Copyright	(c) Justin Le 2019
License	BSD3
Maintainer	[email protected]
Stability	experimental
Portability	non-portable
Safe Haskell	None
Language	Haskell2010

Data.HFunctor.Chain

Contents

Chain
Chain1
- Matchable
Orphan instances

Description

This module provides an Interpretable data type of "linked list of tensor applications".

The type Chain t, for any Tensor t, is meant to be the same as ListBy t (the monoidal functor combinator for t), and represents "zero or more" applications of f to t.

The type Chain1 t, for any Associative t, is meant to be the same as NonEmptyBy t (the semigroupoidal functor combinator for t) and represents "one or more" applications of f to t.

The advantage of using Chain and Chain1 over ListBy or NonEmptyBy is that they provide a universal interface for pattern matching and constructing such values, which may simplify working with new such functor combinators you might encounter.

Synopsis

data Chain (t :: k -> (k1 -> Type) -> k1 -> Type) (i :: k1 -> Type) (f :: k) (a :: k1)
- = Done (i a)
- | More (t f (Chain t i f) a)
foldChain :: forall {k} (t :: (k -> Type) -> (k -> Type) -> k -> Type) (i :: k -> Type) (f :: k -> Type) (g :: k -> Type). HBifunctor t => (i ~> g) -> (t f g ~> g) -> Chain t i f ~> g
foldChainA :: forall {k} t h i g (f :: k -> Type) (a :: k). (HBifunctor t, Functor h) => (forall (x :: k). i x -> h (g x)) -> (forall (x :: k). t f (Comp h g) x -> h (g x)) -> Chain t i f a -> h (g a)
unfoldChain :: forall (t :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (f :: Type -> Type) (g :: Type -> Type) (i :: Type -> Type). HBifunctor t => (g ~> (i :+: t f g)) -> g ~> Chain t i f
unroll :: forall (t :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (i :: Type -> Type) (f :: Type -> Type). Tensor t i => ListBy t f ~> Chain t i f
reroll :: forall (t :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (i :: Type -> Type) (f :: Type -> Type). Tensor t i => Chain t i f ~> ListBy t f
unrolling :: forall (t :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (i :: Type -> Type) (f :: Type -> Type). Tensor t i => ListBy t f <~> Chain t i f
appendChain :: forall (t :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (i :: Type -> Type) (f :: Type -> Type). Tensor t i => t (Chain t i f) (Chain t i f) ~> Chain t i f
splittingChain :: forall {k1} {k2} (t :: k1 -> (k2 -> Type) -> k2 -> Type) (i :: k2 -> Type) (f :: k1) p (a :: k2). Profunctor p => p ((i :+: t f (Chain t i f)) a) ((i :+: t f (Chain t i f)) a) -> p (Chain t i f a) (Chain t i f a)
toChain :: forall (t :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (i :: Type -> Type) (f :: Type -> Type). Tensor t i => t f f ~> Chain t i f
injectChain :: forall (t :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (i :: Type -> Type) (f :: Type -> Type). Tensor t i => f ~> Chain t i f
unconsChain :: forall {k1} {k2} (t :: k1 -> (k2 -> Type) -> k2 -> Type) (i :: k2 -> Type) (f :: k1) (x :: k2). Chain t i f x -> (i :+: t f (Chain t i f)) x
data Chain1 (t :: (k -> Type) -> (k -> Type) -> k -> Type) (f :: k -> Type) (a :: k)
- = Done1 (f a)
- | More1 (t f (Chain1 t f) a)
foldChain1 :: forall {k} (t :: (k -> Type) -> (k -> Type) -> k -> Type) (f :: k -> Type) (g :: k -> Type). HBifunctor t => (f ~> g) -> (t f g ~> g) -> Chain1 t f ~> g
foldChain1A :: forall {k} t h f g (a :: k). (HBifunctor t, Functor h) => (forall (x :: k). f x -> h (g x)) -> (forall (x :: k). t f (Comp h g) x -> h (g x)) -> Chain1 t f a -> h (g a)
unfoldChain1 :: forall (t :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (f :: Type -> Type) (g :: Type -> Type). HBifunctor t => (g ~> (f :+: t f g)) -> g ~> Chain1 t f
unrollingNE :: forall (t :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (f :: Type -> Type). (Associative t, FunctorBy t f) => NonEmptyBy t f <~> Chain1 t f
unrollNE :: forall (t :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (f :: Type -> Type). (Associative t, FunctorBy t f) => NonEmptyBy t f ~> Chain1 t f
rerollNE :: forall (t :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (f :: Type -> Type). Associative t => Chain1 t f ~> NonEmptyBy t f
appendChain1 :: forall (t :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (f :: Type -> Type). (Associative t, FunctorBy t f) => t (Chain1 t f) (Chain1 t f) ~> Chain1 t f
fromChain1 :: forall (t :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (i :: Type -> Type) (f :: Type -> Type). Tensor t i => Chain1 t f ~> Chain t i f
matchChain1 :: forall {k} (t :: (k -> Type) -> (k -> Type) -> k -> Type) (f :: k -> Type) (x :: k). Chain1 t f x -> (f :+: t f (Chain1 t f)) x
toChain1 :: forall {k} (t :: (k -> Type) -> (k -> Type) -> k -> Type) (f :: k -> Type). HBifunctor t => t f f ~> Chain1 t f
injectChain1 :: forall {k} f (t :: (k -> Type) -> (k -> Type) -> k -> Type) (x :: k). f x -> Chain1 t f x
splittingChain1 :: forall (t :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (i :: Type -> Type) (f :: Type -> Type). (Matchable t i, FunctorBy t f) => Chain1 t f <~> t f (Chain t i f)
splitChain1 :: forall (t :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (i :: Type -> Type) (f :: Type -> Type). Tensor t i => Chain1 t f ~> t f (Chain t i f)
matchingChain :: forall (t :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (i :: Type -> Type) (f :: Type -> Type). (Matchable t i, FunctorBy t f) => Chain t i f <~> (i :+: Chain1 t f)
unmatchChain :: forall (t :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (i :: Type -> Type) (f :: Type -> Type). Tensor t i => (i :+: Chain1 t f) ~> Chain t i f

`Chain`

data Chain (t :: k -> (k1 -> Type) -> k1 -> Type) (i :: k1 -> Type) (f :: k) (a :: k1) Source #

A useful construction that works like a "linked list" of t f applied to itself multiple times. That is, it contains t f f, t f (t f f), t f (t f (t f f)), etc, with f occuring zero or more times. It is meant to be the same as ListBy t.

If t is Tensor, then it means we can "collapse" this linked list into some final type ListBy t (reroll), and also extract it back into a linked list (unroll).

So, a value of type Chain t i f a is one of either:

```
i a
```
```
f a
```
```
t f f a
```
```
t f (t f f) a
```
```
t f (t f (t f f)) a
```
.. etc.

Note that this is exactly what an ListBy t is supposed to be. Using Chain allows us to work with all ListBy ts in a uniform way, with normal pattern matching and normal constructors.

You can fully "collapse" a Chain t i f into an f with retract, if you have MonoidIn t i f; this could be considered a fundamental property of monoid-ness.

Another way of thinking of this is that Chain t i is the "free MonoidIn t i". Given any functor f, Chain t i f is a monoid in the monoidal category of endofunctors enriched by t. So, Chain Comp Identity is the "free Monad", Chain Day Identity is the "free Applicative", etc. You "lift" from f a to Chain t i f a using inject.

Note: this instance doesn't exist directly because of restrictions in typeclasses, but is implemented as

Tensor t i => MonoidIn (WrapHBF t) (WrapF i) (Chain t i f)

where pureT is Done and biretract is appendChain.

This construction is inspired by http://oleg.fi/gists/posts/2018-02-21-single-free.html

Constructors

Done (i a)
More (t f (Chain t i f) a)

Instances

Instances details

HBifunctor t => HFunctor (Chain t i :: (k1 -> Type) -> k1 -> Type) Source #
Instance details Defined in Data.HFunctor.Chain.Internal Methods hmap :: forall (f :: k1 -> Type) (g :: k1 -> Type). (f ~> g) -> Chain t i f ~> Chain t i g Source #
Tensor t i => Inject (Chain t i :: (Type -> Type) -> Type -> Type) Source #
Instance details Defined in Data.HFunctor.Chain Methods inject :: forall (f :: Type -> Type). f ~> Chain t i f Source #
MonoidIn t i f => Interpret (Chain t i :: (Type -> Type) -> Type -> Type) (f :: Type -> Type) Source #	We can collapse and interpret an `Chain t i` if we have `Tensor t`.
Instance details Defined in Data.HFunctor.Chain Methods retract :: Chain t i f ~> f Source # interpret :: forall (g :: Type -> Type). (g ~> f) -> Chain t i g ~> f Source #
(Tensor t i, FunctorBy t (Chain t i f)) => MonoidIn (WrapHBF t) (WrapF i) (Chain t i f) Source #	`Chain t i` is the "free `MonoidIn t i`". However, we have to wrap `t` in `WrapHBF` and `i` in `WrapF` to prevent overlapping instances.
Instance details Defined in Data.HFunctor.Chain Methods pureT :: WrapF i ~> Chain t i f Source #
(Tensor t i, FunctorBy t (Chain t i f)) => SemigroupIn (WrapHBF t) (Chain t i f) Source #	We have to wrap `t` in `WrapHBF` to prevent overlapping instances.
Instance details Defined in Data.HFunctor.Chain Methods biretract :: WrapHBF t (Chain t i f) (Chain t i f) ~> Chain t i f Source # binterpret :: forall (g :: Type -> Type) (h :: Type -> Type). (g ~> Chain t i f) -> (h ~> Chain t i f) -> WrapHBF t g h ~> Chain t i f Source #
(Eq1 i, Eq1 (t f (Chain t i f))) => Eq1 (Chain t i f) Source #
Instance details Defined in Data.HFunctor.Chain.Internal Methods liftEq :: (a -> b -> Bool) -> Chain t i f a -> Chain t i f b -> Bool #
(Ord1 i, Ord1 (t f (Chain t i f))) => Ord1 (Chain t i f) Source #
Instance details Defined in Data.HFunctor.Chain.Internal Methods liftCompare :: (a -> b -> Ordering) -> Chain t i f a -> Chain t i f b -> Ordering #
(Functor i, Read1 (t f (Chain t i f)), Read1 i) => Read1 (Chain t i f) Source #
Instance details Defined in Data.HFunctor.Chain.Internal Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Chain t i f a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Chain t i f a] # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (Chain t i f a) # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [Chain t i f a] #
(Show1 (t f (Chain t i f)), Show1 i) => Show1 (Chain t i f) Source #
Instance details Defined in Data.HFunctor.Chain.Internal Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Chain t i f a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Chain t i f a] -> ShowS #
(Contravariant i, Contravariant (t f (Chain t i f))) => Contravariant (Chain t i f) Source #
Instance details Defined in Data.HFunctor.Chain.Internal Methods contramap :: (a' -> a) -> Chain t i f a -> Chain t i f a' # (>$) :: b -> Chain t i f b -> Chain t i f a #
Divisible (Chain Day (Proxy :: Type -> Type) f) Source #	`Chain Day Proxy` is the free "monoid in the monoidal category of endofunctors enriched by contravariant `Day`" --- aka, the free `Divisible`. Since: 0.3.0.0
Instance details Defined in Data.HFunctor.Chain Methods divide :: (a -> (b, c)) -> Chain Day (Proxy :: Type -> Type) f b -> Chain Day (Proxy :: Type -> Type) f c -> Chain Day (Proxy :: Type -> Type) f a # conquer :: Chain Day (Proxy :: Type -> Type) f a #
Conclude (Chain Night Not f) Source #	`Chain Night Refutec` is the free "monoid in the monoidal category of endofunctors enriched by `Night`" --- aka, the free `Conclude`. Since: 0.3.0.0
Instance details Defined in Data.HFunctor.Chain Methods conclude :: (a -> Void) -> Chain Night Not f a Source #
Decide (Chain Night Not f) Source #	Since: 0.3.0.0
Instance details Defined in Data.HFunctor.Chain Methods decide :: (a -> Either b c) -> Chain Night Not f b -> Chain Night Not f c -> Chain Night Not f a Source #
Divise (Chain Day (Proxy :: Type -> Type) f) Source #	Since: 0.3.0.0
Instance details Defined in Data.HFunctor.Chain Methods divise :: (a -> (b, c)) -> Chain Day (Proxy :: Type -> Type) f b -> Chain Day (Proxy :: Type -> Type) f c -> Chain Day (Proxy :: Type -> Type) f a Source # divised :: Chain Day (Proxy :: Type -> Type) f a -> Chain Day (Proxy :: Type -> Type) f b -> Chain Day (Proxy :: Type -> Type) f (a, b) Source #
Inplicative (Chain Day Identity f) Source #	Since: 0.4.0.0
Instance details Defined in Data.HFunctor.Chain Methods knot :: a -> Chain Day Identity f a Source #
Inply (Chain Day Identity f) Source #	Since: 0.4.0.0
Instance details Defined in Data.HFunctor.Chain Methods gather :: (b -> c -> a) -> (a -> (b, c)) -> Chain Day Identity f b -> Chain Day Identity f c -> Chain Day Identity f a Source # gathered :: Chain Day Identity f a -> Chain Day Identity f b -> Chain Day Identity f (a, b) Source #
Inalt (Chain Night Not f) Source #	Since: 0.4.0.0
Instance details Defined in Data.HFunctor.Chain Methods swerve :: (b -> a) -> (c -> a) -> (a -> Either b c) -> Chain Night Not f b -> Chain Night Not f c -> Chain Night Not f a Source # swerved :: Chain Night Not f a -> Chain Night Not f b -> Chain Night Not f (Either a b) Source #
Inplus (Chain Night Not f) Source #	Since: 0.4.0.0
Instance details Defined in Data.HFunctor.Chain Methods reject :: (a -> Void) -> Chain Night Not f a Source #
Applicative (Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f) Source #
Instance details Defined in Data.HFunctor.Chain Methods pure :: a -> Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f a # (<>) :: Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f (a -> b) -> Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f a -> Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f b # liftA2 :: (a -> b -> c) -> Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f a -> Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f b -> Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f c # (>) :: Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f a -> Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f b -> Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f b # (<*) :: Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f a -> Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f b -> Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f a #
Applicative (Chain Day Identity f) Source #	`Chain Day Identity` is the free "monoid in the monoidal category of endofunctors enriched by `Day`" --- aka, the free `Applicative`.
Instance details Defined in Data.HFunctor.Chain Methods pure :: a -> Chain Day Identity f a # (<>) :: Chain Day Identity f (a -> b) -> Chain Day Identity f a -> Chain Day Identity f b # liftA2 :: (a -> b -> c) -> Chain Day Identity f a -> Chain Day Identity f b -> Chain Day Identity f c # (>) :: Chain Day Identity f a -> Chain Day Identity f b -> Chain Day Identity f b # (<*) :: Chain Day Identity f a -> Chain Day Identity f b -> Chain Day Identity f a #
(Functor i, Functor (t f (Chain t i f))) => Functor (Chain t i f) Source #
Instance details Defined in Data.HFunctor.Chain.Internal Methods fmap :: (a -> b) -> Chain t i f a -> Chain t i f b # (<$) :: a -> Chain t i f b -> Chain t i f a #
Monad (Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f) Source #	`Chain Comp Identity` is the free "monoid in the monoidal category of endofunctors enriched by `Comp`" --- aka, the free `Monad`.
Instance details Defined in Data.HFunctor.Chain Methods (>>=) :: Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f a -> (a -> Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f b) -> Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f b # (>>) :: Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f a -> Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f b -> Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f b # return :: a -> Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f a #
(Foldable i, Foldable (t f (Chain t i f))) => Foldable (Chain t i f) Source #
Instance details Defined in Data.HFunctor.Chain.Internal Methods fold :: Monoid m => Chain t i f m -> m # foldMap :: Monoid m => (a -> m) -> Chain t i f a -> m # foldMap' :: Monoid m => (a -> m) -> Chain t i f a -> m # foldr :: (a -> b -> b) -> b -> Chain t i f a -> b # foldr' :: (a -> b -> b) -> b -> Chain t i f a -> b # foldl :: (b -> a -> b) -> b -> Chain t i f a -> b # foldl' :: (b -> a -> b) -> b -> Chain t i f a -> b # foldr1 :: (a -> a -> a) -> Chain t i f a -> a # foldl1 :: (a -> a -> a) -> Chain t i f a -> a # toList :: Chain t i f a -> [a] # null :: Chain t i f a -> Bool # length :: Chain t i f a -> Int # elem :: Eq a => a -> Chain t i f a -> Bool # maximum :: Ord a => Chain t i f a -> a # minimum :: Ord a => Chain t i f a -> a # sum :: Num a => Chain t i f a -> a # product :: Num a => Chain t i f a -> a #
(Traversable i, Traversable (t f (Chain t i f))) => Traversable (Chain t i f) Source #
Instance details Defined in Data.HFunctor.Chain.Internal Methods traverse :: Applicative f0 => (a -> f0 b) -> Chain t i f a -> f0 (Chain t i f b) # sequenceA :: Applicative f0 => Chain t i f (f0 a) -> f0 (Chain t i f a) # mapM :: Monad m => (a -> m b) -> Chain t i f a -> m (Chain t i f b) # sequence :: Monad m => Chain t i f (m a) -> m (Chain t i f a) #
(Invariant i, Invariant (t f (Chain t i f))) => Invariant (Chain t i f) Source #
Instance details Defined in Data.HFunctor.Chain.Internal Methods invmap :: (a -> b) -> (b -> a) -> Chain t i f a -> Chain t i f b #
Functor f => Alt (Chain (Product :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (Proxy :: Type -> Type) f) Source #
Instance details Defined in Data.HFunctor.Chain Methods (<!>) :: Chain (Product :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (Proxy :: Type -> Type) f a -> Chain (Product :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (Proxy :: Type -> Type) f a -> Chain (Product :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (Proxy :: Type -> Type) f a # some :: Applicative (Chain (Product :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (Proxy :: Type -> Type) f) => Chain (Product :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (Proxy :: Type -> Type) f a -> Chain (Product :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (Proxy :: Type -> Type) f [a] # many :: Applicative (Chain (Product :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (Proxy :: Type -> Type) f) => Chain (Product :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (Proxy :: Type -> Type) f a -> Chain (Product :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (Proxy :: Type -> Type) f [a] #
Functor f => Alt (Chain ((:*:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (Proxy :: Type -> Type) f) Source #
Instance details Defined in Data.HFunctor.Chain Methods (<!>) :: Chain ((::) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (Proxy :: Type -> Type) f a -> Chain ((::) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (Proxy :: Type -> Type) f a -> Chain ((::) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (Proxy :: Type -> Type) f a # some :: Applicative (Chain ((::) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (Proxy :: Type -> Type) f) => Chain ((::) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (Proxy :: Type -> Type) f a -> Chain ((::) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (Proxy :: Type -> Type) f [a] # many :: Applicative (Chain ((::) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (Proxy :: Type -> Type) f) => Chain ((::) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (Proxy :: Type -> Type) f a -> Chain ((:*:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (Proxy :: Type -> Type) f [a] #
Apply (Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f) Source #
Instance details Defined in Data.HFunctor.Chain Methods (<.>) :: Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f (a -> b) -> Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f a -> Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f b # (.>) :: Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f a -> Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f b -> Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f b # (<.) :: Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f a -> Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f b -> Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f a # liftF2 :: (a -> b -> c) -> Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f a -> Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f b -> Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f c #
Apply (Chain Day Identity f) Source #
Instance details Defined in Data.HFunctor.Chain Methods (<.>) :: Chain Day Identity f (a -> b) -> Chain Day Identity f a -> Chain Day Identity f b # (.>) :: Chain Day Identity f a -> Chain Day Identity f b -> Chain Day Identity f b # (<.) :: Chain Day Identity f a -> Chain Day Identity f b -> Chain Day Identity f a # liftF2 :: (a -> b -> c) -> Chain Day Identity f a -> Chain Day Identity f b -> Chain Day Identity f c #
Bind (Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f) Source #
Instance details Defined in Data.HFunctor.Chain Methods (>>-) :: Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f a -> (a -> Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f b) -> Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f b # join :: Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f (Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f a) -> Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f a #
Functor f => Plus (Chain (Product :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (Proxy :: Type -> Type) f) Source #	`Chain (::) Proxy` is the free "monoid in the monoidal category of endofunctors enriched by `::`" --- aka, the free `Plus`.
Instance details Defined in Data.HFunctor.Chain Methods zero :: Chain (Product :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (Proxy :: Type -> Type) f a #
Functor f => Plus (Chain ((:*:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (Proxy :: Type -> Type) f) Source #	`Chain (::) Proxy` is the free "monoid in the monoidal category of endofunctors enriched by `::`" --- aka, the free `Plus`.
Instance details Defined in Data.HFunctor.Chain Methods zero :: Chain ((:*:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (Proxy :: Type -> Type) f a #
(Read (i a), Read (t f (Chain t i f) a)) => Read (Chain t i f a) Source #
Instance details Defined in Data.HFunctor.Chain.Internal Methods readsPrec :: Int -> ReadS (Chain t i f a) # readList :: ReadS [Chain t i f a] # readPrec :: ReadPrec (Chain t i f a) # readListPrec :: ReadPrec [Chain t i f a] #
(Show (i a), Show (t f (Chain t i f) a)) => Show (Chain t i f a) Source #
Instance details Defined in Data.HFunctor.Chain.Internal Methods showsPrec :: Int -> Chain t i f a -> ShowS # show :: Chain t i f a -> String # showList :: [Chain t i f a] -> ShowS #
(Eq (i a), Eq (t f (Chain t i f) a)) => Eq (Chain t i f a) Source #
Instance details Defined in Data.HFunctor.Chain.Internal Methods (==) :: Chain t i f a -> Chain t i f a -> Bool # (/=) :: Chain t i f a -> Chain t i f a -> Bool #
(Ord (i a), Ord (t f (Chain t i f) a)) => Ord (Chain t i f a) Source #
Instance details Defined in Data.HFunctor.Chain.Internal Methods compare :: Chain t i f a -> Chain t i f a -> Ordering # (<) :: Chain t i f a -> Chain t i f a -> Bool # (<=) :: Chain t i f a -> Chain t i f a -> Bool # (>) :: Chain t i f a -> Chain t i f a -> Bool # (>=) :: Chain t i f a -> Chain t i f a -> Bool # max :: Chain t i f a -> Chain t i f a -> Chain t i f a # min :: Chain t i f a -> Chain t i f a -> Chain t i f a #

foldChain Source #

Arguments

:: forall {k} (t :: (k -> Type) -> (k -> Type) -> k -> Type) (i :: k -> Type) (f :: k -> Type) (g :: k -> Type). HBifunctor t
=> (i ~> g)	Handle `Done`
-> (t f g ~> g)	Handle `More`
-> Chain t i f ~> g

Recursively fold down a Chain. Provide a function on how to handle the "single f case" (nilLB), and how to handle the "combined t f g case", and this will fold the entire Chain t i) f into a single g.

This is a catamorphism.

foldChainA Source #

Arguments

:: forall {k} t h i g (f :: k -> Type) (a :: k). (HBifunctor t, Functor h)
=> (forall (x :: k). i x -> h (g x))	Handle `Done`
-> (forall (x :: k). t f (Comp h g) x -> h (g x))	Handle `More`
-> Chain t i f a
-> h (g a)

An "effectful" version of foldChain, weaving Applicative effects.

Since: 0.3.6.0

unfoldChain :: forall (t :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (f :: Type -> Type) (g :: Type -> Type) (i :: Type -> Type). HBifunctor t => (g ~> (i :+: t f g)) -> g ~> Chain t i f Source #

Recursively build up a Chain. Provide a function that takes some starting seed g and returns either "done" (i) or "continue further" (t f g), and it will create a Chain t i f from a g.

This is an anamorphism.

unroll :: forall (t :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (i :: Type -> Type) (f :: Type -> Type). Tensor t i => ListBy t f ~> Chain t i f Source #

A type ListBy t is supposed to represent the successive application of ts to itself. unroll makes that successive application explicit, buy converting it to a literal Chain of applications of t to itself.

unroll = unfoldChain unconsLB

reroll :: forall (t :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (i :: Type -> Type) (f :: Type -> Type). Tensor t i => Chain t i f ~> ListBy t f Source #

A type ListBy t is supposed to represent the successive application of ts to itself. rerollNE takes an explicit Chain of applications of t to itself and rolls it back up into an ListBy t.

reroll = foldChain nilLB consLB

Because t cannot be inferred from the input or output, you should call this with -XTypeApplications:

reroll @Comp
    :: Chain Comp Identity f a -> Free f a

unrolling :: forall (t :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (i :: Type -> Type) (f :: Type -> Type). Tensor t i => ListBy t f <~> Chain t i f Source #

A type ListBy t is supposed to represent the successive application of ts to itself. The type Chain t i f is an actual concrete ADT that contains successive applications of t to itself, and you can pattern match on each layer.

unrolling states that the two types are isormorphic. Use unroll and reroll to convert between the two.

appendChain :: forall (t :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (i :: Type -> Type) (f :: Type -> Type). Tensor t i => t (Chain t i f) (Chain t i f) ~> Chain t i f Source #

Chain is a monoid with respect to t: we can "combine" them in an associative way. The identity here is anything made with the Done constructor.

This is essentially biretract, but only requiring Tensor t i: it comes from the fact that Chain1 t i is the "free MonoidIn t i". pureT is Done.

Since: 0.1.1.0

splittingChain :: forall {k1} {k2} (t :: k1 -> (k2 -> Type) -> k2 -> Type) (i :: k2 -> Type) (f :: k1) p (a :: k2). Profunctor p => p ((i :+: t f (Chain t i f)) a) ((i :+: t f (Chain t i f)) a) -> p (Chain t i f a) (Chain t i f a) Source #

For completeness, an isomorphism between Chain and its two constructors, to match splittingLB.

Since: 0.3.0.0

toChain :: forall (t :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (i :: Type -> Type) (f :: Type -> Type). Tensor t i => t f f ~> Chain t i f Source #

Convert a tensor value pairing two fs into a two-item Chain. An analogue of toListBy.

Since: 0.3.1.0

injectChain :: forall (t :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (i :: Type -> Type) (f :: Type -> Type). Tensor t i => f ~> Chain t i f Source #

Create a singleton chain.

Since: 0.3.0.0

unconsChain :: forall {k1} {k2} (t :: k1 -> (k2 -> Type) -> k2 -> Type) (i :: k2 -> Type) (f :: k1) (x :: k2). Chain t i f x -> (i :+: t f (Chain t i f)) x Source #

An analogue of unconsLB: match one of the two constructors of a Chain.

Since: 0.3.0.0

`Chain1`

data Chain1 (t :: (k -> Type) -> (k -> Type) -> k -> Type) (f :: k -> Type) (a :: k) Source #

A useful construction that works like a "non-empty linked list" of t f applied to itself multiple times. That is, it contains t f f, t f (t f f), t f (t f (t f f)), etc, with f occuring one or more times. It is meant to be the same as NonEmptyBy t.

A Chain1 t f a is explicitly one of:

```
f a
```
```
t f f a
```
```
t f (t f f) a
```
```
t f (t f (t f f)) a
```
.. etc

Note that this is exactly the description of NonEmptyBy t. And that's "the point": for all instances of Associative, Chain1 t is isomorphic to NonEmptyBy t (witnessed by unrollingNE). That's big picture of NonEmptyBy: it's supposed to be a type that consists of all possible self-applications of f to t.

Chain1 gives you a way to work with all NonEmptyBy t in a uniform way. Unlike for NonEmptyBy t f in general, you can always explicitly /pattern match/ on a Chain1 (with its two constructors) and do what you please with it. You can also construct Chain1 using normal constructors and functions.

You can convert in between NonEmptyBy t f and Chain1 t f with unrollNE and rerollNE. You can fully "collapse" a Chain1 t f into an f with retract, if you have SemigroupIn t f; this could be considered a fundamental property of semigroup-ness.

See Chain for a version that has an "empty" value.

Another way of thinking of this is that Chain1 t is the "free SemigroupIn t". Given any functor f, Chain1 t f is a semigroup in the semigroupoidal category of endofunctors enriched by t. So, Chain1 Comp is the "free Bind", Chain1 Day is the "free Apply", etc. You "lift" from f a to Chain1 t f a using inject.

Note: this instance doesn't exist directly because of restrictions in typeclasses, but is implemented as

Associative t => SemigroupIn (WrapHBF t) (Chain1 t f)

where biretract is appendChain1.

You can fully "collapse" a Chain t i f into an f with retract, if you have MonoidIn t i f; this could be considered a fundamental property of monoid-ness.

This construction is inspired by iteratees and machines.

Constructors

Done1 (f a)
More1 (t f (Chain1 t f) a)

Instances

Instances details

HBifunctor t => HFunctor (Chain1 t :: (k1 -> Type) -> k1 -> Type) Source #

Instance details

:: forall {k} (t :: (k -> Type) -> (k -> Type) -> k -> Type) (f :: k -> Type) (g :: k -> Type). HBifunctor t
=> (f ~> g)	handle `Done1`
-> (t f g ~> g)	handle `More1`
-> Chain1 t f ~> g

:: forall {k} t h f g (a :: k). (HBifunctor t, Functor h)
=> (forall (x :: k). f x -> h (g x))	handle `Done1`
-> (forall (x :: k). t f (Comp h g) x -> h (g x))	handle `More1`
-> Chain1 t f a
-> h (g a)

SemigroupIn t f => Interpret (Chain1 t :: (Type -> Type) -> Type -> Type) (f :: Type -> Type) Source #
Instance details Methods retract :: Chain1 t f ~> f Source # interpret :: forall (g :: Type -> Type). (g ~> f) -> Chain1 t g ~> f Source #
Tensor t i => Inject (Chain t i :: (Type -> Type) -> Type -> Type) Source #
Instance details Methods inject :: forall (f :: Type -> Type). f ~> Chain t i f Source #
MonoidIn t i f => Interpret (Chain t i :: (Type -> Type) -> Type -> Type) (f :: Type -> Type) Source #	We can collapse and interpret an `Chain t i` if we have `Tensor t`.
Instance details Methods retract :: Chain t i f ~> f Source # interpret :: forall (g :: Type -> Type). (g ~> f) -> Chain t i g ~> f Source #
Contravariant f => Decide (Chain1 Night f) Source #	`Chain1 Night` is the free "semigroup in the semigroupoidal category of endofunctors enriched by `Night`" --- aka, the free `Decide`. Since: 0.3.0.0
Instance details Methods decide :: (a -> Either b c) -> Chain1 Night f b -> Chain1 Night f c -> Chain1 Night f a Source #
Contravariant f => Divise (Chain1 Day f) Source #	`Chain1 Day` is the free "semigroup in the semigroupoidal category of endofunctors enriched by `Day`" --- aka, the free `Divise`. Since: 0.3.0.0
Instance details Methods divise :: (a -> (b, c)) -> Chain1 Day f b -> Chain1 Day f c -> Chain1 Day f a Source # divised :: Chain1 Day f a -> Chain1 Day f b -> Chain1 Day f (a, b) Source #
Invariant f => Inply (Chain1 Day f) Source #	Since: 0.4.0.0
Instance details Methods gather :: (b -> c -> a) -> (a -> (b, c)) -> Chain1 Day f b -> Chain1 Day f c -> Chain1 Day f a Source # gathered :: Chain1 Day f a -> Chain1 Day f b -> Chain1 Day f (a, b) Source #
Invariant f => Inalt (Chain1 Night f) Source #	Since: 0.4.0.0
Instance details Methods swerve :: (b -> a) -> (c -> a) -> (a -> Either b c) -> Chain1 Night f b -> Chain1 Night f c -> Chain1 Night f a Source # swerved :: Chain1 Night f a -> Chain1 Night f b -> Chain1 Night f (Either a b) Source #
Functor f => Alt (Chain1 (Product :: (Type -> Type) -> (Type -> Type) -> Type -> Type) f) Source #	`Chain1 Product` is the free "semigroup in the semigroupoidal category of endofunctors enriched by `Product`" --- aka, the free `Alt`.
Instance details Methods (<!>) :: Chain1 (Product :: (Type -> Type) -> (Type -> Type) -> Type -> Type) f a -> Chain1 (Product :: (Type -> Type) -> (Type -> Type) -> Type -> Type) f a -> Chain1 (Product :: (Type -> Type) -> (Type -> Type) -> Type -> Type) f a # some :: Applicative (Chain1 (Product :: (Type -> Type) -> (Type -> Type) -> Type -> Type) f) => Chain1 (Product :: (Type -> Type) -> (Type -> Type) -> Type -> Type) f a -> Chain1 (Product :: (Type -> Type) -> (Type -> Type) -> Type -> Type) f [a] # many :: Applicative (Chain1 (Product :: (Type -> Type) -> (Type -> Type) -> Type -> Type) f) => Chain1 (Product :: (Type -> Type) -> (Type -> Type) -> Type -> Type) f a -> Chain1 (Product :: (Type -> Type) -> (Type -> Type) -> Type -> Type) f [a] #
Functor f => Alt (Chain1 ((:*:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) f) Source #	`Chain1 (::)` is the free "semigroup in the semigroupoidal category of endofunctors enriched by `::`" --- aka, the free `Alt`.
Instance details Methods (<!>) :: Chain1 ((::) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) f a -> Chain1 ((::) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) f a -> Chain1 ((::) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) f a # some :: Applicative (Chain1 ((::) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) f) => Chain1 ((::) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) f a -> Chain1 ((::) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) f [a] # many :: Applicative (Chain1 ((::) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) f) => Chain1 ((::) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) f a -> Chain1 ((:*:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) f [a] #
Functor f => Apply (Chain1 (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) f) Source #
Instance details Methods (<.>) :: Chain1 (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) f (a -> b) -> Chain1 (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) f a -> Chain1 (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) f b # (.>) :: Chain1 (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) f a -> Chain1 (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) f b -> Chain1 (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) f b # (<.) :: Chain1 (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) f a -> Chain1 (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) f b -> Chain1 (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) f a # liftF2 :: (a -> b -> c) -> Chain1 (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) f a -> Chain1 (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) f b -> Chain1 (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) f c #
Functor f => Apply (Chain1 Day f) Source #	`Chain1 Day` is the free "semigroup in the semigroupoidal category of endofunctors enriched by `Day`" --- aka, the free `Apply`.
Instance details Methods (<.>) :: Chain1 Day f (a -> b) -> Chain1 Day f a -> Chain1 Day f b # (.>) :: Chain1 Day f a -> Chain1 Day f b -> Chain1 Day f b # (<.) :: Chain1 Day f a -> Chain1 Day f b -> Chain1 Day f a # liftF2 :: (a -> b -> c) -> Chain1 Day f a -> Chain1 Day f b -> Chain1 Day f c #
Functor f => Bind (Chain1 (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) f) Source #	`Chain1 Comp` is the free "semigroup in the semigroupoidal category of endofunctors enriched by `Comp`" --- aka, the free `Bind`.
Instance details Methods (>>-) :: Chain1 (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) f a -> (a -> Chain1 (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) f b) -> Chain1 (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) f b # join :: Chain1 (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) f (Chain1 (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) f a) -> Chain1 (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) f a #
(Tensor t i, FunctorBy t (Chain t i f)) => MonoidIn (WrapHBF t) (WrapF i) (Chain t i f) Source #	`Chain t i` is the "free `MonoidIn t i`". However, we have to wrap `t` in `WrapHBF` and `i` in `WrapF` to prevent overlapping instances.
Instance details Methods pureT :: WrapF i ~> Chain t i f Source #
(Associative t, FunctorBy t f, FunctorBy t (Chain1 t f)) => SemigroupIn (WrapHBF t) (Chain1 t f) Source #	`Chain1 t` is the "free `SemigroupIn t`". However, we have to wrap `t` in `WrapHBF` to prevent overlapping instances.
Instance details Methods biretract :: WrapHBF t (Chain1 t f) (Chain1 t f) ~> Chain1 t f Source # binterpret :: forall (g :: Type -> Type) (h :: Type -> Type). (g ~> Chain1 t f) -> (h ~> Chain1 t f) -> WrapHBF t g h ~> Chain1 t f Source #
(Tensor t i, FunctorBy t (Chain t i f)) => SemigroupIn (WrapHBF t) (Chain t i f) Source #	We have to wrap `t` in `WrapHBF` to prevent overlapping instances.
Instance details Methods biretract :: WrapHBF t (Chain t i f) (Chain t i f) ~> Chain t i f Source # binterpret :: forall (g :: Type -> Type) (h :: Type -> Type). (g ~> Chain t i f) -> (h ~> Chain t i f) -> WrapHBF t g h ~> Chain t i f Source #
Divisible (Chain Day (Proxy :: Type -> Type) f) Source #	`Chain Day Proxy` is the free "monoid in the monoidal category of endofunctors enriched by contravariant `Day`" --- aka, the free `Divisible`. Since: 0.3.0.0
Instance details Methods divide :: (a -> (b, c)) -> Chain Day (Proxy :: Type -> Type) f b -> Chain Day (Proxy :: Type -> Type) f c -> Chain Day (Proxy :: Type -> Type) f a # conquer :: Chain Day (Proxy :: Type -> Type) f a #
Conclude (Chain Night Not f) Source #	`Chain Night Refutec` is the free "monoid in the monoidal category of endofunctors enriched by `Night`" --- aka, the free `Conclude`. Since: 0.3.0.0
Instance details Methods conclude :: (a -> Void) -> Chain Night Not f a Source #
Decide (Chain Night Not f) Source #	Since: 0.3.0.0
Instance details Methods decide :: (a -> Either b c) -> Chain Night Not f b -> Chain Night Not f c -> Chain Night Not f a Source #
Divise (Chain Day (Proxy :: Type -> Type) f) Source #	Since: 0.3.0.0
Instance details Methods divise :: (a -> (b, c)) -> Chain Day (Proxy :: Type -> Type) f b -> Chain Day (Proxy :: Type -> Type) f c -> Chain Day (Proxy :: Type -> Type) f a Source # divised :: Chain Day (Proxy :: Type -> Type) f a -> Chain Day (Proxy :: Type -> Type) f b -> Chain Day (Proxy :: Type -> Type) f (a, b) Source #
Inplicative (Chain Day Identity f) Source #	Since: 0.4.0.0
Instance details Methods knot :: a -> Chain Day Identity f a Source #
Inply (Chain Day Identity f) Source #	Since: 0.4.0.0
Instance details Methods gather :: (b -> c -> a) -> (a -> (b, c)) -> Chain Day Identity f b -> Chain Day Identity f c -> Chain Day Identity f a Source # gathered :: Chain Day Identity f a -> Chain Day Identity f b -> Chain Day Identity f (a, b) Source #
Inalt (Chain Night Not f) Source #	Since: 0.4.0.0
Instance details Methods swerve :: (b -> a) -> (c -> a) -> (a -> Either b c) -> Chain Night Not f b -> Chain Night Not f c -> Chain Night Not f a Source # swerved :: Chain Night Not f a -> Chain Night Not f b -> Chain Night Not f (Either a b) Source #
Inplus (Chain Night Not f) Source #	Since: 0.4.0.0
Instance details Methods reject :: (a -> Void) -> Chain Night Not f a Source #
Applicative (Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f) Source #
Instance details Methods pure :: a -> Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f a # (<>) :: Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f (a -> b) -> Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f a -> Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f b # liftA2 :: (a -> b -> c) -> Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f a -> Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f b -> Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f c # (>) :: Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f a -> Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f b -> Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f b # (<*) :: Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f a -> Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f b -> Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f a #
Applicative (Chain Day Identity f) Source #	`Chain Day Identity` is the free "monoid in the monoidal category of endofunctors enriched by `Day`" --- aka, the free `Applicative`.
Instance details Methods pure :: a -> Chain Day Identity f a # (<>) :: Chain Day Identity f (a -> b) -> Chain Day Identity f a -> Chain Day Identity f b # liftA2 :: (a -> b -> c) -> Chain Day Identity f a -> Chain Day Identity f b -> Chain Day Identity f c # (>) :: Chain Day Identity f a -> Chain Day Identity f b -> Chain Day Identity f b # (<*) :: Chain Day Identity f a -> Chain Day Identity f b -> Chain Day Identity f a #
Monad (Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f) Source #	`Chain Comp Identity` is the free "monoid in the monoidal category of endofunctors enriched by `Comp`" --- aka, the free `Monad`.
Instance details Methods (>>=) :: Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f a -> (a -> Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f b) -> Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f b # (>>) :: Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f a -> Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f b -> Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f b # return :: a -> Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f a #
Functor f => Alt (Chain (Product :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (Proxy :: Type -> Type) f) Source #
Instance details Methods (<!>) :: Chain (Product :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (Proxy :: Type -> Type) f a -> Chain (Product :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (Proxy :: Type -> Type) f a -> Chain (Product :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (Proxy :: Type -> Type) f a # some :: Applicative (Chain (Product :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (Proxy :: Type -> Type) f) => Chain (Product :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (Proxy :: Type -> Type) f a -> Chain (Product :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (Proxy :: Type -> Type) f [a] # many :: Applicative (Chain (Product :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (Proxy :: Type -> Type) f) => Chain (Product :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (Proxy :: Type -> Type) f a -> Chain (Product :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (Proxy :: Type -> Type) f [a] #
Functor f => Alt (Chain ((:*:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (Proxy :: Type -> Type) f) Source #
Instance details Methods (<!>) :: Chain ((::) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (Proxy :: Type -> Type) f a -> Chain ((::) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (Proxy :: Type -> Type) f a -> Chain ((::) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (Proxy :: Type -> Type) f a # some :: Applicative (Chain ((::) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (Proxy :: Type -> Type) f) => Chain ((::) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (Proxy :: Type -> Type) f a -> Chain ((::) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (Proxy :: Type -> Type) f [a] # many :: Applicative (Chain ((::) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (Proxy :: Type -> Type) f) => Chain ((::) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (Proxy :: Type -> Type) f a -> Chain ((:*:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (Proxy :: Type -> Type) f [a] #
Apply (Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f) Source #
Instance details Methods (<.>) :: Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f (a -> b) -> Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f a -> Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f b # (.>) :: Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f a -> Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f b -> Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f b # (<.) :: Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f a -> Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f b -> Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f a # liftF2 :: (a -> b -> c) -> Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f a -> Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f b -> Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f c #
Apply (Chain Day Identity f) Source #
Instance details Methods (<.>) :: Chain Day Identity f (a -> b) -> Chain Day Identity f a -> Chain Day Identity f b # (.>) :: Chain Day Identity f a -> Chain Day Identity f b -> Chain Day Identity f b # (<.) :: Chain Day Identity f a -> Chain Day Identity f b -> Chain Day Identity f a # liftF2 :: (a -> b -> c) -> Chain Day Identity f a -> Chain Day Identity f b -> Chain Day Identity f c #
Bind (Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f) Source #
Instance details Methods (>>-) :: Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f a -> (a -> Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f b) -> Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f b # join :: Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f (Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f a) -> Chain (Comp :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Identity f a #
Functor f => Plus (Chain (Product :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (Proxy :: Type -> Type) f) Source #	`Chain (::) Proxy` is the free "monoid in the monoidal category of endofunctors enriched by `::`" --- aka, the free `Plus`.
Instance details Methods zero :: Chain (Product :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (Proxy :: Type -> Type) f a #
Functor f => Plus (Chain ((:*:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (Proxy :: Type -> Type) f) Source #	`Chain (::) Proxy` is the free "monoid in the monoidal category of endofunctors enriched by `::`" --- aka, the free `Plus`.
Instance details Methods zero :: Chain ((:*:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (Proxy :: Type -> Type) f a #

Chain

Instances

Chain1

Instances

Matchable

Orphan instances

`Chain`

`Chain1`