Calculator Compiler Project

Introduction and Project Vision

Building a calculator compiler is one of the most rewarding first projects in compiler design. Think of it as your "Hello World" for compilers — it is small enough to complete in a weekend, yet teaches you the core concepts that scale up to real programming language compilers. By the end of this project, you will have built a complete pipeline that takes a string like (2 + 3) * 4 and produces the answer 20, going through proper lexing, parsing, and evaluation stages.

The reason this project is so valuable is that it forces you to confront real compiler problems in miniature. You need to handle operator precedence (why does 2 + 3 * 4 equal 14 and not 20?), you need to deal with grouping through parentheses, and you need to build a recursive structure that mirrors mathematical nesting. Every real compiler faces these same challenges, just with more grammar rules.

Project Scope and Features

Our calculator will support the following operations:

• Arithmetic operators: Addition (+), Subtraction (-), Multiplication (*), Division (/), Modulo (%)
• Parentheses for explicit grouping and overriding default precedence
• Operator precedence: Multiplication and division bind tighter than addition and subtraction
• Left-to-right associativity for operators of equal precedence
• Error handling: Division by zero, malformed expressions, unmatched parentheses
• Interactive mode: A REPL (Read-Eval-Print Loop) for continuous input

The Grammar

Every compiler starts with a grammar — a formal specification of what valid input looks like. For our calculator, we use a context-free grammar that naturally encodes operator precedence through the hierarchy of rules:

Notice the elegant trick here. Because term is defined in terms of factor, and expr is defined in terms of term, multiplication automatically binds tighter than addition. When the parser sees 2 + 3 * 4, it first groups 3 * 4 into a term (giving 12), and then adds 2 to that term (giving 14). This is called precedence by grammar structure, and it is the standard technique used in real compilers.

Step 1: The Lexer (Tokenizer)

The lexer reads raw characters and produces tokens. For our calculator, the token types are simple:

The lexer function scans the input string character by character. It skips whitespace, recognizes multi-digit numbers (including decimals), and maps operator characters to their token types. Here is the core logic:

Step 2: The Parser (Recursive Descent)

The parser implements each grammar rule as a function. This technique is called recursive descent parsing because functions call each other recursively to build the expression tree. The beauty of this approach is that the code directly mirrors the grammar:

Step 3: Tracing Through an Example

Let us trace through the input (2 + 3) * 4 to see how parsing works:

Step 4: The Interactive REPL

Wrapping everything in a Read-Eval-Print Loop gives users an interactive experience:

Testing Your Calculator

Always test edge cases systematically:

Extension Ideas

Once your basic calculator works, consider these enhancements to deepen your understanding:

• Variables: Support x = 5; y = x + 3 using a symbol table (hash map storing variable names to values)
• Functions: Add built-in functions like sin(1.57), sqrt(16), abs(-5) by extending the grammar with function call syntax
• History: Store previous results in a variable ans so users can chain computations
• Multi-line expressions: Support expressions that span multiple lines
• AST generation: Instead of evaluating directly, build an Abstract Syntax Tree first, then walk it to evaluate — this separates parsing from execution and prepares you for real compiler architectures

Key Takeaways

This project teaches several fundamental compiler concepts. First, you learn that grammars encode precedence through their hierarchical structure. Second, you see how recursive descent parsing naturally mirrors grammar rules, making the parser easy to write and debug. Third, you discover that even simple languages need careful error handling — a missing parenthesis or unexpected character must be reported gracefully rather than crashing. These lessons scale directly to building compilers for full programming languages, where the grammar is larger but the techniques remain identical.