Counterexamples to termination for the direct sum of term rewriting systems
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In a previous work ("Abstract Data Type Systems", TCS 173(2),1997), the last two authors presented a combined language made of a(strongly normalizing) algebraic rewrite system and a typedλ-calculus enriched by pattern-matching definitionsfollowing a certain format, called the "General Schema", whichgeneralizes the usual recursor definitions for natural numbers andsimilar "basic inductive types". This combined language was shownto be strongly normalizing. The purpose of this paper is toreformulate and extend the General Schema in order to make iteasily extensible, to capture a more general class of inductivetypes, called "strictly positive", and to ease the strongnormalization proof of the resulting system. This result provides acomputation model for the combination of an algebraic specificationlanguage based on abstract data types and of a strongly typedfunctional language with strictly positive inductive types.Copyright 2002 Elsevier Science B.V.