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The research on gradual typing has led to many variations on the GraduallyTyped Lambda Calculus (GTLC) of Siek and Taha (2006) and its underlying castcalculus. For example, Wadler and Findler (2009) added blame tracking, Siek etal. (2009) investigated alternate cast evaluation strategies, and Herman et al.(2010) replaced casts with coercions for space-efficiency. The meta-theory forthe GTLC has also expanded beyond type safety to include blame safety(Tobin-Hochstadt and Felleisen 2006), space consumption (Herman et al. 2010),and the gradual guarantees (Siek et al. 2015). These results have been provenfor some variations of the GTLC but not others. Furthermore, researcherscontinue to develop variations on the GTLC but establishing all of themeta-theory for new variations is time consuming.  This article identifies abstractions that capture similarities between manycast calculi in the form of two parameterized cast calculi, one for thepurposes of language specification and the other to guide space-efficientimplementations. The article then develops reusable meta-theory for these twocalculi, proving type safety, blame safety, the gradual guarantees, and spaceconsumption. Finally, the article instantiates this meta-theory for eight castcalculi including five from the literature and three new calculi. All of thesedefinitions and theorems, including the two parameterized calculi, the reusablemeta-theory, and the eight instantiations, are mechanized in Agda makingextensive use of module parameters and dependent records to define theabstractions.

Parameterized Cast Calculi and Reusable Meta-theory for Gradually Typed Lambda Calculi