Maintainer	gatlin@niltag.net
Safe Haskell	Safe-Inferred
Language	Haskell2010

Nested

Contents

Nested functors
Deconstructing nested functors
Manipulating nested functors

Description

Re-implementation of a library by Kenneth Foner. Upgrades were made to make this compile and functional dependencies have been replaced by type families.

This is used in Sheet especially in order to automatically build and inspect multi-dimensional containers out of nested functors.

Synopsis

data Nested fs a
- = forall f.fs ~ F f => Flat (f a)
- | forall fs' f.fs ~ N fs' f => Nest (Nested fs' (f a))
data F (x :: Type -> Type)
data N (o :: Type) (i :: Type -> Type)
type family UnNest x where ...
unNest :: Nested fs a -> UnNest (Nested fs a)
class NestedCountable (x :: k) where
- type NestedCount x :: Type
nestedCount :: Nested fs a -> Natural (NestedCount fs)
type family NestedNTimes (n :: Type) (f :: Type -> Type) where ...

Nested functors

data Nested fs a Source #

A Nested fs a is the composition of all the layers mentioned in fs, applied to an a. Specifically, the fs parameter is a sort of snoc-list holding type constructors of kind (* -> *). The outermost layer appears as the parameter to Flat; the innermost layer appears as the rightmost argument to the outermost Nest.

Constructors

forall f.fs ~ F f => Flat (f a)
forall fs' f.fs ~ N fs' f => Nest (Nested fs' (f a))

Instances

Instances details

Go Nil (Nested ts :: Type -> Type) Source #
Instance details Defined in Sheet Methods go :: forall (a :: k). RefList Nil -> Nested ts a -> Nested ts a Source #
(Take Nil (Nested ts), Functor (Nested ts)) => Take Nil (Nested (N ts Tape)) Source #
Instance details Defined in Sheet Associated Types type ListFrom (Nested (N ts Tape)) a Source # Methods take :: RefList Nil -> Nested (N ts Tape) a -> ListFrom (Nested (N ts Tape)) a Source #
View Nil (Nested (F Tape)) Source #
Instance details Defined in Sheet Associated Types type StreamFrom (Nested (F Tape)) a Source # Methods view :: RefList Nil -> Nested (F Tape) a -> StreamFrom (Nested (F Tape)) a Source #
(View Nil (Nested ts), Functor (Nested ts)) => View Nil (Nested (N ts Tape)) Source #
Instance details Defined in Sheet Associated Types type StreamFrom (Nested (N ts Tape)) a Source # Methods view :: RefList Nil -> Nested (N ts Tape) a -> StreamFrom (Nested (N ts Tape)) a Source #
InsertBase l => InsertNested (Nested (F l) :: Type -> Type) (Nested (F Tape)) Source #
Instance details Defined in Sheet Methods insertNested :: forall (a :: k). Nested (F l) a -> Nested (F Tape) a -> Nested (F Tape) a Source #
(InsertBase l, InsertNested (Nested ls) (Nested ts), Functor (Nested ls), Applicative (Nested ts)) => InsertNested (Nested (N ls l) :: Type -> Type) (Nested (N ts Tape) :: Type -> Type) Source #
Instance details Defined in Sheet Methods insertNested :: forall (a :: k). Nested (N ls l) a -> Nested (N ts Tape) a -> Nested (N ts Tape) a Source #
(NestedAs x (Nested ts y), AsDimensionalAs x (Nested ts y) ~ AsNestedAs x (Nested ts y)) => DimensionalAs x (Nested ts y) Source #
Instance details Defined in Sheet Associated Types type AsDimensionalAs x (Nested ts y) Source # Methods asDimensionalAs :: x -> Nested ts y -> AsDimensionalAs x (Nested ts y) Source #
Go ('Relative :-: Nil) (Nested (F Tape)) Source #
Instance details Defined in Sheet Methods go :: forall (a :: k). RefList ('Relative :-: Nil) -> Nested (F Tape) a -> Nested (F Tape) a Source #
(Go rs (Nested ts), Functor (Nested ts)) => Go ('Relative :-: rs) (Nested (N ts Tape) :: Type -> Type) Source #
Instance details Defined in Sheet Methods go :: forall (a :: k). RefList ('Relative :-: rs) -> Nested (N ts Tape) a -> Nested (N ts Tape) a Source #
Representable f => Representable (Nested (F f)) Source #
Instance details Defined in Nested Associated Types type Rep (Nested (F f)) Methods tabulate :: (Rep (Nested (F f)) -> a) -> Nested (F f) a index :: Nested (F f) a -> Rep (Nested (F f)) -> a
(Representable f, fs ~ NestedNTimes (NestedCount fs) f, Representable (Nested fs), Rep (Nested fs) ~ Counted (NestedCount fs) (Rep f)) => Representable (Nested (N fs f)) Source #
Instance details Defined in Nested Associated Types type Rep (Nested (N fs f)) Methods tabulate :: (Rep (Nested (N fs f)) -> a) -> Nested (N fs f) a index :: Nested (N fs f) a -> Rep (Nested (N fs f)) -> a
Foldable f => Foldable (Nested (F f)) Source #
Instance details Defined in Nested Methods fold :: Monoid m => Nested (F f) m -> m Source # foldMap :: Monoid m => (a -> m) -> Nested (F f) a -> m Source # foldMap' :: Monoid m => (a -> m) -> Nested (F f) a -> m Source # foldr :: (a -> b -> b) -> b -> Nested (F f) a -> b Source # foldr' :: (a -> b -> b) -> b -> Nested (F f) a -> b Source # foldl :: (b -> a -> b) -> b -> Nested (F f) a -> b Source # foldl' :: (b -> a -> b) -> b -> Nested (F f) a -> b Source # foldr1 :: (a -> a -> a) -> Nested (F f) a -> a Source # foldl1 :: (a -> a -> a) -> Nested (F f) a -> a Source # toList :: Nested (F f) a -> [a] Source # null :: Nested (F f) a -> Bool Source # length :: Nested (F f) a -> Int Source # elem :: Eq a => a -> Nested (F f) a -> Bool Source # maximum :: Ord a => Nested (F f) a -> a Source # minimum :: Ord a => Nested (F f) a -> a Source # sum :: Num a => Nested (F f) a -> a Source # product :: Num a => Nested (F f) a -> a Source #
(Foldable f, Foldable (Nested fs)) => Foldable (Nested (N fs f)) Source #
Instance details Defined in Nested Methods fold :: Monoid m => Nested (N fs f) m -> m Source # foldMap :: Monoid m => (a -> m) -> Nested (N fs f) a -> m Source # foldMap' :: Monoid m => (a -> m) -> Nested (N fs f) a -> m Source # foldr :: (a -> b -> b) -> b -> Nested (N fs f) a -> b Source # foldr' :: (a -> b -> b) -> b -> Nested (N fs f) a -> b Source # foldl :: (b -> a -> b) -> b -> Nested (N fs f) a -> b Source # foldl' :: (b -> a -> b) -> b -> Nested (N fs f) a -> b Source # foldr1 :: (a -> a -> a) -> Nested (N fs f) a -> a Source # foldl1 :: (a -> a -> a) -> Nested (N fs f) a -> a Source # toList :: Nested (N fs f) a -> [a] Source # null :: Nested (N fs f) a -> Bool Source # length :: Nested (N fs f) a -> Int Source # elem :: Eq a => a -> Nested (N fs f) a -> Bool Source # maximum :: Ord a => Nested (N fs f) a -> a Source # minimum :: Ord a => Nested (N fs f) a -> a Source # sum :: Num a => Nested (N fs f) a -> a Source # product :: Num a => Nested (N fs f) a -> a Source #
Traversable f => Traversable (Nested (F f)) Source #
Instance details Defined in Nested Methods traverse :: Applicative f0 => (a -> f0 b) -> Nested (F f) a -> f0 (Nested (F f) b) Source # sequenceA :: Applicative f0 => Nested (F f) (f0 a) -> f0 (Nested (F f) a) Source # mapM :: Monad m => (a -> m b) -> Nested (F f) a -> m (Nested (F f) b) Source # sequence :: Monad m => Nested (F f) (m a) -> m (Nested (F f) a) Source #
(Traversable f, Traversable (Nested fs)) => Traversable (Nested (N fs f)) Source #
Instance details Defined in Nested Methods traverse :: Applicative f0 => (a -> f0 b) -> Nested (N fs f) a -> f0 (Nested (N fs f) b) Source # sequenceA :: Applicative f0 => Nested (N fs f) (f0 a) -> f0 (Nested (N fs f) a) Source # mapM :: Monad m => (a -> m b) -> Nested (N fs f) a -> m (Nested (N fs f) b) Source # sequence :: Monad m => Nested (N fs f) (m a) -> m (Nested (N fs f) a) Source #
Alternative f => Alternative (Nested (F f)) Source #
Instance details Defined in Nested Methods empty :: Nested (F f) a Source # (<\|>) :: Nested (F f) a -> Nested (F f) a -> Nested (F f) a Source # some :: Nested (F f) a -> Nested (F f) [a] Source # many :: Nested (F f) a -> Nested (F f) [a] Source #
(Applicative f, Alternative (Nested fs)) => Alternative (Nested (N fs f)) Source #
Instance details Defined in Nested Methods empty :: Nested (N fs f) a Source # (<\|>) :: Nested (N fs f) a -> Nested (N fs f) a -> Nested (N fs f) a Source # some :: Nested (N fs f) a -> Nested (N fs f) [a] Source # many :: Nested (N fs f) a -> Nested (N fs f) [a] Source #
Applicative f => Applicative (Nested (F f)) Source #
Instance details Defined in Nested Methods pure :: a -> Nested (F f) a Source # (<>) :: Nested (F f) (a -> b) -> Nested (F f) a -> Nested (F f) b Source # liftA2 :: (a -> b -> c) -> Nested (F f) a -> Nested (F f) b -> Nested (F f) c Source # (>) :: Nested (F f) a -> Nested (F f) b -> Nested (F f) b Source # (<*) :: Nested (F f) a -> Nested (F f) b -> Nested (F f) a Source #
(Applicative f, Applicative (Nested fs)) => Applicative (Nested (N fs f)) Source #
Instance details Defined in Nested Methods pure :: a -> Nested (N fs f) a Source # (<>) :: Nested (N fs f) (a -> b) -> Nested (N fs f) a -> Nested (N fs f) b Source # liftA2 :: (a -> b -> c) -> Nested (N fs f) a -> Nested (N fs f) b -> Nested (N fs f) c Source # (>) :: Nested (N fs f) a -> Nested (N fs f) b -> Nested (N fs f) b Source # (<*) :: Nested (N fs f) a -> Nested (N fs f) b -> Nested (N fs f) a Source #
Functor f => Functor (Nested (F f)) Source #
Instance details Defined in Nested Methods fmap :: (a -> b) -> Nested (F f) a -> Nested (F f) b Source # (<$) :: a -> Nested (F f) b -> Nested (F f) a Source #
(Functor f, Functor (Nested fs)) => Functor (Nested (N fs f)) Source #
Instance details Defined in Nested Methods fmap :: (a -> b) -> Nested (N fs f) a -> Nested (N fs f) b Source # (<$) :: a -> Nested (N fs f) b -> Nested (N fs f) a Source #
Comonad f => Comonad (Nested (F f)) Source #
Instance details Defined in Nested Methods extract :: Nested (F f) a -> a duplicate :: Nested (F f) a -> Nested (F f) (Nested (F f) a) extend :: (Nested (F f) a -> b) -> Nested (F f) a -> Nested (F f) b
(Comonad f, Comonad (Nested fs), Functor (Nested (N fs f)), Distributive f) => Comonad (Nested (N fs f)) Source #
Instance details Defined in Nested Methods extract :: Nested (N fs f) a -> a duplicate :: Nested (N fs f) a -> Nested (N fs f) (Nested (N fs f) a) extend :: (Nested (N fs f) a -> b) -> Nested (N fs f) a -> Nested (N fs f) b
ComonadApply f => ComonadApply (Nested (F f)) Source #
Instance details Defined in Nested Methods (<@>) :: Nested (F f) (a -> b) -> Nested (F f) a -> Nested (F f) b (@>) :: Nested (F f) a -> Nested (F f) b -> Nested (F f) b (<@) :: Nested (F f) a -> Nested (F f) b -> Nested (F f) a
(ComonadApply f, Distributive f, ComonadApply (Nested fs)) => ComonadApply (Nested (N fs f)) Source #
Instance details Defined in Nested Methods (<@>) :: Nested (N fs f) (a -> b) -> Nested (N fs f) a -> Nested (N fs f) b (@>) :: Nested (N fs f) a -> Nested (N fs f) b -> Nested (N fs f) b (<@) :: Nested (N fs f) a -> Nested (N fs f) b -> Nested (N fs f) a
Distributive f => Distributive (Nested (F f)) Source #
Instance details Defined in Nested Methods distribute :: Functor f0 => f0 (Nested (F f) a) -> Nested (F f) (f0 a) collect :: Functor f0 => (a -> Nested (F f) b) -> f0 a -> Nested (F f) (f0 b) distributeM :: Monad m => m (Nested (F f) a) -> Nested (F f) (m a) collectM :: Monad m => (a -> Nested (F f) b) -> m a -> Nested (F f) (m b)
(Distributive f, Distributive (Nested fs)) => Distributive (Nested (N fs f)) Source #
Instance details Defined in Nested Methods distribute :: Functor f0 => f0 (Nested (N fs f) a) -> Nested (N fs f) (f0 a) collect :: Functor f0 => (a -> Nested (N fs f) b) -> f0 a -> Nested (N fs f) (f0 b) distributeM :: Monad m => m (Nested (N fs f) a) -> Nested (N fs f) (m a) collectM :: Monad m => (a -> Nested (N fs f) b) -> m a -> Nested (N fs f) (m b)
Take ('Relative :-: Nil) (Nested (F Tape)) Source #
Instance details Defined in Sheet Associated Types type ListFrom (Nested (F Tape)) a Source # Methods take :: RefList ('Relative :-: Nil) -> Nested (F Tape) a -> ListFrom (Nested (F Tape)) a Source #
(Functor (Nested ts), Take rs (Nested ts)) => Take ('Relative :-: rs) (Nested (N ts Tape)) Source #
Instance details Defined in Sheet Associated Types type ListFrom (Nested (N ts Tape)) a Source # Methods take :: RefList ('Relative :-: rs) -> Nested (N ts Tape) a -> ListFrom (Nested (N ts Tape)) a Source #
View ('Relative :-: Nil) (Nested (F Tape)) Source #
Instance details Defined in Sheet Associated Types type StreamFrom (Nested (F Tape)) a Source # Methods view :: RefList ('Relative :-: Nil) -> Nested (F Tape) a -> StreamFrom (Nested (F Tape)) a Source #
(Functor (Nested ts), View rs (Nested ts)) => View ('Relative :-: rs) (Nested (N ts Tape)) Source #
Instance details Defined in Sheet Associated Types type StreamFrom (Nested (N ts Tape)) a Source # Methods view :: RefList ('Relative :-: rs) -> Nested (N ts Tape) a -> StreamFrom (Nested (N ts Tape)) a Source #
type AsDimensionalAs x (Nested ts y) Source #
Instance details Defined in Sheet type AsDimensionalAs x (Nested ts y) = AsNestedAs x (Nested ts y)
type Rep (Nested (F f)) Source #
Instance details Defined in Nested type Rep (Nested (F f)) = Counted (S Z) (Rep f)
type Rep (Nested (N fs f)) Source #
Instance details Defined in Nested type Rep (Nested (N fs f)) = Counted (S (NestedCount fs)) (Rep f)
type ListFrom (Nested (F Tape)) a Source #
Instance details Defined in Sheet type ListFrom (Nested (F Tape)) a = [a]
type ListFrom (Nested (N ts Tape)) a Source #
Instance details Defined in Sheet type ListFrom (Nested (N ts Tape)) a = ListFrom (Nested ts) [a]
type ListFrom (Nested (N ts Tape)) a Source #
Instance details Defined in Sheet type ListFrom (Nested (N ts Tape)) a = ListFrom (Nested ts) [a]
type StreamFrom (Nested (F Tape)) a Source #
Instance details Defined in Sheet type StreamFrom (Nested (F Tape)) a = Stream a
type StreamFrom (Nested (F Tape)) a Source #
Instance details Defined in Sheet type StreamFrom (Nested (F Tape)) a = Stream a
type StreamFrom (Nested (N ts Tape)) a Source #
Instance details Defined in Sheet type StreamFrom (Nested (N ts Tape)) a = StreamFrom (Nested ts) (Stream a)
type StreamFrom (Nested (N ts Tape)) a Source #
Instance details Defined in Sheet type StreamFrom (Nested (N ts Tape)) a = StreamFrom (Nested ts) (Stream a)

data F (x :: Type -> Type) Source #

Instances

Instances details

NestedCountable (F f :: Type) Source #
Instance details Defined in Nested Associated Types type NestedCount (F f) Source #
View Nil (Nested (F Tape)) Source #
Instance details Defined in Sheet Associated Types type StreamFrom (Nested (F Tape)) a Source # Methods view :: RefList Nil -> Nested (F Tape) a -> StreamFrom (Nested (F Tape)) a Source #
InsertBase l => InsertNested (Nested (F l) :: Type -> Type) (Nested (F Tape)) Source #
Instance details Defined in Sheet Methods insertNested :: forall (a :: k). Nested (F l) a -> Nested (F Tape) a -> Nested (F Tape) a Source #
Go ('Relative :-: Nil) (Nested (F Tape)) Source #
Instance details Defined in Sheet Methods go :: forall (a :: k). RefList ('Relative :-: Nil) -> Nested (F Tape) a -> Nested (F Tape) a Source #
Representable f => Representable (Nested (F f)) Source #
Instance details Defined in Nested Associated Types type Rep (Nested (F f)) Methods tabulate :: (Rep (Nested (F f)) -> a) -> Nested (F f) a index :: Nested (F f) a -> Rep (Nested (F f)) -> a
Foldable f => Foldable (Nested (F f)) Source #
Instance details Defined in Nested Methods fold :: Monoid m => Nested (F f) m -> m Source # foldMap :: Monoid m => (a -> m) -> Nested (F f) a -> m Source # foldMap' :: Monoid m => (a -> m) -> Nested (F f) a -> m Source # foldr :: (a -> b -> b) -> b -> Nested (F f) a -> b Source # foldr' :: (a -> b -> b) -> b -> Nested (F f) a -> b Source # foldl :: (b -> a -> b) -> b -> Nested (F f) a -> b Source # foldl' :: (b -> a -> b) -> b -> Nested (F f) a -> b Source # foldr1 :: (a -> a -> a) -> Nested (F f) a -> a Source # foldl1 :: (a -> a -> a) -> Nested (F f) a -> a Source # toList :: Nested (F f) a -> [a] Source # null :: Nested (F f) a -> Bool Source # length :: Nested (F f) a -> Int Source # elem :: Eq a => a -> Nested (F f) a -> Bool Source # maximum :: Ord a => Nested (F f) a -> a Source # minimum :: Ord a => Nested (F f) a -> a Source # sum :: Num a => Nested (F f) a -> a Source # product :: Num a => Nested (F f) a -> a Source #
Traversable f => Traversable (Nested (F f)) Source #
Instance details Defined in Nested Methods traverse :: Applicative f0 => (a -> f0 b) -> Nested (F f) a -> f0 (Nested (F f) b) Source # sequenceA :: Applicative f0 => Nested (F f) (f0 a) -> f0 (Nested (F f) a) Source # mapM :: Monad m => (a -> m b) -> Nested (F f) a -> m (Nested (F f) b) Source # sequence :: Monad m => Nested (F f) (m a) -> m (Nested (F f) a) Source #
Alternative f => Alternative (Nested (F f)) Source #
Instance details Defined in Nested Methods empty :: Nested (F f) a Source # (<\|>) :: Nested (F f) a -> Nested (F f) a -> Nested (F f) a Source # some :: Nested (F f) a -> Nested (F f) [a] Source # many :: Nested (F f) a -> Nested (F f) [a] Source #
Applicative f => Applicative (Nested (F f)) Source #
Instance details Defined in Nested Methods pure :: a -> Nested (F f) a Source # (<>) :: Nested (F f) (a -> b) -> Nested (F f) a -> Nested (F f) b Source # liftA2 :: (a -> b -> c) -> Nested (F f) a -> Nested (F f) b -> Nested (F f) c Source # (>) :: Nested (F f) a -> Nested (F f) b -> Nested (F f) b Source # (<*) :: Nested (F f) a -> Nested (F f) b -> Nested (F f) a Source #
Functor f => Functor (Nested (F f)) Source #
Instance details Defined in Nested Methods fmap :: (a -> b) -> Nested (F f) a -> Nested (F f) b Source # (<$) :: a -> Nested (F f) b -> Nested (F f) a Source #
Comonad f => Comonad (Nested (F f)) Source #
Instance details Defined in Nested Methods extract :: Nested (F f) a -> a duplicate :: Nested (F f) a -> Nested (F f) (Nested (F f) a) extend :: (Nested (F f) a -> b) -> Nested (F f) a -> Nested (F f) b
ComonadApply f => ComonadApply (Nested (F f)) Source #
Instance details Defined in Nested Methods (<@>) :: Nested (F f) (a -> b) -> Nested (F f) a -> Nested (F f) b (@>) :: Nested (F f) a -> Nested (F f) b -> Nested (F f) b (<@) :: Nested (F f) a -> Nested (F f) b -> Nested (F f) a
Distributive f => Distributive (Nested (F f)) Source #
Instance details Defined in Nested Methods distribute :: Functor f0 => f0 (Nested (F f) a) -> Nested (F f) (f0 a) collect :: Functor f0 => (a -> Nested (F f) b) -> f0 a -> Nested (F f) (f0 b) distributeM :: Monad m => m (Nested (F f) a) -> Nested (F f) (m a) collectM :: Monad m => (a -> Nested (F f) b) -> m a -> Nested (F f) (m b)
Take ('Relative :-: Nil) (Nested (F Tape)) Source #
Instance details Defined in Sheet Associated Types type ListFrom (Nested (F Tape)) a Source # Methods take :: RefList ('Relative :-: Nil) -> Nested (F Tape) a -> ListFrom (Nested (F Tape)) a Source #
View ('Relative :-: Nil) (Nested (F Tape)) Source #
Instance details Defined in Sheet Associated Types type StreamFrom (Nested (F Tape)) a Source # Methods view :: RefList ('Relative :-: Nil) -> Nested (F Tape) a -> StreamFrom (Nested (F Tape)) a Source #
type NestedCount (F f :: Type) Source #
Instance details Defined in Nested type NestedCount (F f :: Type) = S Z
type Rep (Nested (F f)) Source #
Instance details Defined in Nested type Rep (Nested (F f)) = Counted (S Z) (Rep f)
type ListFrom (Nested (F Tape)) a Source #
Instance details Defined in Sheet type ListFrom (Nested (F Tape)) a = [a]
type StreamFrom (Nested (F Tape)) a Source #
Instance details Defined in Sheet type StreamFrom (Nested (F Tape)) a = Stream a
type StreamFrom (Nested (F Tape)) a Source #
Instance details Defined in Sheet type StreamFrom (Nested (F Tape)) a = Stream a

data N (o :: Type) (i :: Type -> Type) Source #

Instances

Instances details

(Take Nil (Nested ts), Functor (Nested ts)) => Take Nil (Nested (N ts Tape)) Source #
Instance details Defined in Sheet Associated Types type ListFrom (Nested (N ts Tape)) a Source # Methods take :: RefList Nil -> Nested (N ts Tape) a -> ListFrom (Nested (N ts Tape)) a Source #
(View Nil (Nested ts), Functor (Nested ts)) => View Nil (Nested (N ts Tape)) Source #
Instance details Defined in Sheet Associated Types type StreamFrom (Nested (N ts Tape)) a Source # Methods view :: RefList Nil -> Nested (N ts Tape) a -> StreamFrom (Nested (N ts Tape)) a Source #
(InsertBase l, InsertNested (Nested ls) (Nested ts), Functor (Nested ls), Applicative (Nested ts)) => InsertNested (Nested (N ls l) :: Type -> Type) (Nested (N ts Tape) :: Type -> Type) Source #
Instance details Defined in Sheet Methods insertNested :: forall (a :: k). Nested (N ls l) a -> Nested (N ts Tape) a -> Nested (N ts Tape) a Source #
NestedCountable (N fs f :: Type) Source #
Instance details Defined in Nested Associated Types type NestedCount (N fs f) Source #
(Go rs (Nested ts), Functor (Nested ts)) => Go ('Relative :-: rs) (Nested (N ts Tape) :: Type -> Type) Source #
Instance details Defined in Sheet Methods go :: forall (a :: k). RefList ('Relative :-: rs) -> Nested (N ts Tape) a -> Nested (N ts Tape) a Source #
(Representable f, fs ~ NestedNTimes (NestedCount fs) f, Representable (Nested fs), Rep (Nested fs) ~ Counted (NestedCount fs) (Rep f)) => Representable (Nested (N fs f)) Source #
Instance details Defined in Nested Associated Types type Rep (Nested (N fs f)) Methods tabulate :: (Rep (Nested (N fs f)) -> a) -> Nested (N fs f) a index :: Nested (N fs f) a -> Rep (Nested (N fs f)) -> a
(Foldable f, Foldable (Nested fs)) => Foldable (Nested (N fs f)) Source #
Instance details Defined in Nested Methods fold :: Monoid m => Nested (N fs f) m -> m Source # foldMap :: Monoid m => (a -> m) -> Nested (N fs f) a -> m Source # foldMap' :: Monoid m => (a -> m) -> Nested (N fs f) a -> m Source # foldr :: (a -> b -> b) -> b -> Nested (N fs f) a -> b Source # foldr' :: (a -> b -> b) -> b -> Nested (N fs f) a -> b Source # foldl :: (b -> a -> b) -> b -> Nested (N fs f) a -> b Source # foldl' :: (b -> a -> b) -> b -> Nested (N fs f) a -> b Source # foldr1 :: (a -> a -> a) -> Nested (N fs f) a -> a Source # foldl1 :: (a -> a -> a) -> Nested (N fs f) a -> a Source # toList :: Nested (N fs f) a -> [a] Source # null :: Nested (N fs f) a -> Bool Source # length :: Nested (N fs f) a -> Int Source # elem :: Eq a => a -> Nested (N fs f) a -> Bool Source # maximum :: Ord a => Nested (N fs f) a -> a Source # minimum :: Ord a => Nested (N fs f) a -> a Source # sum :: Num a => Nested (N fs f) a -> a Source # product :: Num a => Nested (N fs f) a -> a Source #
(Traversable f, Traversable (Nested fs)) => Traversable (Nested (N fs f)) Source #
Instance details Defined in Nested Methods traverse :: Applicative f0 => (a -> f0 b) -> Nested (N fs f) a -> f0 (Nested (N fs f) b) Source # sequenceA :: Applicative f0 => Nested (N fs f) (f0 a) -> f0 (Nested (N fs f) a) Source # mapM :: Monad m => (a -> m b) -> Nested (N fs f) a -> m (Nested (N fs f) b) Source # sequence :: Monad m => Nested (N fs f) (m a) -> m (Nested (N fs f) a) Source #
(Applicative f, Alternative (Nested fs)) => Alternative (Nested (N fs f)) Source #
Instance details Defined in Nested Methods empty :: Nested (N fs f) a Source # (<\|>) :: Nested (N fs f) a -> Nested (N fs f) a -> Nested (N fs f) a Source # some :: Nested (N fs f) a -> Nested (N fs f) [a] Source # many :: Nested (N fs f) a -> Nested (N fs f) [a] Source #
(Applicative f, Applicative (Nested fs)) => Applicative (Nested (N fs f)) Source #
Instance details Defined in Nested Methods pure :: a -> Nested (N fs f) a Source # (<>) :: Nested (N fs f) (a -> b) -> Nested (N fs f) a -> Nested (N fs f) b Source # liftA2 :: (a -> b -> c) -> Nested (N fs f) a -> Nested (N fs f) b -> Nested (N fs f) c Source # (>) :: Nested (N fs f) a -> Nested (N fs f) b -> Nested (N fs f) b Source # (<*) :: Nested (N fs f) a -> Nested (N fs f) b -> Nested (N fs f) a Source #
(Functor f, Functor (Nested fs)) => Functor (Nested (N fs f)) Source #
Instance details Defined in Nested Methods fmap :: (a -> b) -> Nested (N fs f) a -> Nested (N fs f) b Source # (<$) :: a -> Nested (N fs f) b -> Nested (N fs f) a Source #
(Comonad f, Comonad (Nested fs), Functor (Nested (N fs f)), Distributive f) => Comonad (Nested (N fs f)) Source #
Instance details Defined in Nested Methods extract :: Nested (N fs f) a -> a duplicate :: Nested (N fs f) a -> Nested (N fs f) (Nested (N fs f) a) extend :: (Nested (N fs f) a -> b) -> Nested (N fs f) a -> Nested (N fs f) b
(ComonadApply f, Distributive f, ComonadApply (Nested fs)) => ComonadApply (Nested (N fs f)) Source #
Instance details Defined in Nested Methods (<@>) :: Nested (N fs f) (a -> b) -> Nested (N fs f) a -> Nested (N fs f) b (@>) :: Nested (N fs f) a -> Nested (N fs f) b -> Nested (N fs f) b (<@) :: Nested (N fs f) a -> Nested (N fs f) b -> Nested (N fs f) a
(Distributive f, Distributive (Nested fs)) => Distributive (Nested (N fs f)) Source #
Instance details Defined in Nested Methods distribute :: Functor f0 => f0 (Nested (N fs f) a) -> Nested (N fs f) (f0 a) collect :: Functor f0 => (a -> Nested (N fs f) b) -> f0 a -> Nested (N fs f) (f0 b) distributeM :: Monad m => m (Nested (N fs f) a) -> Nested (N fs f) (m a) collectM :: Monad m => (a -> Nested (N fs f) b) -> m a -> Nested (N fs f) (m b)
(Functor (Nested ts), Take rs (Nested ts)) => Take ('Relative :-: rs) (Nested (N ts Tape)) Source #
Instance details Defined in Sheet Associated Types type ListFrom (Nested (N ts Tape)) a Source # Methods take :: RefList ('Relative :-: rs) -> Nested (N ts Tape) a -> ListFrom (Nested (N ts Tape)) a Source #
(Functor (Nested ts), View rs (Nested ts)) => View ('Relative :-: rs) (Nested (N ts Tape)) Source #
Instance details Defined in Sheet Associated Types type StreamFrom (Nested (N ts Tape)) a Source # Methods view :: RefList ('Relative :-: rs) -> Nested (N ts Tape) a -> StreamFrom (Nested (N ts Tape)) a Source #
type NestedCount (N fs f :: Type) Source #
Instance details Defined in Nested type NestedCount (N fs f :: Type) = S (NestedCount fs)
type Rep (Nested (N fs f)) Source #
Instance details Defined in Nested type Rep (Nested (N fs f)) = Counted (S (NestedCount fs)) (Rep f)
type ListFrom (Nested (N ts Tape)) a Source #
Instance details Defined in Sheet type ListFrom (Nested (N ts Tape)) a = ListFrom (Nested ts) [a]
type ListFrom (Nested (N ts Tape)) a Source #
Instance details Defined in Sheet type ListFrom (Nested (N ts Tape)) a = ListFrom (Nested ts) [a]
type StreamFrom (Nested (N ts Tape)) a Source #
Instance details Defined in Sheet type StreamFrom (Nested (N ts Tape)) a = StreamFrom (Nested ts) (Stream a)
type StreamFrom (Nested (N ts Tape)) a Source #
Instance details Defined in Sheet type StreamFrom (Nested (N ts Tape)) a = StreamFrom (Nested ts) (Stream a)

Deconstructing nested functors

type family UnNest x where ... Source #

Equations

UnNest (Nested (F f) a) = f a
UnNest (Nested (N fs f) a) = Nested fs (f a)

unNest :: Nested fs a -> UnNest (Nested fs a) Source #

Manipulating nested functors

class NestedCountable (x :: k) Source #

Associated Types

type NestedCount x :: Type Source #

Instances

Instances details

NestedCountable (F f :: Type) Source #
Instance details Defined in Nested Associated Types type NestedCount (F f) Source #
NestedCountable (N fs f :: Type) Source #
Instance details Defined in Nested Associated Types type NestedCount (N fs f) Source #

nestedCount :: Nested fs a -> Natural (NestedCount fs) Source #

type family NestedNTimes (n :: Type) (f :: Type -> Type) where ... Source #

Equations

NestedNTimes (S Z) f = F f
NestedNTimes (S n) f = N (NestedNTimes n f) f