A Blame for All (revised)

Several programming languages are beginning to integrate static and dynamic typing, including Racket, Microsoft’s C# 4.0 (Hejlsberg 2010) and TypeScript (Hejlsberg, 2012), Facebook’s PHP (Verlaguet, 2013), and the research languages Sage (Gronski, Knowles, Tomb, Freund, and Flanagan, 2006) and Thorn (Wrigstad, Eugster, Field, Nystrom, and Vitek, 2009). However, an important open question remains, which is how to add parametric polymorphism to languages that combine static and dynamic typing. We present a system that permits a value of dynamic type to be cast to a polymorphic type and vice versa, with relational parametricity enforced by a kind of dynamic sealing along the lines proposed by Matthews and Ahmed (2008) and Neis, Dreyer, and Rossberg (2009). Our development is supported by a variant of the polymorphic lambda calculus that may be of independent interest. It uses type bindings and static casts to maintain a syntactic certificate of parametricity throughout program evaluation. Our system includes a notion of blame, which allows us to show that when casting between a more precise type and a less precise type, any cast failures are due to the less-precisely-typed portion of the program. We also want to show that a cast from a subtype to a supertype cannot fail. This property holds for a relatively weak notion of subtyping (STOP 2009) but we have found a flaw in our proof for the stronger notion of subtyping, which we explain here. Finally, we show that existentials for untyped programs can be encoded in terms of casts through polymorphic types.