Data Definitions in the ACL2 Sedan

We present a data definition framework that enables the convenient specification of data types in ACL2s, the ACL2 Sedan. Our primary motivation for developing the data definition framework was pedagogical. We were teaching undergraduate students how to reason about programs using ACL2s and wanted to provide them with an effective method for defining, testing, and reasoning about data types in the context of an untyped theorem prover. Our framework is now routinely used not only for pedagogical purposes, but also by advanced users. Our framework concisely supports common data definition patterns, e.g., list types, map types, and record types. It also provides support for polymorphic functions. A distinguishing feature of our approach is that we maintain both a predicative and an enumerative characterization of data definitions. In this paper we present our data definition framework via a sequence of examples. We give a complete characterization in terms of tau rules of the inclusion/exclusion relations a data definition induces, under suitable restrictions. The data definition framework is a key component of counterexample generation support in ACL2s, but can be independently used in ACL2, and is available as a community book.