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Narrowing Trees for Syntactically Deterministic Conditional Term Rewriting Systems

Authors Naoki Nishida , Yuya Maeda

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Naoki Nishida
  • Graduate School of Informatics, Nagoya University, Nagoya, Japan
Yuya Maeda
  • Graduate School of Informatics, Nagoya University, Nagoya, Japan

Funding

This work was partially supported by JSPS KAKENHI Grant Number JP17H01722.

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Naoki Nishida and Yuya Maeda. Narrowing Trees for Syntactically Deterministic Conditional Term Rewriting Systems. In 3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 108, pp. 26:1-26:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018) https://doi.org/10.4230/LIPIcs.FSCD.2018.26

Abstract

A narrowing tree for a constructor term rewriting system and a pair of terms is a finite representation for the space of all possible innermost-narrowing derivations that start with the pair and end with non-narrowable terms. Narrowing trees have grammar representations that can be considered regular tree grammars. Innermost narrowing is a counterpart of constructor-based rewriting, and thus, narrowing trees can be used in analyzing constructor-based rewriting to normal forms. In this paper, using grammar representations, we extend narrowing trees to syntactically deterministic conditional term rewriting systems that are constructor systems. We show that narrowing trees are useful to prove two properties of a normal conditional term rewriting system: one is infeasibility of conditional critical pairs and the other is quasi-reducibility.

Subject Classification

ACM Subject Classification
  • Theory of computation → Rewrite systems
Keywords
  • conditional term rewriting
  • innermost narrowing
  • regular tree grammar

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