1st part (E for Everyone): A concise introduction to logical relations

Logical relations are a powerful technique to prove properties about programs. In particular, for proving that two programs are contextually equivalent.

In this talk, we will see that, in System F (aka the polymorphic lambda calculus), the only program of type ∀ a, a → a is the identity.

I will also sketch how to extend logical relations to realistic languages such as ML.

2nd part (POPL talk rehearsal):

A Logical Relation for Monadic Encapsulation of State

We present a logical relations model of a higher-order functional programming language with impredicative polymorphism, recursive types, and a Haskell-style ST monad type with runST. We use our logical relations model to show that runST provides proper encapsulation of state, by showing that effectful computations encapsulated by runST are heap independent. Furthermore, we show that contextual refinements and equivalences that are expected to hold for pure computations do indeed hold in the presence of runST. This is the first time such relational results have been proven for a language with monadic encapsulation of state. We have formalized all the technical development and results in Coq.