba Journal of Mathematics, vol.1, pp.125-135
  3. Existence property by means of a normalization method, 1978, Commentariorum
    Mathematicorum Universitatis Sancti Pauli, XXVII, pp.97-100.
  4. Derived rules related to a constructive theory of metric spaces in intuitionistic
    higher order arithmetic without countable choice, 1980, Annals of Mathematical
    Logic, 19, pp.33-65
  5. On set theories in toposes, 1981, Logic Symposia, Hakone 1979 -1980, Springer
    Lecture Notes in Math. 891, Springer-Verlag, Muller, G.H., Takeuti, G., Tugue,
    T. (eds), pp.23-29
  6. A note on the bar induction rule, 1982, The L.E.J. Brouwer Centenary Symposium,
    North-Holland, Troelstra, A.S., van Dalen, D. (eds.), pp.149-163
  7. Extracting Lisp programs from constructive proofs: a formal theory of constructive
    mathematics based on Lisp, 1983, Publications of the Research Institute for
    Mathematical Sciences, Kyoto University, vol. 19, pp.169-191
  8. 代数仕様とカテゴリー, 1985, コンピュータ・ソフトウェア, vol. 2 pp.30-40
  9. Self-similar sets as Tarski's fixed points, 1985, Publications of the Research
    Institute for Mathematical Sciences, Kyoto University, 21, pp.1059-1066
  10. Adjunction of semifunctors: categorical structures in non-extensional lambda
    calculus, 1985, Theoretical Computer Sciences,41, pp.95-104
  11. PX: a system extracting programs from proofs, 1987, Proceedings of the
    IFIP TC 2/WG 2.2 Working Conference on Formal Description of Programming Concepts,
    M. Wirsing ed., North-Holland, 3, pp. 99-124
  12. Category theory for algebraic specifications, 1988, vol. 1, Advances in
    Software Science and Technology, pp. 169-185.
  13. An introduction to PX, 1990, Logical Foundations
    of Functional Programming, G. Huet ed., Addison-Wesley, pp. 432-486.
  14. Constructive Mathematics and Computer-Aided Reasoning
    , 1990, MATHEMATICAL LOGIC, P.P. Petkov ed., Plenum Press, pp.
  15. Lifschit'z Logic of Calculable Numbers and Optimizations
    in Program Extraction
    , 1994, Festschrift for Prof. S. Takasu (N. Jones,
    M. Hagiya and M. Sato eds.), Lecture Notes in Computer Science, Springer,
    vol. 792, pp. 1-9, S. Hayashi and Y. Takayama
  16. A functional system with transfinitely defined types, 1994, Festschrift
    for Prof. S. Takasu (N. Jones, M. Hagiya and M. Sato eds. Lecture Notes in
    Computer Science, Springer, vol. 792, pp. 31-60, M. Yasugi and S. Hayashi
  17. Singleton, Union, and Intersection Types for Program
    , 1994, Information and Computation, vol. 109, pp. 174-210
  18. Interpretations of transfinite recursion and parametric abstraction in
    type, 1994, in Words, Languages and Combinatorics II, M. Ito and H. Jurgensen,
    eds. World Scientific Publish. Co., Singapore, pp. 452-464, M. Yasugi and
    S. Hayashi
  19. Logic of refinement types, 1994, Proceedings
    of Esprit Basic Research Action, Types for Proofs and Programs workshop, Nijmegen,
    The Netherlands,Lecture Notes in Computer Science, Springer, vol. 806
  20. 変貌する数学観 -そのとき形式化は?-

    科学基礎論研究 Vol. 22, No. 1,1994,pp. 1-6
  21. A New Formalization of Feferman's System of
    Functions and Classes and its Relation to Frege Structure
    , International
    Journal of Foundations of Computer Science, Vol. 6, No. 3, 1995, pp. 187-202,
    S. Hayashi and S. Kobayashi
  22. Two extensions of PX system (extended abstract),
    in Linear Logic 96 Tokyo Meeting, Keio University, Tokyo, 1996, in Electronic
    Notes of Theoretical Computer Science, Vol. 3,
    http://www.elsevier.nl/mcs/tcs/pc/Menu.html, Elsevier-Science Publishing,
    S. Hayashi, M. Ishikawa, S. Kobayashi, H. Nakano, S. Nakazaki
  23. Constructive programming - a personal
    view -, in Combinatorics, Complexity, Logic, Proceedings of DMTCS'96, Springer-Verlag,
    Singapore, 1996, pp.38-51, D. S. Bridges, C. Calude, J. Gibbons, S. Reeves,
    I. Witten (eds.)
  24. "山口昌哉「複雑系科学の哲学に不足しているもの」"に対するコメント、日本ファジイ学会誌, 9(5), 611-613, 1997.
  25. Susumu Hayashi, Ryosuke Sumitomo; Testing Proofs
    by Examples, in Advances in Computing Science, Asian '98 : 4th Asian Computing
    Science Conference, Manila, the Philippines, December 1998, J. Xiang and Ohori,
    eds., Lecture notes in Computer Science No. 1538, pp.1-3, 1998.
  26. 証明アニメーション支援環境の構築、コンピュータソフトウェア、Vol.16, No.3 (1999), pp.71-74, 住友亮翼, 林晋
  27. Hayashi S., Sumitomo R., and Shii K.:Towards Animation of Proofs -testing
    proofs by examples-:, Theoretical Computer Science, 272, pp.177--195, 2002
  28. A limiting first order realizability interpretation, Masahiro
    Nakata and Susumu Hayashi: Scientificae Mathematicae Japonicae http://www.jams.or.jp/scmjol/5.html,
    paper number 5-49: dvi, ps, pdf, 2001
  29. Towards Limit Computable Mathematics, Susumu Hayashi and Masahiro Nakata:
    in Types for Proofs and Programs, International Workshop, TYPES 2000, Durham,
    UK, December 2000, Selected Paper, P. Challanghan, Z. Luo, J. McKinna, R.
    Pollack, eds., Springer Lecture Notes in Computer Science 2277, pp.125-144.
  30. Hayashi S.: Mathematics based on Learning, Algorithmic Learning Theory,
    Lecture Notes in Artificial Intelligence 2533, Springer, pp.7-21.
  31. Akama, Y., Berardi, S., Hayashi, S., Kohlenbach, U.: An Arithmetical Hierarchy
    of the Law of Excluded Middle and Related Principles. LICS 2004: 192-201
  32. Hayashi, S., Pan Y., Sato M., et al.: Test Driven Development of UML Models with SMART modeling system, in Baars et al. eds.,UML 2004, LNCS. 3273,pp. 395-409, 2004.
  33. Hayashi, S.: Can proofs be animated by gamess?, in P. Urzyczyn ed., TLCA 2005, LNCS 3461, pp.11-22, 2005, invited paper.
  34. Stefano Berardi, Thierry Coquand, Susumu Hayashi: Games with 1-backtracking. GALOP 2005: 210-225
  35. Hayashi, S.:Mathematics based on Incremental Learning -Excluded middle and Inductive inference-, Theoretical Computer Science 350 (1), 2006, pp. 125-139, exteded journal version of 28.
  36. Hayashi, S.: Can proofs be animated by games?, Fundamenta Informaticae 77 (2007), pp.1-13, in print, exteded journal version of 33.