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  • "Saïbi [20] describes an elaboration mechanism inserting coercions between types."
    • Amokrane Saïbi. Typing algorithm in type theory with inheritance. Proceedings of the 24th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages - POPL ’97, 1997. doi:10.1145/263699.263742.
  • https://arxiv.org/pdf/2011.10618.pdf
    • "Hybrid typing... In a similar manner, [Tanter and Tabareau 2015] introduce casts for subset types with decidable properties in Coq. They use an axiom to denote failure, which breaks weak canonicity. Dependent interoperability [Dagand et al. 2018; Osera et al. 2012] supports the combination of dependent and non-dependent typing through deep conversions. All these approaches are more intended as programming languages than as type theories, and none support the notion of (im)precision that is at the heart of gradual typing. Dependent contracts. [Greenberg et al. 2010] relates hybrid typing to dependent contracts, which are dynamically-checked assertions that can relate the result of a function application to its argument [Findler and Felleisen 2002]. The semantics of dependent contracts are subtle because contracts include arbitrary code, and in particular one must be careful not to violate the precondition on the argument in the definition of the postcondition contract [Blume and McAllester 2006]. Also, blame assignment when the result and/or argument are themselves higher-order is subtle. Different variants of dependent contracts have been studied in the literature, which differ in terms of the violations they report and the way they assign blame [Dimoulas et al. 2011; Greenberg et al. 2010]. An in-depth exploration of blame assignment for gradual dependent type theories such as GCIC is an important perspective for future work. Gradual typing. The blame calculus of Wadler and Findler [2009] considers subset types on base types, where the refinement is an arbitrary term, as in hybrid type checking [Knowles and Flanagan 2010]. It however lacks the dependent function types found in other works. Lehmann and Tanter [2017] exploit the Abstracting Gradual Typing (AGT) methodology [Garcia et al. 2016] to design a language with imprecise formulas and implication. They support dependent function types, but gradual refinements are only on base types refined with decidable logical predicates." "[Eremondi et al. 2019]... study the dynamic gradual guarantee, but not its reformulation as graduality [New and Ahmed 2018], which as we explain is strictly stronger in the full dependent setting. Finally, while AGT provided valuable intuitions for this work, graduality as embedding-projection pairs was the key technical driver in the design of CastCIC."

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