Monads as a Solution for Generalized Opacity

In this paper we discuss a conservative extension of the simply-typed lambda calculus in order to model a class of expressions that generalize the notion of opaque contexts. Our extension is based on previous work in the semantics of programming languages aimed at providing a mathematical characterization of computations that produce some kind of side effect (Moggi, 1989), and is based on the notion of monads, a construction in category theory that, intuitively, maps a collection of “simple” values and “simple” functions into a more complex value space, in a canonical way. The main advantages of our approach with respect to traditional analyses of opacity are the fact that we are able to explain in a uniform way a set of different but related phenomena, and that we do so in a principled way that has been shown to also explain other linguistic phenomena (Shan, 2001).