# divarvel/Arithmetic-Trees

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A simple datastructure used to describe arithmetic expressions.

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# Arithmetic Trees

## Purpose

This is just the port of Java practicals at École Centrale de Nantes. The goal is to describe polynomials as trees, then evaluate them or derive them. Since I'm fairly new to Haskell, this code has been written just for fun. Comments are welcome !

## Usage

### Define a tree

``````let plus = Binary Plus (Leaf (Val 2)) (Leaf X) -- (2 + x)
let cos = Unary Cos (Leaf X)  -- cos(x)
``````

The following binary operators are supported

``````Plus, Minus, Times, Div, Pow
``````

The following unary operators are supported

``````Cos, Sin, Tan
``````

`Tree` is an instance of `Show`. The expressions are displayed in a nice infix notation.

((42 + 10) * x)

### Evaluate a tree

eval (Binary Pow (Leaf (Val x)) (Leaf (Val 2))) -- 4

### Evaluate a tree for a given value

eval (replace (Binary Pow (Leaf (Val x)) (Leaf (Val 2))) 2) -- 4

### Derive a tree

derive (Binary Plus (Binary Times (Leaf (X)) (Leaf (Val 12))) (Leaf (X)))

### Clean a tree

The derived tree is often unnecessarily cluttered. You can clean it by simplifying (`1*x`, `0*x`, `0+x` and so on).

clean (Binary Times (Val (Leaf 0)) (Val (Leaf 1)))

Again, this is just me playing with Haskell. If you have comments / suggestions, I'll be glad to hear them.

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