(Not who you are replying to) Not sure if it’s specifically related to DBSP but checkout incremental DataFun (slide ~55 of https://www.rntz.net/files/stl2017-da

(Not who you are replying to) Not sure if it’s specifically related to DBSP but checkout incremental DataFun (slide ~55 of https://www.rntz.net/files/stl2017-datafun-slides.pdf https://www.rntz.net/files/stl2017-datafun-slides.pdf) and the paper cited there: A Theory of Changes for Higher Order Languages: Incrementalizing Lambda-calculi by Static Differentiation (Cai et. al, PLDI 2014).