A decorated proof system for exceptions

In this paper, we first provide a careful description of the denotational semantics of exceptions in an object-oriented setting. Then we define a proof system for exceptions which is sound with respect to this denotational semantics. Our proof system is close to the syntax, as in effect systems, in the sense that the exceptions do not appear explicitly in the type of expressions which may raise them, much like compiler qualifiers or specifiers. But our system also involves different kind of equations, in order to separate the verification of properties that are true only up to effects from the verification of generic properties. Thanks to a duality between the global state effect and the core part of the exception effect, the proofs are in two parts: the first part is generic and can be directly dualized from the proofs on global states, while the second part uses specific rules. These specific rules are related to the encapsulation of the core part into some control for the conditional raising and handling of exceptions.