A System F with Call-by-Name Exceptions

We present an extension of System F with call-by-name exceptions. The type system is enriched with two syntactic constructs: a union type A ? ∪{ε} for programs of type A whose execution may raise the exception ε at top level, and a corruption type A{ε} for programs that may raise the exception ε in any evaluation context (not necessarily at top level). We present the syntax and reduction rules of the system, as well as its typing and subtyping rules. We then study its properties, such as confluence. Finally, we construct a realizability model using orthogonality techniques, from which we deduce that well-typed programs are weakly normalizing and that the ones who have the type of natural numbers really compute a natural number, without raising exceptions.