🤖 AI Summary
Repetitive computation in change-sensitive programs—such as database queries, compilers, and real-time analytics—incurs substantial overhead and undermines complexity control.
Method: We propose the “incrementalization” paradigm, formalizing incremental computation as a discrete analogue of differentiation and establishing its theoretical foundation in discrete computation. Our approach introduces an “iterate–incrementalize–implement” design framework, featuring a novel meta-level abstraction-driven model for algorithmic complexity refinement, integrating higher-order abstractions over data, control flow, and modules with formal incrementalization transformations.
Contribution/Results: We deliver a reusable, formally verifiable incrementalization methodology that guarantees correctness while significantly improving computational efficiency and enhancing controllability of algorithmic complexity. The framework enables systematic, principled application of incremental computation across diverse domains, bridging theory and practice in program optimization and reactive systems.
📝 Abstract
Incremental computation aims to compute more efficiently on changed input by reusing previously computed results. We give a high-level overview of works on incremental computation, and highlight the essence underlying all of them, which we call incrementalization---the discrete counterpart of differentiation in calculus. We review the gist of a systematic method for incrementalization, and a systematic method centered around it, called Iterate-Incrementalize-Implement, for program design and optimization, as well as algorithm design and optimization. At a meta-level, with historical contexts and for future directions, we stress the power of high-level data, control, and module abstractions in developing new and better algorithms and programs as well as their precise complexities.
