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The present paper discusses a head-needed strategy and its decidable classes of higher-order rewrite systems (HRSs), which is an extension of the headneeded strategy of term rewriting systems (TRSs). We discuss strong sequential and NV-sequential classes having the following three properties, which are mandatory for practical use: (1) the strategy reducing a head-needed redex is head normalizing (2) whether a redex is head-needed is decidable, and (3) whether an HRS belongs to the class is decidable. The main difficulty in realizing (1) is caused by the β-reductions induced from the higher-order reductions. Since β-reduction changes the structure of higher-order terms, the definition of descendants for HRSs becomes complicated. In order to overcome this difficulty, we introduce a function, PV, to follow occurrences moved by β-reductions. We present a concrete definition of descendants for HRSs by using PV and then show property (1) for orthogonal systems. We also show properties (2) and (3) using tree automata techniques, a ground tree transducer (GTT), and recognizability of redexes.
The present paper discusses a head-needed strategy and its decidable classes of higher-order rewrite systems (HRSs), which is an extension of the headneeded strategy of term rewriting systems (TRSs). We discuss strong sequential and NV-sequential classes having the following three properties, which are mandatory for practical use: (1) the strategy reducing a head-needed redex is head normalizing (2) whether a redex is head-needed is decidable, and (3) whether an HRS belongs to the class is decidable. The main difficulty in realizing (1) is caused by the β-reductions induced from the higher-order reductions. Since β-reduction changes the structure of higher-order terms, the definition of descendants for HRSs becomes complicated. In order to overcome this difficulty, we introduce a function, PV, to follow occurrences moved by β-reductions. We present a concrete definition of descendants for HRSs by using PV and then show property (1) for orthogonal systems. We also show properties (2) and (3) using tree automata techniques, a ground tree transducer (GTT), and recognizability of redexes.
収録刊行物
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- 情報処理学会論文誌プログラミング(PRO)
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情報処理学会論文誌プログラミング(PRO) 2 (2), 144-165, 2009-03-23
東京 : 情報処理学会
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詳細情報 詳細情報について
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- CRID
- 1050282812871133696
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- NII論文ID
- 110007970897
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- NII書誌ID
- AA11464814
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- ISSN
- 18827802
- 18827772
- 03875806
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- NDL書誌ID
- 024320762
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- 本文言語コード
- en
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- article
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- IRDB
- NDL
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