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Proof Animation -testing proofs by constructive programming-

Research Project

Project/Area Number 10480063
Research Category

Grant-in-Aid for Scientific Research (B).

Allocation TypeSingle-year Grants
Section一般
Research Field 計算機科学
Research InstitutionKobe University

Principal Investigator

HAYASHI Susumu  Kobe University, Department of Computer and Systems Engineering, Professor, 工学部, 教授 (40156443)

Co-Investigator(Kenkyū-buntansha) SATO Masahiko  Kyoto University, Graduate School, Department of Computer Science, Professor, 大学院・工学研究科, 教授 (20027387)
YASUGI Mariko  Kyoto Sangyo University, Department of Computer Science, Professor, 理学部, 教授 (90022277)
TAMURA Naoyuki  Kobe University, Department of Computer and Systems Engineering, Associate Professor, 工学部, 助教授 (60207248)
Project Period (FY) 1998 – 2000
Project Status Completed (Fiscal Year 2000)
Budget Amount *help
¥6,300,000 (Direct Cost: ¥6,300,000)
Fiscal Year 2000: ¥1,300,000 (Direct Cost: ¥1,300,000)
Fiscal Year 1999: ¥1,500,000 (Direct Cost: ¥1,500,000)
Fiscal Year 1998: ¥3,500,000 (Direct Cost: ¥3,500,000)
Keywordsconstructive programming / program verification / program logic / learning theory / classical proof execution / 学習理論
Research Abstract

Some theories of classical proof exectution were examined if they are good for proof animation. We implemented an environment for PA by Ogata-theory and it was tested on simple examles. Berardi theory was also deeply examined theoretically and practically by a computer experiment. It turned out that existing theory are short for the aim.
To break through the limitation of the existing theories, we developed a new theory of classical proof execution. It is based on the ideas from algorithmic learning theory and is entirely different from the existing theories. The theory is called LCM(Limit Computable Mathematics).
Application of LCM to PA was investigated. Maybe, even more importantly, it turned out that LCM has a lot of deep connections to various theories in computer science and logic. Examples are computation on real numbers, basis theorems in recursion theory, reverse mathematics of principles of classical logic, concurrent computation, computer algebra of invariant theory, etc. etc.. This idea stimulated many researchers and some projects independent from and/or collaborated with us are taking place.

Report

(4 results)
  • 2000 Annual Research Report   Final Research Report Summary
  • 1999 Annual Research Report
  • 1998 Annual Research Report
  • Research Products

    (21 results)

All Other

All Publications (21 results)

  • [Publications] S. Hayashi: "Towards Animation of Proofs"Theoretical Computer Science. (未定). (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] S. Hayashi: "Formalized Mathematics, Proof Animation, and Limit Computable Mathematics"Relevance and Feasibility of Mathematical Analysis on the Computer, RIMS, Kyoto, March 21/22, 数理解析研究所講究録. (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] M. Yasugi: "Effective properties of sets and functions in metric spaces with computability srtucture"Theoretical Computer Science. 219. 467-486 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] S. Hayashi: "Testing Proofs by Examples"Lecture Notes in Computer Science. 1538. 1-3 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] M. Banbara: "Compiling Resources in a Linear Logic Programming Language"Proc. of Workshop on Parallelism and Implementation Technology for Logic Programming Languages. 32-45 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] M. Yasugi: "Computability problem of Gaussian function"Computability and Complexity in Analysis ed.by K-I.Ko et.al. 157-165 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] M.Nakata and S.Hayashi: "Limiting first order realizability interpretation"Math.Sci.Japonica. (submitted). (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] S.Hayashi, et al.: "Towards Animation of Proofs"Theoretical Computer Science. (in print). (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] 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. 1-3 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] R.Sumitomo, S.Hayashi: "A proof animation environment"Computer Software(in Japanese). Vol.16, No.3. 71-74 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] M.Yasugi: "Effective properties of sets and functions in metric spaces with computability structure"Theoretical Computer Science. vol.219. 467-486 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] S.Hayashi: "Formalized Mathematics, Proof Animation, and Limit Computable Mathematics"Relevance and Feasibility of Mathematical Analysis on the Computer, RIMS, Kyoto, March 21/22, RIMS Kokyu-Roku. (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] M.Banbara and N.Tamura: "Compiling Resources in a Linear Logic Programming Language"Proc.of Workshop on Parallelism and Implementation Techonology for Logic Programming Languages. 32-45 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] M.Yasugi: "Computability problem of Gaussian function"in Computability and Complexity in Analysis ed.by K-I.KO et.al. 157-165 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] S.Hayashi: "Towards Animation of Proofs"Theoretical Computer Science. (未定). (2001)

    • Related Report
      2000 Annual Research Report
  • [Publications] S.Hayashi: "Formalized Mathematics, Proof Animation, and Limit Computable Mathematics"Relevance and Feasibility of Mathematical Analysis on the Computer, RIMS, Kyoto, March 21/22, 数理解析研究所講究録. (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] S.Hayashi: "Towerds Animation of Proofs"Theoretical Computer Science. (未定). (2000)

    • Related Report
      1999 Annual Research Report
  • [Publications] M.Yasugi: "Effective properties of sets and functions in metric spaces with computability structure"Theoretical Computer Science. 219. 467-486 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] S.Hayashi: "Testing Proofs by Examples" Lecture Notes in Computer Science. 1538. 1-3 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] M.Banbara: "Compiling Resources in a Linear Logic Programming Language" Proc.of Workshop on Parallelism and Implementation Technology for Logic Programming Languages. 32-45 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] M.Yasugi: "Computability problem of Gaussian function" Computability and Complexity in Analysis ed. by K-I.Ko et.al. 157-165 (1998)

    • Related Report
      1998 Annual Research Report

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Published: 1998-04-01   Modified: 2016-04-21  

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