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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, supportsdoi:10.1145/2666356.2594304 fatcat:fuvusucaandoziye7wkrrmluoq