Modular reasoning about concurrent higher-order imperative programs

Modern mainstream programming languages permit a powerful combination of language features: concurrency, higher-order functions, and mutable shared data structures. These features are all very important for programming in practice. However, it is wellknown that the combination of them makes it difficult to write correct and secure programs, and it is therefore important to develop mathematically-based techniques for formal reasoning about correctness and security of programs with these features. To get scalable methods that apply to realistic programs, it is crucial that the mathematical models and logics support modular reasoning, meaning that (1) specifications and proofs are compositional wrt. the program structure; and (2) specifications and proofs can concentrate on the resources that a program actually acts upon, instead of its entire state. In this talk I will give an overview of some of the central developments that my group has worked on when generalizing reasoning techniques for simpler programming languages to concurrent, higher-order, imperative languages. I will consider both relational models and program logics based on higher-order separation logic.