srtree: A symbolic regression expression tree structure.

srtree is a Haskell library with a data structure and supporting functions to manipulate expression trees for symbolic regression.

The tree-like structure is parameterized by the type of the variables indexing and the return value when evaluating the tree. The most common is to index the variables with Int starting at $0$ and to return a Double. The Functor instance changes the type of the stored/returned values.

The tree supports leaf nodes containing a variable, a free parameter, or a constant value; internal nodes that represents binary operators such as the four basic math operations, logarithm with custom base, and the power of two expressions; and unary functions specified by Function data type.

This library also defines the OptInt class with the operator ^. that represents the integral power. This is needed to automatically simplify some constructs of the tree and also when using interval arithmetic, that requires a special case of integral power.

The SRTree structure has instances for Num, Fractional, Floating which allows to create an expression as a valid Haskell expression such as:

x = Var 0
y = Var 1
expr = x * 2 + sin(y * pi + x) :: SRTree Int Double

There is also a Bifunctor instance that allows to change the type of both parameters, and an Applicative, Foldable, Traversable instances. To traverse by the index type, there is a function called traverseIx.

Other features:

• simplification algorithm (simplify)
• derivative w.r.t. a variable (deriveBy) and w.r.t. a parameter (deriveParamBy)
• evaluation (evalTree)
• relabel free parameters sequentially (relabelParams)
• relabel variables couting their occurrence (relabelOccurrences, used with interval arithmetic)

TODO:

• support more advanced functions
• support conditional branching (IF-THEN-ELSE)