kotlin-mathematical-modeling

What problem does it solve?

Translating formal mathematical and logical specifications into Kotlin code often leads to subtle runtime errors, incorrect invariants, and mixing of incompatible types. This Skill presents design patterns that push correctness to compile time by modeling closed universes, enforcing type safety, guaranteeing immutability, and enabling lazy representations of infinite structures.

Core Features & Use Cases

• Sealed types for closed universes: Encode disjoint unions and force exhaustiveness in pattern matching to eliminate unhandled cases.
• Value classes for zero-cost type safety: Create distinct numeric and domain types that compile down to primitives to avoid accidental mixing while keeping performance.
• Immutability and persistent structures: Design extensional sets and other collections where operations return new instances, aligning code with mathematical definitions and improving thread safety.
• Lazy sequences for infinite structures: Represent infinite sets like the naturals and compose lazily-evaluated transformations without materializing large collections.
• Use Case: Build a Cardinality hierarchy (Finite, CountablyInfinite, Aleph, Unknown), a NaturalNumber value class, an immutable ExtensionalSet, and a NaturalNumbers lazy sequence to model and test mathematical properties in a Kotlin library.

Quick Start

Create a Kotlin module that models cardinality using sealed types, defines NaturalNumber as a value class, implements an immutable ExtensionalSet, and exposes a lazy sequence of natural numbers for testing and composition.