A relational realizability model for higher-order stateful ADTs

We present a realizability model for reasoning about contextual equivalence of higher-order programs with impredicative polymorphism, recursive types, and higher-order mutable state. The model combines the virtues of two recent earlier models: (1) Ahmed, Dreyer, and Rossberg’s step-indexed logical relations model, which was designed to facilitate proofs of representation independence for “state-dependent” ADTs and (2) Birkedal, Støvring, and Thamsborg’s realizability logical relations model, which was designed to facilitate abstract proofs without tedious step-index arithmetic. The resulting model can be used to give abstract proofs of representation independence for “state-dependent” ADTs.