Interpretations of the gradually-typed lambda calculus

Gradual typing is an approach to integrating static and dynamic type checking within the same language [Siek and Taha 2006]. Given the name "gradual typing", one might think that the most interesting aspect is the type system. It turns out that the dynamic semantics of gradually-typed languages is more complex than the static semantics, with many points in the design space [Wadler and Findler 2009; Siek et al. 2009] and many challenges concerning efficiency [Herman et al. 2007; Hansen 2007; Siek and Taha 2007; Siek and Wadler 2010; Wrigstad et al. 2010; Rastogi et al. 2012]. In this distilled tutorial, we explore the meaning of gradual typing and the challenges to efficient implementation by writing several definitional interpreters and abstract machines in Scheme for the gradually-typed lambda calculus.