Normalization of Infinite Terms

Proving Infinitary Normalization

“…Note that the global properties are special cases of the local ones. In that sense our results generalize those of [9].…”

“…Zantema [9] initiated the development of proof methods for infinitary normalization by adapting the weakly monotone algebras to the infinitary setting. As a matter of fact, Zantema also studies a weaker notion than SN ∞ , which he calls SN ω , and which states that all rewrite sequences of length ω are convergent, in the sense that throughout the infinite reduction any position is rewritten at most finitely often.…”

“…1 The properties SN ∞ and SN ω can be viewed locally, as properties of individual terms or of sets of terms in a TRS, or globally: the entire TRS is SN ∞ (or SN ω ) if all its terms are. In [9] only the global versions are investigated, obtaining characterization theorems for the global properties SN ω and SN ∞ .…”

“…A (possibly infinite) term is SN ∞ if along every rewrite sequence each fixed position is rewritten only finitely often. In [9], SN ∞ has been investigated as a system-wide property, i.e. SN ∞ for all terms of a given rewrite system.…”

“…Moreover, in practice one usually is interested in SN ∞ of a certain set of initial terms. We give a complete characterization of this (more general) 'local version' of SN ∞ using interpretations into weakly monotone algebras (as employed in [9]). Actually, we strengthen this notion to continuous weakly monotone algebras (somewhat akin to [5]).…”