In the self-adjusting computation model, programs can respond automatically and efficiently to input changes by tracking the dynamic data dependencies of the computation and incrementally updating the output as needed. After a run from scratch, the input can be changed and the output can be updated via change-propagation, a mechanism for re-executing the portions of the computation affected by the changes while reusing the unaffected parts. Previous research shows that self-adjusting computation can be effective at achieving near-optimal update bounds for various applications. We address the question of how to write and reason about self-adjusting programs.

We propose a language-based technique for annotating ordinary programs and compiling them into equivalent self-adjusting versions. We also provide a cost semantics and a concept of trace distance that enables reasoning about the effectiveness of self-adjusting computation at the source level. To facilitate asymptotic analysis, we propose techniques for composing and generalizing concrete distances via trace contexts (traces with holes). The translation preserves the extensional semantics of the source programs, the intensional cost of from-scratch runs, and ensures that change-propagation between two evaluations takes time bounded by their relative distance