REPL Calculators

01. Overview

Developed a dual-purpose Read-Eval-Print Loop (REPL) system in Scala designed to handle complex mathematical operations for both standard integers and custom multisets. The project emphasizes the core principles of functional programming, including immutability, recursion, and advanced pattern matching.

The system consists of two distinct calculators sharing a common architectural base, allowing for seamless expression evaluation, variable binding, and automated algebraic simplification.

02. Engineering & Design

The project utilizes a modular inheritance structure where a generic base class manages the core logic, while specific implementations handle unique data types.

• Tree Construction: Implemented a two-stage parsing pipeline that converts infix notation into Reverse Polish Notation via the Shunting Yard algorithm before generating a recursive parse tree.
• Logic Reuse: Leveraged Scala's associated types to create a unified evaluation engine that supports both primitive integers and complex multiset structures without code duplication.
• Pretty Printing: Developed an intelligent output formatter that applies operator precedence rules to minimize unnecessary parentheses, ensuring that simplified expressions remain human-readable.
• Multiset Arithmetic: Engineered custom operators for multiset summation, intersection, and subtraction by managing element multiplicities through immutable Map structures.

03. Algebraic Simplification

A key feature of the system is the simplification engine, which uses deep pattern matching to transform complex expression trees into their most efficient forms.

The engine applies a suite of reduction rules, such as identity properties and distributivity laws, to recursively clean the tree. By utilizing a bottom-up simplification tactic, the system ensures that even deeply nested redundant operations, like adding zero or multiplying by one, are fully resolved. This project highlights the power of functional dispatch in building robust, maintainable software tools.