General supervised learning as change propagation with delta lenses

TL;DR

This paper extends delta lenses with a learning framework over parameterized model transformations, organizing them into a symmetric monoidal category and demonstrating compositional properties.

Contribution

It introduces asymmetric learning delta lenses with amendments and formalizes their structure within a symmetric monoidal category.

Findings

Ala-lenses can be composed sequentially and in parallel while maintaining well-behaved properties.

Well-behaved ala-lenses form a full symmetric monoidal subcategory.

The framework integrates learning into the delta lens formalism for bidirectional transformations.

Abstract

Delta lenses are an established mathematical framework for modelling and designing bidirectional model transformations. Following the recent observations by Fong et al, the paper extends the delta lens framework with a a new ingredient: learning over a parameterized space of model transformations seen as functors. We define a notion of an asymmetric learning delta lens with amendment (ala-lens), and show how ala-lenses can be organized into a symmetric monoidal (sm) category. We also show that sequential and parallel composition of well-behaved ala-lenses are also well-behaved so that well-behaved ala-lenses constitute a full sm-subcategory of ala-lenses.