Functional differentiation

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Functional differentiation means computing or approximating the derivative of a function. There are several ways to do this:

  • Approximate the derivative by where is close to zero. (or at best the square root of the machine precision .
  • Compute the derivative of symbolically. This approach is particularly interesting for Haskell.

Functional analysis

If you want to explain the terms Higher order function and Currying to mathematicians, this is certainly a good example. The mathematician writes

and the Haskell programmer writes

derive :: (Fractional a) => a -> (a -> a) -> (a -> a)
derive h f x = (f (x+h) - f x) / h    .

Haskell's derive h approximates the mathematician's . In functional analysis is called a (linear) function operator, because it maps functions to functions. In Haskell derive h is called a higher order function for the same reason. is in curried form. If it would be uncurried, you would write .

Blog Posts

There have been several blog posts on this recently. I think we should gather the information together and make a nice wiki article on it here. For now, here are links to articles on the topic.