Description

This code implements an automatic differentiation algorithm known as forward mode. It operates on a small functional language.

How to calculate my derivatives?

From the Main.hs module, the function differentiateWrapper can be run. This function takes an expression, possibly a function, and evaluates it given a list of arguments. Since we are talking derivatives, these arguments should all be pairs. There are some example Wrapper calls in Main.hs.

The function differentiateWrapper prints results both for exact differentiation using forward mode, and approximate differentiation using finite differences.

Code Structure

To just run examples, Main.hs should be sufficient. Here, a wrapper is defined that calculates the derivative in multiple ways and prints the result.

Language.hs defines the language (its types and possible expressions) this implementation of forward mode operates on. The file includes some "syntactic sugar" to make the concrete syntax examples of our language easier to read. The algebra is defined in Algebra.hs. The PrettyPrint.hs module contains example of an algebra instance of the language and its types, namely a pretty printer.

Preprocessing

Annotate.hs fills in all empty BinOp types. Variable.hs renames all variables to a unique one.

StaticCheck.hs can be used for type-checking.

Differentiation

The differentiation algorithm is a simple fold defined in Forward.hs.

Numerical differentiation (for validation tests) is implemented in Numerical.hs.

Evaluation

An evaluate function is given both in FoldMachine.hs and StackMachine.hs.