{-
	Copyright (C) 2018 Dr. Alistair Ward

	This file is part of BishBosh.

	BishBosh is free software: you can redistribute it and/or modify
	it under the terms of the GNU General Public License as published by
	the Free Software Foundation, either version 3 of the License, or
	(at your option) any later version.

	BishBosh is distributed in the hope that it will be useful,
	but WITHOUT ANY WARRANTY; without even the implied warranty of
	MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
	GNU General Public License for more details.

	You should have received a copy of the GNU General Public License
	along with BishBosh.  If not, see <http://www.gnu.org/licenses/>.
-}
{- |
 [@AUTHOR@]	Dr. Alistair Ward

 [@DESCRIPTION@]	Defines the relative value of a specific /rank/ of piece, occupying a specific /coordinate/ on the board, at a specific stage in the game.
-}

module BishBosh.Component.PieceSquareByCoordinatesByRank(
-- * Types
-- ** Type-synonyms
--	PieceSquareValueByNPieces,
--	EitherPieceSquareValueByNPiecesByCoordinates,
-- ** Data-types
	PieceSquareByCoordinatesByRank(
--		MkPieceSquareByCoordinatesByRank,
--		deconstruct
	),
-- * Constants
	nPiecesBounds,
	gnuPlotComment,
-- * Functions
	findPieceSquareValue,
	interpolatePieceSquareValues,
	formatForGNUPlot,
-- ** Constructor
	mkPieceSquareByCoordinatesByRank
) where

import			Control.Arrow((&&&), (|||))
import			Data.Array.IArray((!))
import qualified	BishBosh.Attribute.LogicalColour	as Attribute.LogicalColour
import qualified	BishBosh.Attribute.Rank			as Attribute.Rank
import qualified	BishBosh.Cartesian.Abscissa		as Cartesian.Abscissa
import qualified	BishBosh.Cartesian.Coordinates		as Cartesian.Coordinates
import qualified	BishBosh.Component.Piece		as Component.Piece
import qualified	BishBosh.Property.FixedMembership	as Property.FixedMembership
import qualified	BishBosh.Property.Reflectable		as Property.Reflectable
import qualified	BishBosh.Text.ShowList			as Text.ShowList
import qualified	BishBosh.Type.Count			as Type.Count
import qualified	Control.DeepSeq
import qualified	Data.Array.IArray
import qualified	Data.Foldable
import qualified	Data.List

-- | The piece-square value may vary as the game progresses.
type PieceSquareValueByNPieces pieceSquareValue	= Data.Array.IArray.Array Type.Count.NPieces pieceSquareValue

-- | The bounds of the number of pieces on the board, at the end-game & opening-game respectively.
nPiecesBounds :: (Type.Count.NPieces, Type.Count.NPieces)
nPiecesBounds :: (NPieces, NPieces)
nPiecesBounds	= (
	NPieces
3 {-minimum sufficient material-},
	NPieces -> NPieces
forall a b. (Integral a, Num b) => a -> b
fromIntegral NPieces
Attribute.LogicalColour.nDistinctLogicalColours NPieces -> NPieces -> NPieces
forall a. Num a => a -> a -> a
* NPieces
Component.Piece.nPiecesPerSide
 )

-- | Self-documentation.
type EitherPieceSquareValueByNPiecesByCoordinates pieceSquareValue	= Either (
	Cartesian.Coordinates.ArrayByCoordinates pieceSquareValue	-- Uninterpolated.
 ) (
	Cartesian.Coordinates.ArrayByCoordinates (PieceSquareValueByNPieces pieceSquareValue)	-- Interpolated.
 )

-- | The value for each type of /piece/ of occupying each coordinate, at each stage in the lifetime of the game.
newtype PieceSquareByCoordinatesByRank pieceSquareValue	= MkPieceSquareByCoordinatesByRank {
	PieceSquareByCoordinatesByRank pieceSquareValue
-> ArrayByRank
     (EitherPieceSquareValueByNPiecesByCoordinates pieceSquareValue)
deconstruct	:: Attribute.Rank.ArrayByRank (EitherPieceSquareValueByNPiecesByCoordinates pieceSquareValue)
} deriving (PieceSquareByCoordinatesByRank pieceSquareValue
-> PieceSquareByCoordinatesByRank pieceSquareValue -> Bool
(PieceSquareByCoordinatesByRank pieceSquareValue
 -> PieceSquareByCoordinatesByRank pieceSquareValue -> Bool)
-> (PieceSquareByCoordinatesByRank pieceSquareValue
    -> PieceSquareByCoordinatesByRank pieceSquareValue -> Bool)
-> Eq (PieceSquareByCoordinatesByRank pieceSquareValue)
forall pieceSquareValue.
Eq pieceSquareValue =>
PieceSquareByCoordinatesByRank pieceSquareValue
-> PieceSquareByCoordinatesByRank pieceSquareValue -> Bool
forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
/= :: PieceSquareByCoordinatesByRank pieceSquareValue
-> PieceSquareByCoordinatesByRank pieceSquareValue -> Bool
$c/= :: forall pieceSquareValue.
Eq pieceSquareValue =>
PieceSquareByCoordinatesByRank pieceSquareValue
-> PieceSquareByCoordinatesByRank pieceSquareValue -> Bool
== :: PieceSquareByCoordinatesByRank pieceSquareValue
-> PieceSquareByCoordinatesByRank pieceSquareValue -> Bool
$c== :: forall pieceSquareValue.
Eq pieceSquareValue =>
PieceSquareByCoordinatesByRank pieceSquareValue
-> PieceSquareByCoordinatesByRank pieceSquareValue -> Bool
Eq, NPieces -> PieceSquareByCoordinatesByRank pieceSquareValue -> ShowS
[PieceSquareByCoordinatesByRank pieceSquareValue] -> ShowS
PieceSquareByCoordinatesByRank pieceSquareValue -> String
(NPieces
 -> PieceSquareByCoordinatesByRank pieceSquareValue -> ShowS)
-> (PieceSquareByCoordinatesByRank pieceSquareValue -> String)
-> ([PieceSquareByCoordinatesByRank pieceSquareValue] -> ShowS)
-> Show (PieceSquareByCoordinatesByRank pieceSquareValue)
forall pieceSquareValue.
Show pieceSquareValue =>
NPieces -> PieceSquareByCoordinatesByRank pieceSquareValue -> ShowS
forall pieceSquareValue.
Show pieceSquareValue =>
[PieceSquareByCoordinatesByRank pieceSquareValue] -> ShowS
forall pieceSquareValue.
Show pieceSquareValue =>
PieceSquareByCoordinatesByRank pieceSquareValue -> String
forall a.
(NPieces -> a -> ShowS)
-> (a -> String) -> ([a] -> ShowS) -> Show a
showList :: [PieceSquareByCoordinatesByRank pieceSquareValue] -> ShowS
$cshowList :: forall pieceSquareValue.
Show pieceSquareValue =>
[PieceSquareByCoordinatesByRank pieceSquareValue] -> ShowS
show :: PieceSquareByCoordinatesByRank pieceSquareValue -> String
$cshow :: forall pieceSquareValue.
Show pieceSquareValue =>
PieceSquareByCoordinatesByRank pieceSquareValue -> String
showsPrec :: NPieces -> PieceSquareByCoordinatesByRank pieceSquareValue -> ShowS
$cshowsPrec :: forall pieceSquareValue.
Show pieceSquareValue =>
NPieces -> PieceSquareByCoordinatesByRank pieceSquareValue -> ShowS
Show)

instance Control.DeepSeq.NFData pieceSquareValue => Control.DeepSeq.NFData (PieceSquareByCoordinatesByRank pieceSquareValue) where
	rnf :: PieceSquareByCoordinatesByRank pieceSquareValue -> ()
rnf MkPieceSquareByCoordinatesByRank { deconstruct :: forall pieceSquareValue.
PieceSquareByCoordinatesByRank pieceSquareValue
-> ArrayByRank
     (EitherPieceSquareValueByNPiecesByCoordinates pieceSquareValue)
deconstruct = ArrayByRank
  (EitherPieceSquareValueByNPiecesByCoordinates pieceSquareValue)
byRank }	= ArrayByRank
  (EitherPieceSquareValueByNPiecesByCoordinates pieceSquareValue)
-> ()
forall a. NFData a => a -> ()
Control.DeepSeq.rnf ArrayByRank
  (EitherPieceSquareValueByNPiecesByCoordinates pieceSquareValue)
byRank

-- | Constructor.
mkPieceSquareByCoordinatesByRank
	:: (Attribute.Rank.Rank -> EitherPieceSquareValueByNPiecesByCoordinates pieceSquareValue)	-- ^ Convert a /rank/ into either (a /pieceSquareValue/ or a /pieceSquareValue/ which linearly varies with the number of /piece/s remaining) by /coordinates/.
	-> PieceSquareByCoordinatesByRank pieceSquareValue
mkPieceSquareByCoordinatesByRank :: (Rank
 -> EitherPieceSquareValueByNPiecesByCoordinates pieceSquareValue)
-> PieceSquareByCoordinatesByRank pieceSquareValue
mkPieceSquareByCoordinatesByRank	= ArrayByRank
  (EitherPieceSquareValueByNPiecesByCoordinates pieceSquareValue)
-> PieceSquareByCoordinatesByRank pieceSquareValue
forall pieceSquareValue.
ArrayByRank
  (EitherPieceSquareValueByNPiecesByCoordinates pieceSquareValue)
-> PieceSquareByCoordinatesByRank pieceSquareValue
MkPieceSquareByCoordinatesByRank (ArrayByRank
   (EitherPieceSquareValueByNPiecesByCoordinates pieceSquareValue)
 -> PieceSquareByCoordinatesByRank pieceSquareValue)
-> ((Rank
     -> EitherPieceSquareValueByNPiecesByCoordinates pieceSquareValue)
    -> ArrayByRank
         (EitherPieceSquareValueByNPiecesByCoordinates pieceSquareValue))
-> (Rank
    -> EitherPieceSquareValueByNPiecesByCoordinates pieceSquareValue)
-> PieceSquareByCoordinatesByRank pieceSquareValue
forall b c a. (b -> c) -> (a -> b) -> a -> c
. [EitherPieceSquareValueByNPiecesByCoordinates pieceSquareValue]
-> ArrayByRank
     (EitherPieceSquareValueByNPiecesByCoordinates pieceSquareValue)
forall (a :: * -> * -> *) e. IArray a e => [e] -> a Rank e
Attribute.Rank.listArrayByRank ([EitherPieceSquareValueByNPiecesByCoordinates pieceSquareValue]
 -> ArrayByRank
      (EitherPieceSquareValueByNPiecesByCoordinates pieceSquareValue))
-> ((Rank
     -> EitherPieceSquareValueByNPiecesByCoordinates pieceSquareValue)
    -> [EitherPieceSquareValueByNPiecesByCoordinates pieceSquareValue])
-> (Rank
    -> EitherPieceSquareValueByNPiecesByCoordinates pieceSquareValue)
-> ArrayByRank
     (EitherPieceSquareValueByNPiecesByCoordinates pieceSquareValue)
forall b c a. (b -> c) -> (a -> b) -> a -> c
. ((Rank
 -> EitherPieceSquareValueByNPiecesByCoordinates pieceSquareValue)
-> [Rank]
-> [EitherPieceSquareValueByNPiecesByCoordinates pieceSquareValue]
forall a b. (a -> b) -> [a] -> [b]
`map` [Rank]
forall a. FixedMembership a => [a]
Property.FixedMembership.members)

-- | Find the piece-square value, at a stage in the game's lifetime defined by the total number of pieces remaining, for the specified /rank/ & /coordinates/.
findPieceSquareValue
	:: PieceSquareByCoordinatesByRank pieceSquareValue
	-> Type.Count.NPieces				-- ^ The progress through the game.
	-> Attribute.LogicalColour.LogicalColour	-- ^ The /piece/'s /logical colour/.
	-> Attribute.Rank.Rank				-- ^ The /piece/'s /rank/.
	-> Cartesian.Coordinates.Coordinates		-- ^ The /piece/'s location.
	-> pieceSquareValue
findPieceSquareValue :: PieceSquareByCoordinatesByRank pieceSquareValue
-> NPieces
-> LogicalColour
-> Rank
-> Coordinates
-> pieceSquareValue
findPieceSquareValue MkPieceSquareByCoordinatesByRank { deconstruct :: forall pieceSquareValue.
PieceSquareByCoordinatesByRank pieceSquareValue
-> ArrayByRank
     (EitherPieceSquareValueByNPiecesByCoordinates pieceSquareValue)
deconstruct = ArrayByRank
  (EitherPieceSquareValueByNPiecesByCoordinates pieceSquareValue)
byRank } NPieces
nPieces LogicalColour
logicalColour Rank
rank	= (
	(!) (Array Coordinates pieceSquareValue
 -> Coordinates -> pieceSquareValue)
-> (Array Coordinates (Array NPieces pieceSquareValue)
    -> Coordinates -> pieceSquareValue)
-> EitherPieceSquareValueByNPiecesByCoordinates pieceSquareValue
-> Coordinates
-> pieceSquareValue
forall (a :: * -> * -> *) b d c.
ArrowChoice a =>
a b d -> a c d -> a (Either b c) d
||| (
		\Array Coordinates (Array NPieces pieceSquareValue)
byNPiecesByCoordinates	-> (Array NPieces pieceSquareValue -> NPieces -> pieceSquareValue
forall (a :: * -> * -> *) e i.
(IArray a e, Ix i) =>
a i e -> i -> e
! NPieces
nPieces) (Array NPieces pieceSquareValue -> pieceSquareValue)
-> (Coordinates -> Array NPieces pieceSquareValue)
-> Coordinates
-> pieceSquareValue
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (Array Coordinates (Array NPieces pieceSquareValue)
byNPiecesByCoordinates Array Coordinates (Array NPieces pieceSquareValue)
-> Coordinates -> Array NPieces pieceSquareValue
forall (a :: * -> * -> *) e i.
(IArray a e, Ix i) =>
a i e -> i -> e
!)
	) (EitherPieceSquareValueByNPiecesByCoordinates pieceSquareValue
 -> Coordinates -> pieceSquareValue)
-> EitherPieceSquareValueByNPiecesByCoordinates pieceSquareValue
-> Coordinates
-> pieceSquareValue
forall a b. (a -> b) -> a -> b
$ ArrayByRank
  (EitherPieceSquareValueByNPiecesByCoordinates pieceSquareValue)
byRank ArrayByRank
  (EitherPieceSquareValueByNPiecesByCoordinates pieceSquareValue)
-> Rank
-> EitherPieceSquareValueByNPiecesByCoordinates pieceSquareValue
forall (a :: * -> * -> *) e i.
(IArray a e, Ix i) =>
a i e -> i -> e
! Rank
rank
 ) (Coordinates -> pieceSquareValue)
-> (Coordinates -> Coordinates) -> Coordinates -> pieceSquareValue
forall b c a. (b -> c) -> (a -> b) -> a -> c
. if LogicalColour -> Bool
Attribute.LogicalColour.isBlack LogicalColour
logicalColour
	then Coordinates -> Coordinates
forall a. ReflectableOnX a => a -> a
Property.Reflectable.reflectOnX
	else Coordinates -> Coordinates
forall a. a -> a
id

-- | Given the bounds over which two piece-square values vary as the game progresses from opening to end, return linearly interpolated values for all stages.
interpolatePieceSquareValues
	:: Fractional pieceSquareValue
	=> pieceSquareValue	-- ^ Opening-game.
	-> pieceSquareValue	-- ^ End-game.
	-> PieceSquareValueByNPieces pieceSquareValue
interpolatePieceSquareValues :: pieceSquareValue
-> pieceSquareValue -> PieceSquareValueByNPieces pieceSquareValue
interpolatePieceSquareValues pieceSquareValue
openingGame pieceSquareValue
endGame	= (NPieces, NPieces)
-> [pieceSquareValue] -> PieceSquareValueByNPieces pieceSquareValue
forall (a :: * -> * -> *) e i.
(IArray a e, Ix i) =>
(i, i) -> [e] -> a i e
Data.Array.IArray.listArray (NPieces, NPieces)
nPiecesBounds ([pieceSquareValue] -> PieceSquareValueByNPieces pieceSquareValue)
-> ([NPieces] -> [pieceSquareValue])
-> [NPieces]
-> PieceSquareValueByNPieces pieceSquareValue
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (NPieces -> pieceSquareValue) -> [NPieces] -> [pieceSquareValue]
forall a b. (a -> b) -> [a] -> [b]
map (
	(pieceSquareValue -> pieceSquareValue -> pieceSquareValue)
-> (pieceSquareValue, pieceSquareValue) -> pieceSquareValue
forall a b c. (a -> b -> c) -> (a, b) -> c
uncurry pieceSquareValue -> pieceSquareValue -> pieceSquareValue
forall a. Num a => a -> a -> a
(+) ((pieceSquareValue, pieceSquareValue) -> pieceSquareValue)
-> (NPieces -> (pieceSquareValue, pieceSquareValue))
-> NPieces
-> pieceSquareValue
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (
		(pieceSquareValue -> pieceSquareValue -> pieceSquareValue
forall a. Num a => a -> a -> a
* pieceSquareValue
openingGame) (pieceSquareValue -> pieceSquareValue)
-> (pieceSquareValue -> pieceSquareValue)
-> pieceSquareValue
-> (pieceSquareValue, pieceSquareValue)
forall (a :: * -> * -> *) b c c'.
Arrow a =>
a b c -> a b c' -> a b (c, c')
&&& (pieceSquareValue -> pieceSquareValue -> pieceSquareValue
forall a. Num a => a -> a -> a
* pieceSquareValue
endGame) (pieceSquareValue -> pieceSquareValue)
-> (pieceSquareValue -> pieceSquareValue)
-> pieceSquareValue
-> pieceSquareValue
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (pieceSquareValue
1 pieceSquareValue -> pieceSquareValue -> pieceSquareValue
forall a. Num a => a -> a -> a
-)
	) (pieceSquareValue -> (pieceSquareValue, pieceSquareValue))
-> (NPieces -> pieceSquareValue)
-> NPieces
-> (pieceSquareValue, pieceSquareValue)
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (
		pieceSquareValue -> pieceSquareValue -> pieceSquareValue
forall a. Fractional a => a -> a -> a
/ NPieces -> pieceSquareValue
forall a b. (Integral a, Num b) => a -> b
fromIntegral (
			(NPieces -> NPieces -> NPieces) -> (NPieces, NPieces) -> NPieces
forall a b c. (a -> b -> c) -> (a, b) -> c
uncurry NPieces -> NPieces -> NPieces
forall a. Num a => a -> a -> a
subtract (NPieces, NPieces)
nPiecesBounds	-- N.B.: this can't reasonably be zero.
		) -- map into the closed unit-interval [0,1].
	) (pieceSquareValue -> pieceSquareValue)
-> (NPieces -> pieceSquareValue) -> NPieces -> pieceSquareValue
forall b c a. (b -> c) -> (a -> b) -> a -> c
. NPieces -> pieceSquareValue
forall a b. (Integral a, Num b) => a -> b
fromIntegral (NPieces -> pieceSquareValue)
-> (NPieces -> NPieces) -> NPieces -> pieceSquareValue
forall b c a. (b -> c) -> (a -> b) -> a -> c
. NPieces -> NPieces -> NPieces
forall a. Num a => a -> a -> a
subtract (
		(NPieces, NPieces) -> NPieces
forall a b. (a, b) -> a
fst {-minimum-} (NPieces, NPieces)
nPiecesBounds
	)
 ) ([NPieces] -> PieceSquareValueByNPieces pieceSquareValue)
-> [NPieces] -> PieceSquareValueByNPieces pieceSquareValue
forall a b. (a -> b) -> a -> b
$ (NPieces -> NPieces -> [NPieces])
-> (NPieces, NPieces) -> [NPieces]
forall a b c. (a -> b -> c) -> (a, b) -> c
uncurry NPieces -> NPieces -> [NPieces]
forall a. Enum a => a -> a -> [a]
enumFromTo (NPieces, NPieces)
nPiecesBounds

-- | The character used in __GNUPlot__ to denote a comment.
gnuPlotComment :: Char
gnuPlotComment :: Char
gnuPlotComment	= Char
'#'

-- | Format the data for input to __GNUPlot__.
formatForGNUPlot
	:: (pieceSquareValue -> ShowS)						-- ^ Format a /pieceSquareValue/.
	-> ShowS								-- ^ The column-delimiter.
	-> (PieceSquareValueByNPieces pieceSquareValue -> pieceSquareValue)	-- ^ Select one /pieceSquareValue/ from interpolated values.
	-> PieceSquareByCoordinatesByRank pieceSquareValue
	-> ShowS
formatForGNUPlot :: (pieceSquareValue -> ShowS)
-> ShowS
-> (PieceSquareValueByNPieces pieceSquareValue -> pieceSquareValue)
-> PieceSquareByCoordinatesByRank pieceSquareValue
-> ShowS
formatForGNUPlot pieceSquareValue -> ShowS
pieceSquareValueFormatter ShowS
columnDelimiter PieceSquareValueByNPieces pieceSquareValue -> pieceSquareValue
selector MkPieceSquareByCoordinatesByRank { deconstruct :: forall pieceSquareValue.
PieceSquareByCoordinatesByRank pieceSquareValue
-> ArrayByRank
     (EitherPieceSquareValueByNPiecesByCoordinates pieceSquareValue)
deconstruct = ArrayByRank
  (EitherPieceSquareValueByNPiecesByCoordinates pieceSquareValue)
byRank }	= (
	[ShowS] -> ShowS
showsRow (
		Char -> ShowS
showChar Char
gnuPlotComment ShowS -> ShowS -> ShowS
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Char -> ShowS
showChar Char
'x' ShowS -> [ShowS] -> [ShowS]
forall a. a -> [a] -> [a]
: Char -> ShowS
showChar Char
'y' ShowS -> [ShowS] -> [ShowS]
forall a. a -> [a] -> [a]
: (Rank -> ShowS) -> [Rank] -> [ShowS]
forall a b. (a -> b) -> [a] -> [b]
map Rank -> ShowS
forall a. Show a => a -> ShowS
shows [Rank]
Attribute.Rank.range	-- Header comment.
	) ShowS -> ShowS -> ShowS
forall b c a. (b -> c) -> (a -> b) -> a -> c
.
 ) (ShowS -> ShowS)
-> ([EitherPieceSquareValueByNPiecesByCoordinates pieceSquareValue]
    -> ShowS)
-> [EitherPieceSquareValueByNPiecesByCoordinates pieceSquareValue]
-> ShowS
forall b c a. (b -> c) -> (a -> b) -> a -> c
. ((Coordinates, [pieceSquareValue]) -> ShowS -> ShowS)
-> ShowS -> [(Coordinates, [pieceSquareValue])] -> ShowS
forall (t :: * -> *) a b.
Foldable t =>
(a -> b -> b) -> b -> t a -> b
foldr (
	\(Coordinates
coordinates, [pieceSquareValue]
byRank') ShowS
showS	-> let
		(NPieces
x, NPieces
y)	= Coordinates -> NPieces
Cartesian.Coordinates.getX (Coordinates -> NPieces)
-> (Coordinates -> NPieces) -> Coordinates -> (NPieces, NPieces)
forall (a :: * -> * -> *) b c c'.
Arrow a =>
a b c -> a b c' -> a b (c, c')
&&& Coordinates -> NPieces
Cartesian.Coordinates.getY (Coordinates -> (NPieces, NPieces))
-> Coordinates -> (NPieces, NPieces)
forall a b. (a -> b) -> a -> b
$ Coordinates
coordinates
	in [ShowS] -> ShowS
showsRow (
		NPieces -> ShowS
forall a. Show a => a -> ShowS
shows NPieces
x ShowS -> [ShowS] -> [ShowS]
forall a. a -> [a] -> [a]
: NPieces -> ShowS
forall a. Show a => a -> ShowS
shows NPieces
y ShowS -> [ShowS] -> [ShowS]
forall a. a -> [a] -> [a]
: (pieceSquareValue -> ShowS) -> [pieceSquareValue] -> [ShowS]
forall a b. (a -> b) -> [a] -> [b]
map pieceSquareValue -> ShowS
pieceSquareValueFormatter [pieceSquareValue]
byRank'
	) ShowS -> ShowS -> ShowS
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (
		if NPieces
x NPieces -> NPieces -> Bool
forall a. Eq a => a -> a -> Bool
== NPieces
Cartesian.Abscissa.xMax
			then ShowS
terminateRow	-- Separate isolines.
			else ShowS
forall a. a -> a
id
	) ShowS -> ShowS -> ShowS
forall b c a. (b -> c) -> (a -> b) -> a -> c
. ShowS
showS
 ) ShowS
forall a. a -> a
id ([(Coordinates, [pieceSquareValue])] -> ShowS)
-> ([EitherPieceSquareValueByNPiecesByCoordinates pieceSquareValue]
    -> [(Coordinates, [pieceSquareValue])])
-> [EitherPieceSquareValueByNPiecesByCoordinates pieceSquareValue]
-> ShowS
forall b c a. (b -> c) -> (a -> b) -> a -> c
. [Coordinates]
-> [[pieceSquareValue]] -> [(Coordinates, [pieceSquareValue])]
forall a b. [a] -> [b] -> [(a, b)]
zip (
	[Coordinates]
forall a. FixedMembership a => [a]
Property.FixedMembership.members	:: [Cartesian.Coordinates.Coordinates]
 ) ([[pieceSquareValue]] -> [(Coordinates, [pieceSquareValue])])
-> ([EitherPieceSquareValueByNPiecesByCoordinates pieceSquareValue]
    -> [[pieceSquareValue]])
-> [EitherPieceSquareValueByNPiecesByCoordinates pieceSquareValue]
-> [(Coordinates, [pieceSquareValue])]
forall b c a. (b -> c) -> (a -> b) -> a -> c
. [[pieceSquareValue]] -> [[pieceSquareValue]]
forall a. [[a]] -> [[a]]
Data.List.transpose ([[pieceSquareValue]] -> [[pieceSquareValue]])
-> ([EitherPieceSquareValueByNPiecesByCoordinates pieceSquareValue]
    -> [[pieceSquareValue]])
-> [EitherPieceSquareValueByNPiecesByCoordinates pieceSquareValue]
-> [[pieceSquareValue]]
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (EitherPieceSquareValueByNPiecesByCoordinates pieceSquareValue
 -> [pieceSquareValue])
-> [EitherPieceSquareValueByNPiecesByCoordinates pieceSquareValue]
-> [[pieceSquareValue]]
forall a b. (a -> b) -> [a] -> [b]
map (
	Array Coordinates pieceSquareValue -> [pieceSquareValue]
forall (t :: * -> *) a. Foldable t => t a -> [a]
Data.Foldable.toList (Array Coordinates pieceSquareValue -> [pieceSquareValue])
-> (Array Coordinates (PieceSquareValueByNPieces pieceSquareValue)
    -> [pieceSquareValue])
-> EitherPieceSquareValueByNPiecesByCoordinates pieceSquareValue
-> [pieceSquareValue]
forall (a :: * -> * -> *) b d c.
ArrowChoice a =>
a b d -> a c d -> a (Either b c) d
||| (PieceSquareValueByNPieces pieceSquareValue -> pieceSquareValue)
-> [PieceSquareValueByNPieces pieceSquareValue]
-> [pieceSquareValue]
forall a b. (a -> b) -> [a] -> [b]
map PieceSquareValueByNPieces pieceSquareValue -> pieceSquareValue
selector {-select one pieceSquareValue from interpolated values-} ([PieceSquareValueByNPieces pieceSquareValue]
 -> [pieceSquareValue])
-> (Array Coordinates (PieceSquareValueByNPieces pieceSquareValue)
    -> [PieceSquareValueByNPieces pieceSquareValue])
-> Array Coordinates (PieceSquareValueByNPieces pieceSquareValue)
-> [pieceSquareValue]
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Array Coordinates (PieceSquareValueByNPieces pieceSquareValue)
-> [PieceSquareValueByNPieces pieceSquareValue]
forall (t :: * -> *) a. Foldable t => t a -> [a]
Data.Foldable.toList {-ByCoordinates-}
 ) ([EitherPieceSquareValueByNPiecesByCoordinates pieceSquareValue]
 -> ShowS)
-> [EitherPieceSquareValueByNPiecesByCoordinates pieceSquareValue]
-> ShowS
forall a b. (a -> b) -> a -> b
$ ArrayByRank
  (EitherPieceSquareValueByNPiecesByCoordinates pieceSquareValue)
-> [EitherPieceSquareValueByNPiecesByCoordinates pieceSquareValue]
forall (t :: * -> *) a. Foldable t => t a -> [a]
Data.Foldable.toList {-ByRank-} ArrayByRank
  (EitherPieceSquareValueByNPiecesByCoordinates pieceSquareValue)
byRank where
	terminateRow :: ShowS
terminateRow	= Char -> ShowS
showChar Char
'\n'
	showsRow :: [ShowS] -> ShowS
showsRow	= ShowS -> ShowS -> ShowS -> [ShowS] -> ShowS
Text.ShowList.showsDelimitedList ShowS
columnDelimiter ShowS
forall a. a -> a
id ShowS
terminateRow