## ＜テクニカルレポート＞Combinatory Logic and λ-Calculus for Classical Logic

作成者 作成者名 所属機関 所属機関名 Graduate School of Information Science and Electrical Engineering, Kyushu University 九州大学大学院システム情報科学府 作成者名 所属機関 所属機関名 Department of Information Science, Kyoto University 京都大学工学部情報学科計算機科学コース 著者識別子 作成者名 所属機関 所属機関名 Computer Center, Kyushu University 九州大学大型計算機センター 英語 Department of Informatics, Kyushu University 九州大学大学院システム情報科学研究院情報理学部門 2000-08-18 176 Accepted Manuscript open access DOI Technical Report || 176 http://www.i.kyushu-u.ac.jp/research/report.html DOI Technical Report || 176 http://www.i.kyushu-u.ac.jp/research/report.html DOI Technical Report || 176 http://www.i.kyushu-u.ac.jp/research/report.html Since Griffin's work in 1990, classical logic has been an attractive target for extracting computational contents. However, the classical principle used in Griffin's type system is the double-negation...-elimination rule, which prevents one to analyze the intuitionistic part and the purely classical part separately. By formulating a calculus with J (for the elimination rule of falsehood) and P (for Peirce formula which is concerned with purely classical reasoning) combinators, we can separate these two parts. This paper studies the λPJ calculus with P and J combinators and the λC calculus with C combinator(for the double-negation-elimination rule). We also propose two λ-calculi which correspond to λPJ and λC. We give four classes of reduction rules for each calculus, and systematically study their relationship by simulating reduction rules in one calculus by the corresponding one in the other. It is shown that, by restricting the type of P, simulation succeeds for several choices of reduction rules, but that simulating the full calculus λPJ in λC succeeds only for one class. Some programming examples of our calculi such as encoding of conjunction and disjunction are also given.続きを見る

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レコードID 3034 査読無 テクニカルレポート 2009.04.22 2017.01.20