{-# LANGUAGE CPP #-}
{-
	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.Rank			as Attribute.Rank
import qualified	BishBosh.Cartesian.Abscissa		as Cartesian.Abscissa
import qualified	BishBosh.Cartesian.Coordinates		as Cartesian.Coordinates
import qualified	BishBosh.Colour.LogicalColour		as Colour.LogicalColour
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	BishBosh.Type.Mass			as Type.Mass
import qualified	Control.DeepSeq
import qualified	Data.Array.IArray
import qualified	Data.Foldable
import qualified	Data.List

#if defined(USE_UNBOXED_ARRAYS) && !(defined(USE_NEWTYPE_WRAPPERS) || defined(USE_PRECISION))
#define UNBOX
import qualified	Data.Array.Unboxed
#endif

-- | The piece-square value may vary as the game progresses.
type PieceSquareValueByNPieces =
#ifdef UNBOX
	Data.Array.Unboxed.UArray
#else
	Data.Array.IArray.Array
#endif
		Type.Count.NPieces Type.Mass.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
Colour.LogicalColour.nDistinctLogicalColours NPieces -> NPieces -> NPieces
forall a. Num a => a -> a -> a
* NPieces
Component.Piece.nPiecesPerSide
 )

-- | Self-documentation.
type EitherPieceSquareValueByNPiecesByCoordinates	= Either (
#ifdef UNBOX
	Cartesian.Coordinates.UArrayByCoordinates
#else
	Cartesian.Coordinates.ArrayByCoordinates
#endif
		Type.Mass.PieceSquareValue	-- Uninterpolated.
 ) (
	Cartesian.Coordinates.ArrayByCoordinates PieceSquareValueByNPieces	-- Interpolated.
 )

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

instance Control.DeepSeq.NFData PieceSquareByCoordinatesByRank where
	rnf :: PieceSquareByCoordinatesByRank -> ()
rnf
#ifdef UNBOX
		_								= ()
#else
		MkPieceSquareByCoordinatesByRank { deconstruct :: PieceSquareByCoordinatesByRank
-> ArrayByRank EitherPieceSquareValueByNPiecesByCoordinates
deconstruct = ArrayByRank EitherPieceSquareValueByNPiecesByCoordinates
byRank }	= ArrayByRank EitherPieceSquareValueByNPiecesByCoordinates -> ()
forall a. NFData a => a -> ()
Control.DeepSeq.rnf ArrayByRank EitherPieceSquareValueByNPiecesByCoordinates
byRank
#endif

-- | Constructor.
mkPieceSquareByCoordinatesByRank
	:: (Attribute.Rank.Rank -> EitherPieceSquareValueByNPiecesByCoordinates)	-- ^ Convert a /rank/ into either (a /pieceSquareValue/ or a /pieceSquareValue/ which linearly varies with the number of /piece/s remaining) by /coordinates/.
	-> PieceSquareByCoordinatesByRank
mkPieceSquareByCoordinatesByRank :: (Rank -> EitherPieceSquareValueByNPiecesByCoordinates)
-> PieceSquareByCoordinatesByRank
mkPieceSquareByCoordinatesByRank	= ArrayByRank EitherPieceSquareValueByNPiecesByCoordinates
-> PieceSquareByCoordinatesByRank
MkPieceSquareByCoordinatesByRank (ArrayByRank EitherPieceSquareValueByNPiecesByCoordinates
 -> PieceSquareByCoordinatesByRank)
-> ((Rank -> EitherPieceSquareValueByNPiecesByCoordinates)
    -> ArrayByRank EitherPieceSquareValueByNPiecesByCoordinates)
-> (Rank -> EitherPieceSquareValueByNPiecesByCoordinates)
-> PieceSquareByCoordinatesByRank
forall b c a. (b -> c) -> (a -> b) -> a -> c
. [EitherPieceSquareValueByNPiecesByCoordinates]
-> ArrayByRank EitherPieceSquareValueByNPiecesByCoordinates
forall (a :: * -> * -> *) e. IArray a e => [e] -> a Rank e
Attribute.Rank.listArrayByRank ([EitherPieceSquareValueByNPiecesByCoordinates]
 -> ArrayByRank EitherPieceSquareValueByNPiecesByCoordinates)
-> ((Rank -> EitherPieceSquareValueByNPiecesByCoordinates)
    -> [EitherPieceSquareValueByNPiecesByCoordinates])
-> (Rank -> EitherPieceSquareValueByNPiecesByCoordinates)
-> ArrayByRank EitherPieceSquareValueByNPiecesByCoordinates
forall b c a. (b -> c) -> (a -> b) -> a -> c
. ((Rank -> EitherPieceSquareValueByNPiecesByCoordinates)
-> [Rank] -> [EitherPieceSquareValueByNPiecesByCoordinates]
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
	-> Type.Count.NPieces			-- ^ The progress through the game.
	-> Colour.LogicalColour.LogicalColour	-- ^ The /piece/'s /logical colour/.
	-> Attribute.Rank.Rank			-- ^ The /piece/'s /rank/.
	-> Cartesian.Coordinates.Coordinates	-- ^ The /piece/'s location.
	-> Type.Mass.PieceSquareValue
findPieceSquareValue :: PieceSquareByCoordinatesByRank
-> NPieces
-> LogicalColour
-> Rank
-> Coordinates
-> PieceSquareValue
findPieceSquareValue MkPieceSquareByCoordinatesByRank { deconstruct :: PieceSquareByCoordinatesByRank
-> ArrayByRank EitherPieceSquareValueByNPiecesByCoordinates
deconstruct = ArrayByRank EitherPieceSquareValueByNPiecesByCoordinates
byRank } NPieces
nPieces LogicalColour
logicalColour Rank
rank	= (
	(!) (Array Coordinates PieceSquareValue
 -> Coordinates -> PieceSquareValue)
-> (Array Coordinates (Array NPieces PieceSquareValue)
    -> Coordinates -> PieceSquareValue)
-> EitherPieceSquareValueByNPiecesByCoordinates
-> 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
 -> Coordinates -> PieceSquareValue)
-> EitherPieceSquareValueByNPiecesByCoordinates
-> Coordinates
-> PieceSquareValue
forall a b. (a -> b) -> a -> b
$ ArrayByRank EitherPieceSquareValueByNPiecesByCoordinates
byRank ArrayByRank EitherPieceSquareValueByNPiecesByCoordinates
-> Rank -> EitherPieceSquareValueByNPiecesByCoordinates
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
Colour.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
	:: Type.Mass.PieceSquareValue	-- ^ Opening-game.
	-> Type.Mass.PieceSquareValue	-- ^ End-game.
	-> PieceSquareValueByNPieces
interpolatePieceSquareValues :: PieceSquareValue
-> PieceSquareValue -> Array NPieces PieceSquareValue
interpolatePieceSquareValues PieceSquareValue
openingGame PieceSquareValue
endGame	= (NPieces, NPieces)
-> [PieceSquareValue] -> Array NPieces PieceSquareValue
forall (a :: * -> * -> *) e i.
(IArray a e, Ix i) =>
(i, i) -> [e] -> a i e
Data.Array.IArray.listArray (NPieces, NPieces)
nPiecesBounds ([PieceSquareValue] -> Array NPieces PieceSquareValue)
-> ([NPieces] -> [PieceSquareValue])
-> [NPieces]
-> Array NPieces PieceSquareValue
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (NPieces -> PieceSquareValue) -> [NPieces] -> [PieceSquareValue]
forall a b. (a -> b) -> [a] -> [b]
map (
	Rational -> PieceSquareValue
forall a. Fractional a => Rational -> a
fromRational (Rational -> PieceSquareValue)
-> (NPieces -> Rational) -> NPieces -> PieceSquareValue
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (Rational -> Rational -> Rational)
-> (Rational, Rational) -> Rational
forall a b c. (a -> b -> c) -> (a, b) -> c
uncurry Rational -> Rational -> Rational
forall a. Num a => a -> a -> a
(+) ((Rational, Rational) -> Rational)
-> (NPieces -> (Rational, Rational)) -> NPieces -> Rational
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (
		(Rational -> Rational -> Rational
forall a. Num a => a -> a -> a
* PieceSquareValue -> Rational
forall a. Real a => a -> Rational
toRational PieceSquareValue
openingGame) (Rational -> Rational)
-> (Rational -> Rational) -> Rational -> (Rational, Rational)
forall (a :: * -> * -> *) b c c'.
Arrow a =>
a b c -> a b c' -> a b (c, c')
&&& (Rational -> Rational -> Rational
forall a. Num a => a -> a -> a
* PieceSquareValue -> Rational
forall a. Real a => a -> Rational
toRational PieceSquareValue
endGame) (Rational -> Rational)
-> (Rational -> Rational) -> Rational -> Rational
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (Rational
1 Rational -> Rational -> Rational
forall a. Num a => a -> a -> a
-)
	) (Rational -> (Rational, Rational))
-> (NPieces -> Rational) -> NPieces -> (Rational, Rational)
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (
		Rational -> Rational -> Rational
forall a. Fractional a => a -> a -> a
/ NPieces -> Rational
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].
	) (Rational -> Rational)
-> (NPieces -> Rational) -> NPieces -> Rational
forall b c a. (b -> c) -> (a -> b) -> a -> c
. NPieces -> Rational
forall a b. (Integral a, Num b) => a -> b
fromIntegral (NPieces -> Rational)
-> (NPieces -> NPieces) -> NPieces -> Rational
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] -> Array NPieces PieceSquareValue)
-> [NPieces] -> Array NPieces 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
	:: PieceSquareByCoordinatesByRank
	-> (Type.Mass.PieceSquareValue -> ShowS)			-- ^ Format a /pieceSquareValue/.
	-> ShowS							-- ^ The column-delimiter.
	-> (PieceSquareValueByNPieces -> Type.Mass.PieceSquareValue)	-- ^ Select one /PieceSquareValue/ from interpolated values.
	-> ShowS
formatForGNUPlot :: PieceSquareByCoordinatesByRank
-> (PieceSquareValue -> ShowS)
-> ShowS
-> (Array NPieces PieceSquareValue -> PieceSquareValue)
-> ShowS
formatForGNUPlot MkPieceSquareByCoordinatesByRank { deconstruct :: PieceSquareByCoordinatesByRank
-> ArrayByRank EitherPieceSquareValueByNPiecesByCoordinates
deconstruct = ArrayByRank EitherPieceSquareValueByNPiecesByCoordinates
byRank } PieceSquareValue -> ShowS
pieceSquareValueFormatter ShowS
columnDelimiter Array NPieces PieceSquareValue -> PieceSquareValue
selector	= (
	[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] -> ShowS)
-> [EitherPieceSquareValueByNPiecesByCoordinates]
-> 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]
    -> [(Coordinates, [PieceSquareValue])])
-> [EitherPieceSquareValueByNPiecesByCoordinates]
-> 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]])
-> [EitherPieceSquareValueByNPiecesByCoordinates]
-> [(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]])
-> [EitherPieceSquareValueByNPiecesByCoordinates]
-> [[PieceSquareValue]]
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (EitherPieceSquareValueByNPiecesByCoordinates
 -> [PieceSquareValue])
-> [EitherPieceSquareValueByNPiecesByCoordinates]
-> [[PieceSquareValue]]
forall a b. (a -> b) -> [a] -> [b]
map (
	Array Coordinates PieceSquareValue -> [PieceSquareValue]
forall (a :: * -> * -> *) e i. (IArray a e, Ix i) => a i e -> [e]
Data.Array.IArray.elems (Array Coordinates PieceSquareValue -> [PieceSquareValue])
-> (Array Coordinates (Array NPieces PieceSquareValue)
    -> [PieceSquareValue])
-> EitherPieceSquareValueByNPiecesByCoordinates
-> [PieceSquareValue]
forall (a :: * -> * -> *) b d c.
ArrowChoice a =>
a b d -> a c d -> a (Either b c) d
||| (Array NPieces PieceSquareValue -> PieceSquareValue)
-> [Array NPieces PieceSquareValue] -> [PieceSquareValue]
forall a b. (a -> b) -> [a] -> [b]
map Array NPieces PieceSquareValue -> PieceSquareValue
selector {-select one PieceSquareValue from interpolated values-} ([Array NPieces PieceSquareValue] -> [PieceSquareValue])
-> (Array Coordinates (Array NPieces PieceSquareValue)
    -> [Array NPieces PieceSquareValue])
-> Array Coordinates (Array NPieces PieceSquareValue)
-> [PieceSquareValue]
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Array Coordinates (Array NPieces PieceSquareValue)
-> [Array NPieces PieceSquareValue]
forall (t :: * -> *) a. Foldable t => t a -> [a]
Data.Foldable.toList {-ByCoordinates-}
 ) ([EitherPieceSquareValueByNPiecesByCoordinates] -> ShowS)
-> [EitherPieceSquareValueByNPiecesByCoordinates] -> ShowS
forall a b. (a -> b) -> a -> b
$ ArrayByRank EitherPieceSquareValueByNPiecesByCoordinates
-> [EitherPieceSquareValueByNPiecesByCoordinates]
forall (t :: * -> *) a. Foldable t => t a -> [a]
Data.Foldable.toList {-ByRank-} ArrayByRank EitherPieceSquareValueByNPiecesByCoordinates
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