{-# LANGUAGE
  EmptyDataDecls,
  TypeFamilies,
  UndecidableInstances
  #-}
module Types.Data.Graph.RootPath
    ( GetLPath
    , GetDistance
    , GetLPathNodes
    )
    where

import qualified Types.Data.List     as L
import qualified Types.Data.List.Ops as L

import Types.Data.Bool
import Types.Data.Graph
import Types.Data.Ord

-- NodeID
type family   NodeID lNode
type instance NodeID (LNode nodeID nodeLabel) = nodeID

-- NodeIDA
data NodeIDA
type instance L.App NodeIDA lNode = NodeID lNode

-- NodeLabel
type family   NodeLabel lNode
type instance NodeLabel (LNode nodeID nodeLabel) = nodeLabel

-- FindP
type family   FindP node lPaths
type instance FindP n L.Null                     = L.Null
type instance FindP n (L.Cons (LPath L.Null) ps) = FindP n ps
type instance FindP n (L.Cons (LPath (L.Cons (LNode n' l) ns)) ps)
    = If (n :==: n')
         (L.Cons (LNode n' l) ns)
         (FindP n ps)

-- GetLPath
type GetLPath node lPaths
    = LPath (GetLPath' node lPaths)

-- GetLPath'
type GetLPath' node lPaths
    = L.Reverse (FindP node lPaths)

-- GetDistance
type GetDistance node lPaths
    = NodeLabel (L.Head (FindP node lPaths))

-- GetLPathNodes
type GetLPathNodes node lPaths
    = L.Map NodeIDA (GetLPath' node lPaths)