{-# LANGUAGE
CPP
, FlexibleContexts
, MonoLocalBinds
, ScopedTypeVariables
, TypeApplications
, UndecidableInstances
#-}
{-# OPTIONS_GHC -fno-warn-orphans #-}
{-# OPTIONS_GHC -fno-warn-unused-imports #-}
module Data.Group.Generics
( )
where
import Data.Functor.Const
( Const(..) )
import Data.Functor.Identity
( Identity(..) )
import Data.Ord
( Down(..) )
import Data.Proxy
( Proxy(..) )
import GHC.Generics
( Generic(..)
, U1(..), Rec1(..), M1(..), K1(..), Par1(..)
, (:*:)(..), (:.:)(..)
)
import Generic.Data
( Generically(..), GenericProduct(..) )
import Data.Group
( Group(..), Abelian )
ginvert :: forall g. ( Generic g, Group ( Rep g () ) ) => g -> g
ginvert :: g -> g
ginvert = Rep g () -> g
forall a x. Generic a => Rep a x -> a
to (Rep g () -> g) -> (g -> Rep g ()) -> g -> g
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Group (Rep g ()) => Rep g () -> Rep g ()
forall m. Group m => m -> m
invert @( Rep g () ) (Rep g () -> Rep g ()) -> (g -> Rep g ()) -> g -> Rep g ()
forall b c a. (b -> c) -> (a -> b) -> a -> c
. g -> Rep g ()
forall a x. Generic a => a -> Rep a x
from
gpow :: forall n g. ( Integral n, Generic g, Group ( Rep g () ) ) => g -> n -> g
gpow :: g -> n -> g
gpow g
x n
n = Rep g () -> g
forall a x. Generic a => Rep a x -> a
to ( Rep g () -> n -> Rep g ()
forall m x. (Group m, Integral x) => m -> x -> m
pow @( Rep g () ) ( g -> Rep g ()
forall a x. Generic a => a -> Rep a x
from g
x ) n
n )
instance
( Generic g
, Monoid ( GenericProduct g )
, Group ( Rep g () )
)
=> Group ( GenericProduct g ) where
invert :: GenericProduct g -> GenericProduct g
invert = GenericProduct g -> GenericProduct g
forall g. (Generic g, Group (Rep g ())) => g -> g
ginvert
pow :: GenericProduct g -> x -> GenericProduct g
pow GenericProduct g
x x
n = GenericProduct g -> x -> GenericProduct g
forall n g.
(Integral n, Generic g, Group (Rep g ())) =>
g -> n -> g
gpow GenericProduct g
x x
n
instance
( Generic g
, Semigroup g
, Monoid ( Generically g )
, Group ( Rep g () )
)
=> Group ( Generically g ) where
invert :: Generically g -> Generically g
invert = Generically g -> Generically g
forall g. (Generic g, Group (Rep g ())) => g -> g
ginvert
pow :: Generically g -> x -> Generically g
pow Generically g
x x
n = Generically g -> x -> Generically g
forall n g.
(Integral n, Generic g, Group (Rep g ())) =>
g -> n -> g
gpow Generically g
x x
n
instance Group (U1 p) where
invert :: U1 p -> U1 p
invert U1 p
_ = U1 p
forall k (p :: k). U1 p
U1
pow :: U1 p -> x -> U1 p
pow U1 p
_ x
_ = U1 p
forall k (p :: k). U1 p
U1
instance Group (f p) => Group (Rec1 f p) where
invert :: Rec1 f p -> Rec1 f p
invert (Rec1 f p
g) = f p -> Rec1 f p
forall k (f :: k -> *) (p :: k). f p -> Rec1 f p
Rec1 (f p -> f p
forall m. Group m => m -> m
invert f p
g)
pow :: Rec1 f p -> x -> Rec1 f p
pow (Rec1 f p
g) x
n = f p -> Rec1 f p
forall k (f :: k -> *) (p :: k). f p -> Rec1 f p
Rec1 (f p -> x -> f p
forall m x. (Group m, Integral x) => m -> x -> m
pow f p
g x
n)
instance Group (f p) => Group (M1 i c f p) where
invert :: M1 i c f p -> M1 i c f p
invert (M1 f p
g) = f p -> M1 i c f p
forall k i (c :: Meta) (f :: k -> *) (p :: k). f p -> M1 i c f p
M1 (f p -> f p
forall m. Group m => m -> m
invert f p
g)
pow :: M1 i c f p -> x -> M1 i c f p
pow (M1 f p
g) x
n = f p -> M1 i c f p
forall k i (c :: Meta) (f :: k -> *) (p :: k). f p -> M1 i c f p
M1 (f p -> x -> f p
forall m x. (Group m, Integral x) => m -> x -> m
pow f p
g x
n)
instance Group g => Group (K1 i g p) where
invert :: K1 i g p -> K1 i g p
invert (K1 g
g) = g -> K1 i g p
forall k i c (p :: k). c -> K1 i c p
K1 (g -> g
forall m. Group m => m -> m
invert g
g)
pow :: K1 i g p -> x -> K1 i g p
pow (K1 g
g) x
n = g -> K1 i g p
forall k i c (p :: k). c -> K1 i c p
K1 (g -> x -> g
forall m x. (Group m, Integral x) => m -> x -> m
pow g
g x
n)
instance Group g => Group (Par1 g) where
invert :: Par1 g -> Par1 g
invert (Par1 g
g) = g -> Par1 g
forall p. p -> Par1 p
Par1 (g -> g
forall m. Group m => m -> m
invert g
g)
pow :: Par1 g -> x -> Par1 g
pow (Par1 g
g) x
n = g -> Par1 g
forall p. p -> Par1 p
Par1 (g -> x -> g
forall m x. (Group m, Integral x) => m -> x -> m
pow g
g x
n)
#if !MIN_VERSION_groups(0,5,0)
instance (Group (f1 p), Group (f2 p) ) => Group ((:*:) f1 f2 p) where
invert ( g1 :*: g2 ) = ( invert g1 :*: invert g2 )
pow ( g1 :*: g2 ) n = ( pow g1 n :*: pow g2 n )
instance Group (f (g p)) => Group ((:.:) f g p) where
invert (Comp1 g) = Comp1 (invert g)
pow (Comp1 g) n = Comp1 (pow g n)
instance Group a => Group (Down a) where
invert (Down a) = Down (invert a)
pow (Down a) n = Down (pow a n)
instance Group a => Group (Identity a) where
invert (Identity a) = Identity (invert a)
pow (Identity a) n = Identity (pow a n)
instance Group a => Group (Const a b) where
invert (Const a) = Const (invert a)
pow (Const a) n = Const (pow a n)
instance Group (Proxy s) where
invert _ = Proxy
pow _ _ = Proxy
#endif
instance
( Generic g
, Monoid ( GenericProduct g )
, Abelian ( Rep g () )
)
=> Abelian ( GenericProduct g )
instance
( Generic g
, Semigroup g
, Monoid ( Generically g )
, Abelian ( Rep g () )
)
=> Abelian ( Generically g )
#if !MIN_VERSION_groups(0,5,0)
instance Abelian (U1 p)
instance Abelian (f p) => Abelian (Rec1 f p)
instance Abelian (f p) => Abelian (M1 i c f p)
instance Abelian g => Abelian (K1 i g p)
instance Abelian g => Abelian (Par1 g)
instance (Abelian (f1 p), Abelian (f2 p)) => Abelian ((:*:) f1 f2 p)
instance Abelian (f (g p)) => Abelian ((:.:) f g p)
instance Abelian a => Abelian (Down a)
instance Abelian a => Abelian (Identity a) where
instance Abelian a => Abelian (Const a b) where
instance Abelian (Proxy s) where
#endif