This is the homepage for the Incremental λ-Calculus project. Our goal is to extend database technology for low-overhead incremental computation, based on finite differencing, and apply it to higher-order languages.
A theory of changes for higher-order languages — incrementalizing λ-calculi by static differentiation (updated version). With Yufei Cai, Tillmann Rendel, and Klaus Ostermann. PLDI ’14, pp. 145–155.
If the result of an expensive computation is invalidated by a small change to the input, the old result should be updated incrementally instead of reexecuting the whole computation. We incrementalize programs through their derivative. A derivative maps changes in the program’s input directly to changes in the program’s output, without reexecuting the original program. We present a program transformation taking programs to their derivatives, which is fully static and automatic, supports first-class functions, and produces derivatives amenable to standard optimization.
We prove the program transformation correct in Agda for a family of simply-typed λ-calculi, parameterized by base types and primitives. A precise interface specifies what is required to incrementalize the chosen primitives.
We investigate performance by a case study: We implement in Scala the program transformation, a plugin and improve performance of a nontrivial program by orders of magnitude.
This project benefited from code and ideas of many different people:
Further acknowledgments in the paper itself.
For any question or suggestion, feel free to contact me, Paolo G. Giarrusso, at paolo !dot! giarrusso (at) uni-tuebingen !dot! de.