{-# LANGUAGE ConstraintKinds #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE TupleSections #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE RankNTypes #-}
module Data.Semiring.V3 where
import Data.Dioid
import Data.Distributive
import Data.Foldable as Foldable (fold, foldl')
import Data.Functor.Rep
import Data.Group
import Data.Prd
import Data.Ring
import Data.Semigroup.Foldable as Foldable1
import Data.Semiring
import Data.Semiring.Module
import Prelude hiding (sum, negate)
data V3 a = V3 !a !a !a deriving (Eq,Ord,Show)
infixl 7 <@>
(<@>) :: Ring a => V3 a -> V3 a -> V3 a
(<@>) (V3 a b c) (V3 d e f) = V3 (b><f << c><e) (c><d << a><f) (a><e << b><d)
{-# INLINABLE (<@>) #-}
triple :: Ring a => V3 a -> V3 a -> V3 a -> a
triple a b c = a <.> b <@> c
{-# INLINE triple #-}
instance Prd a => Prd (V3 a) where
V3 a b c <~ V3 d e f = a <~ d && b <~ e && c <~ f
instance Semigroup a => Semigroup (V3 a) where
(<>) = mzipWithRep (<>)
instance Monoid a => Monoid (V3 a) where
mempty = pureRep mempty
instance Unital a => Semiring (V3 a) where
(><) = mzipWithRep (><)
fromBoolean = pureRep . fromBoolean
instance (Monoid a, Dioid a) => Dioid (V3 a) where
fromNatural = pureRep . fromNatural
instance Group a => Group (V3 a) where
(<<) = mzipWithRep (<<)
instance Functor V3 where
fmap f (V3 a b c) = V3 (f a) (f b) (f c)
{-# INLINE fmap #-}
a <$ _ = V3 a a a
{-# INLINE (<$) #-}
instance Foldable V3 where
foldMap f (V3 a b c) = f a <> f b <> f c
{-# INLINE foldMap #-}
null _ = False
length _ = 3
instance Foldable1 V3 where
foldMap1 f (V3 a b c) = f a <> f b <> f c
{-# INLINE foldMap1 #-}
instance Distributive V3 where
distribute f = V3 (fmap (\(V3 x _ _) -> x) f) (fmap (\(V3 _ y _) -> y) f) (fmap (\(V3 _ _ z) -> z) f)
{-# INLINE distribute #-}
instance Representable V3 where
type Rep V3 = I3
tabulate f = V3 (f I31) (f I32) (f I33)
{-# INLINE tabulate #-}
index (V3 x _ _) I31 = x
index (V3 _ y _) I32 = y
index (V3 _ _ z) I33 = z
{-# INLINE index #-}
data I3 = I31 | I32 | I33 deriving (Eq, Ord, Show)
instance Prd I3 where
(<~) = (<=)
(>~) = (>=)
pcompare = pcompareOrd
instance Minimal I3 where
minimal = I31
instance Maximal I3 where
maximal = I33