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A variety of logical frameworks support the use of Higher-Order Abstract Syntax (HOAS) in representing formal systems given via axioms and inference rules and reasoning about them. In such frameworks, object-level binding is encoded directly using meta-level binding. Although these systems seem superficially the same, they differ in a variety of ways; for example, in how they handle a context of assumptions and in what theorems about a given formal system can be expressed and proven. In this paper, the authors present several case studies which highlight a variety of different aspects of reasoning using HOAS, with the intention of providing a basis for qualitative comparison of different systems.
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