Crate set_theory 

Set Theory Library

A comprehensive mathematical set theory library implementing standard set operations, multisets, and set laws verification following discrete mathematics principles.

Overview

This library provides:

• CustomSet: Mutable set with unique elements following mathematical set theory
• FrozenSet: Immutable set for thread-safe operations
• MultiSet: Set allowing duplicate elements with multiplicity tracking
• Set Operations: Union, intersection, complement, difference, symmetric difference
• Advanced Operations: Cartesian product, power set, partition validation
• Set Laws: Verification of standard set theory laws (De Morgan, Distributive, etc.)

Features

• Implements standard Rust collection traits (IntoIterator, Eq, Hash)
• Lazy evaluation for expensive operations (power set, cartesian product)
• Type-safe generic implementations
• Comprehensive unit tests and benchmarks
• Optional serialization support (serde)

Quick Start

use set_theory::models::CustomSet;
use set_theory::operations::basic_ops::SetOperations;

// Create sets
let a = CustomSet::from(vec![1, 2, 3, 4]);
let b = CustomSet::from(vec![3, 4, 5, 6]);

// Perform operations
let union = SetOperations::union(&a, &b);
let intersection = SetOperations::intersection(&a, &b);

println!("A ∪ B = {}", union);
println!("A ∩ B = {}", intersection);

Module Structure

• traits: Core traits for set operations
• models: Set implementations (CustomSet, FrozenSet, MultiSet)
• operations: Basic and advanced set operations
• laws: Set theory law verification
• utils: Helper utilities (equality, pretty printing)

Re-exports

pub use laws::set_laws::SetLaws;

pub use models::custom_set::CustomSet;

pub use models::frozen_set::FrozenSet;

pub use models::multiset::MultiSet;

pub use operations::advanced_ops::AdvancedSetOperations;

pub use operations::basic_ops::SetOperations;

Modules

laws

Laws Module

models

Models Module

operations

Operations Module

traits

Traits Module

utils

Utils Module