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.
This work was partially supported by a grant from Japan Society for the Promotion of Science, No. 14780187.
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References
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Aoto, T., Yamada, T. (2003). Termination of Simply Typed Term Rewriting by Translation and Labelling. In: Nieuwenhuis, R. (eds) Rewriting Techniques and Applications. RTA 2003. Lecture Notes in Computer Science, vol 2706. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44881-0_27
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DOI: https://doi.org/10.1007/3-540-44881-0_27
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