4 research outputs found
Counterexamples in Infinitary Rewriting with Non-Fully-Extended Rules
We show counterexamples exist to confluence modulo hypercollapsing subterms, fair normalisation, and the normal form property in orthogonal infinitary higher-order rewriting with non-fully-extended rules. This sets these systems apart from both fully-extended and finite systems, where no such counterexamples are possible
Comparing Böhm-Like Trees
Extending the infinitary rewriting definition of Böhm-like trees to infinitary Combinatory Reduction Systems (iCRSs), we show that each Böhm-like tree defined by means of infinitary rewriting can also be defined by means of a direct approximant function. In addition, we show that counterexamples exists to the reverse implication
Infinitary Combinatory Reduction Systems: Confluence
We study confluence in the setting of higher-order infinitary rewriting, in
particular for infinitary Combinatory Reduction Systems (iCRSs). We prove that
fully-extended, orthogonal iCRSs are confluent modulo identification of
hypercollapsing subterms. As a corollary, we obtain that fully-extended,
orthogonal iCRSs have the normal form property and the unique normal form
property (with respect to reduction). We also show that, unlike the case in
first-order infinitary rewriting, almost non-collapsing iCRSs are not
necessarily confluent
Infinitary Combinatory Reduction Systems: Normalising Reduction Strategies
We study normalising reduction strategies for infinitary Combinatory
Reduction Systems (iCRSs). We prove that all fair, outermost-fair, and
needed-fair strategies are normalising for orthogonal, fully-extended iCRSs.
These facts properly generalise a number of results on normalising strategies
in first-order infinitary rewriting and provide the first examples of
normalising strategies for infinitary lambda calculus