{-# LANGUAGE DisambiguateRecordFields #-}
{-# LANGUAGE DuplicateRecordFields    #-}

{-|
    Hoon's `map` and `set` types and conversions to/from Nouns.
-}
module Urbit.Noun.Tree
    ( HoonSet, setToHoonSet, setFromHoonSet
    , HoonMap, mapToHoonMap, mapFromHoonMap
    , mug
    ) where

import ClassyPrelude
import Control.Lens  hiding (non)

import Urbit.Atom
import Urbit.Noun.Conversions ()
import Urbit.Noun.Convert
import Urbit.Noun.Core
import Urbit.Noun.TH

import Data.Bits        (shiftR, xor)
import Data.Hash.Murmur (murmur3)
import GHC.Natural      (Natural)


-- Types -----------------------------------------------------------------------

data NounVal a = NounVal
    { non ∷ Noun
    , val ∷ !a
    }

data HoonTreeNode a = NTN
    { n ∷ NounVal a
    , l ∷ HoonTree a
    , r ∷ HoonTree a
    }
  deriving (Eq, Ord, Show)

data HoonTree a = E | Node (HoonTreeNode a)
  deriving (Eq, Ord, Show)

pattern N n l r = Node (NTN n l r)

newtype HoonSet a = HoonSet { unHoonSet ∷ HoonTree a }
  deriving newtype (Eq, Ord, Show, FromNoun, ToNoun)

newtype HoonMap k v = HoonMap { unHoonMap ∷ HoonTree (k, v) }
  deriving newtype (Eq, Ord, Show, FromNoun, ToNoun)


-- Instances -------------------------------------------------------------------

instance Eq (NounVal a) where
  (==) = on (==) non

instance Ord (NounVal a) where
  compare = comparing non

instance ToNoun (NounVal a) where
  toNoun = non

instance Show a ⇒ Show (NounVal a) where
  show = show . val

instance FromNoun a ⇒ FromNoun (NounVal a) where
    parseNoun x = NounVal x <$> parseNoun x

instance ToNoun a ⇒ ToNoun (HoonTree a) where
    toNoun E        = A 0
    toNoun (Node n) = toNoun n

instance FromNoun a ⇒ FromNoun (HoonTree a) where
    parseNoun (A 0) = pure E
    parseNoun n     = Node <$> parseNoun n

deriveNoun ''HoonTreeNode


-- Mug -------------------------------------------------------------------------

type Nat = Natural

slowMug ∷ Noun → Nat
slowMug = trim 0xcafe_babe . \case
    A a   → a
    C h t → mix (slowMug h) $ mix 0x7fff_ffff (slowMug t)
  where
    trim ∷ Nat → Nat → Nat
    trim syd key =
        if 0/=ham then ham else trim (succ syd) key
      where
        haz = muk syd (met 3 key) key
        ham = mix (rsh 0 31 haz) (end 0 31 haz)

mix ∷ Nat → Nat → Nat
mix = xor

-- Murmur3
muk ∷ Nat → Nat → Nat → Nat
muk seed len =
    fromIntegral . murmur3 (word32 seed) . resize . atomBytes
  where
    resize ∷ ByteString → ByteString
    resize buf =
      case compare (length buf) (int len) of
          EQ → buf
          LT → error "bad-muk"
          GT → error "bad-muk"
--        LT → buf <> replicate (len - length buf) 0
--        GT → take len buf

int ∷ Integral i ⇒ i → Int
int = fromIntegral

word32 ∷ Integral i ⇒ i → Word32
word32 = fromIntegral

bex ∷ Nat → Nat
bex = (2^)

end ∷ Nat → Nat → Nat → Nat
end blockSize blocks n =
  n `mod` (bex (bex blockSize * blocks))

rsh ∷ Nat → Nat → Nat → Nat
rsh blockSize blocks n =
    shiftR n $ fromIntegral $ (bex blockSize * blocks)

met ∷ Nat → Nat → Nat
met bloq = go 0
  where
    go c 0 = c
    go c n = go (succ c) (rsh bloq 1 n)

-- XX TODO
mug ∷ Noun → Nat
mug = slowMug


-- Order -----------------------------------------------------------------------

{-
    Orders in ascending double mug hash order, collisions fall back to dor.
-}
mor ∷ Noun → Noun → Bool
mor a b = if c == d then dor a b else c < d
  where
    c = mug $ A $ mug a
    d = mug $ A $ mug b

{-
    Orders in ascending tree depth.
-}
dor ∷ Noun → Noun → Bool
dor a       b       | a == b = True
dor (A a)   (C _ _)          = True
dor (C x y) (A b)            = False
dor (A a)   (A b)            = a < b
dor (C x y) (C p q) | x == p = dor y q
dor (C x y) (C p q)          = dor x p

{-
    Orders in ascending +mug hash order.

    Collisions fall back to dor.
-}
gor ∷ Noun → Noun → Bool
gor a b = if c==d then dor a b else c<d
  where (c, d) = (mug a, mug b)

morVal, gorVal ∷ NounVal a → NounVal a → Bool
morVal = on mor non
gorVal = on gor non


--------------------------------------------------------------------------------

nounVal ∷ ToNoun a ⇒ Iso' a (NounVal a)
nounVal = iso to val
  where
    to x = NounVal (toNoun x) x

treeToList ∷ ∀a. HoonTree a → [a]
treeToList = go []
  where
    go ∷ [a] → HoonTree a → [a]
    go acc = \case
        E                → acc
        Node (NTN v l r) → go (go (val v : acc) l) r

setFromHoonSet ∷ Ord a ⇒ HoonSet a → Set a
setFromHoonSet = setFromList . treeToList . unHoonSet

mapFromHoonMap ∷ Ord k ⇒ HoonMap k v → Map k v
mapFromHoonMap = mapFromList . treeToList . unHoonMap

setToHoonSet ∷ ∀a. (Ord a, ToNoun a) ⇒ Set a → HoonSet a
setToHoonSet = HoonSet . foldr put E . fmap (view nounVal) . setToList
  where
    put x = \case
        E                       → N x E E
        Node a | x == n a       → Node a
        Node a | gorVal x (n a) → lef x a
        Node a                  → rit x a

    rit x a = put x (r a) & \case
        E                           → error "bad-put-set"
        Node c | morVal (n a) (n c) → N (n a) (l a) (Node c)
        Node c                      → N (n c) (N (n a) (l a) (l c)) (r c)

    lef x a = put x (l a) & \case
        E                           → error "bad-put-set"
        Node c | morVal (n a) (n c) → N (n a) (Node c) (r a)
        Node c                      → N (n c) (l c) (N (n a) (r c) (r a))

p ∷ (ToNoun a, ToNoun b) ⇒ NounVal (a,b) → NounVal a
p = view (from nounVal . to fst . nounVal)

pq ∷ (ToNoun a, ToNoun b) ⇒ NounVal (a,b) → (NounVal a, NounVal b)
pq = boof . view (from nounVal)
  where
    boof (x, y) = (x ^. nounVal, y ^. nounVal)

mapToHoonMap ∷ ∀k v. (ToNoun k, ToNoun v, Ord k, Ord v) ⇒ Map k v → HoonMap k v
mapToHoonMap = HoonMap . foldr put E . fmap (view nounVal) . mapToList
  where
    put ∷ NounVal (k, v) → HoonTree (k, v) → HoonTree (k, v)
    put kv@(pq -> (b, c)) = \case
      E                            → N kv E E
      Node a | kv == n a           → Node a
      Node a | b  == p (n a)       → N kv (l a) (r a)
      Node a | gorVal b (p $ n a)  → lef kv a
      Node a                       → rit kv a

    lef kv@(pq -> (b, c)) a = put kv (l a) & \case
      E                                   → error "bad-put-map"
      Node d | morVal (p $ n a) (p $ n d) → N (n a) (Node d) (r a)
      Node d                              → N (n d) (l d) (N (n a) (r d) (r a))

    rit kv@(pq -> (b, c)) a = put kv (r a) & \case
      E                                   → error "bad-put-map"
      Node d | morVal (p $ n a) (p $ n d) → N (n a) (l a) (Node d)
      Node d                              → N (n d) (N (n a) (l a) (l d)) (r d)