Safe Haskell	Safe
Language	Haskell2010

Generics.MRSOP.Util

Contents

Utility Functions and Types
Poly-kind indexed product functionality
Poly-kind indexed sums
Type-level Naturals
Type-level Lists
Type-level List Lookup
Higher-order Eq and Show

Description

Useful utilities we need accross multiple modules.

Synopsis

(&&&) :: Arrow a => a b c -> a b c' -> a b (c, c')
(***) :: Arrow a => a b c -> a b' c' -> a (b, b') (c, c')
type (:->) f g = forall n. f n -> g n
(<.>) :: Monad m => (b -> m c) -> (a -> m b) -> a -> m c
data Product (f :: k -> Type) (g :: k -> Type) (a :: k) :: forall k. (k -> Type) -> (k -> Type) -> k -> Type = Pair (f a) (g a)
type (:*:) = Product
pattern (:*:) :: f a -> g a -> Product f g a
type Delta f = Product f f
curry' :: (Product f g x -> a) -> f x -> g x -> a
uncurry' :: (f x -> g x -> a) -> Product f g x -> a
delta :: f :-> Delta f
data Sum (f :: k -> Type) (g :: k -> Type) (a :: k) :: forall k. (k -> Type) -> (k -> Type) -> k -> Type
- = InL (f a)
- | InR (g a)
either' :: (f :-> r) -> (g :-> r) -> Sum f g :-> r
either'' :: (forall x. f x -> a) -> (forall y. g y -> a) -> Sum f g r -> a
data Nat
- = S Nat
- | Z
proxyUnsuc :: Proxy (S n) -> Proxy n
data SNat :: Nat -> * where
- SZ :: SNat Z
- SS :: SNat n -> SNat (S n)
snat2int :: SNat n -> Integer
class IsNat (n :: Nat) where
- getSNat :: Proxy n -> SNat n
getNat :: IsNat n => Proxy n -> Integer
getSNat' :: forall (n :: Nat). IsNat n => SNat n
data ListPrf :: [k] -> * where
- LP_Nil :: ListPrf '[]
- LP_Cons :: ListPrf l -> ListPrf (x ': l)
class IsList (xs :: [k]) where
- listPrf :: ListPrf xs
type L1 xs = IsList xs
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 ...
appendIsListLemma :: ListPrf xs -> ListPrf ys -> ListPrf (xs :++: ys)
type family Lkup (n :: Nat) (ks :: [k]) :: k where ...
type family Idx (ty :: k) (xs :: [k]) :: Nat where ...
data El :: [*] -> Nat -> * where
- El :: IsNat ix => {..} -> El fam ix
getElSNat :: forall ix ls. El ls ix -> SNat ix
into :: forall fam ty ix. (ix ~ Idx ty fam, Lkup ix fam ~ ty, IsNat ix) => ty -> El fam ix
class EqHO (f :: ki -> *) where
- eqHO :: forall k. f k -> f k -> Bool
class ShowHO (f :: ki -> *) where
- showHO :: forall k. f k -> String
- showsPrecHO :: forall k. Int -> f k -> ShowS

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 Source #

Natural transformations

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

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)
Instance details 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) Source #
Instance details Defined in Generics.MRSOP.Util Methods showHO :: Product f g k -> String Source # showsPrecHO :: Int -> Product f g k -> ShowS Source #
(EqHO f, EqHO g) => EqHO (Product f g :: ki -> Type) Source #
Instance details Defined in Generics.MRSOP.Util Methods eqHO :: Product f g k -> Product f g k -> Bool Source #
(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 # fail :: String -> 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 # 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 :: (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)
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)	Since: base-4.9.0.0
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)	Since: base-4.9.0.0
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))))

type (:*:) = Product Source #

Convenient type synonym for Product

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

Convnient pattern synonym for Pair

type Delta f = Product f f Source #

Diagonal indexed functor

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

Lifted curry

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

Lifted uncurry

delta :: f :-> Delta f Source #

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)
Instance details 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) Source #
Instance details Defined in Generics.MRSOP.Util Methods showHO :: Sum f g k -> String Source # showsPrecHO :: Int -> Sum f g k -> ShowS Source #
(EqHO f, EqHO g) => EqHO (Sum f g :: ki -> Type) Source #
Instance details Defined in Generics.MRSOP.Util Methods eqHO :: Sum f g k -> Sum f g k -> Bool Source #
(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 # 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 :: (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)
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)	Since: base-4.9.0.0
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)	Since: base-4.9.0.0
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))))

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

Higher-order sum eliminator

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

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

Type-level Naturals

data Nat Source #

Type-level Peano Naturals

Constructors

S Nat
Z

Instances

Eq Nat Source #
Instance details Defined in Generics.MRSOP.Util Methods (==) :: Nat -> Nat -> Bool # (/=) :: Nat -> Nat -> Bool #
Show Nat Source #
Instance details Defined in Generics.MRSOP.Util Methods showsPrec :: Int -> Nat -> ShowS # show :: Nat -> String # showList :: [Nat] -> ShowS #
TestEquality SNat Source #
Instance details Defined in Generics.MRSOP.Util Methods testEquality :: SNat a -> SNat b -> Maybe (a :~: b) #
TestEquality (Constr codes :: Nat -> Type) Source #
Instance details Defined in Generics.MRSOP.Base.Universe Methods testEquality :: Constr codes a -> Constr codes b -> Maybe (a :~: b) #
ShowHO ki => ShowHO (Fix ki codes :: Nat -> Type) Source #
Instance details Defined in Generics.MRSOP.Base.Universe Methods showHO :: Fix ki codes k -> String Source # showsPrecHO :: Int -> Fix ki codes k -> ShowS Source #
EqHO ki => EqHO (Fix ki codes :: Nat -> Type) Source #
Instance details Defined in Generics.MRSOP.Base.Universe Methods eqHO :: Fix ki codes k -> Fix ki codes k -> Bool Source #

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

Typelevel predecessor operation

data SNat :: Nat -> * where Source #

Singleton Term-level natural

Constructors

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

Instances

TestEquality SNat Source #
Instance details Defined in Generics.MRSOP.Util Methods testEquality :: SNat a -> SNat b -> Maybe (a :~: b) #

snat2int :: SNat n -> Integer Source #

Returns n as a first class integer.

class IsNat (n :: Nat) where Source #

And their conversion to term-level integers.

Methods

getSNat :: Proxy n -> SNat n Source #

Instances

IsNat Z Source #
Instance details Defined in Generics.MRSOP.Util Methods getSNat :: Proxy Z -> SNat Z Source #
IsNat n => IsNat (S n) Source #
Instance details Defined in Generics.MRSOP.Util Methods getSNat :: Proxy (S n) -> SNat (S n) Source #

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

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

Type-level Lists

data ListPrf :: [k] -> * where Source #

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

LP_Nil :: ListPrf '[]
LP_Cons :: ListPrf l -> ListPrf (x ': l)

class IsList (xs :: [k]) where Source #

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

Methods

listPrf :: ListPrf xs Source #

Instances

IsList ([] :: [k]) Source #
Instance details Defined in Generics.MRSOP.Util Methods listPrf :: ListPrf [] Source #
IsList xs => IsList (x ': xs :: [k]) Source #
Instance details Defined in Generics.MRSOP.Util Methods listPrf :: ListPrf (x ': xs) Source #

type L1 xs = IsList xs Source #

Convenient constraint synonyms

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

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

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

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

Appending type-level lists

Equations

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

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

Concatenation of lists is also a list.

Type-level List Lookup

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

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 ... Source #

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 Source #

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 Source #

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 Source #

Smart constructor into El

Higher-order Eq and Show

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

Higher order , poly kinded, version of Eq @since 2.3.0

Methods

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

Instances

EqHO Singl Source #
Instance details Defined in Generics.MRSOP.Opaque Methods eqHO :: Singl k -> Singl k -> Bool Source #
Eq a => EqHO (Const a :: ki -> Type) Source #
Instance details Defined in Generics.MRSOP.Util Methods eqHO :: Const a k -> Const a k -> Bool Source #
(EqHO f, EqHO g) => EqHO (Sum f g :: ki -> Type) Source #
Instance details Defined in Generics.MRSOP.Util Methods eqHO :: Sum f g k -> Sum f g k -> Bool Source #
(EqHO f, EqHO g) => EqHO (Product f g :: ki -> Type) Source #
Instance details Defined in Generics.MRSOP.Util Methods eqHO :: Product f g k -> Product f g k -> Bool Source #
EqHO ki => EqHO (Fix ki codes :: Nat -> Type) Source #
Instance details Defined in Generics.MRSOP.Base.Universe Methods eqHO :: Fix ki codes k -> Fix ki codes k -> Bool Source #
EqHO f => EqHO (NS f :: [k] -> Type) Source #	Since: 2.3.0
Instance details Defined in Generics.MRSOP.Base.NS Methods eqHO :: NS f k0 -> NS f k0 -> Bool Source #
EqHO f => EqHO (NP f :: [k] -> Type) Source #	Since: 2.3.0
Instance details Defined in Generics.MRSOP.Base.NP Methods eqHO :: NP f k0 -> NP f k0 -> Bool Source #
(EqHO phi, EqHO ki) => EqHO (Rep ki phi :: [[Atom kon]] -> Type) Source #
Instance details Defined in Generics.MRSOP.Base.Universe Methods eqHO :: Rep ki phi k -> Rep ki phi k -> Bool Source #
(EqHO phi, EqHO ki) => EqHO (NA ki phi :: Atom kon -> Type) Source #
Instance details Defined in Generics.MRSOP.Base.Universe Methods eqHO :: NA ki phi k -> NA ki phi k -> Bool Source #
(EqHO phi, EqHO ki) => EqHO (Holes ki codes phi :: Atom kon -> Type) Source #
Instance details Defined in Generics.MRSOP.Holes Methods eqHO :: Holes ki codes phi k -> Holes ki codes phi k -> Bool Source #

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

Higher order, poly kinded, version of Show; We provide the same showsPrec mechanism. The documentation of Text.Show has a good example of the correct usage of showsPrec:

infixr 5 :^:
data Tree a =  Leaf a  |  Tree a :^: Tree a

instance (Show a) => Show (Tree a) where
  showsPrec d (Leaf m) = showParen (d > app_prec) $
       showString "Leaf " . showsPrec (app_prec+1) m
    where app_prec = 10

  showsPrec d (u :^: v) = showParen (d > up_prec) $
       showsPrec (up_prec+1) u .
       showString " :^: "      .
       showsPrec (up_prec+1) v
    where up_prec = 5

Since: 2.3.0

Minimal complete definition

showHO | showsPrecHO

Methods

showHO :: forall k. f k -> String Source #

showsPrecHO :: forall k. Int -> f k -> ShowS Source #

Instances

ShowHO Singl Source #
Instance details Defined in Generics.MRSOP.Opaque Methods showHO :: Singl k -> String Source # showsPrecHO :: Int -> Singl k -> ShowS Source #
Show a => ShowHO (Const a :: ki -> Type) Source #
Instance details Defined in Generics.MRSOP.Util Methods showHO :: Const a k -> String Source # showsPrecHO :: Int -> Const a k -> ShowS Source #
(ShowHO f, ShowHO g) => ShowHO (Sum f g :: ki -> Type) Source #
Instance details Defined in Generics.MRSOP.Util Methods showHO :: Sum f g k -> String Source # showsPrecHO :: Int -> Sum f g k -> ShowS Source #
(ShowHO f, ShowHO g) => ShowHO (Product f g :: ki -> Type) Source #
Instance details Defined in Generics.MRSOP.Util Methods showHO :: Product f g k -> String Source # showsPrecHO :: Int -> Product f g k -> ShowS Source #
ShowHO ki => ShowHO (Fix ki codes :: Nat -> Type) Source #
Instance details Defined in Generics.MRSOP.Base.Universe Methods showHO :: Fix ki codes k -> String Source # showsPrecHO :: Int -> Fix ki codes k -> ShowS Source #
ShowHO f => ShowHO (NS f :: [k] -> Type) Source #	Since: 2.3.0
Instance details Defined in Generics.MRSOP.Base.NS Methods showHO :: NS f k0 -> String Source # showsPrecHO :: Int -> NS f k0 -> ShowS Source #
ShowHO f => ShowHO (NP f :: [k] -> Type) Source #	Since: 2.3.0
Instance details Defined in Generics.MRSOP.Base.NP Methods showHO :: NP f k0 -> String Source # showsPrecHO :: Int -> NP f k0 -> ShowS Source #
(ShowHO ki, ShowHO phi) => ShowHO (Rep ki phi :: [[Atom kon]] -> Type) Source #
Instance details Defined in Generics.MRSOP.Base.Universe Methods showHO :: Rep ki phi k -> String Source # showsPrecHO :: Int -> Rep ki phi k -> ShowS Source #
(ShowHO phi, ShowHO ki) => ShowHO (NA ki phi :: Atom kon -> Type) Source #
Instance details Defined in Generics.MRSOP.Base.Universe Methods showHO :: NA ki phi k -> String Source # showsPrecHO :: Int -> NA ki phi k -> ShowS Source #
(HasDatatypeInfo ki fam codes, ShowHO ki, ShowHO f, ShowHO ann) => ShowHO (HolesAnn ann ki codes f :: Atom kon -> Type) Source #
Instance details Defined in Generics.MRSOP.Holes Methods showHO :: HolesAnn ann ki codes f k -> String Source # showsPrecHO :: Int -> HolesAnn ann ki codes f k -> ShowS Source #