On Normalisation of Infinitary Combinatory Reduction Systems

For fully-extended, orthogonal infinitary Combinatory Reduction Systems, we prove that terms with perpetual reductions starting from them do not have (head) normal forms. Using this, we show that needed reduction strategies are normalising for fully-extended, orthogonal infinitary Combinatory Reduct...

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Bibliographic Details
Published inRewriting Techniques and Applications pp. 172 - 186
Main Author Ketema, Jeroen
Format Book Chapter
LanguageEnglish
Published Berlin, Heidelberg Springer Berlin Heidelberg
SeriesLecture Notes in Computer Science
Subjects
Complete Development
Continuous Reduction
Normal Form
Reduction Step
Strong Convergence
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Summary:For fully-extended, orthogonal infinitary Combinatory Reduction Systems, we prove that terms with perpetual reductions starting from them do not have (head) normal forms. Using this, we show that needed reduction strategies are normalising for fully-extended, orthogonal infinitary Combinatory Reduction Systems, and thatweak and strong normalisation coincide for such systems as a whole and, in case reductions are non-erasing, also for terms.
ISBN:9783540705888
3540705880
ISSN:0302-9743
1611-3349
DOI:10.1007/978-3-540-70590-1_12