Refinement Types as Higher-Order Dependency Pairs

Author Cody Roux

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Cody Roux

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Cody Roux. Refinement Types as Higher-Order Dependency Pairs. In 22nd International Conference on Rewriting Techniques and Applications (RTA'11). Leibniz International Proceedings in Informatics (LIPIcs), Volume 10, pp. 299-312, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)


Refinement types are a well-studied manner of performing in-depth analysis on functional programs. The dependency pair method is a very powerful method used to prove termination of rewrite systems; however its extension to higher-order rewrite systems is still the subject of active research. We observe that a variant of refinement types allows us to express a form of higher-order dependency pair method: from the rewrite system labeled with typing information, we build a type-level approximated dependency graph, and describe a type level embedding preorder. We describe a syntactic termination criterion involving the graph and the preorder, which generalizes the simple projection criterion of Middeldorp and Hirokawa, and prove our main result: if the graph passes the criterion, then every well-typed term is strongly normalizing.
  • Dependency Pairs
  • Higher-Order
  • Refinement Types


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