The Next 700 Challenge Problems for Reasoning with Higher-Order Abstract Syntax Representations Part 2—A Survey

Over the past three decades, a variety of meta-reasoning systems which support reasoning about higher-order abstract specifications have been designed and developed. In this paper, we survey and compare four meta-reasoning systems, Twelf, Beluga, Abella and Hybrid, using several benchmarks from the open repository ORBI that describes challenge problems for reasoning with higher-order abstract syntax representations. In particular, we investigate how these systems mechanize and support reasoning using a context of assumptions. This highlights commonalities and differences in these systems and is a first step towards translating between them.