-- Hoogle documentation, generated by Haddock
-- See Hoogle, http://www.haskell.org/hoogle/
-- | Semigroupoids: Category sans id
--
-- Provides a wide array of (semi)groupoids and operations for working
-- with them.
--
-- A Semigroupoid is a Category without the requirement of
-- identity arrows for every object in the category.
--
-- A Category is any Semigroupoid for which the Yoneda
-- lemma holds.
--
-- When working with comonads you often have the <*>
-- portion of an Applicative, but not the pure. This
-- was captured in Uustalu and Vene's "Essence of Dataflow Programming"
-- in the form of the ComonadZip class in the days before
-- Applicative. Apply provides a weaker invariant, but for the
-- comonads used for data flow programming (found in the streams
-- package), this invariant is preserved. Applicative function
-- composition forms a semigroupoid.
--
-- Similarly many structures are nearly a comonad, but not quite, for
-- instance lists provide a reasonable extend operation in the
-- form of tails, but do not always contain a value.
--
-- Ideally the following relationships would hold:
--
--
-- Foldable ----> Traversable <--- Functor ------> Alt ---------> Plus Semigroupoid
-- | | | | |
-- v v v v v
-- Foldable1 ---> Traversable1 Apply --------> Applicative -> Alternative Category
-- | | | |
-- v v v v
-- Bind ---------> Monad -------> MonadPlus Arrow
--
--
-- Apply, Bind, and Extend (not shown) give rise the Static, Kleisli and
-- Cokleisli semigroupoids respectively.
--
-- This lets us remove many of the restrictions from various monad
-- transformers as in many cases the binding operation or
-- <*> operation does not require them.
--
-- Finally, to work with these weaker structures it is beneficial to have
-- containers that can provide stronger guarantees about their contents,
-- so versions of Traversable and Foldable that can be
-- folded with just a Semigroup are added.
@package semigroupoids
@version 5.2
-- | Re-exports from the `base-orphans` and `transformers-compat` packages.
module Data.Traversable.Instances
module Data.Semigroup.Foldable.Class
class Foldable t => Foldable1 t where foldMap1 f = maybe (error "foldMap1") id . getOption . foldMap (Option . Just . f) fold1 = foldMap1 id
fold1 :: (Foldable1 t, Semigroup m) => t m -> m
foldMap1 :: (Foldable1 t, Semigroup m) => (a -> m) -> t a -> m
class Bifoldable t => Bifoldable1 t where bifold1 = bifoldMap1 id id bifoldMap1 f g = maybe (error "bifoldMap1") id . getOption . bifoldMap (Option . Just . f) (Option . Just . g)
bifold1 :: (Bifoldable1 t, Semigroup m) => t m m -> m
bifoldMap1 :: (Bifoldable1 t, Semigroup m) => (a -> m) -> (b -> m) -> t a b -> m
instance Data.Semigroup.Foldable.Class.Foldable1 f => Data.Semigroup.Foldable.Class.Foldable1 (GHC.Generics.Rec1 f)
instance Data.Semigroup.Foldable.Class.Foldable1 f => Data.Semigroup.Foldable.Class.Foldable1 (GHC.Generics.M1 i c f)
instance Data.Semigroup.Foldable.Class.Foldable1 GHC.Generics.Par1
instance (Data.Semigroup.Foldable.Class.Foldable1 f, Data.Semigroup.Foldable.Class.Foldable1 g) => Data.Semigroup.Foldable.Class.Foldable1 (f GHC.Generics.:*: g)
instance (Data.Semigroup.Foldable.Class.Foldable1 f, Data.Semigroup.Foldable.Class.Foldable1 g) => Data.Semigroup.Foldable.Class.Foldable1 (f GHC.Generics.:+: g)
instance Data.Semigroup.Foldable.Class.Foldable1 GHC.Generics.V1
instance (Data.Semigroup.Foldable.Class.Foldable1 f, Data.Semigroup.Foldable.Class.Foldable1 g) => Data.Semigroup.Foldable.Class.Foldable1 (f GHC.Generics.:.: g)
instance Data.Semigroup.Foldable.Class.Bifoldable1 Data.Semigroup.Arg
instance Data.Semigroup.Foldable.Class.Bifoldable1 Data.Either.Either
instance Data.Semigroup.Foldable.Class.Bifoldable1 (,)
instance Data.Semigroup.Foldable.Class.Bifoldable1 ((,,) x)
instance Data.Semigroup.Foldable.Class.Bifoldable1 ((,,,) x y)
instance Data.Semigroup.Foldable.Class.Bifoldable1 ((,,,,) x y z)
instance Data.Semigroup.Foldable.Class.Bifoldable1 Data.Functor.Const.Const
instance Data.Semigroup.Foldable.Class.Bifoldable1 Data.Tagged.Tagged
instance (Data.Semigroup.Foldable.Class.Bifoldable1 p, Data.Semigroup.Foldable.Class.Foldable1 f, Data.Semigroup.Foldable.Class.Foldable1 g) => Data.Semigroup.Foldable.Class.Bifoldable1 (Data.Bifunctor.Biff.Biff p f g)
instance Data.Semigroup.Foldable.Class.Foldable1 f => Data.Semigroup.Foldable.Class.Bifoldable1 (Data.Bifunctor.Clown.Clown f)
instance Data.Semigroup.Foldable.Class.Bifoldable1 p => Data.Semigroup.Foldable.Class.Bifoldable1 (Data.Bifunctor.Flip.Flip p)
instance Data.Semigroup.Foldable.Class.Bifoldable1 p => Data.Semigroup.Foldable.Class.Foldable1 (Data.Bifunctor.Join.Join p)
instance Data.Semigroup.Foldable.Class.Foldable1 g => Data.Semigroup.Foldable.Class.Bifoldable1 (Data.Bifunctor.Joker.Joker g)
instance (Data.Semigroup.Foldable.Class.Bifoldable1 f, Data.Semigroup.Foldable.Class.Bifoldable1 g) => Data.Semigroup.Foldable.Class.Bifoldable1 (Data.Bifunctor.Product.Product f g)
instance (Data.Semigroup.Foldable.Class.Foldable1 f, Data.Semigroup.Foldable.Class.Bifoldable1 p) => Data.Semigroup.Foldable.Class.Bifoldable1 (Data.Bifunctor.Tannen.Tannen f p)
instance Data.Semigroup.Foldable.Class.Bifoldable1 p => Data.Semigroup.Foldable.Class.Bifoldable1 (Data.Bifunctor.Wrapped.WrappedBifunctor p)
instance Data.Semigroup.Foldable.Class.Foldable1 Data.Tree.Tree
instance Data.Semigroup.Foldable.Class.Foldable1 Data.Functor.Identity.Identity
instance Data.Semigroup.Foldable.Class.Foldable1 (Data.Tagged.Tagged a)
instance Data.Semigroup.Foldable.Class.Foldable1 m => Data.Semigroup.Foldable.Class.Foldable1 (Control.Monad.Trans.Identity.IdentityT m)
instance Data.Semigroup.Foldable.Class.Foldable1 f => Data.Semigroup.Foldable.Class.Foldable1 (Control.Applicative.Backwards.Backwards f)
instance (Data.Semigroup.Foldable.Class.Foldable1 f, Data.Semigroup.Foldable.Class.Foldable1 g) => Data.Semigroup.Foldable.Class.Foldable1 (Data.Functor.Compose.Compose f g)
instance Data.Semigroup.Foldable.Class.Foldable1 f => Data.Semigroup.Foldable.Class.Foldable1 (Control.Applicative.Lift.Lift f)
instance (Data.Semigroup.Foldable.Class.Foldable1 f, Data.Semigroup.Foldable.Class.Foldable1 g) => Data.Semigroup.Foldable.Class.Foldable1 (Data.Functor.Product.Product f g)
instance Data.Semigroup.Foldable.Class.Foldable1 f => Data.Semigroup.Foldable.Class.Foldable1 (Data.Functor.Reverse.Reverse f)
instance (Data.Semigroup.Foldable.Class.Foldable1 f, Data.Semigroup.Foldable.Class.Foldable1 g) => Data.Semigroup.Foldable.Class.Foldable1 (Data.Functor.Sum.Sum f g)
instance Data.Semigroup.Foldable.Class.Foldable1 Data.List.NonEmpty.NonEmpty
instance Data.Semigroup.Foldable.Class.Foldable1 ((,) a)
instance Data.Semigroup.Foldable.Class.Foldable1 g => Data.Semigroup.Foldable.Class.Foldable1 (Data.Bifunctor.Joker.Joker g a)
module Data.Functor.Extend
class Functor w => Extend w where extended f = fmap f . duplicated duplicated = extended id
-- |
-- duplicated = extended id
-- fmap (fmap f) . duplicated = duplicated . fmap f
--
duplicated :: Extend w => w a -> w (w a)
-- |
-- extended f = fmap f . duplicated
--
extended :: Extend w => (w a -> b) -> w a -> w b
instance Data.Functor.Extend.Extend []
instance Data.Functor.Extend.Extend (Data.Tagged.Tagged a)
instance Data.Functor.Extend.Extend Data.Proxy.Proxy
instance Data.Functor.Extend.Extend GHC.Base.Maybe
instance Data.Functor.Extend.Extend (Data.Either.Either a)
instance Data.Functor.Extend.Extend ((,) e)
instance Data.Semigroup.Semigroup m => Data.Functor.Extend.Extend ((->) m)
instance Data.Functor.Extend.Extend Data.Sequence.Seq
instance Data.Functor.Extend.Extend Data.Tree.Tree
instance Data.Functor.Extend.Extend w => Data.Functor.Extend.Extend (Control.Comonad.Trans.Env.EnvT e w)
instance Data.Functor.Extend.Extend w => Data.Functor.Extend.Extend (Control.Comonad.Trans.Store.StoreT s w)
instance (Data.Functor.Extend.Extend w, Data.Semigroup.Semigroup m) => Data.Functor.Extend.Extend (Control.Comonad.Trans.Traced.TracedT m w)
instance Data.Functor.Extend.Extend Data.Functor.Identity.Identity
instance Data.Functor.Extend.Extend w => Data.Functor.Extend.Extend (Control.Monad.Trans.Identity.IdentityT w)
instance Data.Functor.Extend.Extend Data.List.NonEmpty.NonEmpty
instance (Data.Functor.Extend.Extend f, Data.Functor.Extend.Extend g) => Data.Functor.Extend.Extend (Data.Functor.Sum.Sum f g)
-- | This module is used to resolve the cyclic we get from defining these
-- classes here rather than in a package upstream. Otherwise we'd get
-- orphaned heads for many instances on the types in
-- transformers and bifunctors.
module Data.Functor.Bind.Class
-- | A strong lax semi-monoidal endofunctor. This is equivalent to an
-- Applicative without pure.
--
-- Laws:
--
--
-- (.) <$> u <.> v <.> w = u <.> (v <.> w)
-- x <.> (f <$> y) = (. f) <$> x <.> y
-- f <$> (x <.> y) = (f .) <$> x <.> y
--
--
-- The laws imply that .> and <. really ignore their
-- left and right results, respectively, and really return their right
-- and left results, respectively. Specifically,
--
--
-- (mf <$> m) .> (nf <$> n) = nf <$> (m .> n)
-- (mf <$> m) <. (nf <$> n) = mf <$> (m <. n)
--
class Functor f => Apply f where a .> b = const id <$> a <.> b a <. b = const <$> a <.> b
(<.>) :: Apply f => f (a -> b) -> f a -> f b
-- |
-- a .> b = const id <$> a <.> b
--
(.>) :: Apply f => f a -> f b -> f b
-- |
-- a <. b = const <$> a <.> b
--
(<.) :: Apply f => f a -> f b -> f a
-- | Wrap an Applicative to be used as a member of Apply
newtype WrappedApplicative f a
WrapApplicative :: f a -> WrappedApplicative f a
[unwrapApplicative] :: WrappedApplicative f a -> f a
-- | Transform a Apply into an Applicative by adding a unit.
newtype MaybeApply f a
MaybeApply :: Either (f a) a -> MaybeApply f a
[runMaybeApply] :: MaybeApply f a -> Either (f a) a
-- | A Monad sans return.
--
-- Minimal definition: Either join or >>-
--
-- If defining both, then the following laws (the default definitions)
-- must hold:
--
--
-- join = (>>- id)
-- m >>- f = join (fmap f m)
--
--
-- Laws:
--
--
-- induced definition of <.>: f <.> x = f >>- (<$> x)
--
--
-- Finally, there are two associativity conditions:
--
--
-- associativity of (>>-): (m >>- f) >>- g == m >>- (\x -> f x >>- g)
-- associativity of join: join . join = join . fmap join
--
--
-- These can both be seen as special cases of the constraint that
--
--
-- associativity of (->-): (f ->- g) ->- h = f ->- (g ->- h)
--
class Apply m => Bind m where m >>- f = join (fmap f m) join = (>>- id)
(>>-) :: Bind m => m a -> (a -> m b) -> m b
join :: Bind m => m (m a) -> m a
apDefault :: Bind f => f (a -> b) -> f a -> f b
returning :: Functor f => f a -> (a -> b) -> f b
class Bifunctor p => Biapply p where a .>> b = bimap (const id) (const id) <<$>> a <<.>> b a <<. b = bimap const const <<$>> a <<.>> b
(<<.>>) :: Biapply p => p (a -> b) (c -> d) -> p a c -> p b d
-- |
-- a .> b ≡ const id <$> a <.> b
--
(.>>) :: Biapply p => p a b -> p c d -> p c d
-- |
-- a <. b ≡ const <$> a <.> b
--
(<<.) :: Biapply p => p a b -> p c d -> p a b
instance Data.Functor.Bind.Class.Apply (Data.Tagged.Tagged a)
instance Data.Functor.Bind.Class.Apply Data.Proxy.Proxy
instance Data.Functor.Bind.Class.Apply f => Data.Functor.Bind.Class.Apply (Control.Applicative.Backwards.Backwards f)
instance (Data.Functor.Bind.Class.Apply f, Data.Functor.Bind.Class.Apply g) => Data.Functor.Bind.Class.Apply (Data.Functor.Compose.Compose f g)
instance Data.Semigroup.Semigroup f => Data.Functor.Bind.Class.Apply (Data.Functor.Constant.Constant f)
instance Data.Functor.Bind.Class.Apply f => Data.Functor.Bind.Class.Apply (Control.Applicative.Lift.Lift f)
instance (Data.Functor.Bind.Class.Apply f, Data.Functor.Bind.Class.Apply g) => Data.Functor.Bind.Class.Apply (Data.Functor.Product.Product f g)
instance Data.Functor.Bind.Class.Apply f => Data.Functor.Bind.Class.Apply (Data.Functor.Reverse.Reverse f)
instance Data.Semigroup.Semigroup m => Data.Functor.Bind.Class.Apply ((,) m)
instance Data.Functor.Bind.Class.Apply Data.List.NonEmpty.NonEmpty
instance Data.Functor.Bind.Class.Apply (Data.Either.Either a)
instance Data.Semigroup.Semigroup m => Data.Functor.Bind.Class.Apply (Data.Functor.Const.Const m)
instance Data.Functor.Bind.Class.Apply ((->) m)
instance Data.Functor.Bind.Class.Apply Control.Applicative.ZipList
instance Data.Functor.Bind.Class.Apply []
instance Data.Functor.Bind.Class.Apply GHC.Types.IO
instance Data.Functor.Bind.Class.Apply GHC.Base.Maybe
instance Data.Functor.Bind.Class.Apply Data.Semigroup.Option
instance Data.Functor.Bind.Class.Apply Data.Functor.Identity.Identity
instance Data.Functor.Bind.Class.Apply w => Data.Functor.Bind.Class.Apply (Control.Monad.Trans.Identity.IdentityT w)
instance GHC.Base.Monad m => Data.Functor.Bind.Class.Apply (Control.Applicative.WrappedMonad m)
instance Control.Arrow.Arrow a => Data.Functor.Bind.Class.Apply (Control.Applicative.WrappedArrow a b)
instance GHC.Classes.Ord k => Data.Functor.Bind.Class.Apply (Data.Map.Base.Map k)
instance Data.Functor.Bind.Class.Apply Data.IntMap.Base.IntMap
instance Data.Functor.Bind.Class.Apply Data.Sequence.Seq
instance Data.Functor.Bind.Class.Apply Data.Tree.Tree
instance (GHC.Base.Functor m, GHC.Base.Monad m) => Data.Functor.Bind.Class.Apply (Control.Monad.Trans.Maybe.MaybeT m)
instance (GHC.Base.Functor m, GHC.Base.Monad m) => Data.Functor.Bind.Class.Apply (Control.Monad.Trans.Error.ErrorT e m)
instance (GHC.Base.Functor m, GHC.Base.Monad m) => Data.Functor.Bind.Class.Apply (Control.Monad.Trans.Except.ExceptT e m)
instance Data.Functor.Bind.Class.Apply m => Data.Functor.Bind.Class.Apply (Control.Monad.Trans.Reader.ReaderT e m)
instance Data.Functor.Bind.Class.Apply m => Data.Functor.Bind.Class.Apply (Control.Monad.Trans.List.ListT m)
instance (Data.Functor.Bind.Class.Apply m, Data.Semigroup.Semigroup w) => Data.Functor.Bind.Class.Apply (Control.Monad.Trans.Writer.Strict.WriterT w m)
instance (Data.Functor.Bind.Class.Apply m, Data.Semigroup.Semigroup w) => Data.Functor.Bind.Class.Apply (Control.Monad.Trans.Writer.Lazy.WriterT w m)
instance Data.Functor.Bind.Class.Bind m => Data.Functor.Bind.Class.Apply (Control.Monad.Trans.State.Strict.StateT s m)
instance Data.Functor.Bind.Class.Bind m => Data.Functor.Bind.Class.Apply (Control.Monad.Trans.State.Lazy.StateT s m)
instance (Data.Functor.Bind.Class.Bind m, Data.Semigroup.Semigroup w) => Data.Functor.Bind.Class.Apply (Control.Monad.Trans.RWS.Strict.RWST r w s m)
instance (Data.Functor.Bind.Class.Bind m, Data.Semigroup.Semigroup w) => Data.Functor.Bind.Class.Apply (Control.Monad.Trans.RWS.Lazy.RWST r w s m)
instance Data.Functor.Bind.Class.Apply (Control.Monad.Trans.Cont.ContT r m)
instance (Data.Semigroup.Semigroup e, Data.Functor.Bind.Class.Apply w) => Data.Functor.Bind.Class.Apply (Control.Comonad.Trans.Env.EnvT e w)
instance (Data.Functor.Bind.Class.Apply w, Data.Semigroup.Semigroup s) => Data.Functor.Bind.Class.Apply (Control.Comonad.Trans.Store.StoreT s w)
instance Data.Functor.Bind.Class.Apply w => Data.Functor.Bind.Class.Apply (Control.Comonad.Trans.Traced.TracedT m w)
instance GHC.Base.Functor f => GHC.Base.Functor (Data.Functor.Bind.Class.WrappedApplicative f)
instance GHC.Base.Applicative f => Data.Functor.Bind.Class.Apply (Data.Functor.Bind.Class.WrappedApplicative f)
instance GHC.Base.Applicative f => GHC.Base.Applicative (Data.Functor.Bind.Class.WrappedApplicative f)
instance GHC.Base.Alternative f => GHC.Base.Alternative (Data.Functor.Bind.Class.WrappedApplicative f)
instance GHC.Base.Functor f => GHC.Base.Functor (Data.Functor.Bind.Class.MaybeApply f)
instance Data.Functor.Bind.Class.Apply f => Data.Functor.Bind.Class.Apply (Data.Functor.Bind.Class.MaybeApply f)
instance Data.Functor.Bind.Class.Apply f => GHC.Base.Applicative (Data.Functor.Bind.Class.MaybeApply f)
instance Data.Functor.Extend.Extend f => Data.Functor.Extend.Extend (Data.Functor.Bind.Class.MaybeApply f)
instance Control.Comonad.Comonad f => Control.Comonad.Comonad (Data.Functor.Bind.Class.MaybeApply f)
instance Data.Functor.Bind.Class.Apply (Control.Comonad.Cokleisli w a)
instance Data.Semigroup.Semigroup m => Data.Functor.Bind.Class.Bind ((,) m)
instance Data.Functor.Bind.Class.Bind (Data.Tagged.Tagged a)
instance Data.Functor.Bind.Class.Bind Data.Proxy.Proxy
instance Data.Functor.Bind.Class.Bind (Data.Either.Either a)
instance (Data.Functor.Bind.Class.Bind f, Data.Functor.Bind.Class.Bind g) => Data.Functor.Bind.Class.Bind (Data.Functor.Product.Product f g)
instance Data.Functor.Bind.Class.Bind ((->) m)
instance Data.Functor.Bind.Class.Bind []
instance Data.Functor.Bind.Class.Bind Data.List.NonEmpty.NonEmpty
instance Data.Functor.Bind.Class.Bind GHC.Types.IO
instance Data.Functor.Bind.Class.Bind GHC.Base.Maybe
instance Data.Functor.Bind.Class.Bind Data.Semigroup.Option
instance Data.Functor.Bind.Class.Bind Data.Functor.Identity.Identity
instance Data.Functor.Bind.Class.Bind m => Data.Functor.Bind.Class.Bind (Control.Monad.Trans.Identity.IdentityT m)
instance GHC.Base.Monad m => Data.Functor.Bind.Class.Bind (Control.Applicative.WrappedMonad m)
instance (GHC.Base.Functor m, GHC.Base.Monad m) => Data.Functor.Bind.Class.Bind (Control.Monad.Trans.Maybe.MaybeT m)
instance (Data.Functor.Bind.Class.Apply m, GHC.Base.Monad m) => Data.Functor.Bind.Class.Bind (Control.Monad.Trans.List.ListT m)
instance (GHC.Base.Functor m, GHC.Base.Monad m) => Data.Functor.Bind.Class.Bind (Control.Monad.Trans.Error.ErrorT e m)
instance (GHC.Base.Functor m, GHC.Base.Monad m) => Data.Functor.Bind.Class.Bind (Control.Monad.Trans.Except.ExceptT e m)
instance Data.Functor.Bind.Class.Bind m => Data.Functor.Bind.Class.Bind (Control.Monad.Trans.Reader.ReaderT e m)
instance (Data.Functor.Bind.Class.Bind m, Data.Semigroup.Semigroup w) => Data.Functor.Bind.Class.Bind (Control.Monad.Trans.Writer.Lazy.WriterT w m)
instance (Data.Functor.Bind.Class.Bind m, Data.Semigroup.Semigroup w) => Data.Functor.Bind.Class.Bind (Control.Monad.Trans.Writer.Strict.WriterT w m)
instance Data.Functor.Bind.Class.Bind m => Data.Functor.Bind.Class.Bind (Control.Monad.Trans.State.Lazy.StateT s m)
instance Data.Functor.Bind.Class.Bind m => Data.Functor.Bind.Class.Bind (Control.Monad.Trans.State.Strict.StateT s m)
instance (Data.Functor.Bind.Class.Bind m, Data.Semigroup.Semigroup w) => Data.Functor.Bind.Class.Bind (Control.Monad.Trans.RWS.Lazy.RWST r w s m)
instance (Data.Functor.Bind.Class.Bind m, Data.Semigroup.Semigroup w) => Data.Functor.Bind.Class.Bind (Control.Monad.Trans.RWS.Strict.RWST r w s m)
instance Data.Functor.Bind.Class.Bind (Control.Monad.Trans.Cont.ContT r m)
instance GHC.Classes.Ord k => Data.Functor.Bind.Class.Bind (Data.Map.Base.Map k)
instance Data.Functor.Bind.Class.Bind Data.IntMap.Base.IntMap
instance Data.Functor.Bind.Class.Bind Data.Sequence.Seq
instance Data.Functor.Bind.Class.Bind Data.Tree.Tree
instance Data.Functor.Bind.Class.Biapply (,)
instance Data.Functor.Bind.Class.Biapply Data.Semigroup.Arg
instance Data.Semigroup.Semigroup x => Data.Functor.Bind.Class.Biapply ((,,) x)
instance (Data.Semigroup.Semigroup x, Data.Semigroup.Semigroup y) => Data.Functor.Bind.Class.Biapply ((,,,) x y)
instance (Data.Semigroup.Semigroup x, Data.Semigroup.Semigroup y, Data.Semigroup.Semigroup z) => Data.Functor.Bind.Class.Biapply ((,,,,) x y z)
instance Data.Functor.Bind.Class.Biapply Data.Functor.Const.Const
instance Data.Functor.Bind.Class.Biapply Data.Tagged.Tagged
instance (Data.Functor.Bind.Class.Biapply p, Data.Functor.Bind.Class.Apply f, Data.Functor.Bind.Class.Apply g) => Data.Functor.Bind.Class.Biapply (Data.Bifunctor.Biff.Biff p f g)
instance Data.Functor.Bind.Class.Apply f => Data.Functor.Bind.Class.Biapply (Data.Bifunctor.Clown.Clown f)
instance Data.Functor.Bind.Class.Biapply p => Data.Functor.Bind.Class.Biapply (Data.Bifunctor.Flip.Flip p)
instance Data.Functor.Bind.Class.Apply g => Data.Functor.Bind.Class.Biapply (Data.Bifunctor.Joker.Joker g)
instance Data.Functor.Bind.Class.Biapply p => Data.Functor.Bind.Class.Apply (Data.Bifunctor.Join.Join p)
instance (Data.Functor.Bind.Class.Biapply p, Data.Functor.Bind.Class.Biapply q) => Data.Functor.Bind.Class.Biapply (Data.Bifunctor.Product.Product p q)
instance (Data.Functor.Bind.Class.Apply f, Data.Functor.Bind.Class.Biapply p) => Data.Functor.Bind.Class.Biapply (Data.Bifunctor.Tannen.Tannen f p)
instance Data.Functor.Bind.Class.Biapply p => Data.Functor.Bind.Class.Biapply (Data.Bifunctor.Wrapped.WrappedBifunctor p)
module Data.Functor.Apply
-- | The Functor class is used for types that can be mapped over.
-- Instances of Functor should satisfy the following laws:
--
--
-- fmap id == id
-- fmap (f . g) == fmap f . fmap g
--
--
-- The instances of Functor for lists, Maybe and IO
-- satisfy these laws.
class Functor (f :: * -> *)
fmap :: Functor f => (a -> b) -> f a -> f b
-- | Replace all locations in the input with the same value. The default
-- definition is fmap . const, but this may be
-- overridden with a more efficient version.
(<$) :: Functor f => a -> f b -> f a
-- | An infix synonym for fmap.
--
-- The name of this operator is an allusion to $. Note the
-- similarities between their types:
--
--
-- ($) :: (a -> b) -> a -> b
-- (<$>) :: Functor f => (a -> b) -> f a -> f b
--
--
-- Whereas $ is function application, <$> is
-- function application lifted over a Functor.
--
-- Examples
--
-- Convert from a Maybe Int to a
-- Maybe String using show:
--
--
-- >>> show <$> Nothing
-- Nothing
--
-- >>> show <$> Just 3
-- Just "3"
--
--
-- Convert from an Either Int Int to
-- an Either Int String using
-- show:
--
--
-- >>> show <$> Left 17
-- Left 17
--
-- >>> show <$> Right 17
-- Right "17"
--
--
-- Double each element of a list:
--
--
-- >>> (*2) <$> [1,2,3]
-- [2,4,6]
--
--
-- Apply even to the second element of a pair:
--
--
-- >>> even <$> (2,2)
-- (2,True)
--
(<$>) :: Functor f => (a -> b) -> f a -> f b
infixl 4 <$>
-- | Flipped version of <$.
--
-- Examples
--
-- Replace the contents of a Maybe Int with a
-- constant String:
--
--
-- >>> Nothing $> "foo"
-- Nothing
--
-- >>> Just 90210 $> "foo"
-- Just "foo"
--
--
-- Replace the contents of an Either Int
-- Int with a constant String, resulting in an
-- Either Int String:
--
--
-- >>> Left 8675309 $> "foo"
-- Left 8675309
--
-- >>> Right 8675309 $> "foo"
-- Right "foo"
--
--
-- Replace each element of a list with a constant String:
--
--
-- >>> [1,2,3] $> "foo"
-- ["foo","foo","foo"]
--
--
-- Replace the second element of a pair with a constant String:
--
--
-- >>> (1,2) $> "foo"
-- (1,"foo")
--
($>) :: Functor f => f a -> b -> f b
infixl 4 $>
-- | A strong lax semi-monoidal endofunctor. This is equivalent to an
-- Applicative without pure.
--
-- Laws:
--
--
-- (.) <$> u <.> v <.> w = u <.> (v <.> w)
-- x <.> (f <$> y) = (. f) <$> x <.> y
-- f <$> (x <.> y) = (f .) <$> x <.> y
--
--
-- The laws imply that .> and <. really ignore their
-- left and right results, respectively, and really return their right
-- and left results, respectively. Specifically,
--
--
-- (mf <$> m) .> (nf <$> n) = nf <$> (m .> n)
-- (mf <$> m) <. (nf <$> n) = mf <$> (m <. n)
--
class Functor f => Apply f where a .> b = const id <$> a <.> b a <. b = const <$> a <.> b
(<.>) :: Apply f => f (a -> b) -> f a -> f b
-- |
-- a .> b = const id <$> a <.> b
--
(.>) :: Apply f => f a -> f b -> f b
-- |
-- a <. b = const <$> a <.> b
--
(<.) :: Apply f => f a -> f b -> f a
-- | A variant of <.> with the arguments reversed.
(<..>) :: Apply w => w a -> w (a -> b) -> w b
infixl 4 <..>
-- | Lift a binary function into a comonad with zipping
liftF2 :: Apply w => (a -> b -> c) -> w a -> w b -> w c
-- | Lift a ternary function into a comonad with zipping
liftF3 :: Apply w => (a -> b -> c -> d) -> w a -> w b -> w c -> w d
-- | Wrap an Applicative to be used as a member of Apply
newtype WrappedApplicative f a
WrapApplicative :: f a -> WrappedApplicative f a
[unwrapApplicative] :: WrappedApplicative f a -> f a
-- | Transform a Apply into an Applicative by adding a unit.
newtype MaybeApply f a
MaybeApply :: Either (f a) a -> MaybeApply f a
[runMaybeApply] :: MaybeApply f a -> Either (f a) a
module Data.Functor.Bind
-- | The Functor class is used for types that can be mapped over.
-- Instances of Functor should satisfy the following laws:
--
--
-- fmap id == id
-- fmap (f . g) == fmap f . fmap g
--
--
-- The instances of Functor for lists, Maybe and IO
-- satisfy these laws.
class Functor (f :: * -> *)
fmap :: Functor f => (a -> b) -> f a -> f b
-- | Replace all locations in the input with the same value. The default
-- definition is fmap . const, but this may be
-- overridden with a more efficient version.
(<$) :: Functor f => a -> f b -> f a
-- | An infix synonym for fmap.
--
-- The name of this operator is an allusion to $. Note the
-- similarities between their types:
--
--
-- ($) :: (a -> b) -> a -> b
-- (<$>) :: Functor f => (a -> b) -> f a -> f b
--
--
-- Whereas $ is function application, <$> is
-- function application lifted over a Functor.
--
-- Examples
--
-- Convert from a Maybe Int to a
-- Maybe String using show:
--
--
-- >>> show <$> Nothing
-- Nothing
--
-- >>> show <$> Just 3
-- Just "3"
--
--
-- Convert from an Either Int Int to
-- an Either Int String using
-- show:
--
--
-- >>> show <$> Left 17
-- Left 17
--
-- >>> show <$> Right 17
-- Right "17"
--
--
-- Double each element of a list:
--
--
-- >>> (*2) <$> [1,2,3]
-- [2,4,6]
--
--
-- Apply even to the second element of a pair:
--
--
-- >>> even <$> (2,2)
-- (2,True)
--
(<$>) :: Functor f => (a -> b) -> f a -> f b
infixl 4 <$>
-- | Flipped version of <$.
--
-- Examples
--
-- Replace the contents of a Maybe Int with a
-- constant String:
--
--
-- >>> Nothing $> "foo"
-- Nothing
--
-- >>> Just 90210 $> "foo"
-- Just "foo"
--
--
-- Replace the contents of an Either Int
-- Int with a constant String, resulting in an
-- Either Int String:
--
--
-- >>> Left 8675309 $> "foo"
-- Left 8675309
--
-- >>> Right 8675309 $> "foo"
-- Right "foo"
--
--
-- Replace each element of a list with a constant String:
--
--
-- >>> [1,2,3] $> "foo"
-- ["foo","foo","foo"]
--
--
-- Replace the second element of a pair with a constant String:
--
--
-- >>> (1,2) $> "foo"
-- (1,"foo")
--
($>) :: Functor f => f a -> b -> f b
infixl 4 $>
-- | A strong lax semi-monoidal endofunctor. This is equivalent to an
-- Applicative without pure.
--
-- Laws:
--
--
-- (.) <$> u <.> v <.> w = u <.> (v <.> w)
-- x <.> (f <$> y) = (. f) <$> x <.> y
-- f <$> (x <.> y) = (f .) <$> x <.> y
--
--
-- The laws imply that .> and <. really ignore their
-- left and right results, respectively, and really return their right
-- and left results, respectively. Specifically,
--
--
-- (mf <$> m) .> (nf <$> n) = nf <$> (m .> n)
-- (mf <$> m) <. (nf <$> n) = mf <$> (m <. n)
--
class Functor f => Apply f where a .> b = const id <$> a <.> b a <. b = const <$> a <.> b
(<.>) :: Apply f => f (a -> b) -> f a -> f b
-- |
-- a .> b = const id <$> a <.> b
--
(.>) :: Apply f => f a -> f b -> f b
-- |
-- a <. b = const <$> a <.> b
--
(<.) :: Apply f => f a -> f b -> f a
-- | A variant of <.> with the arguments reversed.
(<..>) :: Apply w => w a -> w (a -> b) -> w b
infixl 4 <..>
-- | Lift a binary function into a comonad with zipping
liftF2 :: Apply w => (a -> b -> c) -> w a -> w b -> w c
-- | Lift a ternary function into a comonad with zipping
liftF3 :: Apply w => (a -> b -> c -> d) -> w a -> w b -> w c -> w d
-- | Wrap an Applicative to be used as a member of Apply
newtype WrappedApplicative f a
WrapApplicative :: f a -> WrappedApplicative f a
[unwrapApplicative] :: WrappedApplicative f a -> f a
-- | Transform a Apply into an Applicative by adding a unit.
newtype MaybeApply f a
MaybeApply :: Either (f a) a -> MaybeApply f a
[runMaybeApply] :: MaybeApply f a -> Either (f a) a
-- | A Monad sans return.
--
-- Minimal definition: Either join or >>-
--
-- If defining both, then the following laws (the default definitions)
-- must hold:
--
--
-- join = (>>- id)
-- m >>- f = join (fmap f m)
--
--
-- Laws:
--
--
-- induced definition of <.>: f <.> x = f >>- (<$> x)
--
--
-- Finally, there are two associativity conditions:
--
--
-- associativity of (>>-): (m >>- f) >>- g == m >>- (\x -> f x >>- g)
-- associativity of join: join . join = join . fmap join
--
--
-- These can both be seen as special cases of the constraint that
--
--
-- associativity of (->-): (f ->- g) ->- h = f ->- (g ->- h)
--
class Apply m => Bind m where m >>- f = join (fmap f m) join = (>>- id)
(>>-) :: Bind m => m a -> (a -> m b) -> m b
join :: Bind m => m (m a) -> m a
(-<<) :: Bind m => (a -> m b) -> m a -> m b
infixr 1 -<<
(-<-) :: Bind m => (b -> m c) -> (a -> m b) -> a -> m c
infixr 1 -<-
(->-) :: Bind m => (a -> m b) -> (b -> m c) -> a -> m c
infixr 1 ->-
apDefault :: Bind f => f (a -> b) -> f a -> f b
returning :: Functor f => f a -> (a -> b) -> f b
module Data.Functor.Bind.Trans
-- | A subset of monad transformers can transform any Bind as well.
class MonadTrans t => BindTrans t
liftB :: (BindTrans t, Bind b) => b a -> t b a
instance Data.Functor.Bind.Trans.BindTrans Control.Monad.Trans.Identity.IdentityT
instance Data.Functor.Bind.Trans.BindTrans (Control.Monad.Trans.Reader.ReaderT e)
instance GHC.Base.Monoid w => Data.Functor.Bind.Trans.BindTrans (Control.Monad.Trans.Writer.Lazy.WriterT w)
instance GHC.Base.Monoid w => Data.Functor.Bind.Trans.BindTrans (Control.Monad.Trans.Writer.Strict.WriterT w)
instance Data.Functor.Bind.Trans.BindTrans (Control.Monad.Trans.State.Lazy.StateT s)
instance Data.Functor.Bind.Trans.BindTrans (Control.Monad.Trans.State.Strict.StateT s)
instance GHC.Base.Monoid w => Data.Functor.Bind.Trans.BindTrans (Control.Monad.Trans.RWS.Lazy.RWST r w s)
instance GHC.Base.Monoid w => Data.Functor.Bind.Trans.BindTrans (Control.Monad.Trans.RWS.Strict.RWST r w s)
instance Data.Functor.Bind.Trans.BindTrans (Control.Monad.Trans.Cont.ContT r)
-- | A semigroupoid satisfies all of the requirements to be a Category
-- except for the existence of identity arrows.
module Data.Semigroupoid
-- | Category sans id
class Semigroupoid c
o :: Semigroupoid c => c j k -> c i j -> c i k
newtype WrappedCategory k a b
WrapCategory :: k a b -> WrappedCategory k a b
[unwrapCategory] :: WrappedCategory k a b -> k a b
newtype Semi m a b
Semi :: m -> Semi m a b
[getSemi] :: Semi m a b -> m
instance Data.Semigroupoid.Semigroupoid (->)
instance Data.Semigroupoid.Semigroupoid (,)
instance Data.Functor.Bind.Class.Bind m => Data.Semigroupoid.Semigroupoid (Control.Arrow.Kleisli m)
instance Data.Functor.Extend.Extend w => Data.Semigroupoid.Semigroupoid (Control.Comonad.Cokleisli w)
instance Data.Semigroupoid.Semigroupoid Data.Functor.Contravariant.Op
instance forall k (k1 :: k -> k -> *). Control.Category.Category k1 => Data.Semigroupoid.Semigroupoid (Data.Semigroupoid.WrappedCategory k1)
instance forall k (k1 :: k -> k -> *). Control.Category.Category k1 => Control.Category.Category (Data.Semigroupoid.WrappedCategory k1)
instance Data.Semigroup.Semigroup m => Data.Semigroupoid.Semigroupoid (Data.Semigroupoid.Semi m)
instance GHC.Base.Monoid m => Control.Category.Category (Data.Semigroupoid.Semi m)
-- | A semigroupoid satisfies all of the requirements to be a Category
-- except for the existence of identity arrows.
module Data.Semigroupoid.Dual
newtype Dual k a b
Dual :: k b a -> Dual k a b
[getDual] :: Dual k a b -> k b a
instance forall k (k1 :: k -> k -> *). Data.Semigroupoid.Semigroupoid k1 => Data.Semigroupoid.Semigroupoid (Data.Semigroupoid.Dual.Dual k1)
instance forall k (k1 :: k -> k -> *). Control.Category.Category k1 => Control.Category.Category (Data.Semigroupoid.Dual.Dual k1)
module Data.Groupoid
-- | semigroupoid with inverses. This technically should be a category with
-- inverses, except we need to use Ob to define the valid objects for the
-- category
class Semigroupoid k => Groupoid k
inv :: Groupoid k => k a b -> k b a
instance forall k (k1 :: k -> k -> *). Data.Groupoid.Groupoid k1 => Data.Groupoid.Groupoid (Data.Semigroupoid.Dual.Dual k1)
module Data.Isomorphism
data Iso k a b
Iso :: k a b -> k b a -> Iso k a b
[embed] :: Iso k a b -> k a b
[project] :: Iso k a b -> k b a
instance forall k (k1 :: k -> k -> *). Data.Semigroupoid.Semigroupoid k1 => Data.Semigroupoid.Semigroupoid (Data.Isomorphism.Iso k1)
instance forall k (k1 :: k -> k -> *). Data.Semigroupoid.Semigroupoid k1 => Data.Groupoid.Groupoid (Data.Isomorphism.Iso k1)
instance forall k (k1 :: k -> k -> *). Control.Category.Category k1 => Control.Category.Category (Data.Isomorphism.Iso k1)
module Data.Semigroupoid.Ob
class Semigroupoid k => Ob k a
semiid :: Ob k a => k a a
instance (Data.Functor.Bind.Class.Bind m, GHC.Base.Monad m) => Data.Semigroupoid.Ob.Ob (Control.Arrow.Kleisli m) a
instance (Data.Functor.Extend.Extend w, Control.Comonad.Comonad w) => Data.Semigroupoid.Ob.Ob (Control.Comonad.Cokleisli w) a
instance Data.Semigroupoid.Ob.Ob (->) a
module Data.Semigroup.Bifoldable
class Bifoldable t => Bifoldable1 t where bifold1 = bifoldMap1 id id bifoldMap1 f g = maybe (error "bifoldMap1") id . getOption . bifoldMap (Option . Just . f) (Option . Just . g)
bifold1 :: (Bifoldable1 t, Semigroup m) => t m m -> m
bifoldMap1 :: (Bifoldable1 t, Semigroup m) => (a -> m) -> (b -> m) -> t a b -> m
bitraverse1_ :: (Bifoldable1 t, Apply f) => (a -> f b) -> (c -> f d) -> t a c -> f ()
bifor1_ :: (Bifoldable1 t, Apply f) => t a c -> (a -> f b) -> (c -> f d) -> f ()
bisequenceA1_ :: (Bifoldable1 t, Apply f) => t (f a) (f b) -> f ()
-- | Usable default for foldMap, but only if you define bifoldMap1 yourself
bifoldMapDefault1 :: (Bifoldable1 t, Monoid m) => (a -> m) -> (b -> m) -> t a b -> m
instance Data.Functor.Bind.Class.Apply f => Data.Semigroup.Semigroup (Data.Semigroup.Bifoldable.Act f a)
instance GHC.Base.Functor f => GHC.Base.Functor (Data.Semigroup.Bifoldable.Act f)
module Data.Functor.Alt
-- | Laws:
--
--
-- <!> is associative: (a <!> b) <!> c = a <!> (b <!> c)
-- <$> left-distributes over <!>: f <$> (a <!> b) = (f <$> a) <!> (f <$> b)
--
--
-- If extended to an Alternative then <!> should
-- equal <|>.
--
-- Ideally, an instance of Alt also satisfies the "left
-- distributon" law of MonadPlus with respect to <.>:
--
--
-- <.> right-distributes over <!>: (a <!> b) <.> c = (a <.> c) <!> (b <.> c)
--
--
-- But Maybe, IO, Either a,
-- ErrorT e m, and STM satisfy the alternative
-- "left catch" law instead:
--
--
-- pure a <!> b = pure a
--
--
-- However, this variation cannot be stated purely in terms of the
-- dependencies of Alt.
--
-- When and if MonadPlus is successfully refactored, this class should
-- also be refactored to remove these instances.
--
-- The right distributive law should extend in the cases where the a
-- Bind or Monad is provided to yield variations of the
-- right distributive law:
--
--
-- (m <!> n) >>- f = (m >>- f) <!> (m >>- f)
-- (m <!> n) >>= f = (m >>= f) <!> (m >>= f)
--
class Functor f => Alt f where some v = some_v where many_v = some_v pure [] some_v = (:) <$> v <*> many_v many v = many_v where many_v = some_v pure [] some_v = (:) <$> v <*> many_v
-- | <|> without a required empty
() :: Alt f => f a -> f a -> f a
some :: (Alt f, Applicative f) => f a -> f [a]
many :: (Alt f, Applicative f) => f a -> f [a]
instance (Data.Functor.Alt.Alt f, Data.Functor.Alt.Alt g) => Data.Functor.Alt.Alt (f GHC.Generics.:*: g)
instance Data.Functor.Alt.Alt f => Data.Functor.Alt.Alt (GHC.Generics.M1 i c f)
instance Data.Functor.Alt.Alt f => Data.Functor.Alt.Alt (GHC.Generics.Rec1 f)
instance Data.Functor.Alt.Alt GHC.Generics.U1
instance Data.Functor.Alt.Alt GHC.Generics.V1
instance Data.Functor.Alt.Alt Data.Proxy.Proxy
instance Data.Functor.Alt.Alt (Data.Either.Either a)
instance Data.Functor.Alt.Alt GHC.Types.IO
instance Data.Functor.Alt.Alt []
instance Data.Functor.Alt.Alt GHC.Base.Maybe
instance Data.Functor.Alt.Alt Data.Semigroup.Option
instance GHC.Base.MonadPlus m => Data.Functor.Alt.Alt (Control.Applicative.WrappedMonad m)
instance Control.Arrow.ArrowPlus a => Data.Functor.Alt.Alt (Control.Applicative.WrappedArrow a b)
instance GHC.Classes.Ord k => Data.Functor.Alt.Alt (Data.Map.Base.Map k)
instance Data.Functor.Alt.Alt Data.IntMap.Base.IntMap
instance Data.Functor.Alt.Alt Data.Sequence.Seq
instance Data.Functor.Alt.Alt Data.List.NonEmpty.NonEmpty
instance GHC.Base.Alternative f => Data.Functor.Alt.Alt (Data.Functor.Bind.Class.WrappedApplicative f)
instance Data.Functor.Alt.Alt f => Data.Functor.Alt.Alt (Control.Monad.Trans.Identity.IdentityT f)
instance Data.Functor.Alt.Alt f => Data.Functor.Alt.Alt (Control.Monad.Trans.Reader.ReaderT e f)
instance (Data.Functor.Bind.Class.Bind f, GHC.Base.Monad f) => Data.Functor.Alt.Alt (Control.Monad.Trans.Maybe.MaybeT f)
instance (Data.Functor.Bind.Class.Bind f, GHC.Base.Monad f) => Data.Functor.Alt.Alt (Control.Monad.Trans.Error.ErrorT e f)
instance (Data.Functor.Bind.Class.Bind f, GHC.Base.Monad f, Data.Semigroup.Semigroup e) => Data.Functor.Alt.Alt (Control.Monad.Trans.Except.ExceptT e f)
instance Data.Functor.Bind.Class.Apply f => Data.Functor.Alt.Alt (Control.Monad.Trans.List.ListT f)
instance Data.Functor.Alt.Alt f => Data.Functor.Alt.Alt (Control.Monad.Trans.State.Strict.StateT e f)
instance Data.Functor.Alt.Alt f => Data.Functor.Alt.Alt (Control.Monad.Trans.State.Lazy.StateT e f)
instance Data.Functor.Alt.Alt f => Data.Functor.Alt.Alt (Control.Monad.Trans.Writer.Strict.WriterT w f)
instance Data.Functor.Alt.Alt f => Data.Functor.Alt.Alt (Control.Monad.Trans.Writer.Lazy.WriterT w f)
instance Data.Functor.Alt.Alt f => Data.Functor.Alt.Alt (Control.Monad.Trans.RWS.Strict.RWST r w s f)
instance Data.Functor.Alt.Alt f => Data.Functor.Alt.Alt (Control.Monad.Trans.RWS.Lazy.RWST r w s f)
instance Data.Functor.Alt.Alt f => Data.Functor.Alt.Alt (Control.Applicative.Backwards.Backwards f)
instance (Data.Functor.Alt.Alt f, GHC.Base.Functor g) => Data.Functor.Alt.Alt (Data.Functor.Compose.Compose f g)
instance Data.Functor.Alt.Alt f => Data.Functor.Alt.Alt (Control.Applicative.Lift.Lift f)
instance (Data.Functor.Alt.Alt f, Data.Functor.Alt.Alt g) => Data.Functor.Alt.Alt (Data.Functor.Product.Product f g)
instance Data.Functor.Alt.Alt f => Data.Functor.Alt.Alt (Data.Functor.Reverse.Reverse f)
module Data.Functor.Plus
-- | Laws:
--
--
-- zero <!> m = m
-- m <!> zero = m
--
--
-- If extended to an Alternative then zero should equal
-- empty.
class Alt f => Plus f
zero :: Plus f => f a
instance Data.Functor.Plus.Plus Data.Proxy.Proxy
instance Data.Functor.Plus.Plus GHC.Generics.U1
instance (Data.Functor.Plus.Plus f, Data.Functor.Plus.Plus g) => Data.Functor.Plus.Plus (f GHC.Generics.:*: g)
instance Data.Functor.Plus.Plus f => Data.Functor.Plus.Plus (GHC.Generics.M1 i c f)
instance Data.Functor.Plus.Plus f => Data.Functor.Plus.Plus (GHC.Generics.Rec1 f)
instance Data.Functor.Plus.Plus GHC.Types.IO
instance Data.Functor.Plus.Plus []
instance Data.Functor.Plus.Plus GHC.Base.Maybe
instance Data.Functor.Plus.Plus Data.Semigroup.Option
instance GHC.Base.MonadPlus m => Data.Functor.Plus.Plus (Control.Applicative.WrappedMonad m)
instance Control.Arrow.ArrowPlus a => Data.Functor.Plus.Plus (Control.Applicative.WrappedArrow a b)
instance GHC.Classes.Ord k => Data.Functor.Plus.Plus (Data.Map.Base.Map k)
instance Data.Functor.Plus.Plus Data.IntMap.Base.IntMap
instance Data.Functor.Plus.Plus Data.Sequence.Seq
instance GHC.Base.Alternative f => Data.Functor.Plus.Plus (Data.Functor.Bind.Class.WrappedApplicative f)
instance Data.Functor.Plus.Plus f => Data.Functor.Plus.Plus (Control.Monad.Trans.Identity.IdentityT f)
instance Data.Functor.Plus.Plus f => Data.Functor.Plus.Plus (Control.Monad.Trans.Reader.ReaderT e f)
instance (Data.Functor.Bind.Class.Bind f, GHC.Base.Monad f) => Data.Functor.Plus.Plus (Control.Monad.Trans.Maybe.MaybeT f)
instance (Data.Functor.Bind.Class.Bind f, GHC.Base.Monad f, Control.Monad.Trans.Error.Error e) => Data.Functor.Plus.Plus (Control.Monad.Trans.Error.ErrorT e f)
instance (Data.Functor.Bind.Class.Bind f, GHC.Base.Monad f, Data.Semigroup.Semigroup e, GHC.Base.Monoid e) => Data.Functor.Plus.Plus (Control.Monad.Trans.Except.ExceptT e f)
instance (Data.Functor.Bind.Class.Apply f, GHC.Base.Applicative f) => Data.Functor.Plus.Plus (Control.Monad.Trans.List.ListT f)
instance Data.Functor.Plus.Plus f => Data.Functor.Plus.Plus (Control.Monad.Trans.State.Strict.StateT e f)
instance Data.Functor.Plus.Plus f => Data.Functor.Plus.Plus (Control.Monad.Trans.State.Lazy.StateT e f)
instance Data.Functor.Plus.Plus f => Data.Functor.Plus.Plus (Control.Monad.Trans.Writer.Strict.WriterT w f)
instance Data.Functor.Plus.Plus f => Data.Functor.Plus.Plus (Control.Monad.Trans.Writer.Lazy.WriterT w f)
instance Data.Functor.Plus.Plus f => Data.Functor.Plus.Plus (Control.Monad.Trans.RWS.Strict.RWST r w s f)
instance Data.Functor.Plus.Plus f => Data.Functor.Plus.Plus (Control.Monad.Trans.RWS.Lazy.RWST r w s f)
instance Data.Functor.Plus.Plus f => Data.Functor.Plus.Plus (Control.Applicative.Backwards.Backwards f)
instance (Data.Functor.Plus.Plus f, GHC.Base.Functor g) => Data.Functor.Plus.Plus (Data.Functor.Compose.Compose f g)
instance Data.Functor.Plus.Plus f => Data.Functor.Plus.Plus (Control.Applicative.Lift.Lift f)
instance (Data.Functor.Plus.Plus f, Data.Functor.Plus.Plus g) => Data.Functor.Plus.Plus (Data.Functor.Product.Product f g)
instance Data.Functor.Plus.Plus f => Data.Functor.Plus.Plus (Data.Functor.Reverse.Reverse f)
module Data.Semigroupoid.Static
newtype Static f a b
Static :: f (a -> b) -> Static f a b
[runStatic] :: Static f a b -> f (a -> b)
instance GHC.Base.Functor f => GHC.Base.Functor (Data.Semigroupoid.Static.Static f a)
instance Data.Functor.Bind.Class.Apply f => Data.Functor.Bind.Class.Apply (Data.Semigroupoid.Static.Static f a)
instance Data.Functor.Alt.Alt f => Data.Functor.Alt.Alt (Data.Semigroupoid.Static.Static f a)
instance Data.Functor.Plus.Plus f => Data.Functor.Plus.Plus (Data.Semigroupoid.Static.Static f a)
instance GHC.Base.Applicative f => GHC.Base.Applicative (Data.Semigroupoid.Static.Static f a)
instance (Data.Functor.Extend.Extend f, Data.Semigroup.Semigroup a) => Data.Functor.Extend.Extend (Data.Semigroupoid.Static.Static f a)
instance (Control.Comonad.Comonad f, GHC.Base.Monoid a) => Control.Comonad.Comonad (Data.Semigroupoid.Static.Static f a)
instance Data.Functor.Bind.Class.Apply f => Data.Semigroupoid.Semigroupoid (Data.Semigroupoid.Static.Static f)
instance GHC.Base.Applicative f => Control.Category.Category (Data.Semigroupoid.Static.Static f)
instance GHC.Base.Applicative f => Control.Arrow.Arrow (Data.Semigroupoid.Static.Static f)
instance GHC.Base.Alternative f => Control.Arrow.ArrowZero (Data.Semigroupoid.Static.Static f)
instance GHC.Base.Alternative f => Control.Arrow.ArrowPlus (Data.Semigroupoid.Static.Static f)
instance GHC.Base.Applicative f => Control.Arrow.ArrowChoice (Data.Semigroupoid.Static.Static f)
module Data.Semigroup.Foldable
class Foldable t => Foldable1 t where foldMap1 f = maybe (error "foldMap1") id . getOption . foldMap (Option . Just . f) fold1 = foldMap1 id
fold1 :: (Foldable1 t, Semigroup m) => t m -> m
foldMap1 :: (Foldable1 t, Semigroup m) => (a -> m) -> t a -> m
-- | Insert an m between each pair of 't m'. Equivalent to
-- intercalateMap1 with id as the second argument.
--
--
-- >>> intercalate1 ", " $ "hello" :| ["how", "are", "you"]
-- "hello, how, are, you"
--
--
--
-- >>> intercalate1 ", " $ "hello" :| []
-- "hello"
--
--
--
-- >>> intercalate1 mempty $ "I" :| ["Am", "Fine", "You?"]
-- "IAmFineYou?"
--
intercalate1 :: (Foldable1 t, Semigroup m) => m -> t m -> m
-- | Insert m between each pair of m derived from
-- a.
--
--
-- >>> intercalateMap1 " " show $ True :| [False, True]
-- "True False True"
--
--
--
-- >>> intercalateMap1 " " show $ True :| []
-- "True"
--
intercalateMap1 :: (Foldable1 t, Semigroup m) => m -> (a -> m) -> t a -> m
traverse1_ :: (Foldable1 t, Apply f) => (a -> f b) -> t a -> f ()
for1_ :: (Foldable1 t, Apply f) => t a -> (a -> f b) -> f ()
sequenceA1_ :: (Foldable1 t, Apply f) => t (f a) -> f ()
-- | Usable default for foldMap, but only if you define foldMap1 yourself
foldMapDefault1 :: (Foldable1 t, Monoid m) => (a -> m) -> t a -> m
asum1 :: (Foldable1 t, Alt m) => t (m a) -> m a
instance Data.Semigroup.Semigroup a => Data.Semigroup.Semigroup (Data.Semigroup.Foldable.JoinWith a)
instance Data.Functor.Bind.Class.Apply f => Data.Semigroup.Semigroup (Data.Semigroup.Foldable.Act f a)
instance GHC.Base.Functor f => GHC.Base.Functor (Data.Semigroup.Foldable.Act f)
instance Data.Functor.Alt.Alt f => Data.Semigroup.Semigroup (Data.Semigroup.Foldable.Alt_ f a)
module Data.Semigroup.Traversable.Class
class (Bifoldable1 t, Bitraversable t) => Bitraversable1 t where bitraverse1 f g = bisequence1 . bimap f g bisequence1 = bitraverse1 id id
bitraverse1 :: (Bitraversable1 t, Apply f) => (a -> f b) -> (c -> f d) -> t a c -> f (t b d)
bisequence1 :: (Bitraversable1 t, Apply f) => t (f a) (f b) -> f (t a b)
class (Foldable1 t, Traversable t) => Traversable1 t where sequence1 = traverse1 id traverse1 f = sequence1 . fmap f
traverse1 :: (Traversable1 t, Apply f) => (a -> f b) -> t a -> f (t b)
sequence1 :: (Traversable1 t, Apply f) => t (f b) -> f (t b)
instance Data.Semigroup.Traversable.Class.Bitraversable1 Data.Semigroup.Arg
instance Data.Semigroup.Traversable.Class.Bitraversable1 Data.Either.Either
instance Data.Semigroup.Traversable.Class.Bitraversable1 (,)
instance Data.Semigroup.Traversable.Class.Bitraversable1 ((,,) x)
instance Data.Semigroup.Traversable.Class.Bitraversable1 ((,,,) x y)
instance Data.Semigroup.Traversable.Class.Bitraversable1 ((,,,,) x y z)
instance Data.Semigroup.Traversable.Class.Bitraversable1 Data.Functor.Const.Const
instance Data.Semigroup.Traversable.Class.Bitraversable1 Data.Tagged.Tagged
instance (Data.Semigroup.Traversable.Class.Bitraversable1 p, Data.Semigroup.Traversable.Class.Traversable1 f, Data.Semigroup.Traversable.Class.Traversable1 g) => Data.Semigroup.Traversable.Class.Bitraversable1 (Data.Bifunctor.Biff.Biff p f g)
instance Data.Semigroup.Traversable.Class.Traversable1 f => Data.Semigroup.Traversable.Class.Bitraversable1 (Data.Bifunctor.Clown.Clown f)
instance Data.Semigroup.Traversable.Class.Bitraversable1 p => Data.Semigroup.Traversable.Class.Bitraversable1 (Data.Bifunctor.Flip.Flip p)
instance Data.Semigroup.Traversable.Class.Bitraversable1 p => Data.Semigroup.Traversable.Class.Traversable1 (Data.Bifunctor.Join.Join p)
instance Data.Semigroup.Traversable.Class.Traversable1 g => Data.Semigroup.Traversable.Class.Bitraversable1 (Data.Bifunctor.Joker.Joker g)
instance (Data.Semigroup.Traversable.Class.Bitraversable1 f, Data.Semigroup.Traversable.Class.Bitraversable1 g) => Data.Semigroup.Traversable.Class.Bitraversable1 (Data.Bifunctor.Product.Product f g)
instance (Data.Semigroup.Traversable.Class.Traversable1 f, Data.Semigroup.Traversable.Class.Bitraversable1 p) => Data.Semigroup.Traversable.Class.Bitraversable1 (Data.Bifunctor.Tannen.Tannen f p)
instance Data.Semigroup.Traversable.Class.Bitraversable1 p => Data.Semigroup.Traversable.Class.Bitraversable1 (Data.Bifunctor.Wrapped.WrappedBifunctor p)
instance Data.Semigroup.Traversable.Class.Traversable1 f => Data.Semigroup.Traversable.Class.Traversable1 (GHC.Generics.Rec1 f)
instance Data.Semigroup.Traversable.Class.Traversable1 f => Data.Semigroup.Traversable.Class.Traversable1 (GHC.Generics.M1 i c f)
instance Data.Semigroup.Traversable.Class.Traversable1 GHC.Generics.Par1
instance Data.Semigroup.Traversable.Class.Traversable1 GHC.Generics.V1
instance (Data.Semigroup.Traversable.Class.Traversable1 f, Data.Semigroup.Traversable.Class.Traversable1 g) => Data.Semigroup.Traversable.Class.Traversable1 (f GHC.Generics.:*: g)
instance (Data.Semigroup.Traversable.Class.Traversable1 f, Data.Semigroup.Traversable.Class.Traversable1 g) => Data.Semigroup.Traversable.Class.Traversable1 (f GHC.Generics.:+: g)
instance (Data.Semigroup.Traversable.Class.Traversable1 f, Data.Semigroup.Traversable.Class.Traversable1 g) => Data.Semigroup.Traversable.Class.Traversable1 (f GHC.Generics.:.: g)
instance Data.Semigroup.Traversable.Class.Traversable1 Data.Functor.Identity.Identity
instance Data.Semigroup.Traversable.Class.Traversable1 f => Data.Semigroup.Traversable.Class.Traversable1 (Control.Monad.Trans.Identity.IdentityT f)
instance Data.Semigroup.Traversable.Class.Traversable1 f => Data.Semigroup.Traversable.Class.Traversable1 (Control.Applicative.Backwards.Backwards f)
instance (Data.Semigroup.Traversable.Class.Traversable1 f, Data.Semigroup.Traversable.Class.Traversable1 g) => Data.Semigroup.Traversable.Class.Traversable1 (Data.Functor.Compose.Compose f g)
instance Data.Semigroup.Traversable.Class.Traversable1 f => Data.Semigroup.Traversable.Class.Traversable1 (Control.Applicative.Lift.Lift f)
instance (Data.Semigroup.Traversable.Class.Traversable1 f, Data.Semigroup.Traversable.Class.Traversable1 g) => Data.Semigroup.Traversable.Class.Traversable1 (Data.Functor.Product.Product f g)
instance Data.Semigroup.Traversable.Class.Traversable1 f => Data.Semigroup.Traversable.Class.Traversable1 (Data.Functor.Reverse.Reverse f)
instance (Data.Semigroup.Traversable.Class.Traversable1 f, Data.Semigroup.Traversable.Class.Traversable1 g) => Data.Semigroup.Traversable.Class.Traversable1 (Data.Functor.Sum.Sum f g)
instance Data.Semigroup.Traversable.Class.Traversable1 (Data.Tagged.Tagged a)
instance Data.Semigroup.Traversable.Class.Traversable1 Data.Tree.Tree
instance Data.Semigroup.Traversable.Class.Traversable1 Data.List.NonEmpty.NonEmpty
instance Data.Semigroup.Traversable.Class.Traversable1 ((,) a)
instance Data.Semigroup.Traversable.Class.Traversable1 g => Data.Semigroup.Traversable.Class.Traversable1 (Data.Bifunctor.Joker.Joker g a)
module Data.Semigroup.Bitraversable
class (Bifoldable1 t, Bitraversable t) => Bitraversable1 t where bitraverse1 f g = bisequence1 . bimap f g bisequence1 = bitraverse1 id id
bitraverse1 :: (Bitraversable1 t, Apply f) => (a -> f b) -> (c -> f d) -> t a c -> f (t b d)
bisequence1 :: (Bitraversable1 t, Apply f) => t (f a) (f b) -> f (t a b)
bifoldMap1Default :: (Bitraversable1 t, Semigroup m) => (a -> m) -> (b -> m) -> t a b -> m
module Data.Semigroup.Traversable
class (Foldable1 t, Traversable t) => Traversable1 t where sequence1 = traverse1 id traverse1 f = sequence1 . fmap f
traverse1 :: (Traversable1 t, Apply f) => (a -> f b) -> t a -> f (t b)
sequence1 :: (Traversable1 t, Apply f) => t (f b) -> f (t b)
foldMap1Default :: (Traversable1 f, Semigroup m) => (a -> m) -> f a -> m
module Data.Bifunctor.Apply
-- | Formally, the class Bifunctor represents a bifunctor from
-- Hask -> Hask.
--
-- Intuitively it is a bifunctor where both the first and second
-- arguments are covariant.
--
-- You can define a Bifunctor by either defining bimap or
-- by defining both first and second.
--
-- If you supply bimap, you should ensure that:
--
--
-- bimap id id ≡ id
--
--
-- If you supply first and second, ensure:
--
--
-- first id ≡ id
-- second id ≡ id
--
--
-- If you supply both, you should also ensure:
--
--
-- bimap f g ≡ first f . second g
--
--
-- These ensure by parametricity:
--
--
-- bimap (f . g) (h . i) ≡ bimap f h . bimap g i
-- first (f . g) ≡ first f . first g
-- second (f . g) ≡ second f . second g
--
class Bifunctor (p :: * -> * -> *)
-- | Map over both arguments at the same time.
--
--
-- bimap f g ≡ first f . second g
--
bimap :: Bifunctor p => (a -> b) -> (c -> d) -> p a c -> p b d
-- | Map covariantly over the first argument.
--
--
-- first f ≡ bimap f id
--
first :: Bifunctor p => (a -> b) -> p a c -> p b c
-- | Map covariantly over the second argument.
--
--
-- second ≡ bimap id
--
second :: Bifunctor p => (b -> c) -> p a b -> p a c
class Bifunctor p => Biapply p where a .>> b = bimap (const id) (const id) <<$>> a <<.>> b a <<. b = bimap const const <<$>> a <<.>> b
(<<.>>) :: Biapply p => p (a -> b) (c -> d) -> p a c -> p b d
-- |
-- a .> b ≡ const id <$> a <.> b
--
(.>>) :: Biapply p => p a b -> p c d -> p c d
-- |
-- a <. b ≡ const <$> a <.> b
--
(<<.) :: Biapply p => p a b -> p c d -> p a b
(<<$>>) :: (a -> b) -> a -> b
infixl 4 <<$>>
(<<..>>) :: Biapply p => p a c -> p (a -> b) (c -> d) -> p b d
infixl 4 <<..>>
-- | Lift binary functions
bilift2 :: Biapply w => (a -> b -> c) -> (d -> e -> f) -> w a d -> w b e -> w c f
-- | Lift ternary functions
bilift3 :: Biapply w => (a -> b -> c -> d) -> (e -> f -> g -> h) -> w a e -> w b f -> w c g -> w d h