Abstract
We define infinitary combinatory reduction systems (iCRSs). This provides the first extension of infinitary rewriting to higher-order rewriting. We lift two well-known results from infinitary term rewriting systems and infinitary λ-calculus to iCRSs:
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1
every reduction sequence in a fully-extended left-linear iCRS is compressible to a reduction sequence of length at most ω, and
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2
every complete development of the same set of redexes in an orthogonal iCRS ends in the same term.
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Ketema, J., Simonsen, J.G. (2005). Infinitary Combinatory Reduction Systems. In: Giesl, J. (eds) Term Rewriting and Applications. RTA 2005. Lecture Notes in Computer Science, vol 3467. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-32033-3_32
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DOI: https://doi.org/10.1007/978-3-540-32033-3_32
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