Towards algorithmic typing for DOT (short paper)

The Dependent Object Types (DOT) calculus formalizes key features of Scala. The D<: calculus is the core of DOT. To date, presentations of D<: have used declarative, as opposed to algorithmic, typing and subtyping rules. Unfortunately, algorithmic typing for full D<: is known to be an undecidable problem. We explore the design space for a restricted version of D<: that has decidable typechecking. Even in this simplified D<:, algorithmic typing and subtyping are tricky, due to the "bad bounds" problem. The Scala compiler bypasses bad bounds at the cost of a loss in expressiveness in its type system. Based on the approach taken in the Scala compiler, we present the Step Typing and Step Subtyping relations for D<:. These relations are sound and decidable. They are not complete with respect to the original D<: typing rules.