When dealing with math expressions, we often need a way to evaluate them and obtain the result. One effective and interesting approach is to use a recursive descent parser. In this guide, you'll learn how to write a recursive descent parser in Python to evaluate math expressions.
What is a Recursive Descent Parser?
A recursive descent parser is a top-down parser that starts with the highest level grammar rule and recursively applies lower-level grammar rules until it reaches the terminal symbols (tokens). It's called "recursive" because it uses recursive functions to traverse the grammar, and "descent" because it works from the top down.
To illustrate the concept, let's consider we have a simple grammar for arithmetic expressions:
factor are non-terminal symbols, while
number and the operators are terminal symbols.
Writing a Recursive Descent Parser in Python
Let's build a recursive descent parser in Python step by step.
First, we need to tokenize the input math expression. Tokenization is the process of breaking down the input string into tokens, which are the smallest meaningful units in the expression.
2. Recursive Parsing Functions
We'll implement the parsing functions based on the grammar rules defined earlier. Each non-terminal symbol will have its own corresponding function.
3. Putting It All Together
Now, we can create a function called
evaluate_expression that combines tokenization and parsing to evaluate the given math expression.
4. Testing the Parser
Let's test our recursive descent parser with some sample expressions:
Congratulations! You've just created a recursive descent parser in Python to evaluate math expressions. You can now extend the grammar rules and parsing functions to handle more complex expressions or even other types of languages.