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1992 Fiscal Year Final Research Report Summary

Co-operative research on foundational theories of programs

Research Project

Project/Area Number 02302009
Research Category

Grant-in-Aid for Co-operative Research (A)

Allocation TypeSingle-year Grants
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionTohoku University

Principal Investigator

SATO Masahiko  Tohoku University,Research Institute of Electrical Communications,Professor, 電気通信研究所, 教授 (20027387)

Co-Investigator(Kenkyū-buntansha) KAMEYAMA Yukiyoshi  Tohoku University,Research Institute of Electrical Communications,Research assoc, 電気通信研究所, 助手 (10195000)
TATSUTA Makoto  Tohoku University,Research Institute of Electrical Communications,Research assoc, 電気通信研究所, 助手 (80216994)
Project Period (FY) 1990 – 1992
KeywordsTheory of programs / Constructive logic / Type theory / Graph theory
Research Abstract

We have studied (1) mathematical foundations,(2) applied mathematics and (3) programming. We have constructed foundational theories of programming,researched methods of software development based on the theories and developed actual application software. By studying variety of foundational theories of programming and discussing relationship among these theories, We have deepened knowledge about these theories. Particularly the research have got the following results.
Sato constructed a logical system RPT, which has proofs as internal objects and gave foundations of theory of programs. Tatsuta studied realizability interpretations of inductive definitions for constructive programming. Kameyama implemented a constructive programming system and studied computer network, which gives infrastructures of the research. Ito studied structured models of concurrent processes and term rewriting systems and implemented software based on the results as an experiment. Hayashi presented a new framework of type theories by singleton, union and intersection types and showed that it is more expressive for constructive programming than other frameworks. Hagiya studied basic techniques to implement computer environment for describing formal proofs, such as user interfaces of a proof checker which include proofs by examples and visualization of proofs. Ono studied semantics of logics without structural rules, decision problems and finite model properties. Noshita developed fast search techniques for game trees and applied it to software which solves Tsume-shogi. Ushijima studied foundational theories and actual implementation of testing and debugging methods of concurrent programs.

  • Research Products

    (24 results)

All Other

All Publications (24 results)

  • [Publications] M.Sato: "Adding Proof Objects and Inductive Definition Mechanisms to Frege Structures" Proceedings of Theoretical Aspects of Computer Software. 53-87 (1991)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M.Tatsuta: "Realizability Interpretation of Coinductive Definitions and Program Synthesis with Streams" Theoretical Computer Science.

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M.Tatsuta: "Uniqueness of normal proofs of minimal formulas" Journal of Symbolic Logic.

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 亀山 幸義: "構成的数学体系RPTに基づく超数学定理の形式化" 情報処理学会第42回全国大学. 1. 47-48 (1991)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 有川 節夫,西野 哲朗: "学習における計算論的アプローチ" 情報処理学会誌. 32-3. 217-225 (1991)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] J.Cheng and K.Ushijima: "Analyzing Ada Tasking Deadlocks and Livelocks Using Extended Petri Nets" Lecture Notes in Computer Science. 499. 125-146 (1991)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] K.Noshita and Y.Nakatani: "A note on deleting the maximum element in nested s-heaps" Trans.ofIECEJ. E73,10. 1725-1726 (1990)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] E.Kiriyama and H.Ono: "The contraction rule and decision problems for logics without structural rules" Studia Logica. 50. 299-319 (1991)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 萩谷 昌己: "高階単一化と証明の一般化" 人工知能学会誌. 6,3. 388-396 (1991)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M.Hagiya: "Synthesis of rewrite programs by higher-order and semantic unification" New Generation Computing. 8,4. 403-420 (1991)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M.Hagiya: "Higher-order unification as a theorem proving procedure" Eighth International Conference on Logic Programming. 270-284 (1991)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 佐藤 雅彦,桜井 貴文: "プログラムの基礎理論" 岩波書店, 348 (1991)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] I.Ito and A.R.Meyer: "Proceedings of Theoretical Aspects of Computer Software" Springer, 770 (1991)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 林 晋,小林 聡: "構成的プログラミングの基礎" 遊星社, 254 (1991)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 龍田 真: "型理論" 近代科学社, 82 (1992)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M.Sato: "Adding Proof Objects and Inductive Definition Mechanisms to Frege Structures" Proceedings of Theoretical Aspects of Computer Software. 53-87 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M.Tatsuta: "Realizability Interpretation of Coinductive Definitions and Program Synthesis with Streams" Theoretical Computer Science.

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M.Tatsuta: "Uniqueness of normal proofs of minimal formulas" Journal of Symbolic Logic.

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] J.Cheng and K.Ushijima: "Analyzing Ada Tasking Deadlocks and Livelocks Using Extended Petri Nets" Lecture Notes in Computer Science. 499. 125-146 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K.Noshita and Y.Nakatani: "A note on deleting the maximum element in nested s-heaps" Trans. of IECEJ E73. 10. 1725-1726 (1990)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] E.Kiriyama and H.Ono: "The contraction rule and decision problems for logics without structural rules" Studia Logica. 50. 299-319 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M.Hagiya: "Synthesis of rewrite programs by higher-order and semantic unification" New Generation Computing 8,4. 403-420 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M.Hagiya: "Higher-order unification as a theorem proving procedure" Eighth International Conference on Logic Programming. 270-284 (1991)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] I.Ito and A.R.Meyer: "Proceedings of Theoretical Aspects of Computer Software" Springer. (1991)

    • Description
      「研究成果報告書概要(欧文)」より

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Published: 1994-03-24  

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