Termination of term rewriting: interpretation and type elimination
Journal of Symbolic Computation - Special issue on conditional term rewriting systems
Initial Algebra Semantics and Continuous Algebras
Journal of the ACM (JACM)
Termination of term rewriting using dependency pairs
Theoretical Computer Science - Trees in algebra and programming
Normalization of Infinite Terms
RTA '08 Proceedings of the 19th international conference on Rewriting Techniques and Applications
Matrix interpretations for proving termination of term rewriting
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
Productivity of stream definitions
FCT'07 Proceedings of the 16th international conference on Fundamentals of Computation Theory
RTA '09 Proceedings of the 20th International Conference on Rewriting Techniques and Applications
Highlights in infinitary rewriting and lambda calculus
Theoretical Computer Science
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We investigate the notion of `infinitary strong normalization' (SN *** ), introduced in [6], the analogue of termination when rewriting infinite terms. 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. This global property frequently fails for trivial reasons. For example, in the presence of the collapsing rule tail(x:*** )****** , the infinite term t =tail(0:t) rewrites to itself only. 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]). We show that tree automata can be used as an automatable instance of our framework; an actual implementation is made available along with this paper.