Membership Conditional Term Rewriting Systems

Yoshihito TOYAMA

Membership Conditional Term Rewriting Systems

Yoshihito TOYAMA

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We propose a new type of conditional term rewriting system: the membership-conditional term rewriting system, in which, each rewriting rule can have membership conditions which restrict the substitution values for the variables occurring in the rule. For example, the rule f(χ, χ, y)g(χ, y) if χT' yields the reduction f(M, M, N)g(M, N) only when M is in the term set T'. We study the confluence of membership-conditional term rewriting systems that are nonterminating and nonlinear. It is shown that a restricted nonlinear term rewriting system in which membership conditions satisfy the closure and termination properties is confluent if the system is nonoverlapping.

Publication: IEICE TRANSACTIONS on transactions Vol.E72-E No.11 pp.1224-1229

Publication Date: 1989/11/25

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Type of Manuscript: PAPER

Category: Automation, Language and Theory of Computing

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Yoshihito TOYAMA

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Yoshihito TOYAMA, "Membership Conditional Term Rewriting Systems" in IEICE TRANSACTIONS on transactions, vol. E72-E, no. 11, pp. 1224-1229, November 1989, doi: .
Abstract: We propose a new type of conditional term rewriting system: the membership-conditional term rewriting system, in which, each rewriting rule can have membership conditions which restrict the substitution values for the variables occurring in the rule. For example, the rule f(χ, χ, y)g(χ, y) if χT' yields the reduction f(M, M, N)g(M, N) only when M is in the term set T'. We study the confluence of membership-conditional term rewriting systems that are nonterminating and nonlinear. It is shown that a restricted nonlinear term rewriting system in which membership conditions satisfy the closure and termination properties is confluent if the system is nonoverlapping.
URL: https://global.ieice.org/en_transactions/transactions/10.1587/e72-e_11_1224/_p

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@ARTICLE{e72-e_11_1224,
author={Yoshihito TOYAMA, },
journal={IEICE TRANSACTIONS on transactions},
title={Membership Conditional Term Rewriting Systems},
year={1989},
volume={E72-E},
number={11},
pages={1224-1229},
abstract={We propose a new type of conditional term rewriting system: the membership-conditional term rewriting system, in which, each rewriting rule can have membership conditions which restrict the substitution values for the variables occurring in the rule. For example, the rule f(χ, χ, y)g(χ, y) if χT' yields the reduction f(M, M, N)g(M, N) only when M is in the term set T'. We study the confluence of membership-conditional term rewriting systems that are nonterminating and nonlinear. It is shown that a restricted nonlinear term rewriting system in which membership conditions satisfy the closure and termination properties is confluent if the system is nonoverlapping.},
keywords={},
doi={},
ISSN={},
month={November},}

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TY - JOUR
TI - Membership Conditional Term Rewriting Systems
T2 - IEICE TRANSACTIONS on transactions
SP - 1224
EP - 1229
AU - Yoshihito TOYAMA
PY - 1989
DO -
JO - IEICE TRANSACTIONS on transactions
SN -
VL - E72-E
IS - 11
JA - IEICE TRANSACTIONS on transactions
Y1 - November 1989
AB - We propose a new type of conditional term rewriting system: the membership-conditional term rewriting system, in which, each rewriting rule can have membership conditions which restrict the substitution values for the variables occurring in the rule. For example, the rule f(χ, χ, y)g(χ, y) if χT' yields the reduction f(M, M, N)g(M, N) only when M is in the term set T'. We study the confluence of membership-conditional term rewriting systems that are nonterminating and nonlinear. It is shown that a restricted nonlinear term rewriting system in which membership conditions satisfy the closure and termination properties is confluent if the system is nonoverlapping.
ER -