Abstract
This paper studies termination of curryfied term rewriting systems (CTRSs), where functional values are introduced by “partial application” The limitations of syntactic simplification orderings for such systems are discussed. A proof method is proposed, based on three techniques: 1) Requirements on stability and monotonicity are relaxed. 2) Variables and inner function symbols of (potentially) functional types are allowed to contribute in the underlying precedence. 3) A standard polymorphic type system is refined so as to express non-functional polymorphism. Founded on this method, the curryfied path ordering with status (CPOS) is introduced. CPOS coincides with the recursive path ordering with status on first-order terms, and is comparable in strength to other approaches for higher-order rewrite systems, but also allows for polymorphism. Under mild restrictions on the underlying precedence, the so called curry rules are oriented correctly under CPOS.
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Kristoffersen, B. (1996). Termination of curryfied rewrite systems. In: Haveraaen, M., Owe, O., Dahl, OJ. (eds) Recent Trends in Data Type Specification. ADT COMPASS 1995 1995. Lecture Notes in Computer Science, vol 1130. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61629-2_51
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DOI: https://doi.org/10.1007/3-540-61629-2_51
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