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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.

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 Bounded Model Checking technique for higherorder programs based on defunctionalization and points-to analysis. The vehicle of our study is a higher-order calculus with general references. Our technique is a symbolic state syntactical translation based on SMT solvers, adapted to a setting where the values passed and stored during computation can be functions of arbitrary order. We prove that our algorithm is sound and provide a prototype implementation with experimental results showcasing its performance. The first novelty of our technique is a presentation of defunctionalization using nominal techniques, which provides a theoretical background to proving soundness of our technique, coupled with SSA adapted to higher-order values. The second novelty is our use of defunctionalization and points-to analysis to directly encode general higher-order functional programs.

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