module Research where

import Control.Monad.State
import Data.List (intercalate)
import Data.Map (Map)

import qualified Data.Map as Map

data T = Leaf | Stem T | Fork T T
  deriving (Show, Eq, Ord)

apply :: T -> T -> T
apply Leaf b                            = Stem b
apply (Stem a) b                        = Fork a b
apply (Fork Leaf a) _                   = a
apply (Fork (Stem a1) a2) b             = apply (apply a1 b) (apply a2 b)
apply (Fork (Fork a1 a2) a3) Leaf       = a1
apply (Fork (Fork a1 a2) a3) (Stem u)   = apply a2 u
apply (Fork (Fork a1 a2) a3) (Fork u v) = apply (apply a3 u) v

reduce :: T -> T
reduce expr =
  let next = step expr
  in if next == expr then expr else reduce next

step :: T -> T
step (Fork left right) = reduce (apply (reduce left) (reduce right))
step (Stem inner) = Stem (reduce inner)
step t = t

-- SKI Combinators
_S :: T
_S = Fork (Stem (Fork Leaf Leaf)) Leaf

_K :: T
_K = Stem Leaf

-- Identity
-- We use the "point-free" style which drops a redundant node
-- Full I form (SKK): Fork (Stem (Stem Leaf)) (Stem Leaf)
_I :: T
_I = Fork (Stem (Stem Leaf)) Leaf 

-- Booleans
_false :: T
_false = Leaf

_true :: T
_true = Stem Leaf

_not :: T
_not = Fork (Fork _true (Fork Leaf _false)) Leaf

-- Marshalling
ofString :: String -> T
ofString str = ofList (map ofNumber (map fromEnum str))

ofNumber :: Int -> T
ofNumber 0 = Leaf
ofNumber n =
  Fork
    (if odd n then Stem Leaf else Leaf)
    (ofNumber (n `div` 2))

ofList :: [T] -> T
ofList [] = Leaf
ofList (x:xs) = Fork x (ofList xs)

toNumber :: T -> Either String Int
toNumber Leaf = Right 0
toNumber (Fork Leaf rest) = case toNumber rest of
  Right n -> Right (2 * n)
  Left err -> Left err
toNumber (Fork (Stem Leaf) rest) = case toNumber rest of
  Right n -> Right (1 + 2 * n)
  Left err -> Left err
toNumber _ = Left "Invalid Tree Calculus number"

toString :: T -> Either String String
toString tc = case toList tc of
  Right list -> traverse (fmap toEnum . toNumber) list
  Left err -> Left "Invalid Tree Calculus string"

toList :: T -> Either String [T]
toList Leaf = Right []
toList (Fork x rest) = case toList rest of
  Right xs -> Right (x : xs)
  Left err -> Left err
toList _ = Left "Invalid Tree Calculus list"

-- Utility
toAscii :: T -> String
toAscii tree = go tree "" True
  where
    go :: T -> String -> Bool -> String
    go Leaf prefix isLast =
      prefix ++ (if isLast then "`-- " else "|-- ") ++ "Leaf\n"
    go (Stem t) prefix isLast =
      prefix ++ (if isLast then "`-- " else "|-- ") ++ "Stem\n"
        ++ go t (prefix ++ (if isLast then "    " else "|   ")) True
    go (Fork left right) prefix isLast =
      prefix ++ (if isLast then "`-- " else "|-- ") ++ "Fork\n"
        ++ go left (prefix ++ (if isLast then "    " else "|   ")) False
        ++ go right (prefix ++ (if isLast then "    " else "|   ")) True

rules :: IO ()
rules = putStr $ header
              ++ (unlines $ tcRules)
              ++ (unlines $ haskellRules)
              ++ footer
  where
    tcRules :: [String]
    tcRules =
      [ "|                                                                               |"
      , "|                  ┌--------- | Tree Calculus | ---------┐                      |"
      , "|                  | 1.  t  t      a b       -> a        |                      |"
      , "|                  | 2.  t (t a)   b c       -> a c (b c)|                      |"
      , "|                  | 3a. t (t a b) c t       -> a        |                      |"
      , "|                  | 3b. t (t a b) c (t u)   -> b u      |                      |"
      , "|                  | 3c. t (t a b) c (t u v) -> c u v    |                      |"
      , "|                  └-------------------------------------┘                      |"
      , "|                                                                               |"
      ]
    haskellRules :: [String]
    haskellRules =
      [ "| ┌------------------------------ | Haskell | --------------------------------┐ |"
      , "| |                                                                           | |"
      , "| | data T = Leaf | Stem T | Fork TT                                          | |"
      , "| |                                                                           | |"
      , "| | apply :: T -> T -> T                                                      | |"
      , "| | apply Leaf b                            = Stem b                          | |"
      , "| | apply (Stem a) b                        = Fork a b                        | |"
      , "| | apply (Fork Leaf a) _                   = a                               | |"
      , "| | apply (Fork (Stem a1) a2) b             = apply (apply a1 b) (apply a2 b) | |"
      , "| | apply (Fork (Fork a1 a2) a3) Leaf       = a1                              | |"
      , "| | apply (Fork (Fork a1 a2) a3) (Stem u)   = apply a2 u                      | |"
      , "| | apply (Fork (Fork a1 a2) a3) (Fork u v) = apply (apply a3 u) v            | |"
      , "| └---------------------------------------------------------------------------┘ |"
      ]
    header :: String
    header = "┌-------------------- | Rules for evaluating Tree Calculus | -------------------┐\n"
    footer :: String
    footer = "└-------------------- | Rules for evaluating Tree Calculus | -------------------┘\n"