期刊名称：Electronic Proceedings in Theoretical Computer Science
电子版ISSN：2075-2180
出版年度：2019
卷号：307
页码：55-67
DOI：10.4204/EPTCS.307.6
语种：English
出版社：Open Publishing Association
摘要：Cedille is a relatively recent tool based on a Curry-style pure type theory, without a primitive datatype system. Using novel techniques based on dependent intersection types, inductive datatypes with their induction principles are derived. One benefit of this approach is that it allows exploration of new or advanced forms of inductive datatypes. This paper reports work in progress on one such form, namely higher-order abstract syntax (HOAS). We consider the nature of HOAS in the setting of pure type theory, comparing with the traditional concept of environment models for lambda calculus. We see an alternative, based on what we term Kripke function-spaces, for which we can derive a weakly initial algebra in Cedille. Several examples are given using the encoding.
