Automatic Differentiation in 38 lines of Haskell

CommunityNews · 18 September 2022 01:01

Automatic Differentiation in 38 lines of Haskell using Operator Overloading and Dual Numbers. Inspired by Beautiful differentiation.
Automatic Differentiation in 38 lines of Haskell using Operator Overloading and Dual Numbers. Inspired by Beautiful differentiation - AD.hs

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https://gist.github.com/ttesmer/948df432cf46ec6db8c1e83ab59b1b21

AD.hs

{-# LANGUAGE TypeSynonymInstances #-}
data Dual d = D Float d deriving Show
type Float' = Float

diff :: (Dual Float' -> Dual Float') -> Float -> Float'
diff f x = y'
  where D y y' = f (D x 1)

class VectorSpace v where
  zero  :: v

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example.md

# Automatic Differentiation in 38 lines of Haskell
(See discussion [on Hacker News](https://news.ycombinator.com/item?id=32879734))

You can now differentiate (almost[^1]) any differentiable hyperbolic, polynomial, exponential, and/or trigonometric function.
Let's use the polynomial $f(x) = 2x^3 + 3x^2 + 4x + 2$, whose straightforward derivative, $f'(x) = 6x^2 + 6x + 4$, can be used to verify the AD program.

```haskell
λ> f x = 2 * x^3 + 3 * x^2 + 4 * x + 2 -- our polynomial
λ> f 10
2342

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