Abstract
The usual definition of context as “a term with a hole” does not properly address the problems of applying rewrite rules to a context and is in particular inadequate in several respects when a context contains variable bindings. We claim that viewing TRSs as (free) preorder-enriched categories provides a smoother concept of context: on the one hand it allows to decompose a reduction step into redex (+ reduction) and context, on the other it allows to rewrite a context.
By generalising Klop's combinatory reduction systems, we can approach the problem of contexts with variable bindings in a similar way. The rewrite relation of a combinatory reduction system can be defined as the preorder of a certain free preorder-enriched category.
The research reported here was partially supported by SERC grant GR/E 78463.
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© 1993 Springer-Verlag Berlin Heidelberg
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Kahrs, S. (1993). Context rewriting. In: Rusinowitch, M., Rémy, JL. (eds) Conditional Term Rewriting Systems. CTRS 1992. Lecture Notes in Computer Science, vol 656. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56393-8_2
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DOI: https://doi.org/10.1007/3-540-56393-8_2
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