Copyright	(c) 2011 Conal Elliott
Maintainer	conal@conal.net
Stability	experimental
Safe Haskell	Safe
Language	Haskell98

Data.FTree.TopDown

Description

Top-down, depth-typed functor trees. In other words, right-associated n-ary functor composition. See http://conal.net/blog/posts/a-trie-for-length-typed-vectors/.

Synopsis

data T :: (* -> *) -> * -> * -> * where
- L :: a -> T f Z a
- B :: IsNat n => f (T f n a) -> T f (S n) a
type (:^) = T
unL :: (f :^ Z) a -> a
unB :: (f :^ S n) a -> f ((f :^ n) a)
foldT :: forall f n a z. Functor f => (a -> z) -> (f z -> z) -> (f :^ n) a -> z
inT :: (a -> b) -> (forall n. IsNat n => f ((f :^ n) a) -> f ((f :^ n) b)) -> forall n. (f :^ n) a -> (f :^ n) b
inT2 :: (a -> b -> c) -> (forall n. IsNat n => f ((f :^ n) a) -> f ((f :^ n) b) -> f ((f :^ n) c)) -> forall n. (f :^ n) a -> (f :^ n) b -> (f :^ n) c
inL :: (a -> b) -> (f :^ Z) a -> (f :^ Z) b
inB :: (f ((f :^ n) a) -> f ((f :^ n) b)) -> (f :^ S n) a -> (f :^ S n) b
inL2 :: (a -> b -> c) -> (f :^ Z) a -> (f :^ Z) b -> (f :^ Z) c
inB2 :: (f ((f :^ n) a) -> f ((f :^ n) b) -> f ((f :^ n) c)) -> (f :^ S n) a -> (f :^ S n) b -> (f :^ S n) c

Documentation

data T :: (* -> *) -> * -> * -> * where Source #

Constructors

L :: a -> T f Z a
B :: IsNat n => f (T f n a) -> T f (S n) a

Instances

Functor f => Functor (f :^ n) Source #
Instance details Defined in Data.FTree.TopDown Methods fmap :: (a -> b) -> (f :^ n) a -> (f :^ n) b # (<$) :: a -> (f :^ n) b -> (f :^ n) a #
(IsNat n, Applicative f) => Applicative (f :^ n) Source #
Instance details Defined in Data.FTree.TopDown Methods pure :: a -> (f :^ n) a # (<>) :: (f :^ n) (a -> b) -> (f :^ n) a -> (f :^ n) b # liftA2 :: (a -> b -> c) -> (f :^ n) a -> (f :^ n) b -> (f :^ n) c # (>) :: (f :^ n) a -> (f :^ n) b -> (f :^ n) b # (<*) :: (f :^ n) a -> (f :^ n) b -> (f :^ n) a #
(Functor f, Foldable f) => Foldable (f :^ n) Source #
Instance details Defined in Data.FTree.TopDown Methods fold :: Monoid m => (f :^ n) m -> m # foldMap :: Monoid m => (a -> m) -> (f :^ n) a -> m # foldr :: (a -> b -> b) -> b -> (f :^ n) a -> b # foldr' :: (a -> b -> b) -> b -> (f :^ n) a -> b # foldl :: (b -> a -> b) -> b -> (f :^ n) a -> b # foldl' :: (b -> a -> b) -> b -> (f :^ n) a -> b # foldr1 :: (a -> a -> a) -> (f :^ n) a -> a # foldl1 :: (a -> a -> a) -> (f :^ n) a -> a # toList :: (f :^ n) a -> [a] # null :: (f :^ n) a -> Bool # length :: (f :^ n) a -> Int # elem :: Eq a => a -> (f :^ n) a -> Bool # maximum :: Ord a => (f :^ n) a -> a # minimum :: Ord a => (f :^ n) a -> a # sum :: Num a => (f :^ n) a -> a # product :: Num a => (f :^ n) a -> a #
Traversable f => Traversable (f :^ n) Source #
Instance details Defined in Data.FTree.TopDown Methods traverse :: Applicative f0 => (a -> f0 b) -> (f :^ n) a -> f0 ((f :^ n) b) # sequenceA :: Applicative f0 => (f :^ n) (f0 a) -> f0 ((f :^ n) a) # mapM :: Monad m => (a -> m b) -> (f :^ n) a -> m ((f :^ n) b) # sequence :: Monad m => (f :^ n) (m a) -> m ((f :^ n) a) #
ShowF f => ShowF (f :^ n) Source #
Instance details Defined in Data.FTree.TopDown Methods showF :: Show a => (f :^ n) a -> String # showsPrecF :: Show a => Int -> (f :^ n) a -> ShowS #
(Foldable f, Applicative f, IsNat n, Eq a) => Eq ((f :^ n) a) Source #
Instance details Defined in Data.FTree.TopDown Methods (==) :: (f :^ n) a -> (f :^ n) a -> Bool # (/=) :: (f :^ n) a -> (f :^ n) a -> Bool #
(Foldable f, Applicative f, IsNat n, Ord a) => Ord ((f :^ n) a) Source #
Instance details Defined in Data.FTree.TopDown Methods compare :: (f :^ n) a -> (f :^ n) a -> Ordering # (<) :: (f :^ n) a -> (f :^ n) a -> Bool # (<=) :: (f :^ n) a -> (f :^ n) a -> Bool # (>) :: (f :^ n) a -> (f :^ n) a -> Bool # (>=) :: (f :^ n) a -> (f :^ n) a -> Bool # max :: (f :^ n) a -> (f :^ n) a -> (f :^ n) a # min :: (f :^ n) a -> (f :^ n) a -> (f :^ n) a #
(ShowF f, Show a) => Show ((f :^ n) a) Source #
Instance details Defined in Data.FTree.TopDown Methods showsPrec :: Int -> (f :^ n) a -> ShowS # show :: (f :^ n) a -> String # showList :: [(f :^ n) a] -> ShowS #
(IsNat n, Applicative f, Semigroup m) => Semigroup ((f :^ n) m) Source #
Instance details Defined in Data.FTree.TopDown Methods (<>) :: (f :^ n) m -> (f :^ n) m -> (f :^ n) m # sconcat :: NonEmpty ((f :^ n) m) -> (f :^ n) m # stimes :: Integral b => b -> (f :^ n) m -> (f :^ n) m #
(IsNat n, Applicative f, Monoid m) => Monoid ((f :^ n) m) Source #
Instance details Defined in Data.FTree.TopDown Methods mempty :: (f :^ n) m # mappend :: (f :^ n) m -> (f :^ n) m -> (f :^ n) m # mconcat :: [(f :^ n) m] -> (f :^ n) m #

type (:^) = T Source #

unL :: (f :^ Z) a -> a Source #

unB :: (f :^ S n) a -> f ((f :^ n) a) Source #

foldT :: forall f n a z. Functor f => (a -> z) -> (f z -> z) -> (f :^ n) a -> z Source #

inT :: (a -> b) -> (forall n. IsNat n => f ((f :^ n) a) -> f ((f :^ n) b)) -> forall n. (f :^ n) a -> (f :^ n) b Source #

Operate inside the representation of `f :^ n` to make another, preserving depth.

inT2 :: (a -> b -> c) -> (forall n. IsNat n => f ((f :^ n) a) -> f ((f :^ n) b) -> f ((f :^ n) c)) -> forall n. (f :^ n) a -> (f :^ n) b -> (f :^ n) c Source #

Operate inside the representation of two `f :^ n` to make another, preserving depth.

inL :: (a -> b) -> (f :^ Z) a -> (f :^ Z) b Source #

inB :: (f ((f :^ n) a) -> f ((f :^ n) b)) -> (f :^ S n) a -> (f :^ S n) b Source #

inL2 :: (a -> b -> c) -> (f :^ Z) a -> (f :^ Z) b -> (f :^ Z) c Source #

inB2 :: (f ((f :^ n) a) -> f ((f :^ n) b) -> f ((f :^ n) c)) -> (f :^ S n) a -> (f :^ S n) b -> (f :^ S n) c Source #