We present the first fully abstract normal form bisimulation for call-by-value PCF (PCF v ). Our model is based on a labelled transition system (LTS) that combines elements from applicative bisimulation, environmental bisimulation and game semantics. In order to obtain completeness while avoiding the use of semantic quotienting, the LTS constructs traces corresponding to interactions with possible functional contexts. The model gives rise to a sound and complete technique for checking of PCF v program equivalence, which we implement in a bounded bisimulation checking tool. We test our tool on known equivalences from the literature and new examples.

We propose Pushdown Normal Form (PDNF) Bisimulation to verify contextual equivalence in higher-order functional programming languages with local state. Similar to previous work on Normal Form (NF) bisimulation, PDNF Bisimulation is sound and complete with respect to contextual equivalence. However, unlike traditional NF Bisimulation, PDNF Bisimulation is also decidable for a class of program terms that can reach configurations of unbounded size, so long as the source of unboundedness is the call stack. Our approach relies on the principle that, in model-checking for reachability, pushdown systems can be simulated by finite-state automata designed to accept their initial/final stack content. We embody this in a stack-less Labelled Transition System (LTS), together with an on-the-fly saturation procedure for call stacks, upon which bisimulation is defined. We develop up-to techniques and a prototype implementation able to verify equivalences from the literature and others inspired by real code, which were out of reach for previous work.

We present the first fully abstract normal form bisimulation for call-by-value PCF (PCFv). Our model is based on a labelled transition system (LTS) that combines elements from applicative bisimulation, environmental bisimulation and game semantics. In order to obtain completeness while avoiding the use of semantic quotiening, the LTS constructs traces corresponding to interactions with possible functional contexts. The model gives rise to a sound and complete technique for checking of PCFvprogram equivalence, which we implement in a bounded bisimulation checking tool. We test our tool on known equivalences from the literature and new examples.

Abstract We present a bounded equivalence verification technique for higher-order programs with local state. This technique combines fully abstract symbolic environmental bisimulations similar to symbolic game semantics, novel up-to techniques, and lightweight state invariant annotations. This yields an equivalence verification technique with no false positives or negatives. The technique is bounded-complete, in that all inequivalences are automatically detected given large enough bounds. Moreover, several hard equivalences are proved automatically or after being annotated with state invariants. We realise the technique in a tool prototype called Hobbit and benchmark it with an extensive set of new and existing examples. Hobbit can prove many classical equivalences including all Meyer and Sieber examples.

We present a framework for symbolically executing and model checking higher-order programs with external (open) methods. We focus on the client-library paradigm and in particular we aim to check libraries with respect to any definable client. We combine traditional symbolic execution techniques with operational game semantics to build a symbolic execution semantics that captures arbitrary external behaviour. We prove the symbolic semantics to be sound and complete. This yields a bounded technique by imposing bounds on the depth of recursion and callbacks. We provide an implementation of our technique in the 𝕂 framework and showcase its performance on a custom benchmark based on higher-order coding errors such as reentrancy bugs.