Environment Classifiers Extended

This paper proposes and develops the basic theory for a new approach to typing multi-stage languages based a notion of environment classifiers. This approach involves explicit but lightweight tracking – at type-checking time – of the origination environment for future-stage computations. Classification is less restrictive than the previously proposed notions of closedness, and allows for both a more expressive typing of the “run” construct and for a unifying account of typed multi-stage programming. The proposed approach to typing requires making crossstage persistence (CSP) explicit in the language. At the same time, it offers concrete new insights into the notion of levels and in turn into CSP itself. Type safety is established in the simply-typed setting. As a first step toward introducing classifiers to the Hindley-Milner setting, we propose an approach to integrating the two, and prove type preservation in this setting.