This module implements an advanced capability-based security model using type-level programming features in Haskell. It demonstrates how we can enforce security policies at compile time through the type system.

The implementation uses:

• DataKinds for representing permission types at the type level
• Type families for validating permissions and paths
• GADTs for ensuring type safety with phantom types
• Type-level functions to encode permission logic in the type system
• Phantom types to carry permission information

This creates a powerful permission system that is checked at compile time rather than runtime, and provides stronger guarantees about security properties.

Benefits over traditional capability systems

• Permission errors are caught at compile-time rather than runtime
• Impossible to accidentally use the wrong permission for an operation
• Better documentation through types - the compiler enforces constraints
• More expressive domain modeling with permissions as first-class types

Example usage

-- Create read-only capability for a specific directory
let readCap = createCapability @'Read ["safedir"]

-- Check if a path is allowed and get a typed path
withPath readCap "safedir/file.txt" $ \pathMaybe -> 
  case pathMaybe of
    Nothing -> putStrLn "Access denied"
    Just typedPath -> do
      -- Type system ensures this is a valid read operation
      content <- readFile readCap typedPath
      print content
      
      -- This would be a compile-time error:
      -- writeFile readCap typedPath "New content"