Safe Haskell  None 

Language  Haskell2010 
Strict variant of SOP
This does not currently attempt to be exhaustive.
Synopsis
 data NP :: (k > Type ) > [k] > Type where
 hd :: NP f (x ': xs) > f x
 singletonNP :: f x > NP f '[x]
 tl :: NP f (x ': xs) > NP f xs
 data NS :: (k > Type ) > [k] > Type where
 index_NS :: forall f xs. NS f xs > Int
 unZ :: NS f '[x] > f x
 type Injection (f :: k > Type ) (xs :: [k]) = f .> K ( NS f xs)
 injections :: forall xs f. SListI xs => NP ( Injection f xs) xs
 data Proxy (t :: k) = Proxy
 ccompare_SOP :: forall k (c :: k > Constraint ) proxy r (f :: k > Type ) (g :: k > Type ) (xss :: [[k]]). All2 c xss => proxy c > r > ( forall (xs :: [k]). All c xs => NP f xs > NP g xs > r) > r > SOP f xss > SOP g xss > r
 compare_SOP :: forall k r (f :: k > Type ) (g :: k > Type ) (xss :: [[k]]). r > ( forall (xs :: [k]). NP f xs > NP g xs > r) > r > SOP f xss > SOP g xss > r
 ccompare_NS :: forall k c proxy r f g (xs :: [k]). All c xs => proxy c > r > ( forall (x :: k). c x => f x > g x > r) > r > NS f xs > NS g xs > r
 compare_NS :: forall k r f g (xs :: [k]). r > ( forall (x :: k). f x > g x > r) > r > NS f xs > NS g xs > r
 apInjs_POP :: forall k (xss :: [[k]]) (f :: k > Type ). SListI xss => POP f xss > [ SOP f xss]
 apInjs_NP :: forall k (xs :: [k]) (f :: k > Type ). SListI xs => NP f xs > [ NS f xs]
 shift :: forall a1 (f :: a1 > Type ) (xs :: [a1]) (a2 :: a1) (x :: a1). Injection f xs a2 > Injection f (x ': xs) a2
 unSOP :: forall k (f :: k > Type ) (xss :: [[k]]). SOP f xss > NS ( NP f) xss
 newtype SOP (f :: k > Type ) (xss :: [[k]]) = SOP ( NS ( NP f) xss)
 hcliftA3' :: forall k (c :: k > Constraint ) (xss :: [[k]]) h proxy f f' f'' f'''. ( All2 c xss, Prod h ~ ( NP :: ([k] > Type ) > [[k]] > Type ), HAp h) => proxy c > ( forall (xs :: [k]). All c xs => f xs > f' xs > f'' xs > f''' xs) > Prod h f xss > Prod h f' xss > h f'' xss > h f''' xss
 hcliftA2' :: forall k (c :: k > Constraint ) (xss :: [[k]]) h proxy f f' f''. ( All2 c xss, Prod h ~ ( NP :: ([k] > Type ) > [[k]] > Type ), HAp h) => proxy c > ( forall (xs :: [k]). All c xs => f xs > f' xs > f'' xs) > Prod h f xss > h f' xss > h f'' xss
 hcliftA' :: forall k (c :: k > Constraint ) (xss :: [[k]]) h proxy f f'. ( All2 c xss, Prod h ~ ( NP :: ([k] > Type ) > [[k]] > Type ), HAp h) => proxy c > ( forall (xs :: [k]). All c xs => f xs > f' xs) > h f xss > h f' xss
 shiftProjection :: forall a1 (f :: a1 > Type ) (xs :: [a1]) (a2 :: a1) (x :: a1). Projection f xs a2 > Projection f (x ': xs) a2
 projections :: forall k (xs :: [k]) (f :: k > Type ). SListI xs => NP ( Projection f xs) xs
 fromList :: forall k (xs :: [k]) a. SListI xs => [a] > Maybe ( NP ( K a :: k > Type ) xs)
 unPOP :: forall k (f :: k > Type ) (xss :: [[k]]). POP f xss > NP ( NP f) xss
 newtype POP (f :: k > Type ) (xss :: [[k]]) = POP ( NP ( NP f) xss)
 type Projection (f :: k > Type ) (xs :: [k]) = ( K ( NP f xs) :: k > Type ) .> f
 lengthSList :: forall k (xs :: [k]) proxy. SListI xs => proxy xs > Int
 shape :: forall k (xs :: [k]). SListI xs => Shape xs
 sList :: forall k (xs :: [k]). SListI xs => SList xs
 case_SList :: forall k (xs :: [k]) r. SListI xs => r ('[] :: [k]) > ( forall (y :: k) (ys :: [k]). SListI ys => r (y ': ys)) > r xs
 para_SList :: forall k (xs :: [k]) r. SListI xs => r ('[] :: [k]) > ( forall (y :: k) (ys :: [k]). SListI ys => r ys > r (y ': ys)) > r xs
 data SList (a :: [k]) where
 data Shape (a :: [k]) where
 htoI :: forall k1 l1 l2 h1 (f :: k1 > Type ) (xs :: l1) (ys :: l2) h2. ( AllZipN ( Prod h1) ( LiftedCoercible f I ) xs ys, HTrans h1 h2) => h1 f xs > h2 I ys
 hfromI :: forall l1 k2 l2 h1 (f :: k2 > Type ) (xs :: l1) (ys :: l2) h2. ( AllZipN ( Prod h1) ( LiftedCoercible I f) xs ys, HTrans h1 h2) => h1 I xs > h2 f ys
 hsequenceK :: forall k l h (xs :: l) f a. ( SListIN h xs, SListIN ( Prod h) xs, Applicative f, HSequence h) => h ( K (f a) :: k > Type ) xs > f (h ( K a :: k > Type ) xs)
 hsequence :: forall l h (xs :: l) f. ( SListIN h xs, SListIN ( Prod h) xs, HSequence h, Applicative f) => h f xs > f (h I xs)
 hcfor :: forall l h c (xs :: l) g proxy f. ( HSequence h, AllN h c xs, Applicative g) => proxy c > h f xs > ( forall a. c a => f a > g a) > g (h I xs)
 hctraverse :: forall l h c (xs :: l) g proxy f. ( HSequence h, AllN h c xs, Applicative g) => proxy c > ( forall a. c a => f a > g a) > h f xs > g (h I xs)
 hcfoldMap :: forall k l h c (xs :: l) m proxy f. ( HTraverse_ h, AllN h c xs, Monoid m) => proxy c > ( forall (a :: k). c a => f a > m) > h f xs > m
 hcfor_ :: forall k l h c (xs :: l) g proxy f. ( HTraverse_ h, AllN h c xs, Applicative g) => proxy c > h f xs > ( forall (a :: k). c a => f a > g ()) > g ()
 hczipWith3 :: forall k l h c (xs :: l) proxy f f' f'' f'''. ( AllN ( Prod h) c xs, HAp h, HAp ( Prod h)) => proxy c > ( forall (a :: k). c a => f a > f' a > f'' a > f''' a) > Prod h f xs > Prod h f' xs > h f'' xs > h f''' xs
 hczipWith :: forall k l h c (xs :: l) proxy f f' f''. ( AllN ( Prod h) c xs, HAp h, HAp ( Prod h)) => proxy c > ( forall (a :: k). c a => f a > f' a > f'' a) > Prod h f xs > h f' xs > h f'' xs
 hcmap :: forall k l h c (xs :: l) proxy f f'. ( AllN ( Prod h) c xs, HAp h) => proxy c > ( forall (a :: k). c a => f a > f' a) > h f xs > h f' xs
 hcliftA3 :: forall k l h c (xs :: l) proxy f f' f'' f'''. ( AllN ( Prod h) c xs, HAp h, HAp ( Prod h)) => proxy c > ( forall (a :: k). c a => f a > f' a > f'' a > f''' a) > Prod h f xs > Prod h f' xs > h f'' xs > h f''' xs
 hcliftA2 :: forall k l h c (xs :: l) proxy f f' f''. ( AllN ( Prod h) c xs, HAp h, HAp ( Prod h)) => proxy c > ( forall (a :: k). c a => f a > f' a > f'' a) > Prod h f xs > h f' xs > h f'' xs
 hcliftA :: forall k l h c (xs :: l) proxy f f'. ( AllN ( Prod h) c xs, HAp h) => proxy c > ( forall (a :: k). c a => f a > f' a) > h f xs > h f' xs
 hzipWith3 :: forall k l h (xs :: l) f f' f'' f'''. ( SListIN ( Prod h) xs, HAp h, HAp ( Prod h)) => ( forall (a :: k). f a > f' a > f'' a > f''' a) > Prod h f xs > Prod h f' xs > h f'' xs > h f''' xs
 hzipWith :: forall k l h (xs :: l) f f' f''. ( SListIN ( Prod h) xs, HAp h, HAp ( Prod h)) => ( forall (a :: k). f a > f' a > f'' a) > Prod h f xs > h f' xs > h f'' xs
 hmap :: forall k l h (xs :: l) f f'. ( SListIN ( Prod h) xs, HAp h) => ( forall (a :: k). f a > f' a) > h f xs > h f' xs
 hliftA3 :: forall k l h (xs :: l) f f' f'' f'''. ( SListIN ( Prod h) xs, HAp h, HAp ( Prod h)) => ( forall (a :: k). f a > f' a > f'' a > f''' a) > Prod h f xs > Prod h f' xs > h f'' xs > h f''' xs
 hliftA2 :: forall k l h (xs :: l) f f' f''. ( SListIN ( Prod h) xs, HAp h, HAp ( Prod h)) => ( forall (a :: k). f a > f' a > f'' a) > Prod h f xs > h f' xs > h f'' xs
 hliftA :: forall k l h (xs :: l) f f'. ( SListIN ( Prod h) xs, HAp h) => ( forall (a :: k). f a > f' a) > h f xs > h f' xs
 fn_4 :: forall k f (a :: k) f' f'' f''' f''''. (f a > f' a > f'' a > f''' a > f'''' a) > (f .> (f' .> (f'' .> (f''' .> f'''')))) a
 fn_3 :: forall k f (a :: k) f' f'' f'''. (f a > f' a > f'' a > f''' a) > (f .> (f' .> (f'' .> f'''))) a
 fn_2 :: forall k f (a :: k) f' f''. (f a > f' a > f'' a) > (f .> (f' .> f'')) a
 fn :: forall k f (a :: k) f'. (f a > f' a) > (f .> f') a
 class HPure (h :: (k > Type ) > l > Type ) where

newtype
((f :: k >
Type
)
.>
(g :: k >
Type
)) (a :: k) =
Fn
{
 apFn :: f a > g a
 type family Prod (h :: (k > Type ) > l > Type ) :: (k > Type ) > l > Type
 class ( Prod ( Prod h) ~ Prod h, HPure ( Prod h)) => HAp (h :: (k > Type ) > l > Type ) where
 type family CollapseTo (h :: (k > Type ) > l > Type ) x

class
HCollapse
(h :: (k >
Type
) > l >
Type
)
where
 hcollapse :: forall (xs :: l) a. SListIN h xs => h ( K a :: k > Type ) xs > CollapseTo h a

class
HTraverse_
(h :: (k >
Type
) > l >
Type
)
where
 hctraverse_ :: forall c (xs :: l) g proxy f. ( AllN h c xs, Applicative g) => proxy c > ( forall (a :: k). c a => f a > g ()) > h f xs > g ()
 htraverse_ :: forall (xs :: l) g f. ( SListIN h xs, Applicative g) => ( forall (a :: k). f a > g ()) > h f xs > g ()

class
HAp
h =>
HSequence
(h :: (k >
Type
) > l >
Type
)
where
 hsequence' :: forall (xs :: l) f (g :: k > Type ). ( SListIN h xs, Applicative f) => h (f :.: g) xs > f (h g xs)
 hctraverse' :: forall c (xs :: l) g proxy f f'. ( AllN h c xs, Applicative g) => proxy c > ( forall (a :: k). c a => f a > g (f' a)) > h f xs > g (h f' xs)
 htraverse' :: forall (xs :: l) g f f'. ( SListIN h xs, Applicative g) => ( forall (a :: k). f a > g (f' a)) > h f xs > g (h f' xs)
 class HIndex (h :: (k > Type ) > l > Type ) where
 type family UnProd (h :: (k > Type ) > l > Type ) :: (k > Type ) > l > Type
 class UnProd ( Prod h) ~ h => HApInjs (h :: (k > Type ) > l > Type ) where
 class HExpand (h :: (k > Type ) > l > Type ) where

class
((
Same
h1 :: (k2 >
Type
) > l2 >
Type
) ~ h2, (
Same
h2 :: (k1 >
Type
) > l1 >
Type
) ~ h1) =>
HTrans
(h1 :: (k1 >
Type
) > l1 >
Type
) (h2 :: (k2 >
Type
) > l2 >
Type
)
where
 htrans :: forall c (xs :: l1) (ys :: l2) proxy f g. AllZipN ( Prod h1) c xs ys => proxy c > ( forall (x :: k1) (y :: k2). c x y => f x > g y) > h1 f xs > h2 g ys
 hcoerce :: forall (f :: k1 > Type ) (g :: k2 > Type ) (xs :: l1) (ys :: l2). AllZipN ( Prod h1) ( LiftedCoercible f g) xs ys => h1 f xs > h2 g ys
 ccase_SList :: forall k c (xs :: [k]) proxy r. All c xs => proxy c > r ('[] :: [k]) > ( forall (y :: k) (ys :: [k]). (c y, All c ys) => r (y ': ys)) > r xs

class
(
AllF
c xs,
SListI
xs) =>
All
(c :: k >
Constraint
) (xs :: [k])
where
 cpara_SList :: proxy c > r ('[] :: [k]) > ( forall (y :: k) (ys :: [k]). (c y, All c ys) => r ys > r (y ': ys)) > r xs
 type SListI2 = All ( SListI :: [k] > Constraint )
 type SListI = All ( Top :: k > Constraint )
 type All2 (c :: k > Constraint ) = All ( All c)
 class ( SListI xs, SListI ys, SameShapeAs xs ys, SameShapeAs ys xs, AllZipF c xs ys) => AllZip (c :: a > b > Constraint ) (xs :: [a]) (ys :: [b])
 type family SameShapeAs (xs :: [a]) (ys :: [b]) where ...
 class Coercible (f x) (g y) => LiftedCoercible (f :: k > k1) (g :: k2 > k1) (x :: k) (y :: k2)
 class ( AllZipF ( AllZip f) xss yss, SListI xss, SListI yss, SameShapeAs xss yss, SameShapeAs yss xss) => AllZip2 (f :: a > b > Constraint ) (xss :: [[a]]) (yss :: [[b]])
 class f (g x) => Compose (f :: k > Constraint ) (g :: k1 > k) (x :: k1)
 class (f x, g x) => And (f :: k > Constraint ) (g :: k > Constraint ) (x :: k)
 class Top (x :: k)
 type family AllN (h :: (k > Type ) > l > Type ) (c :: k > Constraint ) :: l > Constraint
 type family AllZipN (h :: (k > Type ) > l > Type ) (c :: k1 > k2 > Constraint ) :: l1 > l2 > Constraint
 mapKKK :: forall k1 k2 k3 a b c (d :: k1) (e :: k2) (f :: k3). (a > b > c) > K a d > K b e > K c f
 mapKKI :: forall k1 k2 a b c (d :: k1) (e :: k2). (a > b > c) > K a d > K b e > I c
 mapKIK :: forall k1 k2 a b c (d :: k1) (e :: k2). (a > b > c) > K a d > I b > K c e
 mapKII :: forall k a b c (d :: k). (a > b > c) > K a d > I b > I c
 mapIKK :: forall k1 k2 a b c (d :: k1) (e :: k2). (a > b > c) > I a > K b d > K c e
 mapIKI :: forall k a b c (d :: k). (a > b > c) > I a > K b d > I c
 mapIIK :: forall k a b c (d :: k). (a > b > c) > I a > I b > K c d
 mapIII :: (a > b > c) > I a > I b > I c
 mapKK :: forall k1 k2 a b (c :: k1) (d :: k2). (a > b) > K a c > K b d
 mapKI :: forall k a b (c :: k). (a > b) > K a c > I b
 mapIK :: forall k a b (c :: k). (a > b) > I a > K b c
 mapII :: (a > b) > I a > I b
 unComp :: forall l k f (g :: k > l) (p :: k). (f :.: g) p > f (g p)
 unI :: I a > a
 unK :: forall k a (b :: k). K a b > a
 newtype K a (b :: k) = K a
 newtype I a = I a
 newtype ((f :: l > Type ) :.: (g :: k > l)) (p :: k) = Comp (f (g p))
 module Data.SOP.Constraint
NP
data NP :: (k > Type ) > [k] > Type where Source #
Instances
HTrans ( NP :: (k1 > Type ) > [k1] > Type ) ( NP :: (k2 > Type ) > [k2] > Type ) Source #  
Defined in Data.SOP.Strict htrans :: forall c (xs :: l1) (ys :: l2) proxy f g. AllZipN ( Prod NP ) c xs ys => proxy c > ( forall (x :: k10) (y :: k20). c x y => f x > g y) > NP f xs > NP g ys Source # hcoerce :: forall (f :: k10 > Type ) (g :: k20 > Type ) (xs :: l1) (ys :: l2). AllZipN ( Prod NP ) ( LiftedCoercible f g) xs ys => NP f xs > NP g ys Source # 

HPure ( NP :: (k > Type ) > [k] > Type ) Source #  
HAp ( NP :: (k > Type ) > [k] > Type ) Source #  
HCollapse ( NP :: (k > Type ) > [k] > Type ) Source #  
Defined in Data.SOP.Strict 

HTraverse_ ( NP :: (k > Type ) > [k] > Type ) Source #  
Defined in Data.SOP.Strict hctraverse_ :: forall c (xs :: l) g proxy f. ( AllN NP c xs, Applicative g) => proxy c > ( forall (a :: k0). c a => f a > g ()) > NP f xs > g () Source # htraverse_ :: forall (xs :: l) g f. ( SListIN NP xs, Applicative g) => ( forall (a :: k0). f a > g ()) > NP f xs > g () Source # 

HSequence ( NP :: (k > Type ) > [k] > Type ) Source #  
Defined in Data.SOP.Strict hsequence' :: forall (xs :: l) f (g :: k0 > Type ). ( SListIN NP xs, Applicative f) => NP (f :.: g) xs > f ( NP g xs) Source # hctraverse' :: forall c (xs :: l) g proxy f f'. ( AllN NP c xs, Applicative g) => proxy c > ( forall (a :: k0). c a => f a > g (f' a)) > NP f xs > g ( NP f' xs) Source # htraverse' :: forall (xs :: l) g f f'. ( SListIN NP xs, Applicative g) => ( forall (a :: k0). f a > g (f' a)) > NP f xs > g ( NP f' xs) Source # 

All ( Compose Eq f) xs => Eq ( NP f xs) Source #  
( All ( Compose Eq f) xs, All ( Compose Ord f) xs) => Ord ( NP f xs) Source #  
All ( Compose Show f) xs => Show ( NP f xs) Source # 
Copied from sopcore Not derived, since derived instance ignores associativity info 
All ( Compose NoThunks f) xs => NoThunks ( NP f xs) Source #  
type AllZipN ( NP :: (k > Type ) > [k] > Type ) (c :: a > b > Constraint ) Source #  
Defined in Data.SOP.Strict 

type Same ( NP :: (k1 > Type ) > [k1] > Type ) Source #  
type Prod ( NP :: (k > Type ) > [k] > Type ) Source #  
type SListIN ( NP :: (k > Type ) > [k] > Type ) Source #  
Defined in Data.SOP.Strict 

type CollapseTo ( NP :: (k > Type ) > [k] > Type ) a Source #  
Defined in Data.SOP.Strict 

type AllN ( NP :: (k > Type ) > [k] > Type ) (c :: k > Constraint ) Source #  
Defined in Data.SOP.Strict 
singletonNP :: f x > NP f '[x] Source #
NS
data NS :: (k > Type ) > [k] > Type where Source #
Instances
HTrans ( NS :: (k1 > Type ) > [k1] > Type ) ( NS :: (k2 > Type ) > [k2] > Type ) Source #  
Defined in Data.SOP.Strict htrans :: forall c (xs :: l1) (ys :: l2) proxy f g. AllZipN ( Prod NS ) c xs ys => proxy c > ( forall (x :: k10) (y :: k20). c x y => f x > g y) > NS f xs > NS g ys Source # hcoerce :: forall (f :: k10 > Type ) (g :: k20 > Type ) (xs :: l1) (ys :: l2). AllZipN ( Prod NS ) ( LiftedCoercible f g) xs ys => NS f xs > NS g ys Source # 

HAp ( NS :: (k > Type ) > [k] > Type ) Source #  
HCollapse ( NS :: (k > Type ) > [k] > Type ) Source #  
Defined in Data.SOP.Strict 

HSequence ( NS :: (k > Type ) > [k] > Type ) Source #  
Defined in Data.SOP.Strict hsequence' :: forall (xs :: l) f (g :: k0 > Type ). ( SListIN NS xs, Applicative f) => NS (f :.: g) xs > f ( NS g xs) Source # hctraverse' :: forall c (xs :: l) g proxy f f'. ( AllN NS c xs, Applicative g) => proxy c > ( forall (a :: k0). c a => f a > g (f' a)) > NS f xs > g ( NS f' xs) Source # htraverse' :: forall (xs :: l) g f f'. ( SListIN NS xs, Applicative g) => ( forall (a :: k0). f a > g (f' a)) > NS f xs > g ( NS f' xs) Source # 

HExpand ( NS :: (k > Type ) > [k] > Type ) Source #  
All ( Compose Eq f) xs => Eq ( NS f xs) Source #  
( All ( Compose Eq f) xs, All ( Compose Ord f) xs) => Ord ( NS f xs) Source #  
All ( Compose Show f) xs => Show ( NS f xs) Source #  
All ( Compose NoThunks f) xs => NoThunks ( NS f xs) Source #  
type Same ( NS :: (k1 > Type ) > [k1] > Type ) Source #  
type Prod ( NS :: (k > Type ) > [k] > Type ) Source #  
type SListIN ( NS :: (k > Type ) > [k] > Type ) Source #  
Defined in Data.SOP.Strict 

type CollapseTo ( NS :: (k > Type ) > [k] > Type ) a Source #  
Defined in Data.SOP.Strict 

type AllN ( NS :: (k > Type ) > [k] > Type ) (c :: k > Constraint ) Source #  
Defined in Data.SOP.Strict 
Injections
Reexports from
sopcore
Proxy
is a type that holds no data, but has a phantom parameter of
arbitrary type (or even kind). Its use is to provide type information, even
though there is no value available of that type (or it may be too costly to
create one).
Historically,
is a safer alternative to the
Proxy
::
Proxy
a
idiom.
undefined
:: a
>>>
Proxy :: Proxy (Void, Int > Int)
Proxy
Proxy can even hold types of higher kinds,
>>>
Proxy :: Proxy Either
Proxy
>>>
Proxy :: Proxy Functor
Proxy
>>>
Proxy :: Proxy complicatedStructure
Proxy
Instances
Generic1 ( Proxy :: k > Type ) 
Since: base4.6.0.0 
SemialignWithIndex Void ( Proxy :: Type > Type )  
Defined in Data.Semialign.Internal 

ZipWithIndex Void ( Proxy :: Type > Type )  
RepeatWithIndex Void ( Proxy :: Type > Type )  
Monad ( Proxy :: Type > Type ) 
Since: base4.7.0.0 
Functor ( Proxy :: Type > Type ) 
Since: base4.7.0.0 
Applicative ( Proxy :: Type > Type ) 
Since: base4.7.0.0 
Foldable ( Proxy :: Type > Type ) 
Since: base4.7.0.0 
Defined in Data.Foldable fold :: Monoid m => Proxy m > m Source # foldMap :: Monoid m => (a > m) > Proxy a > m Source # foldMap' :: Monoid m => (a > m) > Proxy a > m Source # foldr :: (a > b > b) > b > Proxy a > b Source # foldr' :: (a > b > b) > b > Proxy a > b Source # foldl :: (b > a > b) > b > Proxy a > b Source # foldl' :: (b > a > b) > b > Proxy a > b Source # foldr1 :: (a > a > a) > Proxy a > a Source # foldl1 :: (a > a > a) > Proxy a > a Source # toList :: Proxy a > [a] Source # null :: Proxy a > Bool Source # length :: Proxy a > Int Source # elem :: Eq a => a > Proxy a > Bool Source # maximum :: Ord a => Proxy a > a Source # minimum :: Ord a => Proxy a > a Source # 

Traversable ( Proxy :: Type > Type ) 
Since: base4.7.0.0 
MonadPlus ( Proxy :: Type > Type ) 
Since: base4.9.0.0 
Alternative ( Proxy :: Type > Type ) 
Since: base4.9.0.0 
Contravariant ( Proxy :: Type > Type )  
Eq1 ( Proxy :: Type > Type ) 
Since: base4.9.0.0 
Ord1 ( Proxy :: Type > Type ) 
Since: base4.9.0.0 
Defined in Data.Functor.Classes 

Read1 ( Proxy :: Type > Type ) 
Since: base4.9.0.0 
Defined in Data.Functor.Classes liftReadsPrec :: ( Int > ReadS a) > ReadS [a] > Int > ReadS ( Proxy a) Source # liftReadList :: ( Int > ReadS a) > ReadS [a] > ReadS [ Proxy a] Source # liftReadPrec :: ReadPrec a > ReadPrec [a] > ReadPrec ( Proxy a) Source # liftReadListPrec :: ReadPrec a > ReadPrec [a] > ReadPrec [ Proxy a] Source # 

Show1 ( Proxy :: Type > Type ) 
Since: base4.9.0.0 
NFData1 ( Proxy :: Type > Type ) 
Since: deepseq1.4.3.0 
Defined in Control.DeepSeq 

Hashable1 ( Proxy :: Type > Type )  
Defined in Data.Hashable.Class 

Semialign ( Proxy :: Type > Type )  
Align ( Proxy :: Type > Type )  
Defined in Data.Semialign.Internal 

Unalign ( Proxy :: Type > Type )  
Zip ( Proxy :: Type > Type )  
Repeat ( Proxy :: Type > Type )  
Defined in Data.Semialign.Internal 

Unzip ( Proxy :: Type > Type )  
Bounded ( Proxy t) 
Since: base4.7.0.0 
Enum ( Proxy s) 
Since: base4.7.0.0 
Defined in Data.Proxy succ :: Proxy s > Proxy s Source # pred :: Proxy s > Proxy s Source # toEnum :: Int > Proxy s Source # fromEnum :: Proxy s > Int Source # enumFrom :: Proxy s > [ Proxy s] Source # enumFromThen :: Proxy s > Proxy s > [ Proxy s] Source # enumFromTo :: Proxy s > Proxy s > [ Proxy s] Source # enumFromThenTo :: Proxy s > Proxy s > Proxy s > [ Proxy s] Source # 

Eq ( Proxy s) 
Since: base4.7.0.0 
Ord ( Proxy s) 
Since: base4.7.0.0 
Read ( Proxy t) 
Since: base4.7.0.0 
Show ( Proxy s) 
Since: base4.7.0.0 
Ix ( Proxy s) 
Since: base4.7.0.0 
Generic ( Proxy t) 
Since: base4.6.0.0 
Semigroup ( Proxy s) 
Since: base4.9.0.0 
Monoid ( Proxy s) 
Since: base4.7.0.0 
Hashable ( Proxy a)  
NFData ( Proxy a) 
Since: deepseq1.4.0.0 
Defined in Control.DeepSeq 

Serialise ( Proxy a) 
Since: serialise0.2.0.0 
type Rep1 ( Proxy :: k > Type )  
type Rep ( Proxy t)  
:: forall k (c :: k > Constraint ) proxy r (f :: k > Type ) (g :: k > Type ) (xss :: [[k]]). All2 c xss  
=> proxy c  
> r 
what to do if first is smaller 
> ( forall (xs :: [k]). All c xs => NP f xs > NP g xs > r) 
what to do if both are equal 
> r 
what to do if first is larger 
> SOP f xss  
> SOP g xss  
> r 
Constrained version of
compare_SOP
.
Since: sopcore0.3.2.0
:: forall k r (f :: k > Type ) (g :: k > Type ) (xss :: [[k]]). r 
what to do if first is smaller 
> ( forall (xs :: [k]). NP f xs > NP g xs > r) 
what to do if both are equal 
> r 
what to do if first is larger 
> SOP f xss  
> SOP g xss  
> r 
Compare two sums of products with respect to the choice in the sum they are making.
Only the sum structure is used for comparison.
This is a small wrapper around
ccompare_NS
for
a common special case.
Since: sopcore0.3.2.0
:: forall k c proxy r f g (xs :: [k]). All c xs  
=> proxy c  
> r 
what to do if first is smaller 
> ( forall (x :: k). c x => f x > g x > r) 
what to do if both are equal 
> r 
what to do if first is larger 
> NS f xs  
> NS g xs  
> r 
Constrained version of
compare_NS
.
Since: sopcore0.3.2.0
:: forall k r f g (xs :: [k]). r 
what to do if first is smaller 
> ( forall (x :: k). f x > g x > r) 
what to do if both are equal 
> r 
what to do if first is larger 
> NS f xs  
> NS g xs  
> r 
Compare two sums with respect to the choice they are making.
A value that chooses the first option is considered smaller than one that chooses the second option.
If the choices are different, then either the first (if the first is smaller than the second) or the third (if the first is larger than the second) argument are called. If both choices are equal, then the second argument is called, which has access to the elements contained in the sums.
Since: sopcore0.3.2.0
apInjs_POP :: forall k (xss :: [[k]]) (f :: k > Type ). SListI xss => POP f xss > [ SOP f xss] Source #
Apply injections to a product of product.
This operates on the outer product only. Given a product containing all possible choices (that are products), produce a list of sums (of products) by applying each injection to the appropriate element.
Example:
>>>
apInjs_POP (POP ((I 'x' :* Nil) :* (I True :* I 2 :* Nil) :* Nil))
[SOP (Z (I 'x' :* Nil)),SOP (S (Z (I True :* I 2 :* Nil)))]
apInjs_NP :: forall k (xs :: [k]) (f :: k > Type ). SListI xs => NP f xs > [ NS f xs] Source #
Apply injections to a product.
Given a product containing all possible choices, produce a list of sums by applying each injection to the appropriate element.
Example:
>>>
apInjs_NP (I 'x' :* I True :* I 2 :* Nil)
[Z (I 'x'),S (Z (I True)),S (S (Z (I 2)))]
shift :: forall a1 (f :: a1 > Type ) (xs :: [a1]) (a2 :: a1) (x :: a1). Injection f xs a2 > Injection f (x ': xs) a2 Source #
Shift an injection.
Given an injection, return an injection into a sum that is one component larger.
unSOP :: forall k (f :: k > Type ) (xss :: [[k]]). SOP f xss > NS ( NP f) xss Source #
Unwrap a sum of products.
newtype SOP (f :: k > Type ) (xss :: [[k]]) Source #
A sum of products.
This is a 'newtype' for an
NS
of an
NP
. The elements of the
(inner) products are applications of the parameter
f
. The type
SOP
is indexed by the list of lists that determines the sizes
of both the (outer) sum and all the (inner) products, as well as
the types of all the elements of the inner products.
A
reflects the structure of a normal Haskell datatype.
The sum structure represents the choice between the different
constructors, the product structure represents the arguments of
each constructor.
SOP
I
Instances
HTrans ( SOP :: (k1 > Type ) > [[k1]] > Type ) ( SOP :: (k2 > Type ) > [[k2]] > Type )  
Defined in Data.SOP.NS htrans :: forall c (xs :: l1) (ys :: l2) proxy f g. AllZipN ( Prod SOP ) c xs ys => proxy c > ( forall (x :: k10) (y :: k20). c x y => f x > g y) > SOP f xs > SOP g ys Source # hcoerce :: forall (f :: k10 > Type ) (g :: k20 > Type ) (xs :: l1) (ys :: l2). AllZipN ( Prod SOP ) ( LiftedCoercible f g) xs ys => SOP f xs > SOP g ys Source # 

HAp ( SOP :: (k > Type ) > [[k]] > Type )  
HCollapse ( SOP :: (k > Type ) > [[k]] > Type )  
Defined in Data.SOP.NS 

HTraverse_ ( SOP :: (k > Type ) > [[k]] > Type )  
Defined in Data.SOP.NS hctraverse_ :: forall c (xs :: l) g proxy f. ( AllN SOP c xs, Applicative g) => proxy c > ( forall (a :: k0). c a => f a > g ()) > SOP f xs > g () Source # htraverse_ :: forall (xs :: l) g f. ( SListIN SOP xs, Applicative g) => ( forall (a :: k0). f a > g ()) > SOP f xs > g () Source # 

HSequence ( SOP :: (k > Type ) > [[k]] > Type )  
Defined in Data.SOP.NS hsequence' :: forall (xs :: l) f (g :: k0 > Type ). ( SListIN SOP xs, Applicative f) => SOP (f :.: g) xs > f ( SOP g xs) Source # hctraverse' :: forall c (xs :: l) g proxy f f'. ( AllN SOP c xs, Applicative g) => proxy c > ( forall (a :: k0). c a => f a > g (f' a)) > SOP f xs > g ( SOP f' xs) Source # htraverse' :: forall (xs :: l) g f f'. ( SListIN SOP xs, Applicative g) => ( forall (a :: k0). f a > g (f' a)) > SOP f xs > g ( SOP f' xs) Source # 

HIndex ( SOP :: (k > Type ) > [[k]] > Type )  
HApInjs ( SOP :: (k > Type ) > [[k]] > Type )  
HExpand ( SOP :: (k > Type ) > [[k]] > Type )  
Eq ( NS ( NP f) xss) => Eq ( SOP f xss)  
Ord ( NS ( NP f) xss) => Ord ( SOP f xss)  
Defined in Data.SOP.NS 

Show ( NS ( NP f) xss) => Show ( SOP f xss)  
NFData ( NS ( NP f) xss) => NFData ( SOP f xss) 
Since: sopcore0.2.5.0 
Defined in Data.SOP.NS 

type Same ( SOP :: (k1 > Type ) > [[k1]] > Type )  
type Prod ( SOP :: (k > Type ) > [[k]] > Type )  
type SListIN ( SOP :: (k > Type ) > [[k]] > Type )  
Defined in Data.SOP.NS 

type CollapseTo ( SOP :: (k > Type ) > [[k]] > Type ) a  
Defined in Data.SOP.NS 

type AllN ( SOP :: (k > Type ) > [[k]] > Type ) (c :: k > Constraint )  
Defined in Data.SOP.NS 
hcliftA3' :: forall k (c :: k > Constraint ) (xss :: [[k]]) h proxy f f' f'' f'''. ( All2 c xss, Prod h ~ ( NP :: ([k] > Type ) > [[k]] > Type ), HAp h) => proxy c > ( forall (xs :: [k]). All c xs => f xs > f' xs > f'' xs > f''' xs) > Prod h f xss > Prod h f' xss > h f'' xss > h f''' xss Source #
Like
hcliftA'
, but for ternary functions.
hcliftA2' :: forall k (c :: k > Constraint ) (xss :: [[k]]) h proxy f f' f''. ( All2 c xss, Prod h ~ ( NP :: ([k] > Type ) > [[k]] > Type ), HAp h) => proxy c > ( forall (xs :: [k]). All c xs => f xs > f' xs > f'' xs) > Prod h f xss > h f' xss > h f'' xss Source #
Like
hcliftA'
, but for binary functions.
hcliftA' :: forall k (c :: k > Constraint ) (xss :: [[k]]) h proxy f f'. ( All2 c xss, Prod h ~ ( NP :: ([k] > Type ) > [[k]] > Type ), HAp h) => proxy c > ( forall (xs :: [k]). All c xs => f xs > f' xs) > h f xss > h f' xss Source #
Lift a constrained function operating on a listindexed structure to a function on a listoflistindexed structure.
This is a variant of
hcliftA
.
Specification:
hcliftA'
p f xs =hpure
(fn_2
$ \AllDictC
> f) `hap
`allDict_NP
p `hap
` xs
Instances:
hcliftA'
::All2
c xss => proxy c > (forall xs.All
c xs => f xs > f' xs) >NP
f xss >NP
f' xsshcliftA'
::All2
c xss => proxy c > (forall xs.All
c xs => f xs > f' xs) >NS
f xss >NS
f' xss
shiftProjection :: forall a1 (f :: a1 > Type ) (xs :: [a1]) (a2 :: a1) (x :: a1). Projection f xs a2 > Projection f (x ': xs) a2 Source #
projections :: forall k (xs :: [k]) (f :: k > Type ). SListI xs => NP ( Projection f xs) xs Source #
Compute all projections from an nary product.
Each element of the resulting product contains one of the projections.
fromList :: forall k (xs :: [k]) a. SListI xs => [a] > Maybe ( NP ( K a :: k > Type ) xs) Source #
Construct a homogeneous nary product from a normal Haskell list.
Returns
Nothing
if the length of the list does not exactly match the
expected size of the product.
unPOP :: forall k (f :: k > Type ) (xss :: [[k]]). POP f xss > NP ( NP f) xss Source #
Unwrap a product of products.
newtype POP (f :: k > Type ) (xss :: [[k]]) Source #
A product of products.
This is a 'newtype' for an
NP
of an
NP
. The elements of the
inner products are applications of the parameter
f
. The type
POP
is indexed by the list of lists that determines the lengths
of both the outer and all the inner products, as well as the types
of all the elements of the inner products.
A
POP
is reminiscent of a twodimensional table (but the inner
lists can all be of different length). In the context of the SOP
approach to generic programming, a
POP
is useful to represent
information that is available for all arguments of all constructors
of a datatype.
Instances
HTrans ( POP :: (k1 > Type ) > [[k1]] > Type ) ( POP :: (k2 > Type ) > [[k2]] > Type )  
Defined in Data.SOP.NP htrans :: forall c (xs :: l1) (ys :: l2) proxy f g. AllZipN ( Prod POP ) c xs ys => proxy c > ( forall (x :: k10) (y :: k20). c x y => f x > g y) > POP f xs > POP g ys Source # hcoerce :: forall (f :: k10 > Type ) (g :: k20 > Type ) (xs :: l1) (ys :: l2). AllZipN ( Prod POP ) ( LiftedCoercible f g) xs ys => POP f xs > POP g ys Source # 

HPure ( POP :: (k > Type ) > [[k]] > Type )  
HAp ( POP :: (k > Type ) > [[k]] > Type )  
HCollapse ( POP :: (k > Type ) > [[k]] > Type )  
Defined in Data.SOP.NP 

HTraverse_ ( POP :: (k > Type ) > [[k]] > Type )  
Defined in Data.SOP.NP hctraverse_ :: forall c (xs :: l) g proxy f. ( AllN POP c xs, Applicative g) => proxy c > ( forall (a :: k0). c a => f a > g ()) > POP f xs > g () Source # htraverse_ :: forall (xs :: l) g f. ( SListIN POP xs, Applicative g) => ( forall (a :: k0). f a > g ()) > POP f xs > g () Source # 

HSequence ( POP :: (k > Type ) > [[k]] > Type )  
Defined in Data.SOP.NP hsequence' :: forall (xs :: l) f (g :: k0 > Type ). ( SListIN POP xs, Applicative f) => POP (f :.: g) xs > f ( POP g xs) Source # hctraverse' :: forall c (xs :: l) g proxy f f'. ( AllN POP c xs, Applicative g) => proxy c > ( forall (a :: k0). c a => f a > g (f' a)) > POP f xs > g ( POP f' xs) Source # htraverse' :: forall (xs :: l) g f f'. ( SListIN POP xs, Applicative g) => ( forall (a :: k0). f a > g (f' a)) > POP f xs > g ( POP f' xs) Source # 

Eq ( NP ( NP f) xss) => Eq ( POP f xss)  
Ord ( NP ( NP f) xss) => Ord ( POP f xss)  
Defined in Data.SOP.NP 

Show ( NP ( NP f) xss) => Show ( POP f xss)  
Semigroup ( NP ( NP f) xss) => Semigroup ( POP f xss) 
Since: sopcore0.4.0.0 
Monoid ( NP ( NP f) xss) => Monoid ( POP f xss) 
Since: sopcore0.4.0.0 
NFData ( NP ( NP f) xss) => NFData ( POP f xss) 
Since: sopcore0.2.5.0 
Defined in Data.SOP.NP 

type AllZipN ( POP :: (k > Type ) > [[k]] > Type ) (c :: a > b > Constraint )  
Defined in Data.SOP.NP 

type Same ( POP :: (k1 > Type ) > [[k1]] > Type )  
type Prod ( POP :: (k > Type ) > [[k]] > Type )  
type UnProd ( POP :: (k > Type ) > [[k]] > Type )  
type SListIN ( POP :: (k > Type ) > [[k]] > Type )  
Defined in Data.SOP.NP 

type CollapseTo ( POP :: (k > Type ) > [[k]] > Type ) a  
Defined in Data.SOP.NP 

type AllN ( POP :: (k > Type ) > [[k]] > Type ) (c :: k > Constraint )  
Defined in Data.SOP.NP 
type Projection (f :: k > Type ) (xs :: [k]) = ( K ( NP f xs) :: k > Type ) .> f Source #
The type of projections from an nary product.
A projection is a function from the nary product to a single element.
lengthSList :: forall k (xs :: [k]) proxy. SListI xs => proxy xs > Int Source #
The length of a typelevel list.
Since: sopcore0.2
sList :: forall k (xs :: [k]). SListI xs => SList xs Source #
Get hold of an explicit singleton (that one can then pattern match on) for a typelevel list
case_SList :: forall k (xs :: [k]) r. SListI xs => r ('[] :: [k]) > ( forall (y :: k) (ys :: [k]). SListI ys => r (y ': ys)) > r xs Source #
Case distinction on a typelevel list.
Since: sopcore0.4.0.0
para_SList :: forall k (xs :: [k]) r. SListI xs => r ('[] :: [k]) > ( forall (y :: k) (ys :: [k]). SListI ys => r ys > r (y ': ys)) > r xs Source #
Paramorphism for a typelevel list.
Since: sopcore0.4.0.0
data SList (a :: [k]) where Source #
Explicit singleton list.
A singleton list can be used to reveal the structure of
a typelevel list argument that the function is quantified
over. For every typelevel list
xs
, there is one nonbottom
value of type
.
SList
xs
Note that these singleton lists are polymorphic in the list elements; we do not require a singleton representation for them.
Since: sopcore0.2
SNil :: forall k. SList ('[] :: [k])  
SCons :: forall k (xs :: [k]) (x :: k). SListI xs => SList (x ': xs) 
Instances
Eq ( SList xs)  
Ord ( SList xs)  
Defined in Data.SOP.Sing 

Show ( SList xs)  
data Shape (a :: [k]) where Source #
Occasionally it is useful to have an explicit, termlevel, representation of typelevel lists (esp because of https://ghc.haskell.org/trac/ghc/ticket/9108 )
ShapeNil :: forall k. Shape ('[] :: [k])  
ShapeCons :: forall k (xs :: [k]) (x :: k). SListI xs => Shape xs > Shape (x ': xs) 
Instances
Eq ( Shape xs)  
Ord ( Shape xs)  
Defined in Data.SOP.Sing 

Show ( Shape xs)  
htoI :: forall k1 l1 l2 h1 (f :: k1 > Type ) (xs :: l1) (ys :: l2) h2. ( AllZipN ( Prod h1) ( LiftedCoercible f I ) xs ys, HTrans h1 h2) => h1 f xs > h2 I ys Source #
Specialization of
hcoerce
.
Since: sopcore0.3.1.0
hfromI :: forall l1 k2 l2 h1 (f :: k2 > Type ) (xs :: l1) (ys :: l2) h2. ( AllZipN ( Prod h1) ( LiftedCoercible I f) xs ys, HTrans h1 h2) => h1 I xs > h2 f ys Source #
Specialization of
hcoerce
.
Since: sopcore0.3.1.0
hsequenceK :: forall k l h (xs :: l) f a. ( SListIN h xs, SListIN ( Prod h) xs, Applicative f, HSequence h) => h ( K (f a) :: k > Type ) xs > f (h ( K a :: k > Type ) xs) Source #
Special case of
hsequence'
where
g =
.
K
a
hsequence :: forall l h (xs :: l) f. ( SListIN h xs, SListIN ( Prod h) xs, HSequence h, Applicative f) => h f xs > f (h I xs) Source #
Special case of
hsequence'
where
g =
.
I
hcfor :: forall l h c (xs :: l) g proxy f. ( HSequence h, AllN h c xs, Applicative g) => proxy c > h f xs > ( forall a. c a => f a > g a) > g (h I xs) Source #
Flipped version of
hctraverse
.
Since: sopcore0.3.2.0
hctraverse :: forall l h c (xs :: l) g proxy f. ( HSequence h, AllN h c xs, Applicative g) => proxy c > ( forall a. c a => f a > g a) > h f xs > g (h I xs) Source #
Special case of
hctraverse'
where
f' =
.
I
Since: sopcore0.3.2.0
hcfoldMap :: forall k l h c (xs :: l) m proxy f. ( HTraverse_ h, AllN h c xs, Monoid m) => proxy c > ( forall (a :: k). c a => f a > m) > h f xs > m Source #
Special case of
hctraverse_
.
Since: sopcore0.3.2.0
hcfor_ :: forall k l h c (xs :: l) g proxy f. ( HTraverse_ h, AllN h c xs, Applicative g) => proxy c > h f xs > ( forall (a :: k). c a => f a > g ()) > g () Source #
Flipped version of
hctraverse_
.
Since: sopcore0.3.2.0
hczipWith3 :: forall k l h c (xs :: l) proxy f f' f'' f'''. ( AllN ( Prod h) c xs, HAp h, HAp ( Prod h)) => proxy c > ( forall (a :: k). c a => f a > f' a > f'' a > f''' a) > Prod h f xs > Prod h f' xs > h f'' xs > h f''' xs Source #
Another name for
hcliftA3
.
Since: sopcore0.2
hczipWith :: forall k l h c (xs :: l) proxy f f' f''. ( AllN ( Prod h) c xs, HAp h, HAp ( Prod h)) => proxy c > ( forall (a :: k). c a => f a > f' a > f'' a) > Prod h f xs > h f' xs > h f'' xs Source #
Another name for
hcliftA2
.
Since: sopcore0.2
hcmap :: forall k l h c (xs :: l) proxy f f'. ( AllN ( Prod h) c xs, HAp h) => proxy c > ( forall (a :: k). c a => f a > f' a) > h f xs > h f' xs Source #
Another name for
hcliftA
.
Since: sopcore0.2
hcliftA3 :: forall k l h c (xs :: l) proxy f f' f'' f'''. ( AllN ( Prod h) c xs, HAp h, HAp ( Prod h)) => proxy c > ( forall (a :: k). c a => f a > f' a > f'' a > f''' a) > Prod h f xs > Prod h f' xs > h f'' xs > h f''' xs Source #
hcliftA2 :: forall k l h c (xs :: l) proxy f f' f''. ( AllN ( Prod h) c xs, HAp h, HAp ( Prod h)) => proxy c > ( forall (a :: k). c a => f a > f' a > f'' a) > Prod h f xs > h f' xs > h f'' xs Source #
hcliftA :: forall k l h c (xs :: l) proxy f f'. ( AllN ( Prod h) c xs, HAp h) => proxy c > ( forall (a :: k). c a => f a > f' a) > h f xs > h f' xs Source #
hzipWith3 :: forall k l h (xs :: l) f f' f'' f'''. ( SListIN ( Prod h) xs, HAp h, HAp ( Prod h)) => ( forall (a :: k). f a > f' a > f'' a > f''' a) > Prod h f xs > Prod h f' xs > h f'' xs > h f''' xs Source #
Another name for
hliftA3
.
Since: sopcore0.2
hzipWith :: forall k l h (xs :: l) f f' f''. ( SListIN ( Prod h) xs, HAp h, HAp ( Prod h)) => ( forall (a :: k). f a > f' a > f'' a) > Prod h f xs > h f' xs > h f'' xs Source #
Another name for
hliftA2
.
Since: sopcore0.2
hmap :: forall k l h (xs :: l) f f'. ( SListIN ( Prod h) xs, HAp h) => ( forall (a :: k). f a > f' a) > h f xs > h f' xs Source #
Another name for
hliftA
.
Since: sopcore0.2
hliftA3 :: forall k l h (xs :: l) f f' f'' f'''. ( SListIN ( Prod h) xs, HAp h, HAp ( Prod h)) => ( forall (a :: k). f a > f' a > f'' a > f''' a) > Prod h f xs > Prod h f' xs > h f'' xs > h f''' xs Source #
A generalized form of
liftA3
,
which in turn is a generalized
zipWith3
.
Takes a lifted ternary function and uses it to combine three structures of equal shape into a single structure.
It either takes three product structures to a product structure, or two product structures and one sum structure to a sum structure.
Specification:
hliftA3
f xs ys zs =hpure
(fn_3
f) `hap
` xs `hap
` ys `hap
` zs
Instances:
hliftA3
,liftA3_NP
::SListI
xs => (forall a. f a > f' a > f'' a > f''' a) >NP
f xs >NP
f' xs >NP
f'' xs >NP
f''' xshliftA3
,liftA3_NS
::SListI
xs => (forall a. f a > f' a > f'' a > f''' a) >NP
f xs >NP
f' xs >NS
f'' xs >NS
f''' xshliftA3
,liftA3_POP
::SListI2
xss => (forall a. f a > f' a > f'' a > f''' a) >POP
f xss >POP
f' xss >POP
f'' xss >POP
f''' xshliftA3
,liftA3_SOP
::SListI2
xss => (forall a. f a > f' a > f'' a > f''' a) >POP
f xss >POP
f' xss >SOP
f'' xss >SOP
f''' xs
hliftA2 :: forall k l h (xs :: l) f f' f''. ( SListIN ( Prod h) xs, HAp h, HAp ( Prod h)) => ( forall (a :: k). f a > f' a > f'' a) > Prod h f xs > h f' xs > h f'' xs Source #
A generalized form of
liftA2
,
which in turn is a generalized
zipWith
.
Takes a lifted binary function and uses it to combine two structures of equal shape into a single structure.
It either takes two product structures to a product structure, or one product and one sum structure to a sum structure.
Specification:
hliftA2
f xs ys =hpure
(fn_2
f) `hap
` xs `hap
` ys
Instances:
hliftA2
,liftA2_NP
::SListI
xs => (forall a. f a > f' a > f'' a) >NP
f xs >NP
f' xs >NP
f'' xshliftA2
,liftA2_NS
::SListI
xs => (forall a. f a > f' a > f'' a) >NP
f xs >NS
f' xs >NS
f'' xshliftA2
,liftA2_POP
::SListI2
xss => (forall a. f a > f' a > f'' a) >POP
f xss >POP
f' xss >POP
f'' xsshliftA2
,liftA2_SOP
::SListI2
xss => (forall a. f a > f' a > f'' a) >POP
f xss >SOP
f' xss >SOP
f'' xss
hliftA :: forall k l h (xs :: l) f f'. ( SListIN ( Prod h) xs, HAp h) => ( forall (a :: k). f a > f' a) > h f xs > h f' xs Source #
A generalized form of
liftA
,
which in turn is a generalized
map
.
Takes a lifted function and applies it to every element of a structure while preserving its shape.
Specification:
hliftA
f xs =hpure
(fn
f) `hap
` xs
Instances:
hliftA
,liftA_NP
::SListI
xs => (forall a. f a > f' a) >NP
f xs >NP
f' xshliftA
,liftA_NS
::SListI
xs => (forall a. f a > f' a) >NS
f xs >NS
f' xshliftA
,liftA_POP
::SListI2
xss => (forall a. f a > f' a) >POP
f xss >POP
f' xsshliftA
,liftA_SOP
::SListI2
xss => (forall a. f a > f' a) >SOP
f xss >SOP
f' xss
fn_4 :: forall k f (a :: k) f' f'' f''' f''''. (f a > f' a > f'' a > f''' a > f'''' a) > (f .> (f' .> (f'' .> (f''' .> f'''')))) a Source #
Construct a quarternary lifted function.
fn_3 :: forall k f (a :: k) f' f'' f'''. (f a > f' a > f'' a > f''' a) > (f .> (f' .> (f'' .> f'''))) a Source #
Construct a ternary lifted function.
fn_2 :: forall k f (a :: k) f' f''. (f a > f' a > f'' a) > (f .> (f' .> f'')) a Source #
Construct a binary lifted function.
fn :: forall k f (a :: k) f'. (f a > f' a) > (f .> f') a Source #
Construct a lifted function.
Same as
Fn
. Only available for uniformity with the
higherarity versions.
class HPure (h :: (k > Type ) > l > Type ) where Source #
hpure :: forall (xs :: l) f. SListIN h xs => ( forall (a :: k). f a) > h f xs Source #
Corresponds to
pure
directly.
Instances:
hpure
,pure_NP
::SListI
xs => (forall a. f a) >NP
f xshpure
,pure_POP
::SListI2
xss => (forall a. f a) >POP
f xss
hcpure :: forall c (xs :: l) proxy f. AllN h c xs => proxy c > ( forall (a :: k). c a => f a) > h f xs Source #
A variant of
hpure
that allows passing in a constrained
argument.
Calling
where
hcpure
f s
s :: h f xs
causes
f
to be
applied at all the types that are contained in
xs
. Therefore,
the constraint
c
has to be satisfied for all elements of
xs
,
which is what
states.
AllN
h c xs
Instances:
hcpure
,cpure_NP
:: (All
c xs ) => proxy c > (forall a. c a => f a) >NP
f xshcpure
,cpure_POP
:: (All2
c xss) => proxy c > (forall a. c a => f a) >POP
f xss
type family Prod (h :: (k > Type ) > l > Type ) :: (k > Type ) > l > Type Source #
Maps a structure containing sums to the corresponding product structure.
Instances
type Prod ( NP :: (k > Type ) > [k] > Type ) Source #  
type Prod ( NS :: (k > Type ) > [k] > Type ) Source #  
type Prod ( NS :: (k > Type ) > [k] > Type )  
type Prod ( SOP :: (k > Type ) > [[k]] > Type )  
type Prod ( NP :: (k > Type ) > [k] > Type )  
type Prod ( POP :: (k > Type ) > [[k]] > Type )  
type Prod ( SimpleTelescope :: (k > Type ) > [k] > Type ) Source #  
type Prod ( OptNP empty :: (k > Type ) > [k] > Type ) Source #  
type Prod ( Telescope g :: (k > Type ) > [k] > Type ) Source #  
type Prod ( Mismatch f :: (k > Type ) > [k] > Type ) Source #  
type Prod HardForkState Source #  
class ( Prod ( Prod h) ~ Prod h, HPure ( Prod h)) => HAp (h :: (k > Type ) > l > Type ) where Source #
A generalization of
<*>
.
hap :: forall (f :: k > Type ) (g :: k > Type ) (xs :: l). Prod h (f .> g) xs > h f xs > h g xs Source #
Corresponds to
<*>
.
For products (
NP
) as well as products of products
(
POP
), the correspondence is rather direct. We combine
a structure containing (lifted) functions and a compatible structure
containing corresponding arguments into a compatible structure
containing results.
The same combinator can also be used to combine a product structure of functions with a sum structure of arguments, which then results in another sum structure of results. The sum structure determines which part of the product structure will be used.
Instances:
hap
,ap_NP
::NP
(f .> g) xs >NP
f xs >NP
g xshap
,ap_NS
::NP
(f .> g) xs >NS
f xs >NS
g xshap
,ap_POP
::POP
(f .> g) xss >POP
f xss >POP
g xsshap
,ap_SOP
::POP
(f .> g) xss >SOP
f xss >SOP
g xss
Instances
HAp ( NP :: (k > Type ) > [k] > Type ) Source #  
HAp ( NS :: (k > Type ) > [k] > Type ) Source #  
HAp ( SimpleTelescope :: (k > Type ) > [k] > Type ) Source #  
Defined in Ouroboros.Consensus.HardFork.Combinator.Util.Telescope hap :: forall (f :: k0 > Type ) (g :: k0 > Type ) (xs :: l). Prod SimpleTelescope (f .> g) xs > SimpleTelescope f xs > SimpleTelescope g xs Source # 

HAp ( NP :: (k > Type ) > [k] > Type )  
HAp ( SOP :: (k > Type ) > [[k]] > Type )  
HAp ( NS :: (k > Type ) > [k] > Type )  
HAp ( POP :: (k > Type ) > [[k]] > Type )  
HAp ( OptNP empty :: (k > Type ) > [k] > Type ) Source #  
HAp ( Telescope g :: (k > Type ) > [k] > Type ) Source #  
HAp ( Mismatch f :: (k > Type ) > [k] > Type ) Source #  
HAp HardForkState Source #  
Defined in Ouroboros.Consensus.HardFork.Combinator.State.Instances hap :: forall (f :: k > Type ) (g :: k > Type ) (xs :: l). Prod HardForkState (f .> g) xs > HardForkState f xs > HardForkState g xs Source # 
type family CollapseTo (h :: (k > Type ) > l > Type ) x Source #
Maps products to lists, and sums to identities.
Instances
type CollapseTo ( NP :: (k > Type ) > [k] > Type ) a Source #  
Defined in Data.SOP.Strict 

type CollapseTo ( NS :: (k > Type ) > [k] > Type ) a Source #  
Defined in Data.SOP.Strict 

type CollapseTo ( NS :: (k > Type ) > [k] > Type ) a  
Defined in Data.SOP.NS 

type CollapseTo ( SOP :: (k > Type ) > [[k]] > Type ) a  
Defined in Data.SOP.NS 

type CollapseTo ( NP :: (k > Type ) > [k] > Type ) a  
Defined in Data.SOP.NP 

type CollapseTo ( POP :: (k > Type ) > [[k]] > Type ) a  
Defined in Data.SOP.NP 

type CollapseTo ( SimpleTelescope :: (k > Type ) > [k] > Type ) a Source #  
type CollapseTo HardForkState a Source #  
class HCollapse (h :: (k > Type ) > l > Type ) where Source #
A class for collapsing a heterogeneous structure into a homogeneous one.
hcollapse :: forall (xs :: l) a. SListIN h xs => h ( K a :: k > Type ) xs > CollapseTo h a Source #
Collapse a heterogeneous structure with homogeneous elements into a homogeneous structure.
If a heterogeneous structure is instantiated to the constant
functor
K
, then it is in fact homogeneous. This function
maps such a value to a simpler Haskell datatype reflecting that.
An
contains a single
NS
(
K
a)
a
, and an
contains
a list of
NP
(
K
a)
a
s.
Instances:
hcollapse
,collapse_NP
::NP
(K
a) xs > [a]hcollapse
,collapse_NS
::NS
(K
a) xs > ahcollapse
,collapse_POP
::POP
(K
a) xss > [[a]]hcollapse
,collapse_SOP
::SOP
(K
a) xss > [a]
Instances
HCollapse ( NP :: (k > Type ) > [k] > Type ) Source #  
Defined in Data.SOP.Strict 

HCollapse ( NS :: (k > Type ) > [k] > Type ) Source #  
Defined in Data.SOP.Strict 

HCollapse ( SimpleTelescope :: (k > Type ) > [k] > Type ) Source #  
Defined in Ouroboros.Consensus.HardFork.Combinator.Util.Telescope hcollapse :: forall (xs :: l) a. SListIN SimpleTelescope xs => SimpleTelescope ( K a) xs > CollapseTo SimpleTelescope a Source # 

HCollapse ( SOP :: (k > Type ) > [[k]] > Type )  
Defined in Data.SOP.NS 

HCollapse ( NS :: (k > Type ) > [k] > Type )  
Defined in Data.SOP.NS 

HCollapse ( POP :: (k > Type ) > [[k]] > Type )  
Defined in Data.SOP.NP 

HCollapse ( NP :: (k > Type ) > [k] > Type )  
Defined in Data.SOP.NP 

HCollapse HardForkState Source #  
Defined in Ouroboros.Consensus.HardFork.Combinator.State.Instances hcollapse :: forall (xs :: l) a. SListIN HardForkState xs => HardForkState ( K a) xs > CollapseTo HardForkState a Source # 
class HTraverse_ (h :: (k > Type ) > l > Type ) where Source #
hctraverse_ :: forall c (xs :: l) g proxy f. ( AllN h c xs, Applicative g) => proxy c > ( forall (a :: k). c a => f a > g ()) > h f xs > g () Source #
Corresponds to
traverse_
.
Instances:
hctraverse_
,ctraverse__NP
:: (All
c xs ,Applicative
g) => proxy c > (forall a. c a => f a > g ()) >NP
f xs > g ()hctraverse_
,ctraverse__NS
:: (All2
c xs ,Applicative
g) => proxy c > (forall a. c a => f a > g ()) >NS
f xs > g ()hctraverse_
,ctraverse__POP
:: (All
c xss,Applicative
g) => proxy c > (forall a. c a => f a > g ()) >POP
f xss > g ()hctraverse_
,ctraverse__SOP
:: (All2
c xss,Applicative
g) => proxy c > (forall a. c a => f a > g ()) >SOP
f xss > g ()
Since: sopcore0.3.2.0
htraverse_ :: forall (xs :: l) g f. ( SListIN h xs, Applicative g) => ( forall (a :: k). f a > g ()) > h f xs > g () Source #
Unconstrained version of
hctraverse_
.
Instances:
traverse_
,traverse__NP
:: (SListI
xs ,Applicative
g) => (forall a. f a > g ()) >NP
f xs > g ()traverse_
,traverse__NS
:: (SListI
xs ,Applicative
g) => (forall a. f a > g ()) >NS
f xs > g ()traverse_
,traverse__POP
:: (SListI2
xss,Applicative
g) => (forall a. f a > g ()) >POP
f xss > g ()traverse_
,traverse__SOP
:: (SListI2
xss,Applicative
g) => (forall a. f a > g ()) >SOP
f xss > g ()
Since: sopcore0.3.2.0
Instances
HTraverse_ ( NP :: (k > Type ) > [k] > Type ) Source #  
Defined in Data.SOP.Strict hctraverse_ :: forall c (xs :: l) g proxy f. ( AllN NP c xs, Applicative g) => proxy c > ( forall (a :: k0). c a => f a > g ()) > NP f xs > g () Source # htraverse_ :: forall (xs :: l) g f. ( SListIN NP xs, Applicative g) => ( forall (a :: k0). f a > g ()) > NP f xs > g () Source # 

HTraverse_ ( SimpleTelescope :: (k > Type ) > [k] > Type ) Source #  
Defined in Ouroboros.Consensus.HardFork.Combinator.Util.Telescope hctraverse_ :: forall c (xs :: l) g proxy f. ( AllN SimpleTelescope c xs, Applicative g) => proxy c > ( forall (a :: k0). c a => f a > g ()) > SimpleTelescope f xs > g () Source # htraverse_ :: forall (xs :: l) g f. ( SListIN SimpleTelescope xs, Applicative g) => ( forall (a :: k0). f a > g ()) > SimpleTelescope f xs > g () Source # 

HTraverse_ ( SOP :: (k > Type ) > [[k]] > Type )  
Defined in Data.SOP.NS hctraverse_ :: forall c (xs :: l) g proxy f. ( AllN SOP c xs, Applicative g) => proxy c > ( forall (a :: k0). c a => f a > g ()) > SOP f xs > g () Source # htraverse_ :: forall (xs :: l) g f. ( SListIN SOP xs, Applicative g) => ( forall (a :: k0). f a > g ()) > SOP f xs > g () Source # 

HTraverse_ ( NS :: (k > Type ) > [k] > Type )  
Defined in Data.SOP.NS hctraverse_ :: forall c (xs :: l) g proxy f. ( AllN NS c xs, Applicative g) => proxy c > ( forall (a :: k0). c a => f a > g ()) > NS f xs > g () Source # htraverse_ :: forall (xs :: l) g f. ( SListIN NS xs, Applicative g) => ( forall (a :: k0). f a > g ()) > NS f xs > g () Source # 

HTraverse_ ( POP :: (k > Type ) > [[k]] > Type )  
Defined in Data.SOP.NP hctraverse_ :: forall c (xs :: l) g proxy f. ( AllN POP c xs, Applicative g) => proxy c > ( forall (a :: k0). c a => f a > g ()) > POP f xs > g () Source # htraverse_ :: forall (xs :: l) g f. ( SListIN POP xs, Applicative g) => ( forall (a :: k0). f a > g ()) > POP f xs > g () Source # 

HTraverse_ ( NP :: (k > Type ) > [k] > Type )  
Defined in Data.SOP.NP hctraverse_ :: forall c (xs :: l) g proxy f. ( AllN NP c xs, Applicative g) => proxy c > ( forall (a :: k0). c a => f a > g ()) > NP f xs > g () Source # htraverse_ :: forall (xs :: l) g f. ( SListIN NP xs, Applicative g) => ( forall (a :: k0). f a > g ()) > NP f xs > g () Source # 

HTraverse_ ( Telescope g :: (k > Type ) > [k] > Type ) Source #  
Defined in Ouroboros.Consensus.HardFork.Combinator.Util.Telescope hctraverse_ :: forall c (xs :: l) g0 proxy f. ( AllN ( Telescope g) c xs, Applicative g0) => proxy c > ( forall (a :: k0). c a => f a > g0 ()) > Telescope g f xs > g0 () Source # htraverse_ :: forall (xs :: l) g0 f. ( SListIN ( Telescope g) xs, Applicative g0) => ( forall (a :: k0). f a > g0 ()) > Telescope g f xs > g0 () Source # 
class HAp h => HSequence (h :: (k > Type ) > l > Type ) where Source #
A generalization of
sequenceA
.
hsequence' :: forall (xs :: l) f (g :: k > Type ). ( SListIN h xs, Applicative f) => h (f :.: g) xs > f (h g xs) Source #
Corresponds to
sequenceA
.
Lifts an applicative functor out of a structure.
Instances:
hsequence'
,sequence'_NP
:: (SListI
xs ,Applicative
f) =>NP
(f:.:
g) xs > f (NP
g xs )hsequence'
,sequence'_NS
:: (SListI
xs ,Applicative
f) =>NS
(f:.:
g) xs > f (NS
g xs )hsequence'
,sequence'_POP
:: (SListI2
xss,Applicative
f) =>POP
(f:.:
g) xss > f (POP
g xss)hsequence'
,sequence'_SOP
:: (SListI2
xss,Applicative
f) =>SOP
(f:.:
g) xss > f (SOP
g xss)
hctraverse' :: forall c (xs :: l) g proxy f f'. ( AllN h c xs, Applicative g) => proxy c > ( forall (a :: k). c a => f a > g (f' a)) > h f xs > g (h f' xs) Source #
Corresponds to
traverse
.
Instances:
hctraverse'
,ctraverse'_NP
:: (All
c xs ,Applicative
g) => proxy c > (forall a. c a => f a > g (f' a)) >NP
f xs > g (NP
f' xs )hctraverse'
,ctraverse'_NS
:: (All2
c xs ,Applicative
g) => proxy c > (forall a. c a => f a > g (f' a)) >NS
f xs > g (NS
f' xs )hctraverse'
,ctraverse'_POP
:: (All
c xss,Applicative
g) => proxy c > (forall a. c a => f a > g (f' a)) >POP
f xss > g (POP
f' xss)hctraverse'
,ctraverse'_SOP
:: (All2
c xss,Applicative
g) => proxy c > (forall a. c a => f a > g (f' a)) >SOP
f xss > g (SOP
f' xss)
Since: sopcore0.3.2.0
htraverse' :: forall (xs :: l) g f f'. ( SListIN h xs, Applicative g) => ( forall (a :: k). f a > g (f' a)) > h f xs > g (h f' xs) Source #
Unconstrained variant of
hctraverse
`.
Instances:
htraverse'
,traverse'_NP
:: (SListI
xs ,Applicative
g) => (forall a. c a => f a > g (f' a)) >NP
f xs > g (NP
f' xs )htraverse'
,traverse'_NS
:: (SListI2
xs ,Applicative
g) => (forall a. c a => f a > g (f' a)) >NS
f xs > g (NS
f' xs )htraverse'
,traverse'_POP
:: (SListI
xss,Applicative
g) => (forall a. c a => f a > g (f' a)) >POP
f xss > g (POP
f' xss)htraverse'
,traverse'_SOP
:: (SListI2
xss,Applicative
g) => (forall a. c a => f a > g (f' a)) >SOP
f xss > g (SOP
f' xss)
Since: sopcore0.3.2.0
Instances
HSequence ( NP :: (k > Type ) > [k] > Type ) Source #  
Defined in Data.SOP.Strict hsequence' :: forall (xs :: l) f (g :: k0 > Type ). ( SListIN NP xs, Applicative f) => NP (f :.: g) xs > f ( NP g xs) Source # hctraverse' :: forall c (xs :: l) g proxy f f'. ( AllN NP c xs, Applicative g) => proxy c > ( forall (a :: k0). c a => f a > g (f' a)) > NP f xs > g ( NP f' xs) Source # htraverse' :: forall (xs :: l) g f f'. ( SListIN NP xs, Applicative g) => ( forall (a :: k0). f a > g (f' a)) > NP f xs > g ( NP f' xs) Source # 

HSequence ( NS :: (k > Type ) > [k] > Type ) Source #  
Defined in Data.SOP.Strict hsequence' :: forall (xs :: l) f (g :: k0 > Type ). ( SListIN NS xs, Applicative f) => NS (f :.: g) xs > f ( NS g xs) Source # hctraverse' :: forall c (xs :: l) g proxy f f'. ( AllN NS c xs, Applicative g) => proxy c > ( forall (a :: k0). c a => f a > g (f' a)) > NS f xs > g ( NS f' xs) Source # htraverse' :: forall (xs :: l) g f f'. ( SListIN NS xs, Applicative g) => ( forall (a :: k0). f a > g (f' a)) > NS f xs > g ( NS f' xs) Source # 

HSequence ( SimpleTelescope :: (k > Type ) > [k] > Type ) Source #  
Defined in Ouroboros.Consensus.HardFork.Combinator.Util.Telescope hsequence' :: forall (xs :: l) f (g :: k0 > Type ). ( SListIN SimpleTelescope xs, Applicative f) => SimpleTelescope (f :.: g) xs > f ( SimpleTelescope g xs) Source # hctraverse' :: forall c (xs :: l) g proxy f f'. ( AllN SimpleTelescope c xs, Applicative g) => proxy c > ( forall (a :: k0). c a => f a > g (f' a)) > SimpleTelescope f xs > g ( SimpleTelescope f' xs) Source # htraverse' :: forall (xs :: l) g f f'. ( SListIN SimpleTelescope xs, Applicative g) => ( forall (a :: k0). f a > g (f' a)) > SimpleTelescope f xs > g ( SimpleTelescope f' xs) Source # 

HSequence ( SOP :: (k > Type ) > [[k]] > Type )  
Defined in Data.SOP.NS hsequence' :: forall (xs :: l) f (g :: k0 > Type ). ( SListIN SOP xs, Applicative f) => SOP (f :.: g) xs > f ( SOP g xs) Source # hctraverse' :: forall c (xs :: l) g proxy f f'. ( AllN SOP c xs, Applicative g) => proxy c > ( forall (a :: k0). c a => f a > g (f' a)) > SOP f xs > g ( SOP f' xs) Source # htraverse' :: forall (xs :: l) g f f'. ( SListIN SOP xs, Applicative g) => ( forall (a :: k0). f a > g (f' a)) > SOP f xs > g ( SOP f' xs) Source # 

HSequence ( NS :: (k > Type ) > [k] > Type )  
Defined in Data.SOP.NS hsequence' :: forall (xs :: l) f (g :: k0 > Type ). ( SListIN NS xs, Applicative f) => NS (f :.: g) xs > f ( NS g xs) Source # hctraverse' :: forall c (xs :: l) g proxy f f'. ( AllN NS c xs, Applicative g) => proxy c > ( forall (a :: k0). c a => f a > g (f' a)) > NS f xs > g ( NS f' xs) Source # htraverse' :: forall (xs :: l) g f f'. ( SListIN NS xs, Applicative g) => ( forall (a :: k0). f a > g (f' a)) > NS f xs > g ( NS f' xs) Source # 

HSequence ( POP :: (k > Type ) > [[k]] > Type )  
Defined in Data.SOP.NP hsequence' :: forall (xs :: l) f (g :: k0 > Type ). ( SListIN POP xs, Applicative f) => POP (f :.: g) xs > f ( POP g xs) Source # hctraverse' :: forall c (xs :: l) g proxy f f'. ( AllN POP c xs, Applicative g) => proxy c > ( forall (a :: k0). c a => f a > g (f' a)) > POP f xs > g ( POP f' xs) Source # htraverse' :: forall (xs :: l) g f f'. ( SListIN POP xs, Applicative g) => ( forall (a :: k0). f a > g (f' a)) > POP f xs > g ( POP f' xs) Source # 

HSequence ( NP :: (k > Type ) > [k] > Type )  
Defined in Data.SOP.NP hsequence' :: forall (xs :: l) f (g :: k0 > Type ). ( SListIN NP xs, Applicative f) => NP (f :.: g) xs > f ( NP g xs) Source # hctraverse' :: forall c (xs :: l) g proxy f f'. ( AllN NP c xs, Applicative g) => proxy c > ( forall (a :: k0). c a => f a > g (f' a)) > NP f xs > g ( NP f' xs) Source # htraverse' :: forall (xs :: l) g f f'. ( SListIN NP xs, Applicative g) => ( forall (a :: k0). f a > g (f' a)) > NP f xs > g ( NP f' xs) Source # 

HSequence ( OptNP empty :: (k > Type ) > [k] > Type ) Source #  
Defined in Ouroboros.Consensus.Util.OptNP hsequence' :: forall (xs :: l) f (g :: k0 > Type ). ( SListIN ( OptNP empty) xs, Applicative f) => OptNP empty (f :.: g) xs > f ( OptNP empty g xs) Source # hctraverse' :: forall c (xs :: l) g proxy f f'. ( AllN ( OptNP empty) c xs, Applicative g) => proxy c > ( forall (a :: k0). c a => f a > g (f' a)) > OptNP empty f xs > g ( OptNP empty f' xs) Source # htraverse' :: forall (xs :: l) g f f'. ( SListIN ( OptNP empty) xs, Applicative g) => ( forall (a :: k0). f a > g (f' a)) > OptNP empty f xs > g ( OptNP empty f' xs) Source # 

HSequence ( Telescope g :: (k > Type ) > [k] > Type ) Source #  
Defined in Ouroboros.Consensus.HardFork.Combinator.Util.Telescope hsequence' :: forall (xs :: l) f (g0 :: k0 > Type ). ( SListIN ( Telescope g) xs, Applicative f) => Telescope g (f :.: g0) xs > f ( Telescope g g0 xs) Source # hctraverse' :: forall c (xs :: l) g0 proxy f f'. ( AllN ( Telescope g) c xs, Applicative g0) => proxy c > ( forall (a :: k0). c a => f a > g0 (f' a)) > Telescope g f xs > g0 ( Telescope g f' xs) Source # htraverse' :: forall (xs :: l) g0 f f'. ( SListIN ( Telescope g) xs, Applicative g0) => ( forall (a :: k0). f a > g0 (f' a)) > Telescope g f xs > g0 ( Telescope g f' xs) Source # 

HSequence HardForkState Source #  
Defined in Ouroboros.Consensus.HardFork.Combinator.State.Instances hsequence' :: forall (xs :: l) f (g :: k > Type ). ( SListIN HardForkState xs, Applicative f) => HardForkState (f :.: g) xs > f ( HardForkState g xs) Source # hctraverse' :: forall c (xs :: l) g proxy f f'. ( AllN HardForkState c xs, Applicative g) => proxy c > ( forall (a :: k). c a => f a > g (f' a)) > HardForkState f xs > g ( HardForkState f' xs) Source # htraverse' :: forall (xs :: l) g f f'. ( SListIN HardForkState xs, Applicative g) => ( forall (a :: k). f a > g (f' a)) > HardForkState f xs > g ( HardForkState f' xs) Source # 
class HIndex (h :: (k > Type ) > l > Type ) where Source #
A class for determining which choice in a sumlike structure a value represents.
hindex :: forall (f :: k > Type ) (xs :: l). h f xs > Int Source #
If
h
is a sumlike structure representing a choice
between
n
different options, and
x
is a value of
type
h f xs
, then
returns a number between
hindex
x
0
and
n  1
representing the index of the choice
made by
x
.
Instances:
hindex
,index_NS
::NS
f xs > Inthindex
,index_SOP
::SOP
f xs > Int
Examples:
>>>
hindex (S (S (Z (I False))))
2>>>
hindex (Z (K ()))
0>>>
hindex (SOP (S (Z (I True :* I 'x' :* Nil))))
1
Since: sopcore0.2.4.0
type family UnProd (h :: (k > Type ) > l > Type ) :: (k > Type ) > l > Type Source #
Maps a structure containing products to the corresponding sum structure.
Since: sopcore0.2.4.0
class UnProd ( Prod h) ~ h => HApInjs (h :: (k > Type ) > l > Type ) where Source #
A class for applying all injections corresponding to a sumlike structure to a table containing suitable arguments.
hapInjs :: forall (xs :: l) (f :: k > Type ). SListIN h xs => Prod h f xs > [h f xs] Source #
For a given table (productlike structure), produce a list where each element corresponds to the application of an injection function into the corresponding sumlike structure.
Instances:
hapInjs
,apInjs_NP
::SListI
xs =>NP
f xs > [NS
f xs ]hapInjs
,apInjs_SOP
::SListI2
xss =>POP
f xs > [SOP
f xss]
Examples:
>>>
hapInjs (I 'x' :* I True :* I 2 :* Nil) :: [NS I '[Char, Bool, Int]]
[Z (I 'x'),S (Z (I True)),S (S (Z (I 2)))]
>>>
hapInjs (POP ((I 'x' :* Nil) :* (I True :* I 2 :* Nil) :* Nil)) :: [SOP I '[ '[Char], '[Bool, Int]]]
[SOP (Z (I 'x' :* Nil)),SOP (S (Z (I True :* I 2 :* Nil)))]
Unfortunately the typesignatures are required in GHC7.10 and older.
Since: sopcore0.2.4.0
class HExpand (h :: (k > Type ) > l > Type ) where Source #
A class for expanding sum structures into corresponding product structures, filling in the slots not targeted by the sum with default values.
Since: sopcore0.2.5.0
hexpand :: forall (xs :: l) f. SListIN ( Prod h) xs => ( forall (x :: k). f x) > h f xs > Prod h f xs Source #
Expand a given sum structure into a corresponding product structure by placing the value contained in the sum into the corresponding position in the product, and using the given default value for all other positions.
Instances:
hexpand
,expand_NS
::SListI
xs => (forall x . f x) >NS
f xs >NP
f xshexpand
,expand_SOP
::SListI2
xss => (forall x . f x) >SOP
f xss >POP
f xss
Examples:
>>>
hexpand Nothing (S (Z (Just 3))) :: NP Maybe '[Char, Int, Bool]
Nothing :* Just 3 :* Nothing :* Nil>>>
hexpand [] (SOP (S (Z ([1,2] :* "xyz" :* Nil)))) :: POP [] '[ '[Bool], '[Int, Char] ]
POP (([] :* Nil) :* ([1,2] :* "xyz" :* Nil) :* Nil)
Since: sopcore0.2.5.0
hcexpand :: forall c (xs :: l) proxy f. AllN ( Prod h) c xs => proxy c > ( forall (x :: k). c x => f x) > h f xs > Prod h f xs Source #
Variant of
hexpand
that allows passing a constrained default.
Instances:
hcexpand
,cexpand_NS
::All
c xs => proxy c > (forall x . c x => f x) >NS
f xs >NP
f xshcexpand
,cexpand_SOP
::All2
c xss => proxy c > (forall x . c x => f x) >SOP
f xss >POP
f xss
Examples:
>>>
hcexpand (Proxy :: Proxy Bounded) (I minBound) (S (Z (I 20))) :: NP I '[Bool, Int, Ordering]
I False :* I 20 :* I LT :* Nil>>>
hcexpand (Proxy :: Proxy Num) (I 0) (SOP (S (Z (I 1 :* I 2 :* Nil)))) :: POP I '[ '[Double], '[Int, Int] ]
POP ((I 0.0 :* Nil) :* (I 1 :* I 2 :* Nil) :* Nil)
Since: sopcore0.2.5.0
class (( Same h1 :: (k2 > Type ) > l2 > Type ) ~ h2, ( Same h2 :: (k1 > Type ) > l1 > Type ) ~ h1) => HTrans (h1 :: (k1 > Type ) > l1 > Type ) (h2 :: (k2 > Type ) > l2 > Type ) where Source #
A class for transforming structures into related structures with a different index list, as long as the index lists have the same shape and the elements and interpretation functions are suitably related.
Since: sopcore0.3.1.0
htrans :: forall c (xs :: l1) (ys :: l2) proxy f g. AllZipN ( Prod h1) c xs ys => proxy c > ( forall (x :: k1) (y :: k2). c x y => f x > g y) > h1 f xs > h2 g ys Source #
Transform a structure into a related structure given a conversion function for the elements.
Since: sopcore0.3.1.0
hcoerce :: forall (f :: k1 > Type ) (g :: k2 > Type ) (xs :: l1) (ys :: l2). AllZipN ( Prod h1) ( LiftedCoercible f g) xs ys => h1 f xs > h2 g ys Source #
Safely coerce a structure into a representationally equal structure.
This is a special case of
htrans
, but can be implemented more efficiently;
for example in terms of
unsafeCoerce
.
Examples:
>>>
hcoerce (I (Just LT) :* I (Just 'x') :* I (Just True) :* Nil) :: NP Maybe '[Ordering, Char, Bool]
Just LT :* Just 'x' :* Just True :* Nil>>>
hcoerce (SOP (Z (K True :* K False :* Nil))) :: SOP I '[ '[Bool, Bool], '[Bool] ]
SOP (Z (I True :* I False :* Nil))
Since: sopcore0.3.1.0
Instances
HTrans ( NP :: (k1 > Type ) > [k1] > Type ) ( NP :: (k2 > Type ) > [k2] > Type ) Source #  
Defined in Data.SOP.Strict htrans :: forall c (xs :: l1) (ys :: l2) proxy f g. AllZipN ( Prod NP ) c xs ys => proxy c > ( forall (x :: k10) (y :: k20). c x y => f x > g y) > NP f xs > NP g ys Source # hcoerce :: forall (f :: k10 > Type ) (g :: k20 > Type ) (xs :: l1) (ys :: l2). AllZipN ( Prod NP ) ( LiftedCoercible f g) xs ys => NP f xs > NP g ys Source # 

HTrans ( NS :: (k1 > Type ) > [k1] > Type ) ( NS :: (k2 > Type ) > [k2] > Type ) Source #  
Defined in Data.SOP.Strict htrans :: forall c (xs :: l1) (ys :: l2) proxy f g. AllZipN ( Prod NS ) c xs ys => proxy c > ( forall (x :: k10) (y :: k20). c x y => f x > g y) > NS f xs > NS g ys Source # hcoerce :: forall (f :: k10 > Type ) (g :: k20 > Type ) (xs :: l1) (ys :: l2). AllZipN ( Prod NS ) ( LiftedCoercible f g) xs ys => NS f xs > NS g ys Source # 

HTrans ( SOP :: (k1 > Type ) > [[k1]] > Type ) ( SOP :: (k2 > Type ) > [[k2]] > Type )  
Defined in Data.SOP.NS htrans :: forall c (xs :: l1) (ys :: l2) proxy f g. AllZipN ( Prod SOP ) c xs ys => proxy c > ( forall (x :: k10) (y :: k20). c x y => f x > g y) > SOP f xs > SOP g ys Source # hcoerce :: forall (f :: k10 > Type ) (g :: k20 > Type ) (xs :: l1) (ys :: l2). AllZipN ( Prod SOP ) ( LiftedCoercible f g) xs ys => SOP f xs > SOP g ys Source # 

HTrans ( NS :: (k1 > Type ) > [k1] > Type ) ( NS :: (k2 > Type ) > [k2] > Type )  
Defined in Data.SOP.NS htrans :: forall c (xs :: l1) (ys :: l2) proxy f g. AllZipN ( Prod NS ) c xs ys => proxy c > ( forall (x :: k10) (y :: k20). c x y => f x > g y) > NS f xs > NS g ys Source # hcoerce :: forall (f :: k10 > Type ) (g :: k20 > Type ) (xs :: l1) (ys :: l2). AllZipN ( Prod NS ) ( LiftedCoercible f g) xs ys => NS f xs > NS g ys Source # 

HTrans ( POP :: (k1 > Type ) > [[k1]] > Type ) ( POP :: (k2 > Type ) > [[k2]] > Type )  
Defined in Data.SOP.NP htrans :: forall c (xs :: l1) (ys :: l2) proxy f g. AllZipN ( Prod POP ) c xs ys => proxy c > ( forall (x :: k10) (y :: k20). c x y => f x > g y) > POP f xs > POP g ys Source # hcoerce :: forall (f :: k10 > Type ) (g :: k20 > Type ) (xs :: l1) (ys :: l2). AllZipN ( Prod POP ) ( LiftedCoercible f g) xs ys => POP f xs > POP g ys Source # 

HTrans ( NP :: (k1 > Type ) > [k1] > Type ) ( NP :: (k2 > Type ) > [k2] > Type )  
Defined in Data.SOP.NP htrans :: forall c (xs :: l1) (ys :: l2) proxy f g. AllZipN ( Prod NP ) c xs ys => proxy c > ( forall (x :: k10) (y :: k20). c x y => f x > g y) > NP f xs > NP g ys Source # hcoerce :: forall (f :: k10 > Type ) (g :: k20 > Type ) (xs :: l1) (ys :: l2). AllZipN ( Prod NP ) ( LiftedCoercible f g) xs ys => NP f xs > NP g ys Source # 
ccase_SList :: forall k c (xs :: [k]) proxy r. All c xs => proxy c > r ('[] :: [k]) > ( forall (y :: k) (ys :: [k]). (c y, All c ys) => r (y ': ys)) > r xs Source #
Constrained case distinction on a typelevel list.
Since: sopcore0.4.0.0
class ( AllF c xs, SListI xs) => All (c :: k > Constraint ) (xs :: [k]) where Source #
Require a constraint for every element of a list.
If you have a datatype that is indexed over a typelevel
list, then you can use
All
to indicate that all elements
of that typelevel list must satisfy a given constraint.
Example: The constraint
All Eq '[ Int, Bool, Char ]
is equivalent to the constraint
(Eq Int, Eq Bool, Eq Char)
Example: A type signature such as
f :: All Eq xs => NP I xs > ...
means that
f
can assume that all elements of the nary
product satisfy
Eq
.
Note on superclasses: ghc cannot deduce superclasses from
All
constraints.
You might expect the following to compile
class (Eq a) => MyClass a foo :: (All Eq xs) => NP f xs > z foo = [..] bar :: (All MyClass xs) => NP f xs > x bar = foo
but it will fail with an error saying that it was unable to
deduce the class constraint
(or similar) in the
definition of
AllF
Eq
xs
bar
.
In cases like this you can use
Dict
from
Data.SOP.Dict
to prove conversions between constraints.
See
this answer on SO for more details
.
cpara_SList :: proxy c > r ('[] :: [k]) > ( forall (y :: k) (ys :: [k]). (c y, All c ys) => r ys > r (y ': ys)) > r xs Source #
Constrained paramorphism for a typelevel list.
The advantage of writing functions in terms of
cpara_SList
is that
they are then typically not recursive, and can be unfolded statically if
the typelevel list is statically known.
Since: sopcore0.4.0.0
Instances
All (c :: k > Constraint ) ('[] :: [k])  
Defined in Data.SOP.Constraint cpara_SList :: proxy c > r '[] > ( forall (y :: k0) (ys :: [k0]). (c y, All c ys) => r ys > r (y ': ys)) > r '[] Source # 

(c x, All c xs) => All (c :: a > Constraint ) (x ': xs :: [a])  
Defined in Data.SOP.Constraint cpara_SList :: proxy c > r '[] > ( forall (y :: k) (ys :: [k]). (c y, All c ys) => r ys > r (y ': ys)) > r (x ': xs) Source # 
type SListI2 = All ( SListI :: [k] > Constraint ) Source #
Require a singleton for every inner list in a list of lists.
type SListI = All ( Top :: k > Constraint ) Source #
Implicit singleton list.
A singleton list can be used to reveal the structure of a typelevel list argument that the function is quantified over.
Since 0.4.0.0, this is now defined in terms of
All
.
A singleton list provides a witness for a typelevel list
where the elements need not satisfy any additional
constraints.
Since: sopcore0.4.0.0
type All2 (c :: k > Constraint ) = All ( All c) Source #
Require a constraint for every element of a list of lists.
If you have a datatype that is indexed over a typelevel
list of lists, then you can use
All2
to indicate that all
elements of the inner lists must satisfy a given constraint.
Example: The constraint
All2 Eq '[ '[ Int ], '[ Bool, Char ] ]
is equivalent to the constraint
(Eq Int, Eq Bool, Eq Char)
Example: A type signature such as
f :: All2 Eq xss => SOP I xs > ...
means that
f
can assume that all elements of the sum
of product satisfy
Eq
.
Since 0.4.0.0, this is merely a synonym for 'All (All c)'.
Since: sopcore0.4.0.0
class ( SListI xs, SListI ys, SameShapeAs xs ys, SameShapeAs ys xs, AllZipF c xs ys) => AllZip (c :: a > b > Constraint ) (xs :: [a]) (ys :: [b]) Source #
Require a constraint pointwise for every pair of elements from two lists.
Example: The constraint
AllZip (~) '[ Int, Bool, Char ] '[ a, b, c ]
is equivalent to the constraint
(Int ~ a, Bool ~ b, Char ~ c)
Since: sopcore0.3.1.0
Instances
( SListI xs, SListI ys, SameShapeAs xs ys, SameShapeAs ys xs, AllZipF c xs ys) => AllZip (c :: a > b > Constraint ) (xs :: [a]) (ys :: [b])  
Defined in Data.SOP.Constraint 
type family SameShapeAs (xs :: [a]) (ys :: [b]) where ... Source #
Type family that forces a typelevel list to be of the same shape as the given typelevel list.
Since 0.5.0.0, this only tests the toplevel structure of
the list, and is intended to be used in conjunction with
a separate construct (such as the
AllZip
,
AllZipF
combination to tie the recursive knot). The reason is that
making
SameShapeAs
directly recursive leads to quadratic
compile times.
The main use of this constraint is to help type inference to learn something about otherwise unknown typelevel lists.
Since: sopcore0.5.0.0
SameShapeAs ('[] :: [a]) (ys :: [b]) = ys ~ ('[] :: [b])  
SameShapeAs (x ': xs :: [a1]) (ys :: [a2]) = ys ~ ( Head ys ': Tail ys) 
class Coercible (f x) (g y) => LiftedCoercible (f :: k > k1) (g :: k2 > k1) (x :: k) (y :: k2) Source #
The constraint
is equivalent
to
LiftedCoercible
f g x y
.
Coercible
(f x) (g y)
Since: sopcore0.3.1.0
Instances
Coercible (f x) (g y) => LiftedCoercible (f :: k1 > k2) (g :: k3 > k2) (x :: k1) (y :: k3)  
Defined in Data.SOP.Constraint 
class ( AllZipF ( AllZip f) xss yss, SListI xss, SListI yss, SameShapeAs xss yss, SameShapeAs yss xss) => AllZip2 (f :: a > b > Constraint ) (xss :: [[a]]) (yss :: [[b]]) Source #
Require a constraint pointwise for every pair of elements from two lists of lists.
Instances
( AllZipF ( AllZip f) xss yss, SListI xss, SListI yss, SameShapeAs xss yss, SameShapeAs yss xss) => AllZip2 (f :: a > b > Constraint ) (xss :: [[a]]) (yss :: [[b]])  
Defined in Data.SOP.Constraint 
class f (g x) => Compose (f :: k > Constraint ) (g :: k1 > k) (x :: k1) infixr 9 Source #
Composition of constraints.
Note that the result of the composition must be a constraint,
and therefore, in
, the kind of
Compose
f g
f
is
k >
.
The kind of
Constraint
g
, however, is
l > k
and can thus be a normal
type constructor.
A typical use case is in connection with
All
on an
NP
or an
NS
. For example, in order to denote that all elements on an
satisfy
NP
f xs
Show
, we can say
.
All
(
Compose
Show
f) xs
Since: sopcore0.2
Instances
f (g x) => Compose (f :: k1 > Constraint ) (g :: k2 > k1) (x :: k2)  
Defined in Data.SOP.Constraint 
class (f x, g x) => And (f :: k > Constraint ) (g :: k > Constraint ) (x :: k) infixl 7 Source #
Pairing of constraints.
Since: sopcore0.2
Instances
(f x, g x) => And (f :: k > Constraint ) (g :: k > Constraint ) (x :: k)  
Defined in Data.SOP.Constraint 
A constraint that can always be satisfied.
Since: sopcore0.2
Instances
Top (x :: k)  
Defined in Data.SOP.Constraint 
type family AllN (h :: (k > Type ) > l > Type ) (c :: k > Constraint ) :: l > Constraint Source #
A generalization of
All
and
All2
.
The family
AllN
expands to
All
or
All2
depending on whether
the argument is indexed by a list or a list of lists.
Instances
type AllN ( NP :: (k > Type ) > [k] > Type ) (c :: k > Constraint ) Source #  
Defined in Data.SOP.Strict 

type AllN ( NS :: (k > Type ) > [k] > Type ) (c :: k > Constraint ) Source #  
Defined in Data.SOP.Strict 

type AllN ( NS :: (k > Type ) > [k] > Type ) (c :: k > Constraint )  
Defined in Data.SOP.NS 

type AllN ( SOP :: (k > Type ) > [[k]] > Type ) (c :: k > Constraint )  
Defined in Data.SOP.NS 

type AllN ( NP :: (k > Type ) > [k] > Type ) (c :: k > Constraint )  
Defined in Data.SOP.NP 

type AllN ( POP :: (k > Type ) > [[k]] > Type ) (c :: k > Constraint )  
Defined in Data.SOP.NP 

type AllN ( SimpleTelescope :: (k > Type ) > [k] > Type ) (c :: k > Constraint ) Source #  
type AllN ( OptNP empty :: (k > Type ) > [k] > Type ) (c :: k > Constraint ) Source #  
Defined in Ouroboros.Consensus.Util.OptNP 

type AllN ( Telescope g :: (k > Type ) > [k] > Type ) (c :: k > Constraint ) Source #  
type AllN ( Mismatch f :: (k > Type ) > [k] > Type ) (c :: k > Constraint ) Source #  
type AllN HardForkState (c :: Type > Constraint ) Source #  
type family AllZipN (h :: (k > Type ) > l > Type ) (c :: k1 > k2 > Constraint ) :: l1 > l2 > Constraint Source #
A generalization of
AllZip
and
AllZip2
.
The family
AllZipN
expands to
AllZip
or
AllZip2
depending on
whther the argument is indexed by a list or a list of lists.
Instances
type AllZipN ( NP :: (k > Type ) > [k] > Type ) (c :: a > b > Constraint ) Source #  
Defined in Data.SOP.Strict 

type AllZipN ( NP :: (k > Type ) > [k] > Type ) (c :: a > b > Constraint )  
Defined in Data.SOP.NP 

type AllZipN ( POP :: (k > Type ) > [[k]] > Type ) (c :: a > b > Constraint )  
Defined in Data.SOP.NP 
mapKKK :: forall k1 k2 k3 a b c (d :: k1) (e :: k2) (f :: k3). (a > b > c) > K a d > K b e > K c f Source #
Lift the given function.
Since: sopcore0.2.5.0
mapKKI :: forall k1 k2 a b c (d :: k1) (e :: k2). (a > b > c) > K a d > K b e > I c Source #
Lift the given function.
Since: sopcore0.2.5.0
mapKIK :: forall k1 k2 a b c (d :: k1) (e :: k2). (a > b > c) > K a d > I b > K c e Source #
Lift the given function.
Since: sopcore0.2.5.0
mapKII :: forall k a b c (d :: k). (a > b > c) > K a d > I b > I c Source #
Lift the given function.
Since: sopcore0.2.5.0
mapIKK :: forall k1 k2 a b c (d :: k1) (e :: k2). (a > b > c) > I a > K b d > K c e Source #
Lift the given function.
Since: sopcore0.2.5.0
mapIKI :: forall k a b c (d :: k). (a > b > c) > I a > K b d > I c Source #
Lift the given function.
Since: sopcore0.2.5.0
mapIIK :: forall k a b c (d :: k). (a > b > c) > I a > I b > K c d Source #
Lift the given function.
Since: sopcore0.2.5.0
mapIII :: (a > b > c) > I a > I b > I c Source #
Lift the given function.
Since: sopcore0.2.5.0
mapKK :: forall k1 k2 a b (c :: k1) (d :: k2). (a > b) > K a c > K b d Source #
Lift the given function.
Since: sopcore0.2.5.0
mapKI :: forall k a b (c :: k). (a > b) > K a c > I b Source #
Lift the given function.
Since: sopcore0.2.5.0
mapIK :: forall k a b (c :: k). (a > b) > I a > K b c Source #
Lift the given function.
Since: sopcore0.2.5.0
unComp :: forall l k f (g :: k > l) (p :: k). (f :.: g) p > f (g p) Source #
Extract the contents of a
Comp
value.
The constant type functor.
Like
Constant
, but kindpolymorphic
in its second argument and with a shorter name.
K a 
Instances
Show ( Ticked a) => Show ( Ticked ( K a x)) Source #  
( SListI xs, Show ( Ticked a)) => Show ( Ticked ( HardForkLedgerView_ ( K a :: Type > Type ) xs)) Source #  
Eq2 ( K :: Type > Type > Type ) 
Since: sopcore0.2.4.0 
Ord2 ( K :: Type > Type > Type ) 
Since: sopcore0.2.4.0 
Defined in Data.SOP.BasicFunctors 

Read2 ( K :: Type > Type > Type ) 
Since: sopcore0.2.4.0 
Defined in Data.SOP.BasicFunctors liftReadsPrec2 :: ( Int > ReadS a) > ReadS [a] > ( Int > ReadS b) > ReadS [b] > Int > ReadS ( K a b) Source # liftReadList2 :: ( Int > ReadS a) > ReadS [a] > ( Int > ReadS b) > ReadS [b] > ReadS [ K a b] Source # liftReadPrec2 :: ReadPrec a > ReadPrec [a] > ReadPrec b > ReadPrec [b] > ReadPrec ( K a b) Source # liftReadListPrec2 :: ReadPrec a > ReadPrec [a] > ReadPrec b > ReadPrec [b] > ReadPrec [ K a b] Source # 

Show2 ( K :: Type > Type > Type ) 
Since: sopcore0.2.4.0 
Defined in Data.SOP.BasicFunctors 

NFData2 ( K :: Type > Type > Type ) 
Since: sopcore0.2.5.0 
Defined in Data.SOP.BasicFunctors 

Functor ( K a :: Type > Type )  
( SListI xs, Show a) => Show ( HardForkLedgerView_ ( K a :: Type > Type ) xs) Source #  
Monoid a => Applicative ( K a :: Type > Type )  
Foldable ( K a :: Type > Type )  
Defined in Data.SOP.BasicFunctors fold :: Monoid m => K a m > m Source # foldMap :: Monoid m => (a0 > m) > K a a0 > m Source # foldMap' :: Monoid m => (a0 > m) > K a a0 > m Source # foldr :: (a0 > b > b) > b > K a a0 > b Source # foldr' :: (a0 > b > b) > b > K a a0 > b Source # foldl :: (b > a0 > b) > b > K a a0 > b Source # foldl' :: (b > a0 > b) > b > K a a0 > b Source # foldr1 :: (a0 > a0 > a0) > K a a0 > a0 Source # foldl1 :: (a0 > a0 > a0) > K a a0 > a0 Source # toList :: K a a0 > [a0] Source # null :: K a a0 > Bool Source # length :: K a a0 > Int Source # elem :: Eq a0 => a0 > K a a0 > Bool Source # maximum :: Ord a0 => K a a0 > a0 Source # minimum :: Ord a0 => K a a0 > a0 Source # 

Traversable ( K a :: Type > Type )  
Eq a => Eq1 ( K a :: Type > Type ) 
Since: sopcore0.2.4.0 
Defined in Data.SOP.BasicFunctors liftEq :: (a0 > b > 