{-
	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@]	An interface for vector-like data which is orientated to the edges of the board.
-}

module BishBosh.Property.Orientated (
-- * Type-classes
	Orientated(..)
) where

import	Control.Arrow((&&&), (|||))

{- |
	* An interface for vector-like data.

	* CAVEAT: the default implementations are mutually dependent, & could result in infinite recursion.
-}
class Orientated a where
	isVertical :: a -> Bool	-- ^ Whether the datum is aligned with a file of the board.
	isVertical	= (Bool -> Bool -> Bool) -> (Bool, Bool) -> Bool
forall a b c. (a -> b -> c) -> (a, b) -> c
uncurry Bool -> Bool -> Bool
(&&) ((Bool, Bool) -> Bool) -> (a -> (Bool, Bool)) -> a -> Bool
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (a -> Bool
forall a. Orientated a => a -> Bool
isParallel (a -> Bool) -> (a -> Bool) -> a -> (Bool, Bool)
forall (a :: * -> * -> *) b c c'.
Arrow a =>
a b c -> a b c' -> a b (c, c')
&&& Bool -> Bool
not (Bool -> Bool) -> (a -> Bool) -> a -> Bool
forall b c a. (b -> c) -> (a -> b) -> a -> c
. a -> Bool
forall a. Orientated a => a -> Bool
isHorizontal)	-- Default implementation.

	isHorizontal :: a -> Bool	-- ^ Whether the datum is aligned with a rank of the board.
	isHorizontal	= (Bool -> Bool -> Bool) -> (Bool, Bool) -> Bool
forall a b c. (a -> b -> c) -> (a, b) -> c
uncurry Bool -> Bool -> Bool
(&&) ((Bool, Bool) -> Bool) -> (a -> (Bool, Bool)) -> a -> Bool
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (a -> Bool
forall a. Orientated a => a -> Bool
isParallel (a -> Bool) -> (a -> Bool) -> a -> (Bool, Bool)
forall (a :: * -> * -> *) b c c'.
Arrow a =>
a b c -> a b c' -> a b (c, c')
&&& Bool -> Bool
not (Bool -> Bool) -> (a -> Bool) -> a -> Bool
forall b c a. (b -> c) -> (a -> b) -> a -> c
. a -> Bool
forall a. Orientated a => a -> Bool
isVertical)	-- Default implementation.

	isParallel	:: a -> Bool	-- ^ Whether it is parallel to an edge of the board.
	isParallel	= (Bool -> Bool -> Bool) -> (Bool, Bool) -> Bool
forall a b c. (a -> b -> c) -> (a, b) -> c
uncurry Bool -> Bool -> Bool
(||) ((Bool, Bool) -> Bool) -> (a -> (Bool, Bool)) -> a -> Bool
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (a -> Bool
forall a. Orientated a => a -> Bool
isVertical (a -> Bool) -> (a -> Bool) -> a -> (Bool, Bool)
forall (a :: * -> * -> *) b c c'.
Arrow a =>
a b c -> a b c' -> a b (c, c')
&&& a -> Bool
forall a. Orientated a => a -> Bool
isHorizontal)		-- Default implementation.

	isDiagonal	:: a -> Bool	-- ^ Whether it is diagonal (45 degrees) wrt the edges of the board.
	isDiagonal	= (Bool -> Bool -> Bool) -> (Bool, Bool) -> Bool
forall a b c. (a -> b -> c) -> (a, b) -> c
uncurry Bool -> Bool -> Bool
(&&) ((Bool, Bool) -> Bool) -> (a -> (Bool, Bool)) -> a -> Bool
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (a -> Bool
forall a. Orientated a => a -> Bool
isStraight (a -> Bool) -> (a -> Bool) -> a -> (Bool, Bool)
forall (a :: * -> * -> *) b c c'.
Arrow a =>
a b c -> a b c' -> a b (c, c')
&&& Bool -> Bool
not (Bool -> Bool) -> (a -> Bool) -> a -> Bool
forall b c a. (b -> c) -> (a -> b) -> a -> c
. a -> Bool
forall a. Orientated a => a -> Bool
isParallel)	-- Default implementation.

	isStraight :: a -> Bool
	isStraight	= (Bool -> Bool -> Bool) -> (Bool, Bool) -> Bool
forall a b c. (a -> b -> c) -> (a, b) -> c
uncurry Bool -> Bool -> Bool
(||) ((Bool, Bool) -> Bool) -> (a -> (Bool, Bool)) -> a -> Bool
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (a -> Bool
forall a. Orientated a => a -> Bool
isParallel (a -> Bool) -> (a -> Bool) -> a -> (Bool, Bool)
forall (a :: * -> * -> *) b c c'.
Arrow a =>
a b c -> a b c' -> a b (c, c')
&&& a -> Bool
forall a. Orientated a => a -> Bool
isDiagonal)		-- Default implementation.

instance (Orientated l, Orientated r) => Orientated (Either l r) where
	isVertical :: Either l r -> Bool
isVertical	= l -> Bool
forall a. Orientated a => a -> Bool
isVertical (l -> Bool) -> (r -> Bool) -> Either l r -> Bool
forall (a :: * -> * -> *) b d c.
ArrowChoice a =>
a b d -> a c d -> a (Either b c) d
||| r -> Bool
forall a. Orientated a => a -> Bool
isVertical
	isHorizontal :: Either l r -> Bool
isHorizontal	= l -> Bool
forall a. Orientated a => a -> Bool
isHorizontal (l -> Bool) -> (r -> Bool) -> Either l r -> Bool
forall (a :: * -> * -> *) b d c.
ArrowChoice a =>
a b d -> a c d -> a (Either b c) d
||| r -> Bool
forall a. Orientated a => a -> Bool
isHorizontal
	isDiagonal :: Either l r -> Bool
isDiagonal	= l -> Bool
forall a. Orientated a => a -> Bool
isDiagonal (l -> Bool) -> (r -> Bool) -> Either l r -> Bool
forall (a :: * -> * -> *) b d c.
ArrowChoice a =>
a b d -> a c d -> a (Either b c) d
||| r -> Bool
forall a. Orientated a => a -> Bool
isDiagonal
	isParallel :: Either l r -> Bool
isParallel	= l -> Bool
forall a. Orientated a => a -> Bool
isParallel (l -> Bool) -> (r -> Bool) -> Either l r -> Bool
forall (a :: * -> * -> *) b d c.
ArrowChoice a =>
a b d -> a c d -> a (Either b c) d
||| r -> Bool
forall a. Orientated a => a -> Bool
isParallel
	isStraight :: Either l r -> Bool
isStraight	= l -> Bool
forall a. Orientated a => a -> Bool
isStraight (l -> Bool) -> (r -> Bool) -> Either l r -> Bool
forall (a :: * -> * -> *) b d c.
ArrowChoice a =>
a b d -> a c d -> a (Either b c) d
||| r -> Bool
forall a. Orientated a => a -> Bool
isStraight