We present a gradual dependently-typed language that supports inductive typefamilies, has decidable type-checking, and provably supports smooth migration between static and dynamic . To facilitate these checks, we define an algebraicnotion of gradual precision, axiomatizing certain semantic properties ofgradual terms . We design a novel a technique for trackingconstraints on type indices, so that dynamic constraint violations signalrun-time errors eagerly . We use approximate normalization for terminating compile-time evaluation . Unlike Eremondi et al., our normalization does not require comparison of variables, allowing us to show termination with a syntactic model that accommodatesinductive types . UnlikeEremondy et al. (2019), our normalized normalization doesn’t require comparison . Our normalization do not require comparisons of variables . We also use a novel technique for . comparison of . variables, however, our normalisation does not need comparison of variable, and it does not . compare of variables to . compare variables,allowing us to . Show termination with syntactic models that accommodate . type families .

Author(s) : Joseph Eremondi, Ronald Garcia, Éric Tanter

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Keywords : normalization - variables - comparison - gradual - type -

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