DALI: An Untyped, CBV Functional Language Supporting First-Order Datatypes with Binders

Writing (meta-)programs that manipulate other (object-) programs poses signi cant technical problems when the objectlanguage itself has a notion of binders and variable occurrences. Higher-order abstract syntax is a representation of object programs that has recently been the focus of several studies. This paper points out a number of limitations of using higher order syntax in a functional context, and argues that DALI, a language based on a simple and elegant proposal made by Dale Miller ten years ago can provide superior support for manipulating such object-languages. Miller's original proposal, however, did not provide any formal treatment. To ll this gap, we present both a big-step and a reduction semantics for DALI, and summarize the results of our extensive study of the semantics, including the rather involved proof of the soundness of the reduction semantics with respect to the big-step semantics. Because our formal development is carried out for the untyped version of the language, we hope it will serve as a solid basis for investigating type system(s) for DALI.