Modularity of Confluence: A Simplified Proof
نویسندگان
چکیده
In this note we present a simple proof of a result of Toyama which states that the disjoint union of confluent term rewriting systems is confluent. 1985 Mathematics Subject Classification: 68Q5
منابع مشابه
Modular Church-Rosser Modulo
In [12], Toyama proved that the union of two confluent term-rewriting systems that share absolutely no function symbols or constants is likewise confluent, a property called modularity. The proof of this beautiful modularity result, technically based on slicing terms into an homogeneous cap and a so called alien, possibly heterogeneous substitution, was later substantially simplified in [5, 11]...
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In [19], Toyama proved that the union of two confluent term-rewriting systems that share absolutely no function symbols or constants is likewise confluent, a property called modularity. The proof of this beautiful modularity result, technically based on slicing terms into an homogeneous cap and a so called alien, possibly heterogeneous substitution, was later substantially simplified in [8, 12]...
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We prove modularity of constructive confluence for term rewriting systems using a novel decomposition of terms into tall aliens and bases. The proof is modular itself in that it factors through the decreasing diagrams theorem for abstract rewriting systems.
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A property of term rewriting systems is modular if it is preserved under disjoint union. In the past few years the modularity of properties of term rewriting systems has been extensively studied. The first results in this direction were obtained by Toyama. In (Toyama, 1987a) he showed that confluence is a modular property (see Klop et al. (1994) for a simplified proof) and in (Toyama, 1987b) he...
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عنوان ژورنال:
- Inf. Process. Lett.
دوره 49 شماره
صفحات -
تاریخ انتشار 1994