base-4.4.0.0: Basic libraries

Control.Arrow

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

# Arrows

class Category a => Arrow a whereSource

The basic arrow class.

Minimal complete definition: `arr` and `first`.

The other combinators have sensible default definitions, which may be overridden for efficiency.

Methods

arr :: (b -> c) -> a b cSource

Lift a function to an arrow.

first :: a b c -> a (b, d) (c, d)Source

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)Source

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')Source

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')Source

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 Source

Constructors

 Kleisli FieldsrunKleisli :: a -> m b

Instances

 Monad m => Category (Kleisli m) MonadFix m => ArrowLoop (Kleisli m) Monad m => ArrowApply (Kleisli m) Monad m => ArrowChoice (Kleisli m) MonadPlus m => ArrowPlus (Kleisli m) MonadPlus m => ArrowZero (Kleisli m) Monad m => Arrow (Kleisli m)

## Derived combinators

returnA :: Arrow a => a b bSource

The identity arrow, which plays the role of `return` in arrow notation.

(^>>) :: Arrow a => (b -> c) -> a c d -> a b dSource

Precomposition with a pure function.

(>>^) :: Arrow a => a b c -> (c -> d) -> a b dSource

Postcomposition with a pure function.

(>>>) :: Category cat => cat a b -> cat b c -> cat a cSource

Left-to-right composition

(<<<) :: Category cat => cat b c -> cat a b -> cat a cSource

Right-to-left composition

## Right-to-left variants

(<<^) :: Arrow a => a c d -> (b -> c) -> a b dSource

Precomposition with a pure function (right-to-left variant).

(^<<) :: Arrow a => (c -> d) -> a b c -> a b dSource

Postcomposition with a pure function (right-to-left variant).

# Monoid operations

class Arrow a => ArrowZero a whereSource

Methods

zeroArrow :: a b cSource

Instances

 MonadPlus m => ArrowZero (Kleisli m)

class ArrowZero a => ArrowPlus a whereSource

Methods

(<+>) :: a b c -> a b c -> a b cSource

Instances

 MonadPlus m => ArrowPlus (Kleisli m)

# Conditionals

class Arrow a => ArrowChoice a whereSource

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)Source

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)Source

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')Source

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) dSource

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 whereSource

Some arrows allow application of arrow inputs to other inputs.

Methods

app :: a (a b c, b) cSource

Instances

 ArrowApply (->) Monad m => ArrowApply (Kleisli m)

The `ArrowApply` class is equivalent to `Monad`: any monad gives rise to a `Kleisli` arrow, and any instance of `ArrowApply` defines a monad.

Constructors

Instances

leftApp :: ArrowApply a => a b c -> a (Either b d) (Either c d)Source

Any instance of `ArrowApply` can be made into an instance of `ArrowChoice` by defining `left` = `leftApp`.

# Feedback

class Arrow a => ArrowLoop a whereSource

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 cSource

Instances

 ArrowLoop (->) MonadFix m => ArrowLoop (Kleisli m)