Termination of simply typed term rewriting by translation and labelling

Authors:
Takahito Aoto;Toshiyuki Yamada
Affiliations:
Research Institute of Electrical Communication, Tohoku University, Japan;Faculty of Engineering, Mie University, Japan
Venue:
RTA'03 Proceedings of the 14th international conference on Rewriting techniques and applications
Year:
2003

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Abstract

Simply typed term rewriting proposed by Yamada (RTA 2001) is a framework of term rewriting allowing higher-order functions. In contrast to the usual higher-order term rewriting frameworks, simply typed term rewriting dispenses with bound variables. This paper presents a method for proving termination of simply typed term rewriting systems (STTRSs, for short). We first give a translation of STTRSs into many-sorted first-order TRSs and show that termination problem of STTRSs is reduced to that of many-sorted first-order TRSs. Next, we introduce a labelling method which is applied to first-order TRSs obtained by the translation to facilitate termination proof of them; our labelling employs an extension of semantic labelling where terms are interpreted on a many-sorted algebra.