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We present a novel approach to generic programming over extensible datatypes. Row types capture the structure of records and variants, and can be usedto express record and variant subtyping, record extension, and modularcomposition of case branches. We extend row typing to capture genericprogramming over rows themselves, capturing patterns including liftingoperations to records and variations from their component types, and theduality between cases blocks over variants and records of labeled functions,without placing specific requirements on the fields or constructors present inthe records and variants. We formalize our approach in System R{\omega}, anextension of F{\omega} with row types, and give a denotational semantics for(stratified) R{\omega} in Agda.

Generic Programming with Extensible Data Types; Or, Making Ad Hoc Extensible Data Types Less Ad Hoc