At its core, it is an implementation of the book Structure and Interpretation of Classical Mechanics by Gerald Jay Sussman and Jack Wisdom.

This involves creating a Haskell implementation of the Scheme library scmutils, which includes toolboxes for symbolic algebra, differentiation and integration.

A key feature is that the routines for differentation and integration are agnostic to the underlying type - the same functions are overloaded to work with symbolic expressions or with numerical quantities. For example, we could define a polynomial function

>>> let f a = (1+a)^3

which applies equally to numbers and symbolic expressions:

>>> f 2
27
>>> f x
1.0 + 3.0x + 3.0x² + x³

We can also find the first four derivates both numerically and symbolically:

>>> dTake 4 $ f (dVar 2)
[27,27,18,6]
>>> dTake 4 $ f (dVar x)
[1.0 + 3.0x + 3.0x² + x³,3.0 + 6.0x + 3.0x²,6.0 + 6.0x,6.0]

Eventually the library will include type-agnostic integration routines as well.

Get the book here.

Chris Taylor. You can find me at Stack Overflow or Math.StackExchange or look at my LinkedIn profile or follow me on Twitter.