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二階の書換え系における引数切り落とし法

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Other Title
  • 2カイ ノ カキカエケイ ニ オケル ヒキスウ キリオトシホウ
  • Argument Filtering Method for Second-Order Higher-Order Rewrite Systems

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Abstract

高階書換え系は関数プログラムの計算モデルであり,停止性は重要な性質の一つである.停止性証明法の一つに強計算性に基づく静的依存対法と呼ばれる再帰構造解析法がある.依存対法を用いる際には,引数切り落とし法と呼ばれる手法が重要となる.高階の書換え系に適用可能な引数切り落とし法は既に知られているが,適用する際に,λ抽象に対応していないという問題と,型の構造を破壊してしまうという問題がある.本論文では,これら二つの問題を解決する高階書換え系上の引数切り落とし法を提案する.提案した手法の正当性を一般には証明できなかったが,規則の各辺が堅固または二階の場合には健全であることを証明する.Higher-order rewrite systems are computation models of functional programming languages, and the termination property is one of the most important ones of them. Recently, static dependency pair method based on strong computability was introduced, which proves the termination effectively and efficiently. An argument filtering method plays an important role in this method. However, existing argument filtering method in higher-order rewrite systems has two problems: it cannot handle λ-abstraction, and destructs type structures. In order to overcome these problems, we extend the method. Although we did not show its soundness in general, we prove the soundness under the restriction that both sides of rules are either firmness or second-order.

identifier:http://ci.nii.ac.jp/naid/110006343342

identifier:http://hdl.handle.net/2237/21097

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