{-# LANGUAGE TupleSections #-}
module Diagonal where

import Colonnade
import Data.Profunctor
import Data.Bifunctor

-- Row numbers, as integers with two extra values at the end
data RowNumber = RN Int | Ellipsis | Omega deriving Eq
instance Show RowNumber where
  show (RN n) = show n
  show Ellipsis = "..."
  show Omega = "ω"

-- Rendered cell data, along with its row number and an optional value to show instead
data RenderCell a = RC {
    cellRow :: Maybe RowNumber,  -- Nothing if this is a header; Just . RC otherwise
    cellData :: Either String a  -- Left if fixed display data, a otherwise
  } deriving Functor

-- If a forced value is availaible, use it; otherwise, show the inside
instance Show a => Show (RenderCell a) where
  show (RC _ (Left s))   = s
  show (RC _ (Right x))  = show x

-- Lift a RenderCell over Either to an Either over RenderCells
-- If the force-string is set (cellData is a Left), then a `Left` version is produced
liftRC :: RenderCell (Either a b) -> Either (RenderCell a) (RenderCell b)
liftRC (RC rn (Left x))          = Left $ RC rn $ Left x
liftRC (RC rn (Right (Left v)))  = Left $ RC rn $ Right v
liftRC (RC rn (Right (Right v))) = Right $ RC rn $ Right v

-- Single column with a fixed header and data coming from a row number
newColumn header f = columns f (\_ -> Headed $ RC Nothing (Left header)) [()]

-- Numbered rows of data, as opposed to data for rendering
data DiagRow a = DR {
    rowNumber :: RowNumber,
    rowData :: [a]
  } deriving Functor

-- Same as `newColumn`, but reads into a DiagRow's row numberRows
-- The display function `f` is used to convert the value to a String
newColumnR header f = newColumn header (\_ c -> RC (Just $ rowNumber c) (Left $ f $ rowNumber c))

-- Number rows with the title "Sequence"
numberColumn = newColumnR "Sequence" show
-- Column of ellipses
ellipsisColumn = newColumnR "..." (const "...")

-- Create a Colonnade over DiagRows by mapping them into lists
-- The ellipsis row is mapped to a cells which always display as ellipses
-- The remaining rows are `Right` if they lie on the main diagonal, or `Left` otherwise
diagBox' n = columns cell headCell [0..n]
  where cell _ (DR Ellipsis  _) = RC (Just Ellipsis) (Left "...")
        cell i (DR rn       rd) = RC (Just rn) $ Right $ (if RN i == rn then Right else Left) (rd !! i)
        headCell i = Headed $ RC Nothing (Left $ show i)

diagBox n = numberColumn <> diagBox' n <> ellipsisColumn

displayRows f = (displayTable .) . tagRows'
  where -- Tag rows by (predicate function, extra value) tuples
        tagRows' [] r@(RC rn _) = Left r  -- Tag missing things as left
        tagRows' ((p, f):ps) r@(RC rn _) = if p == rn then Right (f, r) else tagRows' ps r -- Match found, tag right
        displayTable row = case bimap liftRC (fmap liftRC) row of
          (Left (Left r)) -> Left r
          (Left (Right r)) -> Right $ f r
          (Right (g, r)) -> Right $ g $ either id id r

rowsOmega :: [[a]] -> [a] -> [DiagRow a]
rowsOmega xs y = zipWith (\x n -> DR (RN n) x) xs [0..] ++ [DR Ellipsis [], DR Omega y]

diagData = rowsOmega [
    [1, 2, 3, 4, 5, 6],
    [9, 2, 4, 8, 3, 7],
    [2, 2, 8, 2, 2, 2],
    [2, 3, 9, 3, 9, 9],
    [9, 4, 9, 4, 9, 4],
    [8, 1, 2, 5, 7, 9]
  ]
  [2, 3, 9, 4, 0, 0]

displayDiagTable ps = rmap style . diagBox
  where style    = either show id . displayRows (("Red " ++) . show) (map (, ("Green " ++). show) ps)