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Originator: Aart Middeldorp [Mid89]
Date: April 1991
Summary: Is unicity of normal forms with respect to reduction a modular property of left-linear term-rewriting systems?
If R and S are two term-rewriting systems with disjoint vocabularies, such that for each of R and S any two convertible normal forms must be identical, then their union R ∪ S also enjoys this property [Mid89]. Accordingly, we say that unicity of normal forms (UN) is a “modular” property of term-rewriting systems. “Unicity of normal forms with respect to reduction” (UN^{→}) is the weaker property that any two normal forms of the same term must be identical. For non-left-linear systems, this property is not modular. The question remains: Is UN^{→} a modular property of left-linear term-rewriting systems?
A positive solution is given in [Mar94].
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