Safe Haskell	None
Language	Haskell2010

Data.IFunctor.Foldable

Contents

Fixpoint for indexed types
Morphisms
Constructive morphisms
Destructive morphisms
Combined morphisms
Monadic morphisms
Distribution Laws
Constructive distribution laws
Destructive distribution laws
Generalized morphisms
Generalized monadic morphisms
Re-exports

Synopsis

newtype IFix f ix = IFix {
- unIFix :: f (IFix f) ix
}
cata :: IFunctor f => (f a ~~> a) -> IFix f ~~> a
prepro :: IFunctor f => (forall b. f b ~~> f b) -> (f a ~~> a) -> IFix f ~~> a
para :: IFunctor f => (f (Product (IFix f) a) ~~> a) -> IFix f ~~> a
zygo :: IFunctor f => (f b ~~> b) -> (f (Product b a) ~~> a) -> IFix f ~~> a
histo :: IFunctor f => (f (ICofree f a) ~~> a) -> IFix f ~~> a
ana :: IFunctor f => (a ~~> f a) -> a ~~> IFix f
postpro :: IFunctor f => (forall b. f b ~~> f b) -> (a ~~> f a) -> a ~~> IFix f
apo :: IFunctor f => (a ~~> f (Sum (IFix f) a)) -> a ~~> IFix f
gapo :: IFunctor f => (b ~~> f b) -> (a ~~> f (Sum b a)) -> a ~~> IFix f
futu :: IFunctor f => (a ~~> f (IFree f a)) -> a ~~> IFix f
hylo :: IFunctor f => (f b ~~> b) -> (a ~~> f a) -> a ~~> b
dyna :: IFunctor f => (f (ICofree f b) ~~> b) -> (a ~~> f a) -> a ~~> b
chrono :: IFunctor f => (f (ICofree f b) ~~> b) -> (a ~~> f (IFree f a)) -> a ~~> b
meta :: (IFunctor f, IFunctor g) => (f a ~~> a) -> (a ~~> b) -> (b ~~> g b) -> IFix f ~~> IFix g
elgot :: forall f a b. IFunctor f => (f a ~~> a) -> (b ~~> Sum a (f b)) -> b ~~> a
coelgot :: forall f a b. IFunctor f => (Product a (f b) ~~> b) -> (a ~~> f a) -> a ~~> b
cataM :: (ITraversable f, Monad m) => (forall ix. SingI ix => f a ix -> m (a ix)) -> forall ix. SingI ix => IFix f ix -> m (a ix)
paraM :: (ITraversable f, Monad m) => (forall ix. SingI ix => f (Product (IFix f) a) ix -> m (a ix)) -> forall ix. SingI ix => IFix f ix -> m (a ix)
anaM :: (ITraversable f, Monad m) => (forall ix. SingI ix => a ix -> m (f a ix)) -> forall ix. SingI ix => a ix -> m (IFix f ix)
apoM :: (ITraversable f, Monad m) => (forall ix. SingI ix => a ix -> m (f (Sum (IFix f) a) ix)) -> forall ix. SingI ix => a ix -> m (IFix f ix)
hyloM :: (ITraversable f, Monad m) => (forall ix. SingI ix => f b ix -> m (b ix)) -> (forall ix. SingI ix => a ix -> m (f a ix)) -> forall ix. SingI ix => a ix -> m (b ix)
dynaM :: (ITraversable f, Monad m) => (forall ix. SingI ix => f (ICofree f b) ix -> m (b ix)) -> (forall ix. SingI ix => a ix -> m (f a ix)) -> forall ix. SingI ix => a ix -> m (b ix)
type DistLaw f g = forall a. f (g a) ~~> g (f a)
distCata :: IFunctor f => DistLaw f IIdentity
distPara :: IFunctor f => DistLaw f (Product (IFix f))
distZygo :: IFunctor f => (f b ~~> b) -> DistLaw f (Product b)
distHisto :: IFunctor f => DistLaw f (ICofree f)
distAna :: IFunctor f => DistLaw IIdentity f
distApo :: IFunctor f => DistLaw (Sum (IFix f)) f
distGApo :: IFunctor f => (b ~~> f b) -> DistLaw (Sum b) f
distFutu :: IFunctor f => DistLaw (IFree f) f
gfold :: forall f w a. (IFunctor f, IComonad w) => DistLaw f w -> (f (w a) ~~> a) -> IFix f ~~> a
gunfold :: forall f m a. (IFunctor f, IMonad m) => DistLaw m f -> (a ~~> f (m a)) -> a ~~> IFix f
ghylo :: forall f w m a b. (IFunctor f, IComonad w, IMonad m) => DistLaw f w -> DistLaw m f -> (f (w b) ~~> b) -> (a ~~> f (m a)) -> a ~~> b
gprepro :: forall f w a. (IFunctor f, IComonad w) => DistLaw f w -> (forall c. f c ~~> f c) -> (f (w a) ~~> a) -> IFix f ~~> a
gpostpro :: forall f m a. (IFunctor f, IMonad m) => DistLaw m f -> (forall c. f c ~~> f c) -> (a ~~> f (m a)) -> a ~~> IFix f
gfoldM :: forall f w m a. (ITraversable f, ITraversable w, IComonad w, Monad m) => DistLaw f w -> (forall ix. SingI ix => f (w a) ix -> m (a ix)) -> forall ix. SingI ix => IFix f ix -> m (a ix)
gunfoldM :: forall f m a x. (ITraversable f, ITraversable m, IMonad m, Monad x) => DistLaw m f -> (forall ix. SingI ix => a ix -> x (f (m a) ix)) -> forall ix. SingI ix => a ix -> x (IFix f ix)
ghyloM :: forall f w m a b x. (ITraversable f, ITraversable w, ITraversable m, IComonad w, IMonad m, Monad x) => DistLaw f w -> DistLaw m f -> (forall ix. SingI ix => f (w b) ix -> x (b ix)) -> (forall ix. SingI ix => a ix -> x (f (m a) ix)) -> forall ix. SingI ix => a ix -> x (b ix)
newtype Const a (b :: k) = Const {
- getConst :: a
}
data Product (f :: k -> Type) (g :: k -> Type) (a :: k) = Pair (f a) (g a)
data Sum (f :: k -> Type) (g :: k -> Type) (a :: k)
- = InL (f a)
- | InR (g a)
class IFunctor f => IComonad f where
- iextract :: f a ~~> a
- iduplicate :: f a ~~> f (f a)
- iextend :: (f a ~~> b) -> f a ~~> f b
type (~~>) a b = forall ix. SingI ix => a ix -> b ix
class IFunctor f where
- imap :: (a ~~> b) -> f a ~~> f b
module Data.IFunctor.Classes
data ICofree f a ix = (a ix) ::< (f (ICofree f a) ix)
data IFree f a ix
- = IPure (a ix)
- | IFree (f (IFree f a) ix)
data IIdentity f ix = IIdentity {
- runIIdentity :: f ix
}
class IFunctor f => IMonad f where
- ipure :: a ~~> f a
- ijoin :: f (f a) ~~> f a
- ibind :: (a ~~> f b) -> f a ~~> f b
class IFunctor f => ITraversable f where
- itraverse :: (Applicative m, SingI ix) => (forall ix. SingI ix => a ix -> m (b ix)) -> f a ix -> m (f b ix)
imapDefault :: ITraversable f => (a ~~> b) -> f a ~~> f b
class SingI (a :: k) where
- sing :: Sing a

Fixpoint for indexed types

newtype IFix f ix Source #

Fixpoint type

Constructors

IFix
Fields unIFix :: f (IFix f) ix

Instances

Instances details

Generic1 (IFix f :: k -> Type) Source #
Instance details Defined in Data.IFunctor.Foldable Associated Types type Rep1 (IFix f) :: k -> Type # Methods from1 :: forall (a :: k0). IFix f a -> Rep1 (IFix f) a # to1 :: forall (a :: k0). Rep1 (IFix f) a -> IFix f a #
(IEq f, SingI ix) => Eq (IFix f ix) Source #
Instance details Defined in Data.IFunctor.Foldable Methods (==) :: IFix f ix -> IFix f ix -> Bool # (/=) :: IFix f ix -> IFix f ix -> Bool #
(IOrd f, SingI ix) => Ord (IFix f ix) Source #
Instance details Defined in Data.IFunctor.Foldable Methods compare :: IFix f ix -> IFix f ix -> Ordering # (<) :: IFix f ix -> IFix f ix -> Bool # (<=) :: IFix f ix -> IFix f ix -> Bool # (>) :: IFix f ix -> IFix f ix -> Bool # (>=) :: IFix f ix -> IFix f ix -> Bool # max :: IFix f ix -> IFix f ix -> IFix f ix # min :: IFix f ix -> IFix f ix -> IFix f ix #
(IRead f, SingI ix) => Read (IFix f ix) Source #
Instance details Defined in Data.IFunctor.Foldable Methods readsPrec :: Int -> ReadS (IFix f ix) # readList :: ReadS [IFix f ix] # readPrec :: ReadPrec (IFix f ix) # readListPrec :: ReadPrec [IFix f ix] #
(IShow f, SingI ix) => Show (IFix f ix) Source #
Instance details Defined in Data.IFunctor.Foldable Methods showsPrec :: Int -> IFix f ix -> ShowS # show :: IFix f ix -> String # showList :: [IFix f ix] -> ShowS #
Generic (IFix f ix) Source #
Instance details Defined in Data.IFunctor.Foldable Associated Types type Rep (IFix f ix) :: Type -> Type # Methods from :: IFix f ix -> Rep (IFix f ix) x # to :: Rep (IFix f ix) x -> IFix f ix #
type Rep1 (IFix f :: k -> Type) Source #
Instance details Defined in Data.IFunctor.Foldable type Rep1 (IFix f :: k -> Type) = D1 ('MetaData "IFix" "Data.IFunctor.Foldable" "recursion-schemes-ix-0.1.0.0-LBKNYYUUm79APWA4D6g9GS" 'True) (C1 ('MetaCons "IFix" 'PrefixI 'True) (S1 ('MetaSel ('Just "unIFix") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 (f (IFix f)))))
type Rep (IFix f ix) Source #
Instance details Defined in Data.IFunctor.Foldable type Rep (IFix f ix) = D1 ('MetaData "IFix" "Data.IFunctor.Foldable" "recursion-schemes-ix-0.1.0.0-LBKNYYUUm79APWA4D6g9GS" 'True) (C1 ('MetaCons "IFix" 'PrefixI 'True) (S1 ('MetaSel ('Just "unIFix") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (f (IFix f) ix))))

Morphisms

Constructive morphisms

cata :: IFunctor f => (f a ~~> a) -> IFix f ~~> a Source #

Catamorphism, ie. fold

prepro :: IFunctor f => (forall b. f b ~~> f b) -> (f a ~~> a) -> IFix f ~~> a Source #

Fokkinga's prepromorphism

para :: IFunctor f => (f (Product (IFix f) a) ~~> a) -> IFix f ~~> a Source #

Paramorphism

zygo :: IFunctor f => (f b ~~> b) -> (f (Product b a) ~~> a) -> IFix f ~~> a Source #

Zygomorphism

histo :: IFunctor f => (f (ICofree f a) ~~> a) -> IFix f ~~> a Source #

Histomorphism

Destructive morphisms

ana :: IFunctor f => (a ~~> f a) -> a ~~> IFix f Source #

Anamorphism, ie. unfold

postpro :: IFunctor f => (forall b. f b ~~> f b) -> (a ~~> f a) -> a ~~> IFix f Source #

Fokkinga's postpromorphism

apo :: IFunctor f => (a ~~> f (Sum (IFix f) a)) -> a ~~> IFix f Source #

Apomorphism

gapo :: IFunctor f => (b ~~> f b) -> (a ~~> f (Sum b a)) -> a ~~> IFix f Source #

GApomorphism

futu :: IFunctor f => (a ~~> f (IFree f a)) -> a ~~> IFix f Source #

Futumorphism

Combined morphisms

hylo :: IFunctor f => (f b ~~> b) -> (a ~~> f a) -> a ~~> b Source #

Hylomorphism, fold then unfold

dyna :: IFunctor f => (f (ICofree f b) ~~> b) -> (a ~~> f a) -> a ~~> b Source #

Dynamorphism

chrono :: IFunctor f => (f (ICofree f b) ~~> b) -> (a ~~> f (IFree f a)) -> a ~~> b Source #

Chronomorphism

meta :: (IFunctor f, IFunctor g) => (f a ~~> a) -> (a ~~> b) -> (b ~~> g b) -> IFix f ~~> IFix g Source #

Metamorphism TODO: ensure only 1 pass over structure

elgot :: forall f a b. IFunctor f => (f a ~~> a) -> (b ~~> Sum a (f b)) -> b ~~> a Source #

coelgot :: forall f a b. IFunctor f => (Product a (f b) ~~> b) -> (a ~~> f a) -> a ~~> b Source #

Monadic morphisms

cataM :: (ITraversable f, Monad m) => (forall ix. SingI ix => f a ix -> m (a ix)) -> forall ix. SingI ix => IFix f ix -> m (a ix) Source #

Monadic catamorphism

paraM :: (ITraversable f, Monad m) => (forall ix. SingI ix => f (Product (IFix f) a) ix -> m (a ix)) -> forall ix. SingI ix => IFix f ix -> m (a ix) Source #

Monadic Paramorphism

anaM :: (ITraversable f, Monad m) => (forall ix. SingI ix => a ix -> m (f a ix)) -> forall ix. SingI ix => a ix -> m (IFix f ix) Source #

Monadic anamorphism

apoM :: (ITraversable f, Monad m) => (forall ix. SingI ix => a ix -> m (f (Sum (IFix f) a) ix)) -> forall ix. SingI ix => a ix -> m (IFix f ix) Source #

Monadic apomorphism

hyloM :: (ITraversable f, Monad m) => (forall ix. SingI ix => f b ix -> m (b ix)) -> (forall ix. SingI ix => a ix -> m (f a ix)) -> forall ix. SingI ix => a ix -> m (b ix) Source #

Monadic hylomorphism

dynaM :: (ITraversable f, Monad m) => (forall ix. SingI ix => f (ICofree f b) ix -> m (b ix)) -> (forall ix. SingI ix => a ix -> m (f a ix)) -> forall ix. SingI ix => a ix -> m (b ix) Source #

Monadic dynamorphism

Distribution Laws

type DistLaw f g = forall a. f (g a) ~~> g (f a) Source #

Type of distribution laws A Constructive morphism means the second part is a IComonad A Destructive morphism means the first part is an IMonad

Constructive distribution laws

distCata :: IFunctor f => DistLaw f IIdentity Source #

distPara :: IFunctor f => DistLaw f (Product (IFix f)) Source #

distZygo :: IFunctor f => (f b ~~> b) -> DistLaw f (Product b) Source #

distHisto :: IFunctor f => DistLaw f (ICofree f) Source #

Destructive distribution laws

distAna :: IFunctor f => DistLaw IIdentity f Source #

distApo :: IFunctor f => DistLaw (Sum (IFix f)) f Source #

distGApo :: IFunctor f => (b ~~> f b) -> DistLaw (Sum b) f Source #

distFutu :: IFunctor f => DistLaw (IFree f) f Source #

Generalized morphisms

gfold :: forall f w a. (IFunctor f, IComonad w) => DistLaw f w -> (f (w a) ~~> a) -> IFix f ~~> a Source #

Generalized fold

gunfold :: forall f m a. (IFunctor f, IMonad m) => DistLaw m f -> (a ~~> f (m a)) -> a ~~> IFix f Source #

Generalized unfold

ghylo :: forall f w m a b. (IFunctor f, IComonad w, IMonad m) => DistLaw f w -> DistLaw m f -> (f (w b) ~~> b) -> (a ~~> f (m a)) -> a ~~> b Source #

Generalized hylomorphism

gprepro :: forall f w a. (IFunctor f, IComonad w) => DistLaw f w -> (forall c. f c ~~> f c) -> (f (w a) ~~> a) -> IFix f ~~> a Source #

Generalized prepromorphism

gpostpro :: forall f m a. (IFunctor f, IMonad m) => DistLaw m f -> (forall c. f c ~~> f c) -> (a ~~> f (m a)) -> a ~~> IFix f Source #

Generalized postpromorphism

Generalized monadic morphisms

gfoldM :: forall f w m a. (ITraversable f, ITraversable w, IComonad w, Monad m) => DistLaw f w -> (forall ix. SingI ix => f (w a) ix -> m (a ix)) -> forall ix. SingI ix => IFix f ix -> m (a ix) Source #

Generalized monadic fold

gunfoldM :: forall f m a x. (ITraversable f, ITraversable m, IMonad m, Monad x) => DistLaw m f -> (forall ix. SingI ix => a ix -> x (f (m a) ix)) -> forall ix. SingI ix => a ix -> x (IFix f ix) Source #

Generalized monadic unfold

ghyloM :: forall f w m a b x. (ITraversable f, ITraversable w, ITraversable m, IComonad w, IMonad m, Monad x) => DistLaw f w -> DistLaw m f -> (forall ix. SingI ix => f (w b) ix -> x (b ix)) -> (forall ix. SingI ix => a ix -> x (f (m a) ix)) -> forall ix. SingI ix => a ix -> x (b ix) Source #

Generalized monadic hylomorphism

Re-exports

newtype Const a (b :: k) #

The Const functor.

Constructors

Const
Fields getConst :: a

Instances

Instances details

Generic1 (Const a :: k -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Associated Types type Rep1 (Const a) :: k -> Type # Methods from1 :: forall (a0 :: k0). Const a a0 -> Rep1 (Const a) a0 # to1 :: forall (a0 :: k0). Rep1 (Const a) a0 -> Const a a0 #
Functor (Const m :: Type -> Type)	Since: base-2.1
Instance details Defined in Data.Functor.Const Methods fmap :: (a -> b) -> Const m a -> Const m b # (<$) :: a -> Const m b -> Const m a #
Monoid m => Applicative (Const m :: Type -> Type)	Since: base-2.0.1
Instance details Defined in Data.Functor.Const Methods pure :: a -> Const m a # (<>) :: Const m (a -> b) -> Const m a -> Const m b # liftA2 :: (a -> b -> c) -> Const m a -> Const m b -> Const m c # (>) :: Const m a -> Const m b -> Const m b # (<*) :: Const m a -> Const m b -> Const m a #
Foldable (Const m :: Type -> Type)	Since: base-4.7.0.0
Instance details Defined in Data.Functor.Const Methods fold :: Monoid m0 => Const m m0 -> m0 # foldMap :: Monoid m0 => (a -> m0) -> Const m a -> m0 # foldMap' :: Monoid m0 => (a -> m0) -> Const m a -> m0 # foldr :: (a -> b -> b) -> b -> Const m a -> b # foldr' :: (a -> b -> b) -> b -> Const m a -> b # foldl :: (b -> a -> b) -> b -> Const m a -> b # foldl' :: (b -> a -> b) -> b -> Const m a -> b # foldr1 :: (a -> a -> a) -> Const m a -> a # foldl1 :: (a -> a -> a) -> Const m a -> a # toList :: Const m a -> [a] # null :: Const m a -> Bool # length :: Const m a -> Int # elem :: Eq a => a -> Const m a -> Bool # maximum :: Ord a => Const m a -> a # minimum :: Ord a => Const m a -> a # sum :: Num a => Const m a -> a # product :: Num a => Const m a -> a #
Traversable (Const m :: Type -> Type)	Since: base-4.7.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Const m a -> f (Const m b) # sequenceA :: Applicative f => Const m (f a) -> f (Const m a) # mapM :: Monad m0 => (a -> m0 b) -> Const m a -> m0 (Const m b) # sequence :: Monad m0 => Const m (m0 a) -> m0 (Const m a) #
Bounded a => Bounded (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods minBound :: Const a b # maxBound :: Const a b #
Enum a => Enum (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods succ :: Const a b -> Const a b # pred :: Const a b -> Const a b # toEnum :: Int -> Const a b # fromEnum :: Const a b -> Int # enumFrom :: Const a b -> [Const a b] # enumFromThen :: Const a b -> Const a b -> [Const a b] # enumFromTo :: Const a b -> Const a b -> [Const a b] # enumFromThenTo :: Const a b -> Const a b -> Const a b -> [Const a b] #
Eq a => Eq (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods (==) :: Const a b -> Const a b -> Bool # (/=) :: Const a b -> Const a b -> Bool #
Floating a => Floating (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods pi :: Const a b # exp :: Const a b -> Const a b # log :: Const a b -> Const a b # sqrt :: Const a b -> Const a b # (**) :: Const a b -> Const a b -> Const a b # logBase :: Const a b -> Const a b -> Const a b # sin :: Const a b -> Const a b # cos :: Const a b -> Const a b # tan :: Const a b -> Const a b # asin :: Const a b -> Const a b # acos :: Const a b -> Const a b # atan :: Const a b -> Const a b # sinh :: Const a b -> Const a b # cosh :: Const a b -> Const a b # tanh :: Const a b -> Const a b # asinh :: Const a b -> Const a b # acosh :: Const a b -> Const a b # atanh :: Const a b -> Const a b # log1p :: Const a b -> Const a b # expm1 :: Const a b -> Const a b # log1pexp :: Const a b -> Const a b # log1mexp :: Const a b -> Const a b #
Fractional a => Fractional (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods (/) :: Const a b -> Const a b -> Const a b # recip :: Const a b -> Const a b # fromRational :: Rational -> Const a b #
Integral a => Integral (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods quot :: Const a b -> Const a b -> Const a b # rem :: Const a b -> Const a b -> Const a b # div :: Const a b -> Const a b -> Const a b # mod :: Const a b -> Const a b -> Const a b # quotRem :: Const a b -> Const a b -> (Const a b, Const a b) # divMod :: Const a b -> Const a b -> (Const a b, Const a b) # toInteger :: Const a b -> Integer #
(Typeable k, Data a, Typeable b) => Data (Const a b)	Since: base-4.10.0.0
Instance details Defined in Data.Data Methods gfoldl :: (forall d b0. Data d => c (d -> b0) -> d -> c b0) -> (forall g. g -> c g) -> Const a b -> c (Const a b) # gunfold :: (forall b0 r. Data b0 => c (b0 -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Const a b) # toConstr :: Const a b -> Constr # dataTypeOf :: Const a b -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Const a b)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Const a b)) # gmapT :: (forall b0. Data b0 => b0 -> b0) -> Const a b -> Const a b # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Const a b -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Const a b -> r # gmapQ :: (forall d. Data d => d -> u) -> Const a b -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Const a b -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Const a b -> m (Const a b) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Const a b -> m (Const a b) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Const a b -> m (Const a b) #
Num a => Num (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods (+) :: Const a b -> Const a b -> Const a b # (-) :: Const a b -> Const a b -> Const a b # (*) :: Const a b -> Const a b -> Const a b # negate :: Const a b -> Const a b # abs :: Const a b -> Const a b # signum :: Const a b -> Const a b # fromInteger :: Integer -> Const a b #
Ord a => Ord (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods compare :: Const a b -> Const a b -> Ordering # (<) :: Const a b -> Const a b -> Bool # (<=) :: Const a b -> Const a b -> Bool # (>) :: Const a b -> Const a b -> Bool # (>=) :: Const a b -> Const a b -> Bool # max :: Const a b -> Const a b -> Const a b # min :: Const a b -> Const a b -> Const a b #
Read a => Read (Const a b)	This instance would be equivalent to the derived instances of the `Const` newtype if the `getConst` field were removed Since: base-4.8.0.0
Instance details Defined in Data.Functor.Const Methods readsPrec :: Int -> ReadS (Const a b) # readList :: ReadS [Const a b] # readPrec :: ReadPrec (Const a b) # readListPrec :: ReadPrec [Const a b] #
Real a => Real (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods toRational :: Const a b -> Rational #
RealFloat a => RealFloat (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods floatRadix :: Const a b -> Integer # floatDigits :: Const a b -> Int # floatRange :: Const a b -> (Int, Int) # decodeFloat :: Const a b -> (Integer, Int) # encodeFloat :: Integer -> Int -> Const a b # exponent :: Const a b -> Int # significand :: Const a b -> Const a b # scaleFloat :: Int -> Const a b -> Const a b # isNaN :: Const a b -> Bool # isInfinite :: Const a b -> Bool # isDenormalized :: Const a b -> Bool # isNegativeZero :: Const a b -> Bool # isIEEE :: Const a b -> Bool # atan2 :: Const a b -> Const a b -> Const a b #
RealFrac a => RealFrac (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods properFraction :: Integral b0 => Const a b -> (b0, Const a b) # truncate :: Integral b0 => Const a b -> b0 # round :: Integral b0 => Const a b -> b0 # ceiling :: Integral b0 => Const a b -> b0 # floor :: Integral b0 => Const a b -> b0 #
Show a => Show (Const a b)	This instance would be equivalent to the derived instances of the `Const` newtype if the `getConst` field were removed Since: base-4.8.0.0
Instance details Defined in Data.Functor.Const Methods showsPrec :: Int -> Const a b -> ShowS # show :: Const a b -> String # showList :: [Const a b] -> ShowS #
Ix a => Ix (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods range :: (Const a b, Const a b) -> [Const a b] # index :: (Const a b, Const a b) -> Const a b -> Int # unsafeIndex :: (Const a b, Const a b) -> Const a b -> Int # inRange :: (Const a b, Const a b) -> Const a b -> Bool # rangeSize :: (Const a b, Const a b) -> Int # unsafeRangeSize :: (Const a b, Const a b) -> Int #
Generic (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Associated Types type Rep (Const a b) :: Type -> Type # Methods from :: Const a b -> Rep (Const a b) x # to :: Rep (Const a b) x -> Const a b #
Semigroup a => Semigroup (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods (<>) :: Const a b -> Const a b -> Const a b # sconcat :: NonEmpty (Const a b) -> Const a b # stimes :: Integral b0 => b0 -> Const a b -> Const a b #
Monoid a => Monoid (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods mempty :: Const a b # mappend :: Const a b -> Const a b -> Const a b # mconcat :: [Const a b] -> Const a b #
Storable a => Storable (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods sizeOf :: Const a b -> Int # alignment :: Const a b -> Int # peekElemOff :: Ptr (Const a b) -> Int -> IO (Const a b) # pokeElemOff :: Ptr (Const a b) -> Int -> Const a b -> IO () # peekByteOff :: Ptr b0 -> Int -> IO (Const a b) # pokeByteOff :: Ptr b0 -> Int -> Const a b -> IO () # peek :: Ptr (Const a b) -> IO (Const a b) # poke :: Ptr (Const a b) -> Const a b -> IO () #
Bits a => Bits (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods (.&.) :: Const a b -> Const a b -> Const a b # (.\|.) :: Const a b -> Const a b -> Const a b # xor :: Const a b -> Const a b -> Const a b # complement :: Const a b -> Const a b # shift :: Const a b -> Int -> Const a b # rotate :: Const a b -> Int -> Const a b # zeroBits :: Const a b # bit :: Int -> Const a b # setBit :: Const a b -> Int -> Const a b # clearBit :: Const a b -> Int -> Const a b # complementBit :: Const a b -> Int -> Const a b # testBit :: Const a b -> Int -> Bool # bitSizeMaybe :: Const a b -> Maybe Int # bitSize :: Const a b -> Int # isSigned :: Const a b -> Bool # shiftL :: Const a b -> Int -> Const a b # unsafeShiftL :: Const a b -> Int -> Const a b # shiftR :: Const a b -> Int -> Const a b # unsafeShiftR :: Const a b -> Int -> Const a b # rotateL :: Const a b -> Int -> Const a b # rotateR :: Const a b -> Int -> Const a b # popCount :: Const a b -> Int #
FiniteBits a => FiniteBits (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods finiteBitSize :: Const a b -> Int # countLeadingZeros :: Const a b -> Int # countTrailingZeros :: Const a b -> Int #
type Rep1 (Const a :: k -> Type)
Instance details Defined in Data.Functor.Const type Rep1 (Const a :: k -> Type) = D1 ('MetaData "Const" "Data.Functor.Const" "base" 'True) (C1 ('MetaCons "Const" 'PrefixI 'True) (S1 ('MetaSel ('Just "getConst") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))
type Rep (Const a b)
Instance details Defined in Data.Functor.Const type Rep (Const a b) = D1 ('MetaData "Const" "Data.Functor.Const" "base" 'True) (C1 ('MetaCons "Const" 'PrefixI 'True) (S1 ('MetaSel ('Just "getConst") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

data Product (f :: k -> Type) (g :: k -> Type) (a :: k) #

Lifted product of functors.

Constructors

Pair (f a) (g a)

Instances

Instances details

IFunctor (Product a :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Data.IFunctor Methods imap :: forall (a0 :: k0 -> Type) (b :: k0 -> Type). (a0 ~~> b) -> Product a a0 ~~> Product a b Source #
IOrd2 a => IOrd (Product a :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Data.IFunctor.Classes Methods icompare :: forall (ix :: k0) a0. SingI ix => (forall (ix :: k1). SingI ix => a0 ix -> a0 ix -> Ordering) -> Product a a0 ix -> Product a a0 ix -> Ordering Source #
IEq2 a => IEq (Product a :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Data.IFunctor.Classes Methods ieq :: forall (ix :: k0) a0. SingI ix => (forall (ix :: k1). SingI ix => a0 ix -> a0 ix -> Bool) -> Product a a0 ix -> Product a a0 ix -> Bool Source #
IRead2 a => IRead (Product a :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Data.IFunctor.Classes Methods ireadPrec :: forall (ix :: k0) a0. SingI ix => (forall (ix :: k1). SingI ix => ReadPrec (a0 ix)) -> ReadPrec (Product a a0 ix) Source # ireadsPrec :: forall (ix :: k0) a0. SingI ix => (forall (ix :: k1). SingI ix => Int -> ReadS (a0 ix)) -> Int -> ReadS (Product a a0 ix) Source #
IShow2 a => IShow (Product a :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Data.IFunctor.Classes Methods ishowsPrec :: forall (ix :: k0) a0. SingI ix => (forall (ix :: k1). SingI ix => Int -> a0 ix -> ShowS) -> Int -> Product a a0 ix -> ShowS Source # ishow :: forall (ix :: k0) a0. SingI ix => (forall (ix :: k1). SingI ix => Int -> a0 ix -> ShowS) -> Product a a0 ix -> String Source #
ITraversable (Product a :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Data.ITraversable Methods itraverse :: forall m (ix :: k0) a0 b. (Applicative m, SingI ix) => (forall (ix :: k1). SingI ix => a0 ix -> m (b ix)) -> Product a a0 ix -> m (Product a b ix) Source #
IComonad (Product a :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Data.IComonad Methods iextract :: forall (a0 :: k0 -> Type). Product a a0 ~~> a0 Source # iduplicate :: forall (a0 :: k0 -> Type). Product a a0 ~~> Product a (Product a a0) Source # iextend :: forall (a0 :: k0 -> Type) (b :: k0 -> Type). (Product a a0 ~~> b) -> Product a a0 ~~> Product a b Source #
Generic1 (Product f g :: k -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Associated Types type Rep1 (Product f g) :: k -> Type # Methods from1 :: forall (a :: k0). Product f g a -> Rep1 (Product f g) a # to1 :: forall (a :: k0). Rep1 (Product f g) a -> Product f g a #
(Monad f, Monad g) => Monad (Product f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods (>>=) :: Product f g a -> (a -> Product f g b) -> Product f g b # (>>) :: Product f g a -> Product f g b -> Product f g b # return :: a -> Product f g a #
(Functor f, Functor g) => Functor (Product f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods fmap :: (a -> b) -> Product f g a -> Product f g b # (<$) :: a -> Product f g b -> Product f g a #
(MonadFix f, MonadFix g) => MonadFix (Product f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods mfix :: (a -> Product f g a) -> Product f g a #
(Applicative f, Applicative g) => Applicative (Product f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods pure :: a -> Product f g a # (<>) :: Product f g (a -> b) -> Product f g a -> Product f g b # liftA2 :: (a -> b -> c) -> Product f g a -> Product f g b -> Product f g c # (>) :: Product f g a -> Product f g b -> Product f g b # (<*) :: Product f g a -> Product f g b -> Product f g a #
(Foldable f, Foldable g) => Foldable (Product f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods fold :: Monoid m => Product f g m -> m # foldMap :: Monoid m => (a -> m) -> Product f g a -> m # foldMap' :: Monoid m => (a -> m) -> Product f g a -> m # foldr :: (a -> b -> b) -> b -> Product f g a -> b # foldr' :: (a -> b -> b) -> b -> Product f g a -> b # foldl :: (b -> a -> b) -> b -> Product f g a -> b # foldl' :: (b -> a -> b) -> b -> Product f g a -> b # foldr1 :: (a -> a -> a) -> Product f g a -> a # foldl1 :: (a -> a -> a) -> Product f g a -> a # toList :: Product f g a -> [a] # null :: Product f g a -> Bool # length :: Product f g a -> Int # elem :: Eq a => a -> Product f g a -> Bool # maximum :: Ord a => Product f g a -> a # minimum :: Ord a => Product f g a -> a # sum :: Num a => Product f g a -> a # product :: Num a => Product f g a -> a #
(Traversable f, Traversable g) => Traversable (Product f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods traverse :: Applicative f0 => (a -> f0 b) -> Product f g a -> f0 (Product f g b) # sequenceA :: Applicative f0 => Product f g (f0 a) -> f0 (Product f g a) # mapM :: Monad m => (a -> m b) -> Product f g a -> m (Product f g b) # sequence :: Monad m => Product f g (m a) -> m (Product f g a) #
(Eq1 f, Eq1 g) => Eq1 (Product f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods liftEq :: (a -> b -> Bool) -> Product f g a -> Product f g b -> Bool #
(Ord1 f, Ord1 g) => Ord1 (Product f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods liftCompare :: (a -> b -> Ordering) -> Product f g a -> Product f g b -> Ordering #
(Read1 f, Read1 g) => Read1 (Product f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Product f g a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Product f g a] # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (Product f g a) # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [Product f g a] #
(Show1 f, Show1 g) => Show1 (Product f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Product f g a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Product f g a] -> ShowS #
(MonadZip f, MonadZip g) => MonadZip (Product f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods mzip :: Product f g a -> Product f g b -> Product f g (a, b) # mzipWith :: (a -> b -> c) -> Product f g a -> Product f g b -> Product f g c # munzip :: Product f g (a, b) -> (Product f g a, Product f g b) #
(Alternative f, Alternative g) => Alternative (Product f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods empty :: Product f g a # (<\|>) :: Product f g a -> Product f g a -> Product f g a # some :: Product f g a -> Product f g [a] # many :: Product f g a -> Product f g [a] #
(MonadPlus f, MonadPlus g) => MonadPlus (Product f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods mzero :: Product f g a # mplus :: Product f g a -> Product f g a -> Product f g a #
(Eq1 f, Eq1 g, Eq a) => Eq (Product f g a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods (==) :: Product f g a -> Product f g a -> Bool # (/=) :: Product f g a -> Product f g a -> Bool #
(Typeable a, Typeable f, Typeable g, Typeable k, Data (f a), Data (g a)) => Data (Product f g a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g0. g0 -> c g0) -> Product f g a -> c (Product f g a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Product f g a) # toConstr :: Product f g a -> Constr # dataTypeOf :: Product f g a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Product f g a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Product f g a)) # gmapT :: (forall b. Data b => b -> b) -> Product f g a -> Product f g a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Product f g a -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Product f g a -> r # gmapQ :: (forall d. Data d => d -> u) -> Product f g a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Product f g a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Product f g a -> m (Product f g a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Product f g a -> m (Product f g a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Product f g a -> m (Product f g a) #
(Ord1 f, Ord1 g, Ord a) => Ord (Product f g a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods compare :: Product f g a -> Product f g a -> Ordering # (<) :: Product f g a -> Product f g a -> Bool # (<=) :: Product f g a -> Product f g a -> Bool # (>) :: Product f g a -> Product f g a -> Bool # (>=) :: Product f g a -> Product f g a -> Bool # max :: Product f g a -> Product f g a -> Product f g a # min :: Product f g a -> Product f g a -> Product f g a #
(Read1 f, Read1 g, Read a) => Read (Product f g a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods readsPrec :: Int -> ReadS (Product f g a) # readList :: ReadS [Product f g a] # readPrec :: ReadPrec (Product f g a) # readListPrec :: ReadPrec [Product f g a] #
(Show1 f, Show1 g, Show a) => Show (Product f g a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Methods showsPrec :: Int -> Product f g a -> ShowS # show :: Product f g a -> String # showList :: [Product f g a] -> ShowS #
Generic (Product f g a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Product Associated Types type Rep (Product f g a) :: Type -> Type # Methods from :: Product f g a -> Rep (Product f g a) x # to :: Rep (Product f g a) x -> Product f g a #
type Rep1 (Product f g :: k -> Type)
Instance details Defined in Data.Functor.Product type Rep1 (Product f g :: k -> Type) = D1 ('MetaData "Product" "Data.Functor.Product" "base" 'False) (C1 ('MetaCons "Pair" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 f) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 g)))
type Rep (Product f g a)
Instance details Defined in Data.Functor.Product type Rep (Product f g a) = D1 ('MetaData "Product" "Data.Functor.Product" "base" 'False) (C1 ('MetaCons "Pair" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (f a)) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (g a))))

data Sum (f :: k -> Type) (g :: k -> Type) (a :: k) #

Lifted sum of functors.

Constructors

InL (f a)
InR (g a)

Instances

Instances details

IFunctor (Sum a :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Data.IFunctor Methods imap :: forall (a0 :: k0 -> Type) (b :: k0 -> Type). (a0 ~~> b) -> Sum a a0 ~~> Sum a b Source #
IOrd2 a => IOrd (Sum a :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Data.IFunctor.Classes Methods icompare :: forall (ix :: k0) a0. SingI ix => (forall (ix :: k1). SingI ix => a0 ix -> a0 ix -> Ordering) -> Sum a a0 ix -> Sum a a0 ix -> Ordering Source #
IEq2 a => IEq (Sum a :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Data.IFunctor.Classes Methods ieq :: forall (ix :: k0) a0. SingI ix => (forall (ix :: k1). SingI ix => a0 ix -> a0 ix -> Bool) -> Sum a a0 ix -> Sum a a0 ix -> Bool Source #
IRead2 a => IRead (Sum a :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Data.IFunctor.Classes Methods ireadPrec :: forall (ix :: k0) a0. SingI ix => (forall (ix :: k1). SingI ix => ReadPrec (a0 ix)) -> ReadPrec (Sum a a0 ix) Source # ireadsPrec :: forall (ix :: k0) a0. SingI ix => (forall (ix :: k1). SingI ix => Int -> ReadS (a0 ix)) -> Int -> ReadS (Sum a a0 ix) Source #
IShow2 a => IShow (Sum a :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Data.IFunctor.Classes Methods ishowsPrec :: forall (ix :: k0) a0. SingI ix => (forall (ix :: k1). SingI ix => Int -> a0 ix -> ShowS) -> Int -> Sum a a0 ix -> ShowS Source # ishow :: forall (ix :: k0) a0. SingI ix => (forall (ix :: k1). SingI ix => Int -> a0 ix -> ShowS) -> Sum a a0 ix -> String Source #
ITraversable (Sum a :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Data.ITraversable Methods itraverse :: forall m (ix :: k0) a0 b. (Applicative m, SingI ix) => (forall (ix :: k1). SingI ix => a0 ix -> m (b ix)) -> Sum a a0 ix -> m (Sum a b ix) Source #
IMonad (Sum a :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Data.IMonad Methods ipure :: forall (a0 :: k0 -> Type). a0 ~~> Sum a a0 Source # ijoin :: forall (a0 :: k0 -> Type). Sum a (Sum a a0) ~~> Sum a a0 Source # ibind :: forall (a0 :: k0 -> Type) (b :: k0 -> Type). (a0 ~~> Sum a b) -> Sum a a0 ~~> Sum a b Source #
Generic1 (Sum f g :: k -> Type)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Sum Associated Types type Rep1 (Sum f g) :: k -> Type # Methods from1 :: forall (a :: k0). Sum f g a -> Rep1 (Sum f g) a # to1 :: forall (a :: k0). Rep1 (Sum f g) a -> Sum f g a #
(Functor f, Functor g) => Functor (Sum f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Sum Methods fmap :: (a -> b) -> Sum f g a -> Sum f g b # (<$) :: a -> Sum f g b -> Sum f g a #
(Foldable f, Foldable g) => Foldable (Sum f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Sum Methods fold :: Monoid m => Sum f g m -> m # foldMap :: Monoid m => (a -> m) -> Sum f g a -> m # foldMap' :: Monoid m => (a -> m) -> Sum f g a -> m # foldr :: (a -> b -> b) -> b -> Sum f g a -> b # foldr' :: (a -> b -> b) -> b -> Sum f g a -> b # foldl :: (b -> a -> b) -> b -> Sum f g a -> b # foldl' :: (b -> a -> b) -> b -> Sum f g a -> b # foldr1 :: (a -> a -> a) -> Sum f g a -> a # foldl1 :: (a -> a -> a) -> Sum f g a -> a # toList :: Sum f g a -> [a] # null :: Sum f g a -> Bool # length :: Sum f g a -> Int # elem :: Eq a => a -> Sum f g a -> Bool # maximum :: Ord a => Sum f g a -> a # minimum :: Ord a => Sum f g a -> a # sum :: Num a => Sum f g a -> a # product :: Num a => Sum f g a -> a #
(Traversable f, Traversable g) => Traversable (Sum f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Sum Methods traverse :: Applicative f0 => (a -> f0 b) -> Sum f g a -> f0 (Sum f g b) # sequenceA :: Applicative f0 => Sum f g (f0 a) -> f0 (Sum f g a) # mapM :: Monad m => (a -> m b) -> Sum f g a -> m (Sum f g b) # sequence :: Monad m => Sum f g (m a) -> m (Sum f g a) #
(Eq1 f, Eq1 g) => Eq1 (Sum f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Sum Methods liftEq :: (a -> b -> Bool) -> Sum f g a -> Sum f g b -> Bool #
(Ord1 f, Ord1 g) => Ord1 (Sum f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Sum Methods liftCompare :: (a -> b -> Ordering) -> Sum f g a -> Sum f g b -> Ordering #
(Read1 f, Read1 g) => Read1 (Sum f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Sum Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Sum f g a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Sum f g a] # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (Sum f g a) # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [Sum f g a] #
(Show1 f, Show1 g) => Show1 (Sum f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Sum Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Sum f g a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Sum f g a] -> ShowS #
(Eq1 f, Eq1 g, Eq a) => Eq (Sum f g a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Sum Methods (==) :: Sum f g a -> Sum f g a -> Bool # (/=) :: Sum f g a -> Sum f g a -> Bool #
(Typeable a, Typeable f, Typeable g, Typeable k, Data (f a), Data (g a)) => Data (Sum f g a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Sum Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g0. g0 -> c g0) -> Sum f g a -> c (Sum f g a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Sum f g a) # toConstr :: Sum f g a -> Constr # dataTypeOf :: Sum f g a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Sum f g a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Sum f g a)) # gmapT :: (forall b. Data b => b -> b) -> Sum f g a -> Sum f g a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Sum f g a -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Sum f g a -> r # gmapQ :: (forall d. Data d => d -> u) -> Sum f g a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Sum f g a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Sum f g a -> m (Sum f g a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Sum f g a -> m (Sum f g a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Sum f g a -> m (Sum f g a) #
(Ord1 f, Ord1 g, Ord a) => Ord (Sum f g a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Sum Methods compare :: Sum f g a -> Sum f g a -> Ordering # (<) :: Sum f g a -> Sum f g a -> Bool # (<=) :: Sum f g a -> Sum f g a -> Bool # (>) :: Sum f g a -> Sum f g a -> Bool # (>=) :: Sum f g a -> Sum f g a -> Bool # max :: Sum f g a -> Sum f g a -> Sum f g a # min :: Sum f g a -> Sum f g a -> Sum f g a #
(Read1 f, Read1 g, Read a) => Read (Sum f g a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Sum Methods readsPrec :: Int -> ReadS (Sum f g a) # readList :: ReadS [Sum f g a] # readPrec :: ReadPrec (Sum f g a) # readListPrec :: ReadPrec [Sum f g a] #
(Show1 f, Show1 g, Show a) => Show (Sum f g a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Sum Methods showsPrec :: Int -> Sum f g a -> ShowS # show :: Sum f g a -> String # showList :: [Sum f g a] -> ShowS #
Generic (Sum f g a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Sum Associated Types type Rep (Sum f g a) :: Type -> Type # Methods from :: Sum f g a -> Rep (Sum f g a) x # to :: Rep (Sum f g a) x -> Sum f g a #
type Rep1 (Sum f g :: k -> Type)
Instance details Defined in Data.Functor.Sum type Rep1 (Sum f g :: k -> Type) = D1 ('MetaData "Sum" "Data.Functor.Sum" "base" 'False) (C1 ('MetaCons "InL" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 f)) :+: C1 ('MetaCons "InR" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 g)))
type Rep (Sum f g a)
Instance details Defined in Data.Functor.Sum type Rep (Sum f g a) = D1 ('MetaData "Sum" "Data.Functor.Sum" "base" 'False) (C1 ('MetaCons "InL" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (f a))) :+: C1 ('MetaCons "InR" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (g a))))

class IFunctor f => IComonad f where Source #

Comonoid in the category of dependent endofunctors

Minimal complete definition

iextract, (iduplicate | iextend)

Methods

iextract :: f a ~~> a Source #

iduplicate :: f a ~~> f (f a) Source #

iextend :: (f a ~~> b) -> f a ~~> f b Source #

Instances

Instances details

IComonad (IIdentity :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Data.IFunctor.IIdentity Methods iextract :: forall (a :: k0 -> Type). IIdentity a ~~> a Source # iduplicate :: forall (a :: k0 -> Type). IIdentity a ~~> IIdentity (IIdentity a) Source # iextend :: forall (a :: k0 -> Type) (b :: k0 -> Type). (IIdentity a ~~> b) -> IIdentity a ~~> IIdentity b Source #
IComonad (Product a :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Data.IComonad Methods iextract :: forall (a0 :: k0 -> Type). Product a a0 ~~> a0 Source # iduplicate :: forall (a0 :: k0 -> Type). Product a a0 ~~> Product a (Product a a0) Source # iextend :: forall (a0 :: k0 -> Type) (b :: k0 -> Type). (Product a a0 ~~> b) -> Product a a0 ~~> Product a b Source #
IFunctor f => IComonad (ICofree f :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Data.IFunctor.ICofree Methods iextract :: forall (a :: k0 -> Type). ICofree f a ~~> a Source # iduplicate :: forall (a :: k0 -> Type). ICofree f a ~~> ICofree f (ICofree f a) Source # iextend :: forall (a :: k0 -> Type) (b :: k0 -> Type). (ICofree f a ~~> b) -> ICofree f a ~~> ICofree f b Source #

type (~~>) a b = forall ix. SingI ix => a ix -> b ix infixr 4 Source #

Indexed function type

class IFunctor f where Source #

Functor in the category of dependent types

Methods

imap :: (a ~~> b) -> f a ~~> f b Source #

Instances

Instances details

IFunctor (IIdentity :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Data.IFunctor.IIdentity Methods imap :: forall (a :: k0 -> Type) (b :: k0 -> Type). (a ~~> b) -> IIdentity a ~~> IIdentity b Source #
IFunctor (Product a :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Data.IFunctor Methods imap :: forall (a0 :: k0 -> Type) (b :: k0 -> Type). (a0 ~~> b) -> Product a a0 ~~> Product a b Source #
IFunctor (Sum a :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Data.IFunctor Methods imap :: forall (a0 :: k0 -> Type) (b :: k0 -> Type). (a0 ~~> b) -> Sum a a0 ~~> Sum a b Source #
IFunctor f => IFunctor (IFree f :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Data.IFunctor.IFree Methods imap :: forall (a :: k0 -> Type) (b :: k0 -> Type). (a ~~> b) -> IFree f a ~~> IFree f b Source #
IFunctor f => IFunctor (ICofree f :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Data.IFunctor.ICofree Methods imap :: forall (a :: k0 -> Type) (b :: k0 -> Type). (a ~~> b) -> ICofree f a ~~> ICofree f b Source #

module Data.IFunctor.Classes

data ICofree f a ix Source #

Cofree IComonad

Constructors

(a ix) ::< (f (ICofree f a) ix) infixr 5

Instances

Instances details

IFunctor f => IFunctor (ICofree f :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Data.IFunctor.ICofree Methods imap :: forall (a :: k0 -> Type) (b :: k0 -> Type). (a ~~> b) -> ICofree f a ~~> ICofree f b Source #
IOrd f => IOrd (ICofree f :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Data.IFunctor.ICofree Methods icompare :: forall (ix :: k0) a. SingI ix => (forall (ix :: k1). SingI ix => a ix -> a ix -> Ordering) -> ICofree f a ix -> ICofree f a ix -> Ordering Source #
IEq f => IEq (ICofree f :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Data.IFunctor.ICofree Methods ieq :: forall (ix :: k0) a. SingI ix => (forall (ix :: k1). SingI ix => a ix -> a ix -> Bool) -> ICofree f a ix -> ICofree f a ix -> Bool Source #
IRead f => IRead (ICofree f :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Data.IFunctor.ICofree Methods ireadPrec :: forall (ix :: k0) a. SingI ix => (forall (ix :: k1). SingI ix => ReadPrec (a ix)) -> ReadPrec (ICofree f a ix) Source # ireadsPrec :: forall (ix :: k0) a. SingI ix => (forall (ix :: k1). SingI ix => Int -> ReadS (a ix)) -> Int -> ReadS (ICofree f a ix) Source #
IShow f => IShow (ICofree f :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Data.IFunctor.ICofree Methods ishowsPrec :: forall (ix :: k0) a. SingI ix => (forall (ix :: k1). SingI ix => Int -> a ix -> ShowS) -> Int -> ICofree f a ix -> ShowS Source # ishow :: forall (ix :: k0) a. SingI ix => (forall (ix :: k1). SingI ix => Int -> a ix -> ShowS) -> ICofree f a ix -> String Source #
ITraversable f => ITraversable (ICofree f :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Data.IFunctor.ICofree Methods itraverse :: forall m (ix :: k0) a b. (Applicative m, SingI ix) => (forall (ix :: k1). SingI ix => a ix -> m (b ix)) -> ICofree f a ix -> m (ICofree f b ix) Source #
IFunctor f => IComonad (ICofree f :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Data.IFunctor.ICofree Methods iextract :: forall (a :: k0 -> Type). ICofree f a ~~> a Source # iduplicate :: forall (a :: k0 -> Type). ICofree f a ~~> ICofree f (ICofree f a) Source # iextend :: forall (a :: k0 -> Type) (b :: k0 -> Type). (ICofree f a ~~> b) -> ICofree f a ~~> ICofree f b Source #
Generic1 (ICofree f a :: k -> Type) Source #
Instance details Defined in Data.IFunctor.ICofree Associated Types type Rep1 (ICofree f a) :: k -> Type # Methods from1 :: forall (a0 :: k0). ICofree f a a0 -> Rep1 (ICofree f a) a0 # to1 :: forall (a0 :: k0). Rep1 (ICofree f a) a0 -> ICofree f a a0 #
(IEq f, IEq2 a, SingI ix) => Eq (ICofree f a ix) Source #
Instance details Defined in Data.IFunctor.ICofree Methods (==) :: ICofree f a ix -> ICofree f a ix -> Bool # (/=) :: ICofree f a ix -> ICofree f a ix -> Bool #
(IOrd f, IOrd2 a, SingI ix) => Ord (ICofree f a ix) Source #
Instance details Defined in Data.IFunctor.ICofree Methods compare :: ICofree f a ix -> ICofree f a ix -> Ordering # (<) :: ICofree f a ix -> ICofree f a ix -> Bool # (<=) :: ICofree f a ix -> ICofree f a ix -> Bool # (>) :: ICofree f a ix -> ICofree f a ix -> Bool # (>=) :: ICofree f a ix -> ICofree f a ix -> Bool # max :: ICofree f a ix -> ICofree f a ix -> ICofree f a ix # min :: ICofree f a ix -> ICofree f a ix -> ICofree f a ix #
(IRead f, IRead2 a, SingI ix) => Read (ICofree f a ix) Source #
Instance details Defined in Data.IFunctor.ICofree Methods readsPrec :: Int -> ReadS (ICofree f a ix) # readList :: ReadS [ICofree f a ix] # readPrec :: ReadPrec (ICofree f a ix) # readListPrec :: ReadPrec [ICofree f a ix] #
(IShow f, IShow2 a, SingI ix) => Show (ICofree f a ix) Source #
Instance details Defined in Data.IFunctor.ICofree Methods showsPrec :: Int -> ICofree f a ix -> ShowS # show :: ICofree f a ix -> String # showList :: [ICofree f a ix] -> ShowS #
Generic (ICofree f a ix) Source #
Instance details Defined in Data.IFunctor.ICofree Associated Types type Rep (ICofree f a ix) :: Type -> Type # Methods from :: ICofree f a ix -> Rep (ICofree f a ix) x # to :: Rep (ICofree f a ix) x -> ICofree f a ix #
type Rep1 (ICofree f a :: k -> Type) Source #
Instance details Defined in Data.IFunctor.ICofree type Rep1 (ICofree f a :: k -> Type) = D1 ('MetaData "ICofree" "Data.IFunctor.ICofree" "recursion-schemes-ix-0.1.0.0-LBKNYYUUm79APWA4D6g9GS" 'False) (C1 ('MetaCons "::<" ('InfixI 'RightAssociative 5) 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 a) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 (f (ICofree f a)))))
type Rep (ICofree f a ix) Source #
Instance details Defined in Data.IFunctor.ICofree type Rep (ICofree f a ix) = D1 ('MetaData "ICofree" "Data.IFunctor.ICofree" "recursion-schemes-ix-0.1.0.0-LBKNYYUUm79APWA4D6g9GS" 'False) (C1 ('MetaCons "::<" ('InfixI 'RightAssociative 5) 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (a ix)) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (f (ICofree f a) ix))))

data IFree f a ix Source #

Free IMonad

Constructors

IPure (a ix)
IFree (f (IFree f a) ix)

Instances

Instances details

IFunctor f => IFunctor (IFree f :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Data.IFunctor.IFree Methods imap :: forall (a :: k0 -> Type) (b :: k0 -> Type). (a ~~> b) -> IFree f a ~~> IFree f b Source #
IOrd f => IOrd (IFree f :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Data.IFunctor.IFree Methods icompare :: forall (ix :: k0) a. SingI ix => (forall (ix :: k1). SingI ix => a ix -> a ix -> Ordering) -> IFree f a ix -> IFree f a ix -> Ordering Source #
IEq f => IEq (IFree f :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Data.IFunctor.IFree Methods ieq :: forall (ix :: k0) a. SingI ix => (forall (ix :: k1). SingI ix => a ix -> a ix -> Bool) -> IFree f a ix -> IFree f a ix -> Bool Source #
IRead f => IRead (IFree f :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Data.IFunctor.IFree Methods ireadPrec :: forall (ix :: k0) a. SingI ix => (forall (ix :: k1). SingI ix => ReadPrec (a ix)) -> ReadPrec (IFree f a ix) Source # ireadsPrec :: forall (ix :: k0) a. SingI ix => (forall (ix :: k1). SingI ix => Int -> ReadS (a ix)) -> Int -> ReadS (IFree f a ix) Source #
IShow f => IShow (IFree f :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Data.IFunctor.IFree Methods ishowsPrec :: forall (ix :: k0) a. SingI ix => (forall (ix :: k1). SingI ix => Int -> a ix -> ShowS) -> Int -> IFree f a ix -> ShowS Source # ishow :: forall (ix :: k0) a. SingI ix => (forall (ix :: k1). SingI ix => Int -> a ix -> ShowS) -> IFree f a ix -> String Source #
ITraversable f => ITraversable (IFree f :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Data.IFunctor.IFree Methods itraverse :: forall m (ix :: k0) a b. (Applicative m, SingI ix) => (forall (ix :: k1). SingI ix => a ix -> m (b ix)) -> IFree f a ix -> m (IFree f b ix) Source #
IFunctor f => IMonad (IFree f :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Data.IFunctor.IFree Methods ipure :: forall (a :: k0 -> Type). a ~~> IFree f a Source # ijoin :: forall (a :: k0 -> Type). IFree f (IFree f a) ~~> IFree f a Source # ibind :: forall (a :: k0 -> Type) (b :: k0 -> Type). (a ~~> IFree f b) -> IFree f a ~~> IFree f b Source #
Generic1 (IFree f a :: k -> Type) Source #
Instance details Defined in Data.IFunctor.IFree Associated Types type Rep1 (IFree f a) :: k -> Type # Methods from1 :: forall (a0 :: k0). IFree f a a0 -> Rep1 (IFree f a) a0 # to1 :: forall (a0 :: k0). Rep1 (IFree f a) a0 -> IFree f a a0 #
(IEq f, IEq2 a, SingI ix) => Eq (IFree f a ix) Source #
Instance details Defined in Data.IFunctor.IFree Methods (==) :: IFree f a ix -> IFree f a ix -> Bool # (/=) :: IFree f a ix -> IFree f a ix -> Bool #
(IOrd f, IOrd2 a, SingI ix) => Ord (IFree f a ix) Source #
Instance details Defined in Data.IFunctor.IFree Methods compare :: IFree f a ix -> IFree f a ix -> Ordering # (<) :: IFree f a ix -> IFree f a ix -> Bool # (<=) :: IFree f a ix -> IFree f a ix -> Bool # (>) :: IFree f a ix -> IFree f a ix -> Bool # (>=) :: IFree f a ix -> IFree f a ix -> Bool # max :: IFree f a ix -> IFree f a ix -> IFree f a ix # min :: IFree f a ix -> IFree f a ix -> IFree f a ix #
(IRead f, IRead2 a, SingI ix) => Read (IFree f a ix) Source #
Instance details Defined in Data.IFunctor.IFree Methods readsPrec :: Int -> ReadS (IFree f a ix) # readList :: ReadS [IFree f a ix] # readPrec :: ReadPrec (IFree f a ix) # readListPrec :: ReadPrec [IFree f a ix] #
(IShow f, IShow2 a, SingI ix) => Show (IFree f a ix) Source #
Instance details Defined in Data.IFunctor.IFree Methods showsPrec :: Int -> IFree f a ix -> ShowS # show :: IFree f a ix -> String # showList :: [IFree f a ix] -> ShowS #
Generic (IFree f a ix) Source #
Instance details Defined in Data.IFunctor.IFree Associated Types type Rep (IFree f a ix) :: Type -> Type # Methods from :: IFree f a ix -> Rep (IFree f a ix) x # to :: Rep (IFree f a ix) x -> IFree f a ix #
type Rep1 (IFree f a :: k -> Type) Source #
Instance details Defined in Data.IFunctor.IFree type Rep1 (IFree f a :: k -> Type) = D1 ('MetaData "IFree" "Data.IFunctor.IFree" "recursion-schemes-ix-0.1.0.0-LBKNYYUUm79APWA4D6g9GS" 'False) (C1 ('MetaCons "IPure" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 a)) :+: C1 ('MetaCons "IFree" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 (f (IFree f a)))))
type Rep (IFree f a ix) Source #
Instance details Defined in Data.IFunctor.IFree type Rep (IFree f a ix) = D1 ('MetaData "IFree" "Data.IFunctor.IFree" "recursion-schemes-ix-0.1.0.0-LBKNYYUUm79APWA4D6g9GS" 'False) (C1 ('MetaCons "IPure" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (a ix))) :+: C1 ('MetaCons "IFree" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (f (IFree f a) ix))))

data IIdentity f ix Source #

Constructors

IIdentity
Fields runIIdentity :: f ix

Instances

Instances details

IFunctor (IIdentity :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Data.IFunctor.IIdentity Methods imap :: forall (a :: k0 -> Type) (b :: k0 -> Type). (a ~~> b) -> IIdentity a ~~> IIdentity b Source #
IOrd (IIdentity :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Data.IFunctor.IIdentity Methods icompare :: forall (ix :: k0) a. SingI ix => (forall (ix :: k1). SingI ix => a ix -> a ix -> Ordering) -> IIdentity a ix -> IIdentity a ix -> Ordering Source #
IEq (IIdentity :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Data.IFunctor.IIdentity Methods ieq :: forall (ix :: k0) a. SingI ix => (forall (ix :: k1). SingI ix => a ix -> a ix -> Bool) -> IIdentity a ix -> IIdentity a ix -> Bool Source #
IRead (IIdentity :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Data.IFunctor.IIdentity Methods ireadPrec :: forall (ix :: k0) a. SingI ix => (forall (ix :: k1). SingI ix => ReadPrec (a ix)) -> ReadPrec (IIdentity a ix) Source # ireadsPrec :: forall (ix :: k0) a. SingI ix => (forall (ix :: k1). SingI ix => Int -> ReadS (a ix)) -> Int -> ReadS (IIdentity a ix) Source #
IShow (IIdentity :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Data.IFunctor.IIdentity Methods ishowsPrec :: forall (ix :: k0) a. SingI ix => (forall (ix :: k1). SingI ix => Int -> a ix -> ShowS) -> Int -> IIdentity a ix -> ShowS Source # ishow :: forall (ix :: k0) a. SingI ix => (forall (ix :: k1). SingI ix => Int -> a ix -> ShowS) -> IIdentity a ix -> String Source #
ITraversable (IIdentity :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Data.IFunctor.IIdentity Methods itraverse :: forall m (ix :: k0) a b. (Applicative m, SingI ix) => (forall (ix :: k1). SingI ix => a ix -> m (b ix)) -> IIdentity a ix -> m (IIdentity b ix) Source #
IComonad (IIdentity :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Data.IFunctor.IIdentity Methods iextract :: forall (a :: k0 -> Type). IIdentity a ~~> a Source # iduplicate :: forall (a :: k0 -> Type). IIdentity a ~~> IIdentity (IIdentity a) Source # iextend :: forall (a :: k0 -> Type) (b :: k0 -> Type). (IIdentity a ~~> b) -> IIdentity a ~~> IIdentity b Source #
IMonad (IIdentity :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Data.IFunctor.IIdentity Methods ipure :: forall (a :: k0 -> Type). a ~~> IIdentity a Source # ijoin :: forall (a :: k0 -> Type). IIdentity (IIdentity a) ~~> IIdentity a Source # ibind :: forall (a :: k0 -> Type) (b :: k0 -> Type). (a ~~> IIdentity b) -> IIdentity a ~~> IIdentity b Source #
Generic1 (IIdentity f :: k -> Type) Source #
Instance details Defined in Data.IFunctor.IIdentity Associated Types type Rep1 (IIdentity f) :: k -> Type # Methods from1 :: forall (a :: k0). IIdentity f a -> Rep1 (IIdentity f) a # to1 :: forall (a :: k0). Rep1 (IIdentity f) a -> IIdentity f a #
(IEq2 f, SingI ix) => Eq (IIdentity f ix) Source #
Instance details Defined in Data.IFunctor.IIdentity Methods (==) :: IIdentity f ix -> IIdentity f ix -> Bool # (/=) :: IIdentity f ix -> IIdentity f ix -> Bool #
(Typeable ix, Typeable f, Typeable k, Data (f ix)) => Data (IIdentity f ix) Source #
Instance details Defined in Data.IFunctor.IIdentity Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> IIdentity f ix -> c (IIdentity f ix) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (IIdentity f ix) # toConstr :: IIdentity f ix -> Constr # dataTypeOf :: IIdentity f ix -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (IIdentity f ix)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (IIdentity f ix)) # gmapT :: (forall b. Data b => b -> b) -> IIdentity f ix -> IIdentity f ix # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> IIdentity f ix -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> IIdentity f ix -> r # gmapQ :: (forall d. Data d => d -> u) -> IIdentity f ix -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> IIdentity f ix -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> IIdentity f ix -> m (IIdentity f ix) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> IIdentity f ix -> m (IIdentity f ix) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> IIdentity f ix -> m (IIdentity f ix) #
(IOrd2 f, SingI ix) => Ord (IIdentity f ix) Source #
Instance details Defined in Data.IFunctor.IIdentity Methods compare :: IIdentity f ix -> IIdentity f ix -> Ordering # (<) :: IIdentity f ix -> IIdentity f ix -> Bool # (<=) :: IIdentity f ix -> IIdentity f ix -> Bool # (>) :: IIdentity f ix -> IIdentity f ix -> Bool # (>=) :: IIdentity f ix -> IIdentity f ix -> Bool # max :: IIdentity f ix -> IIdentity f ix -> IIdentity f ix # min :: IIdentity f ix -> IIdentity f ix -> IIdentity f ix #
(IRead2 f, SingI ix) => Read (IIdentity f ix) Source #
Instance details Defined in Data.IFunctor.IIdentity Methods readsPrec :: Int -> ReadS (IIdentity f ix) # readList :: ReadS [IIdentity f ix] # readPrec :: ReadPrec (IIdentity f ix) # readListPrec :: ReadPrec [IIdentity f ix] #
(IShow2 f, SingI ix) => Show (IIdentity f ix) Source #
Instance details Defined in Data.IFunctor.IIdentity Methods showsPrec :: Int -> IIdentity f ix -> ShowS # show :: IIdentity f ix -> String # showList :: [IIdentity f ix] -> ShowS #
Generic (IIdentity f ix) Source #
Instance details Defined in Data.IFunctor.IIdentity Associated Types type Rep (IIdentity f ix) :: Type -> Type # Methods from :: IIdentity f ix -> Rep (IIdentity f ix) x # to :: Rep (IIdentity f ix) x -> IIdentity f ix #
type Rep1 (IIdentity f :: k -> Type) Source #
Instance details Defined in Data.IFunctor.IIdentity type Rep1 (IIdentity f :: k -> Type) = D1 ('MetaData "IIdentity" "Data.IFunctor.IIdentity" "recursion-schemes-ix-0.1.0.0-LBKNYYUUm79APWA4D6g9GS" 'False) (C1 ('MetaCons "IIdentity" 'PrefixI 'True) (S1 ('MetaSel ('Just "runIIdentity") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 f)))
type Rep (IIdentity f ix) Source #
Instance details Defined in Data.IFunctor.IIdentity type Rep (IIdentity f ix) = D1 ('MetaData "IIdentity" "Data.IFunctor.IIdentity" "recursion-schemes-ix-0.1.0.0-LBKNYYUUm79APWA4D6g9GS" 'False) (C1 ('MetaCons "IIdentity" 'PrefixI 'True) (S1 ('MetaSel ('Just "runIIdentity") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (f ix))))

class IFunctor f => IMonad f where Source #

Minimal complete definition

ipure, (ijoin | ibind)

Methods

ipure :: a ~~> f a Source #

ijoin :: f (f a) ~~> f a Source #

ibind :: (a ~~> f b) -> f a ~~> f b Source #

Instances

Instances details

IMonad (IIdentity :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Data.IFunctor.IIdentity Methods ipure :: forall (a :: k0 -> Type). a ~~> IIdentity a Source # ijoin :: forall (a :: k0 -> Type). IIdentity (IIdentity a) ~~> IIdentity a Source # ibind :: forall (a :: k0 -> Type) (b :: k0 -> Type). (a ~~> IIdentity b) -> IIdentity a ~~> IIdentity b Source #
IMonad (Sum a :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Data.IMonad Methods ipure :: forall (a0 :: k0 -> Type). a0 ~~> Sum a a0 Source # ijoin :: forall (a0 :: k0 -> Type). Sum a (Sum a a0) ~~> Sum a a0 Source # ibind :: forall (a0 :: k0 -> Type) (b :: k0 -> Type). (a0 ~~> Sum a b) -> Sum a a0 ~~> Sum a b Source #
IFunctor f => IMonad (IFree f :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Data.IFunctor.IFree Methods ipure :: forall (a :: k0 -> Type). a ~~> IFree f a Source # ijoin :: forall (a :: k0 -> Type). IFree f (IFree f a) ~~> IFree f a Source # ibind :: forall (a :: k0 -> Type) (b :: k0 -> Type). (a ~~> IFree f b) -> IFree f a ~~> IFree f b Source #

class IFunctor f => ITraversable f where Source #

Methods

itraverse :: (Applicative m, SingI ix) => (forall ix. SingI ix => a ix -> m (b ix)) -> f a ix -> m (f b ix) Source #

Instances

Instances details

ITraversable (IIdentity :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Data.IFunctor.IIdentity Methods itraverse :: forall m (ix :: k0) a b. (Applicative m, SingI ix) => (forall (ix :: k1). SingI ix => a ix -> m (b ix)) -> IIdentity a ix -> m (IIdentity b ix) Source #
ITraversable (Product a :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Data.ITraversable Methods itraverse :: forall m (ix :: k0) a0 b. (Applicative m, SingI ix) => (forall (ix :: k1). SingI ix => a0 ix -> m (b ix)) -> Product a a0 ix -> m (Product a b ix) Source #
ITraversable (Sum a :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Data.ITraversable Methods itraverse :: forall m (ix :: k0) a0 b. (Applicative m, SingI ix) => (forall (ix :: k1). SingI ix => a0 ix -> m (b ix)) -> Sum a a0 ix -> m (Sum a b ix) Source #
ITraversable f => ITraversable (IFree f :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Data.IFunctor.IFree Methods itraverse :: forall m (ix :: k0) a b. (Applicative m, SingI ix) => (forall (ix :: k1). SingI ix => a ix -> m (b ix)) -> IFree f a ix -> m (IFree f b ix) Source #
ITraversable f => ITraversable (ICofree f :: (k -> Type) -> k -> Type) Source #
Instance details Defined in Data.IFunctor.ICofree Methods itraverse :: forall m (ix :: k0) a b. (Applicative m, SingI ix) => (forall (ix :: k1). SingI ix => a ix -> m (b ix)) -> ICofree f a ix -> m (ICofree f b ix) Source #

imapDefault :: ITraversable f => (a ~~> b) -> f a ~~> f b Source #

Default imap for deriving IFunctor

class SingI (a :: k) where #

Methods

sing :: Sing a #