Abstract Syntax Tree

How does the compiler make sense of my code?

The information is gathered from this link

During my implementation of the Shunting yard algorithm, I used tokens to split the function expression into operators, numbers, functions, etc..

The steps involved in the picture above are:

• The source code is first split into smaller chunks called tokens.
• The tokens are then parsed into a tree called the syntax tree by the parser.

For example, this is how I declared the tokens inside my token.hpp:

enum TokenType { NUMBER, VARIABLE, OPERATOR, FUNCTION, LEFT_PARAN, RIGHT_PARAN};
struct TokenData{
	TokenType type;
	std::string value;
	TokenData(TokenType t, const std::string &expr): type(t), value(expr) {}
};

An Abstract Syntax Tree is an intermediate representation of source code as a tree structure.

One case of this is the Binary Tree which is simply a tree where a node can not have more than 2 children. In this case, the nodes would be operators and the leaves would be operands.

So I will:

• Parse the RPN (Reverse Polish Notation) into a tree structure where each node represents an operation (add, multiply, sin, cos..),
• Traverse the AST and apply differentiation rules recursively,
• Simplify the result,
• Evaluate the Derivative.