A Principled Approach to Ornamentation in ML

Ornaments are a way to describe changes in datatype definitions reorganizing, adding, or dropping some pieces of data so that functions operating on the bare definition can be partially and sometimes totally lifted into functions operating on the ornamented structure. We propose an extension of ML with higher-order ornaments, demonstrate its expressiveness with a few typical examples, including code refactoring, study the metatheoretical properties of ornaments, and describe their elaboration process. We formalize ornamentation via an a posteriori abstraction of the bare code, returning a generic term, which lives in a meta-language above ML. The lifted code is obtained by application of the generic term to well-chosen arguments, followed by staged reduction, and some remaining simplifications. We use logical relations to closely relate the lifted code to the bare code.