We have also applied self-adjusting computation in a number of domains including algorithms, machine learning, and software systems. In these applications, we have solved several important open problems (e.g., geometric problems involving changing and moving data sets, inference algorithms for learning from changing models).
Perhaps the most important idea in self-adjusting computation is the treatment of computation as a "first-class" mathematical and computational object that can be remembered, re-used, and adapted to changes in its environment. Another important idea is the use of type systems that can separate "changeable" computations from "stable" or "invariable" computations that do not and cannot change. The final but crucial idea is the realization of the first class nature of computation as an efficient algorithm. The research overall stands on advances made in what in computer science is known an Theory A and Theory B, combining and fusing techniques from both areas. A key techniques that permeates much of this work is the use of language-based and algorithmic efficiency or cost models that help guarantee efficiency. We have also demonstrated that carefully designed languages and compilers can realize in practice the efficiency predicted by the theoretical efficiency models.