Logical Mobility and Locality Types

We present a type theory characterizing the mobility and locality of program terms in a calculus for distributed computation. The type theory is derived from logical notions of necessity (2A) and possibility (3A) of the modal logic S4 via a Curry-Howard style isomorphism. Logical worlds are interpreted as sites for computation, accessibility corresponds to dependency between processes at those sites. Necessity (2A) describes terms of type A which have a structural kind of mobility or location-independence. Possibility (3A) describes terms of type A located somewhere, perhaps at a remote site. We present the calculus in a setting where the locations are distinguished by stores. Store effects (mutable references) give rise to a class of location-dependent terms, namely the store addresses denoting reference cells. The system of modal types ensures that store addresses are not removed from the location where they are defined.