A Modal Calculus for Exception Handling

The exception monad, while an adequate mechanism for providing the denotational semantics of exceptions, is somewhat awkward to program with. Just as any other monad, it forces a programming style in which exceptional computations are explicitly sequentialized in the program text. In addition, values of computation types must usually be tested before use, in order to determine if they correspond to a raised exception. In this paper we propose a type system that rearranges the monadic formulation, so that the above shortcomings are avoided. Instead of the exception monad, we propose the operator from the modal logic S4 to encode exceptional computation. The way tracking of exceptions is organized in the modal system is exactly dual to the monadic case, reflecting the well-known property that is actually a comonad.