Beautiful differentiation (Conal Elliott)

Automatic differentiation but:

• generalized to arbitrary dimensionality
• generalized to arbitrary order
• employing lazy evaluation – allowing to avoid obfuscation of code

Related

• Constructive solid geometry

External links

Central page linking to all relevant material:

• http://conal.net/papers/beautiful-differentiation/

Actually usable implementation (Haskell library):

• vector-space: Vector & affine spaces, linear maps, and derivatives

vector-space provides classes and generic operations for vector spaces and affine spaces.
It also defines a type of infinite towers of generalized derivatives.
A generalized derivative is a linear transformation rather than one of the common concrete representations (scalars, vectors, matrices, ...).

• Underlying data storage method:
  MemoTrie: Trie-based memo functions

Wikipedia:

• Automatic differentiation