In this dissertation I argue that modal type systems provide an elegant and practical means for controlling local resources in spatially distributed computer programs. A distributed program is one that executes in multiple physical or logical places. It usually does so because those places have local resources that can only be used in those locations. Such resources can include processing power, proximity to data, hardware, or the physical presence of a user. Programmers that write distributed applications therefore need to be able to reason about the places in which their programs will execute. This work provides an elegant and practical way to think about such programs in the form of a type system derived from modal logic. Modal logic allows for reasoning about truth from multiple simultaneous perspectives. These perspectives, called "worlds," are identified with the locations in the distributed program. This enables the programming language to be simultaneously aware of the various hosts involved in a program, their

We introduce a theory of polymorphic concurrent processes, which arises from an interpretation of second-order intuitionistic linear logic propositions as polymorphic session types, in the style of the Girard-Reynolds polymorphic λ-calculus. The interpretation naturally generalizes recent discoveries on the correspondence between linear logic propositions and session types. In our proposed theory, polymorphism accounts for the exchange of abstract communication protocols, and dynamic instantiation of heterogeneous interfaces. Well-typed processes enjoy a strong form of subject reduction (type preservation) and global progress, but also termination (strong normalization) and relational parametricity (representation independence). The latter two properties are obtained by adapting proof techniques in the functional setting to linear session types.

Substructural logics, such as linear logic and ordered logic, have an inherent notion of state and state change. This makes them a natural choice for developing logical frameworks that specify evolving stateful systems. Our previous work has shown that the so-called forward reasoning fragment of ordered linear logic can be used to give clear, concise, and modular specifications of stateful and concurrent features of programming languages. I propose to show that a logical framework based on forward reasoning in ordered linear logic can also be used to formally reason about properties of programming languages in ways that can be verified by both human readers and mechanized proof assistants. 1