Generics.MRSOP.Util

Useful utilities we need accross multiple modules.

Utility Functions and Types

(&&&) :: Arrow a => a b c -> a b c' -> a b (c, c') infixr 3

Fanout: send the input to both argument arrows and combine their output.

The default definition may be overridden with a more efficient version if desired.

(***) :: Arrow a => a b c -> a b' c' -> a (b, b') (c, c') infixr 3

Split the input between the two argument arrows and combine their output. Note that this is in general not a functor.

The default definition may be overridden with a more efficient version if desired.

type (:->) f g = forall n. f n -> g n

Natural transformations

(<.>) :: Monad m => (b -> m c) -> (a -> m b) -> a -> m c infixr 8

Kleisli Composition

Poly-kind indexed product functionality

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

Lifted product of functors.

Constructors

Pair (f a) (g a)

Instances

Generic1 (Product f g :: k -> Type)

Defined in Data.Functor.Product

Associated Types

type Rep1 (Product f g) :: k -> Type

Methods

from1 :: Product f g a -> Rep1 (Product f g) a

to1 :: Rep1 (Product f g) a -> Product f g a

(ShowHO f, ShowHO g) => ShowHO (Product f g :: ki -> Type)

Defined in Generics.MRSOP.Util

Methods

showHO :: Product f g k -> String

(EqHO f, EqHO g) => EqHO (Product f g :: ki -> Type)

Defined in Generics.MRSOP.Util

Methods

eqHO :: Product f g k -> Product f g k -> Bool

(Monad f, Monad g) => Monad (Product f g)

Since: base-4.9.0.0

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

fail :: String -> Product f g a

(Functor f, Functor g) => Functor (Product f g)

Since: base-4.9.0.0

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

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

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

Defined in Data.Functor.Product

Methods

fold :: Monoid m => Product f g m -> 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

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

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

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

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

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

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

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

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

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

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 :: (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

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

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

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)

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)

Since: base-4.9.0.0

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)

Since: base-4.9.0.0

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))))

type (:*:) = Product

pattern (:*:) :: f a -> g a -> Product f g a

type Delta f = Product f f

Diagonal indexed functor

curry' :: (Product f g x -> a) -> f x -> g x -> a

Lifted curry

uncurry' :: (f x -> g x -> a) -> Product f g x -> a

Lifted uncurry

delta :: f :-> Delta f

Duplicates its argument

Poly-kind indexed sums

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

Lifted sum of functors.

Constructors

InL (f a)

InR (g a)

Instances

Generic1 (Sum f g :: k -> Type)

Defined in Data.Functor.Sum

Associated Types

type Rep1 (Sum f g) :: k -> Type

Methods

from1 :: Sum f g a -> Rep1 (Sum f g) a

to1 :: Rep1 (Sum f g) a -> Sum f g a

(ShowHO f, ShowHO g) => ShowHO (Sum f g :: ki -> Type)

Defined in Generics.MRSOP.Util

Methods

showHO :: Sum f g k -> String

(EqHO f, EqHO g) => EqHO (Sum f g :: ki -> Type)

Defined in Generics.MRSOP.Util

Methods

eqHO :: Sum f g k -> Sum f g k -> Bool

(Functor f, Functor g) => Functor (Sum f g)

Since: base-4.9.0.0

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

Defined in Data.Functor.Sum

Methods

fold :: Monoid m => Sum f g m -> 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

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

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

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

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

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

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

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 :: (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

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

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

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)

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)

Since: base-4.9.0.0

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)

Since: base-4.9.0.0

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))))

either' :: (f :-> r) -> (g :-> r) -> Sum f g :-> r

Higher-order sum eliminator

either'' :: (forall x. f x -> a) -> (forall y. g y -> a) -> Sum f g r -> a

Just like either', but the result type is of kind Star

Type-level Naturals

data Nat

Type-level Peano Naturals

Constructors

S Nat

Z

Instances

Eq Nat

Defined in Generics.MRSOP.Util

Methods

(==) :: Nat -> Nat -> Bool

(/=) :: Nat -> Nat -> Bool

Show Nat

Defined in Generics.MRSOP.Util

Methods

showsPrec :: Int -> Nat -> ShowS

show :: Nat -> String

showList :: [Nat] -> ShowS

TestEquality SNat

Defined in Generics.MRSOP.Util

Methods

testEquality :: SNat a -> SNat b -> Maybe (a :~: b)

TestEquality (Constr codes :: Nat -> Type)

Defined in Generics.MRSOP.Base.Universe

Methods

testEquality :: Constr codes a -> Constr codes b -> Maybe (a :~: b)

EqHO ki => EqHO (Fix ki codes :: Nat -> Type)

Defined in Generics.MRSOP.Base.Universe

Methods

eqHO :: Fix ki codes k -> Fix ki codes k -> Bool

proxyUnsuc :: Proxy (S n) -> Proxy n

data SNat :: Nat -> * where

Singleton Term-level natural

Constructors

SZ :: SNat Z

SS :: SNat n -> SNat (S n)

Instances

TestEquality SNat

Defined in Generics.MRSOP.Util

Methods

testEquality :: SNat a -> SNat b -> Maybe (a :~: b)

snat2int :: SNat n -> Integer

class IsNat (n :: Nat) where

And their conversion to term-level integers.

Methods

getSNat :: Proxy n -> SNat n

Instances

IsNat Z

Defined in Generics.MRSOP.Util

Methods

getSNat :: Proxy Z -> SNat Z

IsNat n => IsNat (S n)

Defined in Generics.MRSOP.Util

Methods

getSNat :: Proxy (S n) -> SNat (S n)

getNat :: IsNat n => Proxy n -> Integer

getSNat' :: forall (n :: Nat). IsNat n => SNat n

Type-level Lists

data ListPrf :: [k] -> * where

An inhabitant of ListPrf ls is *not* a singleton! It only proves that ls is, in fact, a type level list. This is useful since it enables us to pattern match on type-level lists whenever we see fit.

Constructors

Nil :: ListPrf '[]

Cons :: ListPrf l -> ListPrf (x ': l)

class IsList (xs :: [k]) where

The IsList class allows us to construct ListPrfs in a straight forward fashion.

Methods

listPrf :: ListPrf xs

Instances

IsList ([] :: [k])

Defined in Generics.MRSOP.Util

Methods

listPrf :: ListPrf []

IsList xs => IsList (x ': xs :: [k])

Defined in Generics.MRSOP.Util

Methods

listPrf :: ListPrf (x ': xs)

type L1 xs = IsList xs

Convenient constraint synonyms

type L2 xs ys = (IsList xs, IsList ys)

type L3 xs ys zs = (IsList xs, IsList ys, IsList zs)

type L4 xs ys zs as = (IsList xs, IsList ys, IsList zs, IsList as)

type family (txs :: [k]) :++: (tys :: [k]) :: [k] where ...

Appending type-level lists

Equations

'[] :++: tys = tys

(tx ': txs) :++: tys = tx ': (txs :++: tys)

appendIsListLemma :: ListPrf xs -> ListPrf ys -> ListPrf (xs :++: ys)

Concatenation of lists is also a list.

Type-level List Lookup

type family Lkup (n :: Nat) (ks :: [k]) :: k where ...

Type-level list lookup

Equations

Lkup Z (k ': ks) = k

Lkup (S n) (k ': ks) = Lkup n ks

Lkup _ '[] = TypeError (Text "Lkup index too big")

type family Idx (ty :: k) (xs :: [k]) :: Nat where ...

Type-level list index

Equations

Idx x (x ': ys) = Z

Idx x (y ': ys) = S (Idx x ys)

Idx x '[] = TypeError (Text "Element not found")

data El :: [*] -> Nat -> * where

Also list lookup, but for kind * only.

Constructors

El

Fields

• :: IsNat ix
• => { unEl :: Lkup ix fam
•    } -> El fam ix

getElSNat :: forall ix ls. El ls ix -> SNat ix

Convenient way to cast an El index to term-level.

into :: forall fam ty ix. (ix ~ Idx ty fam, Lkup ix fam ~ ty, IsNat ix) => ty -> El fam ix

Smart constructor into El

Higher-order Eq and Show

class EqHO (f :: ki -> *) where

Higher order version of Eq

Methods

eqHO :: forall k. f k -> f k -> Bool

Instances

EqHO Singl

Defined in Generics.MRSOP.Opaque

Methods

eqHO :: Singl k -> Singl k -> Bool

Eq a => EqHO (Const a :: ki -> Type)

Defined in Generics.MRSOP.Util

Methods

eqHO :: Const a k -> Const a k -> Bool

(EqHO f, EqHO g) => EqHO (Sum f g :: ki -> Type)

Defined in Generics.MRSOP.Util

Methods

eqHO :: Sum f g k -> Sum f g k -> Bool

(EqHO f, EqHO g) => EqHO (Product f g :: ki -> Type)

Defined in Generics.MRSOP.Util

Methods

eqHO :: Product f g k -> Product f g k -> Bool

EqHO ki => EqHO (Fix ki codes :: Nat -> Type)

Defined in Generics.MRSOP.Base.Universe

Methods

eqHO :: Fix ki codes k -> Fix ki codes k -> Bool

EqHO phi => EqHO (NS phi :: [k] -> Type)

Defined in Generics.MRSOP.Base.NS

Methods

eqHO :: NS phi k0 -> NS phi k0 -> Bool

EqHO phi => EqHO (NP phi :: [k] -> Type)

Defined in Generics.MRSOP.Base.NP

Methods

eqHO :: NP phi k0 -> NP phi k0 -> Bool

(EqHO phi, EqHO ki) => EqHO (Rep ki phi :: [[Atom kon]] -> Type)

Defined in Generics.MRSOP.Base.Universe

Methods

eqHO :: Rep ki phi k -> Rep ki phi k -> Bool

(EqHO phi, EqHO ki) => EqHO (NA ki phi :: Atom kon -> Type)

Defined in Generics.MRSOP.Base.Universe

Methods

eqHO :: NA ki phi k -> NA ki phi k -> Bool

class ShowHO (f :: ki -> *) where

Higher order version of Show

Methods

showHO :: forall k. f k -> String

Instances

ShowHO Singl

Defined in Generics.MRSOP.Opaque

Methods

showHO :: Singl k -> String

Show a => ShowHO (Const a :: ki -> Type)

Defined in Generics.MRSOP.Util

Methods

showHO :: Const a k -> String

(ShowHO f, ShowHO g) => ShowHO (Sum f g :: ki -> Type)

Defined in Generics.MRSOP.Util

Methods

showHO :: Sum f g k -> String

(ShowHO f, ShowHO g) => ShowHO (Product f g :: ki -> Type)

Defined in Generics.MRSOP.Util

Methods

showHO :: Product f g k -> String

ShowHO (ConstructorInfo :: [Atom kon] -> Type)

Defined in Generics.MRSOP.Base.Metadata

Methods

showHO :: ConstructorInfo k -> String

ShowHO (FieldInfo :: Atom kon -> Type)

Defined in Generics.MRSOP.Base.Metadata

Methods

showHO :: FieldInfo k -> String

ShowHO phi => ShowHO (NS phi :: [k] -> Type)

Defined in Generics.MRSOP.Base.NS

Methods

showHO :: NS phi k0 -> String

ShowHO phi => ShowHO (NP phi :: [k] -> Type)

Defined in Generics.MRSOP.Base.NP

Methods

showHO :: NP phi k0 -> String

(ShowHO phi, ShowHO ki) => ShowHO (NA ki phi :: Atom kon -> Type)

Defined in Generics.MRSOP.Base.Universe

Methods

showHO :: NA ki phi k -> String