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Normalization Analysis for Term Rewriting

Research Project

Project/Area Number 17K00011
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Theory of informatics
Research InstitutionJapan Advanced Institute of Science and Technology

Principal Investigator

Hirokawa Nao  北陸先端科学技術大学院大学, 先端科学技術研究科, 准教授 (50467122)

Project Period (FY) 2017-04-01 – 2021-03-31
Project Status Completed (Fiscal Year 2020)
Budget Amount *help
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2020: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2019: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2017: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywords項書換え / 正規化性 / 正規化戦略 / 定理自動証明 / 完備化 / 合流性 / 自動定理証明 / 情報基礎
Outline of Final Research Achievements

We studied foundational techniques for dealing with infinite data structures such as real numbers and infinite lists. Programs that operate on such infinite data often employ potentially non-terminating functions. Therefore, their evaluation requires a special computation method called lazy evaluation. In this research project we showed that in many cases a program can be turned into another form of a program so that a simple calculation by the leftmost outermost strategy achieves lazy evaluation. We also developed an automatic method for verifying termination of lazy evaluation, which is a crucial property for running programs safely.

Academic Significance and Societal Importance of the Research Achievements

本研究において遅延評価の実現方法とその停止性(正規化性)を解析する枠組み・手法を構築した。遅延評価は関数型プログラミング言語のみならず、数学的な定理を証明する定理証明支援システムにおいても採用されている。実数や無限列などの数学的構造を扱う上で必須の技術であり、本研究はそれらをより良く扱うための計算・演繹機構の理論基盤、より良い自動化の枠組みを与えるための技術基盤の確立に貢献する。

Report

(5 results)
  • 2020 Annual Research Report   Final Research Report ( PDF )
  • 2019 Research-status Report
  • 2018 Research-status Report
  • 2017 Research-status Report
  • Research Products

    (17 results)

All 2020 2019 2018 2017 Other

All Int'l Joint Research (6 results) Journal Article (1 results) (of which Int'l Joint Research: 1 results,  Peer Reviewed: 1 results,  Open Access: 1 results) Presentation (5 results) (of which Int'l Joint Research: 5 results,  Invited: 1 results) Remarks (5 results)

  • [Int'l Joint Research] University of Innsbruck(オーストリア)

    • Related Report
      2019 Research-status Report
  • [Int'l Joint Research] Queen Mary University of London(英国)

    • Related Report
      2019 Research-status Report
  • [Int'l Joint Research] University of Innsbruck(オーストリア)

    • Related Report
      2018 Research-status Report
  • [Int'l Joint Research] Queen Mary University of London(英国)

    • Related Report
      2018 Research-status Report
  • [Int'l Joint Research] University of Innsbruck(オーストリア)

    • Related Report
      2017 Research-status Report
  • [Int'l Joint Research] Queen Mary University of London(英国)

    • Related Report
      2017 Research-status Report
  • [Journal Article] Abstract Completion, Formalized2019

    • Author(s)
      Nao Hirokawa, Aart Middeldorp, Christian Sternagel, and Sarah Winkler.
    • Journal Title

      Journal of Logical Methods in Computer Science

      Volume: 15(3)

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Presentation] Parallel Closedness Revisited2020

    • Author(s)
      Kiraku Shintani and Nao Hirokawa
    • Organizer
      9th International Workshop on Confluence (IWC 2020)
    • Related Report
      2020 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Confluence by Critical Pair Analysis Revisited2019

    • Author(s)
      Nao Hirokawa, Julian Nagele, Vincent van Oostrom, and Michio Oyamaguchi
    • Organizer
      Proceedings of the 27th International Conference on Automated Deduction
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research
  • [Presentation] Cops and CoCoWeb: Infrastructure for Confluence Tools2018

    • Author(s)
      Nao Hirokawa, Julian Nagele, and Aart Middeldorp
    • Organizer
      Proceedings of the 9th International Joint Conference on Automated Reasoning, Lecture Notes in Artificial Intelligence 10900, pp. 346-353, 2018
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research
  • [Presentation] Confluence Competition 20182018

    • Author(s)
      Takahito Aoto, Makoto Hamana, Nao Hirokawa, Aart Middeldorp, Julian Nagele, Naoki Nishida, Kiraku Shintani, and Harald Zankl
    • Organizer
      Proceedings of the 3rd International Conference on Formal Structures for Computation and Deduction, Leibnitz International Proceedings in Informatics, pp. 32:1-32:5, 2018
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Infinite Runs in Abstract Completion2017

    • Author(s)
      Nao Hirokawa, Aart Middeldorp, Christian Sternagel, and Sarah Winkler
    • Organizer
      Proceedings of the 2nd International Conference on Formal Structures for Computation and Deduction, Leibnitz International Proceedings in Informatics 84, pp. 19:1-19:16, 2017.
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research
  • [Remarks] 研究代表のホームページ

    • URL

      http://www.jaist.ac.jp/~hirokawa/

    • Related Report
      2020 Annual Research Report 2017 Research-status Report
  • [Remarks] 合流性ツール Saigawa と CoLL のウェブサイト

    • URL

      https://www.jaist.ac.jp/project/saigawa/

    • Related Report
      2020 Annual Research Report
  • [Remarks] ホームページ

    • URL

      https://www.jaist.ac.jp/~hirokawa/

    • Related Report
      2019 Research-status Report
  • [Remarks] 合流性ツール Saigawa

    • URL

      https://www.jaist.ac.jp/project/saigawa/

    • Related Report
      2019 Research-status Report
  • [Remarks] 研究者代表のホームページ

    • URL

      https://www.jaist.ac.jp/~hirokawa/

    • Related Report
      2018 Research-status Report

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Published: 2017-04-28   Modified: 2022-01-27  

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