The Marriage of Bisimulations and Kripke Logical Relations Technical Appendix

A Logical Step Forward in Parametric Bisimulations

In the last several years, a number of effective methods have been developed for reasoning about program equivalence in higher-order imperative languages like ML. Most recently, we proposed parametric bisimulations (PBs), which fruitfully synthesize the direct coinductive style of bisimulations with the flexible invariants on local state afforded by Kripke logical relations, and which furthermo...

Parametric Bisimulations

In the last several years, a number of effective methods have been developed for reasoning about program equivalence in higher-order imperative languages like ML. Most recently, we proposed relation transition systems (RTSs), which fruitfully synthesize the direct coinductive style of bisimulations with the flexible invariants on local state afforded by Kripke logical relations, and which furth...

Kripke Open Bisimulation - A Marriage of Game Semantics and Operational Techniques

Proving that two programs are contextually equivalent is notoriously hard, particularly for functional languages with references (i.e., local states). Many operational techniques have been designed to prove such equivalences, and fully abstract denotational model, using game semantics, have been built for such languages. In this work, we marry ideas coming from trace semantics, an operational v...

Limitations of Applicative Bisimulation (Preliminary Report)

We present a series of examples that illuminate an important aspect of the semantics of higher-order functions with local state. Namely that certain behaviour of such functions can only be observed by providing them with arguments that contain the functions themselves. This provides evidence for the necessity of complex conditions for functions in modern semantics for state, such as logical rel...

Parametric Bisimulations: A Logical Step Forward Technical Appendix