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=== Higher-order rewriting systems === Higher-order rewriting systems are a generalization of first-order term rewriting systems to [[lambda term]]s, allowing higher order functions and bound variables.<ref name=Wolfram>{{cite book |first1=D. A. |last1=Wolfram |title=The Clausal Theory of Types |date=1993 |publisher=Cambridge University Press |pages=47β50 |doi=10.1017/CBO9780511569906|isbn=9780521395380 |s2cid=42331173 }}</ref> Various results about first-order TRSs can be reformulated for HRSs as well.<ref>{{cite book |last1=Nipkow |first1=Tobias |last2=Prehofer |first2=Christian |editor1-last=Bibel |editor1-first=W. |editor2-last=Schmitt |editor2-first=P. |title=Automated Deduction - A Basis for Applications. Volume I: Foundations |date=1998 |publisher=Kluwer |pages=399β430 |chapter=Higher-Order Rewriting and Equational Reasoning |chapter-url=https://www21.in.tum.de/~nipkow/pubs/ded-book.html |access-date=2021-08-16 |archive-date=2021-08-16 |archive-url=https://web.archive.org/web/20210816153129/https://www21.in.tum.de/~nipkow/pubs/ded-book.html |url-status=live }}</ref>
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