{-# OPTIONS_GHC -fglasgow-exts #-}

-- Regular library with functional dependencies

module Regular where

data K a r       = K { unK :: a }
data I r         = I { unI :: r }
data U r         = U
data (f :+: g) r = L (f r) | R (g r)
data (f :*: g) r = f r :*: g r
data C c f r =  C { unC :: f r }

infixr 6 :+:
infixr 7 :*:

class Constructor c where
  conName   :: t c (f :: * -> *) r -> String
  conFixity :: t c (f :: * -> *) r -> Fixity
  conFixity = const Prefix

data Fixity = Prefix | Infix Associativity Int
  deriving (Eq, Show, Ord, Read)

data Associativity = LeftAssociative | RightAssociative | NotAssociative
  deriving (Eq, Show, Ord, Read)

class Regular a where
  type PF a :: * -> *
  from      :: a -> PF a a
  to        :: PF a a -> a