Parameterized cast calculi and reusable meta-theory for gradually typed lambda calculi

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