Type Level Naturals

This page collects information on how to work with type-level natural numbers, as implemented in the Haskell compiler GHC (ticket #4385).

User's Guide

• Type-Level Naturals Basics
• Natural Numbers: From Values to Types
• Type-Level Operations
• Examples

Notes on Design

• Alternative Design For Singletons
• Avoiding Partial Type Functions
• Naturals or Integers?
• Inductive definitions

Notes on the Implementation

• Implementation of GHC.TypeNats
• Axioms for Natural Number Operators
• GHC Interaction Rules (Notational Conventions)
  • Top-Level Interactions
  • Simple Inert Interactions
  • Solving (<=) Predicates
  • XXX: Write the new rules
• Translation to FC
• Precedences for infix predicates such as ~ and <=

External links

• The implementation resides on branch 'type-nats' of the GHC repo. The following GHC-related related repos also have a type-nats branch:
  • libraries/base
  • libraries/template-haskell
  • utils/haddock

• More advanced example: ​https://github.com/yav/memory-arrays/tree/master