Patent 8739137 was granted and assigned to Purdue Research Foundation on May, 2014 by the United States Patent and Trademark Office.
The disclosed system provides a transformation-based implementation of forward-mode and reverse-mode automatic differentiation as a built-in, first-class function in a functional programming language. Each of these constructs imposes only a small constant factor of the computational burden (time) of the function itself, and the forward construct has the same properties in terms of space. The functions can be applied to any function, including those involving derivatives and nested closures.