Type Refinements in an Open World ( Extended

A refinement is a predicate on the elements of a type that describes their execution behavior. Much work has gone into developing refinements in a closed world, in which the classes of values of a type are fixed statically, as in the case of the natural numbers with zero and succ. Relatively little work has gone into developing refinements in an open world in which new classes may be added dynamically. Here we examine the problem of exception tracking, a perennially problematic typing concept for programming languages, from the point of view of refinements in an open world. Exceptions are decomposed into separate control and data mechanisms, the latter motivating the need for open-world refinements. Exception tracking is thereby repositioned as a matter of program verification, rather than structural typing, integrating behavioral typing with theorem proving even in an open world. Some further applications of dynamic classification and openworld refinements are suggested.