Maintainer | gatlin@niltag.net |
---|---|

Safe Haskell | Safe-Inferred |

Language | Haskell2010 |

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 Upgrades were made to make this compile and functional dependencies have been replaced by type families.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
- 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

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`

.

#### Instances

Go Nil (Nested ts :: Type -> Type) Source # | |

(Take Nil (Nested ts), Functor (Nested ts)) => Take Nil (Nested (N ts Tape)) Source # | |

View Nil (Nested (F Tape)) Source # | |

(View Nil (Nested ts), Functor (Nested ts)) => View Nil (Nested (N ts Tape)) Source # | |

InsertBase l => InsertNested (Nested (F l) :: Type -> Type) (Nested (F Tape)) 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 # | |

(NestedAs x (Nested ts y), AsDimensionalAs x (Nested ts y) ~ AsNestedAs x (Nested ts y)) => DimensionalAs x (Nested ts y) Source # | |

Defined in Sheet type AsDimensionalAs x (Nested ts y) Source # asDimensionalAs :: x -> Nested ts y -> AsDimensionalAs x (Nested ts y) Source # | |

Go ('Relative :-: Nil) (Nested (F Tape)) Source # | |

(Go rs (Nested ts), Functor (Nested ts)) => Go ('Relative :-: rs) (Nested (N ts Tape) :: Type -> Type) Source # | |

Representable f => Representable (Nested (F f)) 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 # | |

Foldable f => Foldable (Nested (F f)) Source # | |

Defined in Nested 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 # | |

(Foldable f, Foldable (Nested fs)) => Foldable (Nested (N fs f)) Source # | |

Defined in Nested 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 # | |

Traversable f => Traversable (Nested (F f)) Source # | |

Defined in Nested 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 # | |

Defined in Nested 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 # | |

(Applicative f, Alternative (Nested fs)) => Alternative (Nested (N fs f)) Source # | |

Applicative f => Applicative (Nested (F f)) Source # | |

Defined in Nested 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 # | |

Defined in Nested 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 # | |

(Functor f, Functor (Nested fs)) => Functor (Nested (N fs f)) Source # | |

Comonad f => Comonad (Nested (F f)) Source # | |

(Comonad f, Comonad (Nested fs), Functor (Nested (N fs f)), Distributive f) => Comonad (Nested (N fs f)) Source # | |

ComonadApply f => ComonadApply (Nested (F f)) Source # | |

(ComonadApply f, Distributive f, ComonadApply (Nested fs)) => ComonadApply (Nested (N fs f)) Source # | |

Distributive f => Distributive (Nested (F f)) Source # | |

Defined in Nested | |

(Distributive f, Distributive (Nested fs)) => Distributive (Nested (N fs f)) Source # | |

Defined in Nested 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 # | |

(Functor (Nested ts), Take rs (Nested ts)) => Take ('Relative :-: rs) (Nested (N ts Tape)) Source # | |

View ('Relative :-: Nil) (Nested (F Tape)) Source # | |

(Functor (Nested ts), View rs (Nested ts)) => View ('Relative :-: rs) (Nested (N ts Tape)) Source # | |

type AsDimensionalAs x (Nested ts y) Source # | |

Defined in Sheet | |

type Rep (Nested (F f)) Source # | |

type Rep (Nested (N fs f)) Source # | |

type ListFrom (Nested (F Tape)) a Source # | |

type ListFrom (Nested (N ts Tape)) a Source # | |

type ListFrom (Nested (N ts Tape)) a Source # | |

type StreamFrom (Nested (F Tape)) a Source # | |

type StreamFrom (Nested (F Tape)) a Source # | |

type StreamFrom (Nested (N ts Tape)) a Source # | |

Defined in Sheet | |

type StreamFrom (Nested (N ts Tape)) a Source # | |

Defined in Sheet |

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

#### Instances

NestedCountable (F f :: Type) Source # | |

Defined in Nested type NestedCount (F f) Source # | |

View Nil (Nested (F Tape)) Source # | |

InsertBase l => InsertNested (Nested (F l) :: Type -> Type) (Nested (F Tape)) Source # | |

Go ('Relative :-: Nil) (Nested (F Tape)) Source # | |

Representable f => Representable (Nested (F f)) Source # | |

Foldable f => Foldable (Nested (F f)) Source # | |

Defined in Nested 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 # | |

Traversable f => Traversable (Nested (F f)) Source # | |

Defined in Nested 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 # | |

Applicative f => Applicative (Nested (F f)) Source # | |

Defined in Nested 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 # | |

Comonad f => Comonad (Nested (F f)) Source # | |

ComonadApply f => ComonadApply (Nested (F f)) Source # | |

Distributive f => Distributive (Nested (F f)) Source # | |

Defined in Nested | |

Take ('Relative :-: Nil) (Nested (F Tape)) Source # | |

View ('Relative :-: Nil) (Nested (F Tape)) Source # | |

type NestedCount (F f :: Type) Source # | |

type Rep (Nested (F f)) Source # | |

type ListFrom (Nested (F Tape)) a Source # | |

type StreamFrom (Nested (F Tape)) a Source # | |

type StreamFrom (Nested (F Tape)) a Source # | |

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

#### Instances

(Take Nil (Nested ts), Functor (Nested ts)) => Take Nil (Nested (N ts Tape)) Source # | |

(View Nil (Nested ts), Functor (Nested ts)) => View Nil (Nested (N ts Tape)) 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 # | |

NestedCountable (N fs f :: Type) Source # | |

Defined in Nested type NestedCount (N fs f) Source # | |

(Go rs (Nested ts), Functor (Nested ts)) => Go ('Relative :-: rs) (Nested (N ts Tape) :: Type -> Type) 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 # | |

(Foldable f, Foldable (Nested fs)) => Foldable (Nested (N fs f)) Source # | |

Defined in Nested 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 # | |

(Traversable f, Traversable (Nested fs)) => Traversable (Nested (N fs f)) Source # | |

Defined in Nested 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 # | |

(Applicative f, Applicative (Nested fs)) => Applicative (Nested (N fs f)) Source # | |

Defined in Nested 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 # | |

(Comonad f, Comonad (Nested fs), Functor (Nested (N fs f)), Distributive f) => Comonad (Nested (N fs f)) Source # | |

(ComonadApply f, Distributive f, ComonadApply (Nested fs)) => ComonadApply (Nested (N fs f)) Source # | |

(Distributive f, Distributive (Nested fs)) => Distributive (Nested (N fs f)) Source # | |

Defined in Nested 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 # | |

(Functor (Nested ts), View rs (Nested ts)) => View ('Relative :-: rs) (Nested (N ts Tape)) Source # | |

type NestedCount (N fs f :: Type) Source # | |

Defined in Nested | |

type Rep (Nested (N fs f)) Source # | |

type ListFrom (Nested (N ts Tape)) a Source # | |

type ListFrom (Nested (N ts Tape)) a Source # | |

type StreamFrom (Nested (N ts Tape)) a Source # | |

Defined in Sheet | |

type StreamFrom (Nested (N ts Tape)) a Source # | |

Defined in Sheet |

# Deconstructing nested functors

# Manipulating nested functors

class NestedCountable (x :: k) Source #

type NestedCount x :: Type Source #

#### Instances

NestedCountable (F f :: Type) Source # | |

Defined in Nested type NestedCount (F f) Source # | |

NestedCountable (N fs f :: Type) Source # | |

Defined in Nested type NestedCount (N fs f) Source # |

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

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

NestedNTimes (S Z) f = F f | |

NestedNTimes (S n) f = N (NestedNTimes n f) f |