Refinement Types as Higher-Order Dependency Pairs

Roux, Cody

doi:10.4230/lipics.rta.2011.299

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Implementation and Comparison With Other Criteria And Tools1

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2019

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“…In [30], Roux also uses dependency pairs for the termination of simply-typed higher-order rewriting systems, as well as a restricted form of dependent types where a type constant C is annotated by a pattern l representing the set of terms matching l. This extends to patterns the notion of indexed or sized types [18]. Then, for proving the absence of infinite chains, he uses simple projections [17], which can be seen as a particular case of SCT where strictly decreasing arguments are fixed (SCT can also handle permutations in arguments).…”

Section: Implementation and Comparison With Other Criteria And Toolsmentioning

confidence: 99%

Dependency Pairs Termination in Dependent Type Theory Modulo Rewriting

Blanqui,

Genestier,

Hermant

2019

Preprint

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Dependency pairs are a key concept at the core of modern automated termination provers for first-order term rewriting systems. In this paper, we introduce an extension of this technique for a large class of dependently-typed higher-order rewriting systems. This extends previous results by Wahlstedt on the one hand and the first author on the other hand to strong normalization and non-orthogonal rewriting systems. This new criterion is implemented in the type-checker Dedukti.

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Section: Implementation and Comparison With Other Criteria And Toolsmentioning

confidence: 99%