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The Calculus of Algebraic and Inductive Constructions
, 1998
"... ions can occur in the rewriting rules (either in the lefthand side or in the righthand side). \Delta In higherorder rewrite rules, recursive calls can be compared through a combination of multiset and lexicographic orderings instead of just a multiset ordering. \Delta An adpated version of the ..."
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ions can occur in the rewriting rules (either in the lefthand side or in the righthand side). \Delta In higherorder rewrite rules, recursive calls can be compared through a combination of multiset and lexicographic orderings instead of just a multiset ordering. \Delta An adpated version of the new "General schema" of Jouannaud and Okada [JO97b] catches the recursor rules of any strictly positive inductive type. \Delta For the calculus part, we use a much shorter and simpler strong normalization proof inspired from Geuvers [Geu95]. \Delta For the reducibility of higherorder function symbols, we simplify and improve the proof of Jouannaud and Okada [JO97b]. Definition 2.1 (Algebraic types) Given a set S of sorts, the set T S of algebraic types is inductively defined by the following grammar rule: s := s j (s!s) where s ranges over S. ! associates to the right such that s 1 ! (s 2 !s 3 ) can be written as s 1 !s 2 !s 3 . An algebraic type s 1 ! : : : ! s n is firstorder if s i...