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(HO)RPO Revisited

Frédéric Blanqui
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Abstract

The notion of computability closure has been introduced for proving the termination of the combination of higher-order rewriting and beta-reduction. It is also used for strengthening the higher-order recursive path ordering. In the present paper, we study in more details the relations between the computability closure and the (higher-order) recursive path ordering. We show that the first-order recursive path ordering is equal to an ordering naturally defined from the computability closure. In the higher-order case, we get an ordering containing the higher-order recursive path ordering whose well-foundedness relies on the correctness of the computability closure. This provides a simple way to extend the higher-order recursive path ordering to richer type systems.

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Frédéric Blanqui. 2006-09-08. (HO)RPO Revisited. https://arxiv.org/abs/cs/0609037

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