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Linear CHAMを用いた型付きλ項の評価

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(1)Vol. 42. No. SIG 11(PRO 12). Nov. 2001. 情報処理学会論文誌:プログラミング. 発表概要. Linear CHAM を用いた型付き λ 項の評価 佐. 藤. 伸. 也†. 杉. 徹††. 本. 山. 田. 眞 市††. 古典線形論理は並列計算の新しい理論的基礎を与えるとして期待されている.Abramsky は並行計算 のモデルの一種である CHAM の枠組みを用いて古典線形論理の計算的解釈を与えた.Linear CHAM と名付けられたこの計算体系において,古典線形論理の証明図に対応する項表現は proof expression と呼ばれ,cut 除去手続きに相当する書き換え規則によって簡約が行われる.本発表では,型付き λ 項から proof expression への変換とその逆変換を定義し,それらの変換と Linear CHAM の簡約を 通して,与えられた型付き λ 項の正規形が求められることを示す.. Evaluating Typed λ-terms by Using Linear CHAM Shinya Sato,† Toru Sugimoto†† and Shinichi Yamada†† Classical Linear Logic (CLL) is expected to give new theoretical foundations of parallel computation. Abramsky gave a computational interpretation of CLL using the framework of CHAM. In this computational system which is called Linear CHAM, proof expressions are assigned to proof trees in CLL, and they are reduced by rewriting rules which correspond to cut elimination procedures of CLL. In this presentation, we give a translation from typed λterms into proof expressions and its inverse translation, and show that we can get the normal form of a lambda term through reductions in Linear CHAM and these translations.. ( 平成 13 年 1 月 23 日発表). † 東京理科大学大学院理工学研究科 Graduate School of Science and Technology, Science University of Tokyo †† 東京理科大学理工学部 Faculty of Science and Technology, Science University of Tokyo. 98.

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