Memoization is an interesting technique that could be used to implement a purely functional spreadsheet, without the need of maintaining a dependency graph. I've written a small article on the subject.
There are many ways to implement incremental computation. One popular method - implemented by spreadsheets - is to keep an up-to-date topologically sorted dependency graph of all cells. â€¨After modification of a cell, a spreadsheet can optimally determine which cells need to be recalculated (without recalculating everything) given its dependency graph.
â€¨In this short paper we will discuss another approach that is based on memoization. â€¨An example is given that uses a divide and conquer algorithm to maximally re-use sums of integers. Next to that, we sketch a possible implementation based on uniquely represented confluently persistent treaps.
edit: small typo