Proving Infinitary Normalization
We investigate the notion of ‘infinitary strong normalization’ (SN ∞ ), introduced in , 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 , 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:σ)→σ, 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 ). Actually, we strengthen this notion to continuous weakly monotone algebras (somewhat akin to ). 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.
KeywordsNormal Form Ground Term Tree Automaton Pigeonhole Principle Dependency Pair
Unable to display preview. Download preview PDF.
- 2.Comon, H., Dauchet, M., Gilleron, R., Löding, C., Jacquemard, F., Lugiez, D., Tison, S., Tommasi, M.: Tree Automata Techniques and Applications (2007), http://www.grappa.univ-lille3.fr/tata
- 6.Klop, J.W., de Vrijer, R.C.: Infinitary Normalization. In: Artemov, S., Barringer, H., d’Avila Garcez, A.S., Lamb, L.C., Woods, J. (eds.) We Will Show Them: Essays in Honour of Dov Gabbay, vol. 2, pp. 169–192. College Publ. (2005)Google Scholar
- 7.Terese: Term Rewriting Systems. Cambridge Tracts in Theoretical Computer Science, vol. 55. Cambridge University Press, Cambridge (2003)Google Scholar