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We combine adaptivity and memoization to obtain an incremental computation technique that dramatically improves performance over adaptivity and memoization alone. The key contribution is adaptive memoization, which enables result re-use by matching any subset of the function arguments to a previous function call and updating the result to satisfy the unmatched arguments via adaptivity. We study the technique in the context of a purely functional language, called IFL, and as an ML library. Thedoi:10.1184/r1/6603020 fatcat:uy3psnw6o5abfex2kuq637lkhq