TY - GEN
T1 - Confluent term rewriting systems with membership conditions
AU - Toyama, Yoshihito
N1 - Publisher Copyright:
© 1988, Springer-Verlag.
PY - 1988
Y1 - 1988
N2 - 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(x, x, y) ▹ g(x, y) if x ∈ T' yields the reduction f(M, M, N) → g(M, N) only when M is in the term set T'. Thus, by using membership-conditional rewriting, we can easily provide a strategy for term reduction. 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.
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(x, x, y) ▹ g(x, y) if x ∈ T' yields the reduction f(M, M, N) → g(M, N) only when M is in the term set T'. Thus, by using membership-conditional rewriting, we can easily provide a strategy for term reduction. 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.
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U2 - 10.1007/3-540-19242-5_17
DO - 10.1007/3-540-19242-5_17
M3 - Conference contribution
AN - SCOPUS:85028856291
SN - 9783540192428
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 228
EP - 241
BT - Conditional Term Rewriting Systems - 1st International Workshop, Proceedings
A2 - Kaplan, Stephane
A2 - Jouannaud, Jean-Pierre
PB - Springer Verlag
T2 - 1st International Workshop on Conditional Term Rewriting Systems, 1987
Y2 - 8 July 1987 through 10 July 1987
ER -