Control.Arrow
 Portability portable Stability experimental Maintainer ross@soi.city.ac.uk
 Contents Arrows Derived combinators Right-to-left variants Monoid operations Conditionals Arrow application Feedback
Description
Basic arrow definitions, based on Generalising Monads to Arrows, by John Hughes, Science of Computer Programming 37, pp67-111, May 2000. plus a couple of definitions (returnA and loop) from A New Notation for Arrows, by Ross Paterson, in ICFP 2001, Firenze, Italy, pp229-240. See these papers for the equations these combinators are expected to satisfy. These papers and more information on arrows can be found at http://www.haskell.org/arrows/.
Synopsis
class Arrow a where
 arr :: (b -> c) -> a b c pure :: (b -> c) -> a b c (>>>) :: a b c -> a c d -> a b d first :: a b c -> a (b, d) (c, d) second :: a b c -> a (d, b) (d, c) (***) :: a b c -> a b' c' -> a (b, b') (c, c') (&&&) :: a b c -> a b c' -> a b (c, c')
newtype Kleisli m a b = Kleisli {
 runKleisli :: (a -> m b)
}
returnA :: Arrow a => a b b
(^>>) :: Arrow a => (b -> c) -> a c d -> a b d
(>>^) :: Arrow a => a b c -> (c -> d) -> a b d
(<<<) :: Arrow a => a c d -> a b c -> a b d
(<<^) :: Arrow a => a c d -> (b -> c) -> a b d
(^<<) :: Arrow a => (c -> d) -> a b c -> a b d
class Arrow a => ArrowZero a where
 zeroArrow :: a b c
class ArrowZero a => ArrowPlus a where
 (<+>) :: a b c -> a b c -> a b c
class Arrow a => ArrowChoice a where
 left :: a b c -> a (Either b d) (Either c d) right :: a b c -> a (Either d b) (Either d c) (+++) :: a b c -> a b' c' -> a (Either b b') (Either c c') (|||) :: a b d -> a c d -> a (Either b c) d
class Arrow a => ArrowApply a where
 app :: a (a b c, b) c
newtype ArrowMonad a b = ArrowMonad (a () b)
leftApp :: ArrowApply a => a b c -> a (Either b d) (Either c d)
class Arrow a => ArrowLoop a where
 loop :: a (b, d) (c, d) -> a b c
Arrows
class Arrow a where
The basic arrow class. Any instance must define either arr or pure (which are synonyms), as well as >>> and first. The other combinators have sensible default definitions, which may be overridden for efficiency.
Methods
 arr :: (b -> c) -> a b c Lift a function to an arrow: you must define either this or pure. pure :: (b -> c) -> a b c A synonym for arr: you must define one or other of them. (>>>) :: a b c -> a c d -> a b d Left-to-right composition of arrows. first :: a b c -> a (b, d) (c, d) Send the first component of the input through the argument arrow, and copy the rest unchanged to the output. second :: a b c -> a (d, b) (d, c) A mirror image of first. The default definition may be overridden with a more efficient version if desired. (***) :: a b c -> a b' c' -> a (b, b') (c, c') Split the input between the two argument arrows and combine their output. Note that this is in general not a functor. The default definition may be overridden with a more efficient version if desired. (&&&) :: a b c -> a b c' -> a b (c, c') Fanout: send the input to both argument arrows and combine their output. The default definition may be overridden with a more efficient version if desired.
Instances
 Arrow (->) Monad m => Arrow (Kleisli m)
newtype Kleisli m a b
Kleisli arrows of a monad.
Constructors
Kleisli
 runKleisli :: (a -> m b)
Instances
 Monad m => Arrow (Kleisli m) Monad m => ArrowApply (Kleisli m) Monad m => ArrowChoice (Kleisli m) MonadFix m => ArrowLoop (Kleisli m) MonadPlus m => ArrowPlus (Kleisli m) MonadPlus m => ArrowZero (Kleisli m)
Derived combinators
returnA :: Arrow a => a b b
The identity arrow, which plays the role of return in arrow notation.
(^>>) :: Arrow a => (b -> c) -> a c d -> a b d
Precomposition with a pure function.
(>>^) :: Arrow a => a b c -> (c -> d) -> a b d
Postcomposition with a pure function.
Right-to-left variants
(<<<) :: Arrow a => a c d -> a b c -> a b d
Right-to-left composition, for a better fit with arrow notation.
(<<^) :: Arrow a => a c d -> (b -> c) -> a b d
Precomposition with a pure function (right-to-left variant).
(^<<) :: Arrow a => (c -> d) -> a b c -> a b d
Postcomposition with a pure function (right-to-left variant).
Monoid operations
class Arrow a => ArrowZero a where
Methods
 zeroArrow :: a b c
Instances
 MonadPlus m => ArrowZero (Kleisli m)
class ArrowZero a => ArrowPlus a where
Methods
 (<+>) :: a b c -> a b c -> a b c
Instances
 MonadPlus m => ArrowPlus (Kleisli m)
Conditionals
class Arrow a => ArrowChoice a where
Choice, for arrows that support it. This class underlies the if and case constructs in arrow notation. Any instance must define left. The other combinators have sensible default definitions, which may be overridden for efficiency.
Methods
 left :: a b c -> a (Either b d) (Either c d) Feed marked inputs through the argument arrow, passing the rest through unchanged to the output. right :: a b c -> a (Either d b) (Either d c) A mirror image of left. The default definition may be overridden with a more efficient version if desired. (+++) :: a b c -> a b' c' -> a (Either b b') (Either c c') Split the input between the two argument arrows, retagging and merging their outputs. Note that this is in general not a functor. The default definition may be overridden with a more efficient version if desired. (|||) :: a b d -> a c d -> a (Either b c) d Fanin: Split the input between the two argument arrows and merge their outputs. The default definition may be overridden with a more efficient version if desired.
Instances
 ArrowChoice (->) Monad m => ArrowChoice (Kleisli m)
Arrow application
class Arrow a => ArrowApply a where
Some arrows allow application of arrow inputs to other inputs.
Methods
 app :: a (a b c, b) c
Instances
 ArrowApply (->) Monad m => ArrowApply (Kleisli m)
newtype ArrowMonad a b
The ArrowApply class is equivalent to Monad: any monad gives rise to a Kleisli arrow, and any instance of ArrowApply defines a monad.
Constructors
 ArrowMonad (a () b)
Instances
 ArrowApply a => Monad (ArrowMonad a)
leftApp :: ArrowApply a => a b c -> a (Either b d) (Either c d)
Any instance of ArrowApply can be made into an instance of ArrowChoice by defining left = leftApp.
Feedback
class Arrow a => ArrowLoop a where
The loop operator expresses computations in which an output value is fed back as input, even though the computation occurs only once. It underlies the rec value recursion construct in arrow notation.
Methods
 loop :: a (b, d) (c, d) -> a b c
Instances
 ArrowLoop (->) MonadFix m => ArrowLoop (Kleisli m)
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