ghc-internal-9.1001.0: Basic libraries

GHC.Internal.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.

Synopsis

# Arrows

class Category a => Arrow (a :: Type -> Type -> Type) where Source #

The basic arrow class.

Instances should satisfy the following laws:

• arr id = id
• arr (f >>> g) = arr f >>> arr g
• first (arr f) = arr (first f)
• first (f >>> g) = first f >>> first g
• first f >>> arr fst = arr fst >>> f
• first f >>> arr (id *** g) = arr (id *** g) >>> first f
• first (first f) >>> arr assoc = arr assoc >>> first f

where

assoc ((a,b),c) = (a,(b,c))

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

Minimal complete definition

arr, (first | (***))

Methods

arr :: (b -> c) -> a b c Source #

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') infixr 3 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') infixr 3 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

Instances details
 Monad m => Arrow (Kleisli m) Source # @since base-2.01 Instance detailsDefined in GHC.Internal.Control.Arrow Methodsarr :: (b -> c) -> Kleisli m b c Source #first :: Kleisli m b c -> Kleisli m (b, d) (c, d) Source #second :: Kleisli m b c -> Kleisli m (d, b) (d, c) Source #(***) :: Kleisli m b c -> Kleisli m b' c' -> Kleisli m (b, b') (c, c') Source #(&&&) :: Kleisli m b c -> Kleisli m b c' -> Kleisli m b (c, c') Source # Arrow (->) Source # @since base-2.01 Instance detailsDefined in GHC.Internal.Control.Arrow Methodsarr :: (b -> c) -> b -> c Source #first :: (b -> c) -> (b, d) -> (c, d) Source #second :: (b -> c) -> (d, b) -> (d, c) Source #(***) :: (b -> c) -> (b' -> c') -> (b, b') -> (c, c') Source #(&&&) :: (b -> c) -> (b -> c') -> b -> (c, c') Source #

newtype Kleisli (m :: Type -> Type) a b Source #

Constructors

 Kleisli FieldsrunKleisli :: a -> m b

#### Instances

Instances details
Monad m => Category (Kleisli m :: Type -> Type -> Type) Source #

@since base-3.0

Instance details

Defined in GHC.Internal.Control.Arrow

Methods

id :: Kleisli m a a Source #

(.) :: Kleisli m b c -> Kleisli m a b -> Kleisli m a c Source #

Generic1 (Kleisli m a :: Type -> Type) Source #
Instance details

Defined in GHC.Internal.Control.Arrow

Associated Types

 type Rep1 (Kleisli m a :: Type -> Type) @since base-4.14.0.0 Instance detailsDefined in GHC.Internal.Control.Arrow type Rep1 (Kleisli m a :: Type -> Type) = D1 ('MetaData "Kleisli" "GHC.Internal.Control.Arrow" "ghc-internal" 'True) (C1 ('MetaCons "Kleisli" 'PrefixI 'True) (S1 ('MetaSel ('Just "runKleisli") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) ((FUN 'Many a :: Type -> Type) :.: Rec1 m)))

Methods

from1 :: Kleisli m a a0 -> Rep1 (Kleisli m a) a0 Source #

to1 :: Rep1 (Kleisli m a) a0 -> Kleisli m a a0 Source #

Monad m => Arrow (Kleisli m) Source #

@since base-2.01

Instance details

Defined in GHC.Internal.Control.Arrow

Methods

arr :: (b -> c) -> Kleisli m b c Source #

first :: Kleisli m b c -> Kleisli m (b, d) (c, d) Source #

second :: Kleisli m b c -> Kleisli m (d, b) (d, c) Source #

(***) :: Kleisli m b c -> Kleisli m b' c' -> Kleisli m (b, b') (c, c') Source #

(&&&) :: Kleisli m b c -> Kleisli m b c' -> Kleisli m b (c, c') Source #

Monad m => ArrowApply (Kleisli m) Source #

@since base-2.01

Instance details

Defined in GHC.Internal.Control.Arrow

Methods

app :: Kleisli m (Kleisli m b c, b) c Source #

Monad m => ArrowChoice (Kleisli m) Source #

@since base-2.01

Instance details

Defined in GHC.Internal.Control.Arrow

Methods

left :: Kleisli m b c -> Kleisli m (Either b d) (Either c d) Source #

right :: Kleisli m b c -> Kleisli m (Either d b) (Either d c) Source #

(+++) :: Kleisli m b c -> Kleisli m b' c' -> Kleisli m (Either b b') (Either c c') Source #

(|||) :: Kleisli m b d -> Kleisli m c d -> Kleisli m (Either b c) d Source #

MonadFix m => ArrowLoop (Kleisli m) Source #

Beware that for many monads (those for which the >>= operation is strict) this instance will not satisfy the right-tightening law required by the ArrowLoop class.

@since base-2.01

Instance details

Defined in GHC.Internal.Control.Arrow

Methods

loop :: Kleisli m (b, d) (c, d) -> Kleisli m b c Source #

MonadPlus m => ArrowPlus (Kleisli m) Source #

@since base-2.01

Instance details

Defined in GHC.Internal.Control.Arrow

Methods

(<+>) :: Kleisli m b c -> Kleisli m b c -> Kleisli m b c Source #

MonadPlus m => ArrowZero (Kleisli m) Source #

@since base-2.01

Instance details

Defined in GHC.Internal.Control.Arrow

Methods

zeroArrow :: Kleisli m b c Source #

Alternative m => Alternative (Kleisli m a) Source #

@since base-4.14.0.0

Instance details

Defined in GHC.Internal.Control.Arrow

Methods

empty :: Kleisli m a a0 Source #

(<|>) :: Kleisli m a a0 -> Kleisli m a a0 -> Kleisli m a a0 Source #

some :: Kleisli m a a0 -> Kleisli m a [a0] Source #

many :: Kleisli m a a0 -> Kleisli m a [a0] Source #

Applicative m => Applicative (Kleisli m a) Source #

@since base-4.14.0.0

Instance details

Defined in GHC.Internal.Control.Arrow

Methods

pure :: a0 -> Kleisli m a a0 Source #

(<*>) :: Kleisli m a (a0 -> b) -> Kleisli m a a0 -> Kleisli m a b Source #

liftA2 :: (a0 -> b -> c) -> Kleisli m a a0 -> Kleisli m a b -> Kleisli m a c Source #

(*>) :: Kleisli m a a0 -> Kleisli m a b -> Kleisli m a b Source #

(<*) :: Kleisli m a a0 -> Kleisli m a b -> Kleisli m a a0 Source #

Functor m => Functor (Kleisli m a) Source #

@since base-4.14.0.0

Instance details

Defined in GHC.Internal.Control.Arrow

Methods

fmap :: (a0 -> b) -> Kleisli m a a0 -> Kleisli m a b Source #

(<$) :: a0 -> Kleisli m a b -> Kleisli m a a0 Source # Monad m => Monad (Kleisli m a) Source # @since base-4.14.0.0 Instance details Defined in GHC.Internal.Control.Arrow Methods (>>=) :: Kleisli m a a0 -> (a0 -> Kleisli m a b) -> Kleisli m a b Source # (>>) :: Kleisli m a a0 -> Kleisli m a b -> Kleisli m a b Source # return :: a0 -> Kleisli m a a0 Source # MonadPlus m => MonadPlus (Kleisli m a) Source # @since base-4.14.0.0 Instance details Defined in GHC.Internal.Control.Arrow Methods mzero :: Kleisli m a a0 Source # mplus :: Kleisli m a a0 -> Kleisli m a a0 -> Kleisli m a a0 Source # Generic (Kleisli m a b) Source # Instance details Defined in GHC.Internal.Control.Arrow Associated Types  type Rep (Kleisli m a b) @since base-4.14.0.0 Instance detailsDefined in GHC.Internal.Control.Arrow type Rep (Kleisli m a b) = D1 ('MetaData "Kleisli" "GHC.Internal.Control.Arrow" "ghc-internal" 'True) (C1 ('MetaCons "Kleisli" 'PrefixI 'True) (S1 ('MetaSel ('Just "runKleisli") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (a -> m b)))) Methods from :: Kleisli m a b -> Rep (Kleisli m a b) x Source # to :: Rep (Kleisli m a b) x -> Kleisli m a b Source # type Rep1 (Kleisli m a :: Type -> Type) Source # @since base-4.14.0.0 Instance details Defined in GHC.Internal.Control.Arrow type Rep1 (Kleisli m a :: Type -> Type) = D1 ('MetaData "Kleisli" "GHC.Internal.Control.Arrow" "ghc-internal" 'True) (C1 ('MetaCons "Kleisli" 'PrefixI 'True) (S1 ('MetaSel ('Just "runKleisli") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) ((FUN 'Many a :: Type -> Type) :.: Rec1 m))) type Rep (Kleisli m a b) Source # @since base-4.14.0.0 Instance details Defined in GHC.Internal.Control.Arrow type Rep (Kleisli m a b) = D1 ('MetaData "Kleisli" "GHC.Internal.Control.Arrow" "ghc-internal" 'True) (C1 ('MetaCons "Kleisli" 'PrefixI 'True) (S1 ('MetaSel ('Just "runKleisli") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (a -> m b)))) ## Derived combinators returnA :: Arrow a => a b b Source # The identity arrow, which plays the role of return in arrow notation. (^>>) :: Arrow a => (b -> c) -> a c d -> a b d infixr 1 Source # Precomposition with a pure function. (>>^) :: Arrow a => a b c -> (c -> d) -> a b d infixr 1 Source # Postcomposition with a pure function. (>>>) :: forall {k} cat (a :: k) (b :: k) (c :: k). Category cat => cat a b -> cat b c -> cat a c infixr 1 Source # Left-to-right composition (<<<) :: forall {k} cat (b :: k) (c :: k) (a :: k). Category cat => cat b c -> cat a b -> cat a c infixr 1 Source # Right-to-left composition ## Right-to-left variants (<<^) :: Arrow a => a c d -> (b -> c) -> a b d infixr 1 Source # Precomposition with a pure function (right-to-left variant). (^<<) :: Arrow a => (c -> d) -> a b c -> a b d infixr 1 Source # Postcomposition with a pure function (right-to-left variant). # Monoid operations class Arrow a => ArrowZero (a :: Type -> Type -> Type) where Source # Methods zeroArrow :: a b c Source # #### Instances Instances details  MonadPlus m => ArrowZero (Kleisli m) Source # @since base-2.01 Instance detailsDefined in GHC.Internal.Control.Arrow MethodszeroArrow :: Kleisli m b c Source # class ArrowZero a => ArrowPlus (a :: Type -> Type -> Type) where Source # A monoid on arrows. Methods (<+>) :: a b c -> a b c -> a b c infixr 5 Source # An associative operation with identity zeroArrow. #### Instances Instances details  MonadPlus m => ArrowPlus (Kleisli m) Source # @since base-2.01 Instance detailsDefined in GHC.Internal.Control.Arrow Methods(<+>) :: Kleisli m b c -> Kleisli m b c -> Kleisli m b c Source # # Conditionals class Arrow a => ArrowChoice (a :: Type -> Type -> Type) where Source # Choice, for arrows that support it. This class underlies the if and case constructs in arrow notation. Instances should satisfy the following laws: • left (arr f) = arr (left f) • left (f >>> g) = left f >>> left g • f >>> arr Left = arr Left >>> left f • left f >>> arr (id +++ g) = arr (id +++ g) >>> left f • left (left f) >>> arr assocsum = arr assocsum >>> left f where assocsum (Left (Left x)) = Left x assocsum (Left (Right y)) = Right (Left y) assocsum (Right z) = Right (Right z) The other combinators have sensible default definitions, which may be overridden for efficiency. Minimal complete definition (left | (+++)) 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') infixr 2 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) d infixr 2 Source # 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 Instances details  Monad m => ArrowChoice (Kleisli m) Source # @since base-2.01 Instance detailsDefined in GHC.Internal.Control.Arrow Methodsleft :: Kleisli m b c -> Kleisli m (Either b d) (Either c d) Source #right :: Kleisli m b c -> Kleisli m (Either d b) (Either d c) Source #(+++) :: Kleisli m b c -> Kleisli m b' c' -> Kleisli m (Either b b') (Either c c') Source #(|||) :: Kleisli m b d -> Kleisli m c d -> Kleisli m (Either b c) d Source # ArrowChoice (->) Source # @since base-2.01 Instance detailsDefined in GHC.Internal.Control.Arrow Methodsleft :: (b -> c) -> Either b d -> Either c d Source #right :: (b -> c) -> Either d b -> Either d c Source #(+++) :: (b -> c) -> (b' -> c') -> Either b b' -> Either c c' Source #(|||) :: (b -> d) -> (c -> d) -> Either b c -> d Source # # Arrow application class Arrow a => ArrowApply (a :: Type -> Type -> Type) where Source # Some arrows allow application of arrow inputs to other inputs. Instances should satisfy the following laws: • first (arr (\x -> arr (\y -> (x,y)))) >>> app = id • first (arr (g >>>)) >>> app = second g >>> app • first (arr (>>> h)) >>> app = app >>> h Such arrows are equivalent to monads (see ArrowMonad). Methods app :: a (a b c, b) c Source # #### Instances Instances details  Monad m => ArrowApply (Kleisli m) Source # @since base-2.01 Instance detailsDefined in GHC.Internal.Control.Arrow Methodsapp :: Kleisli m (Kleisli m b c, b) c Source # ArrowApply (->) Source # @since base-2.01 Instance detailsDefined in GHC.Internal.Control.Arrow Methodsapp :: (b -> c, b) -> c Source # newtype ArrowMonad (a :: Type -> Type -> Type) b Source # 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 Instances details  Source # @since base-4.6.0.0 Instance detailsDefined in GHC.Internal.Control.Arrow Methodsempty :: ArrowMonad a a0 Source #(<|>) :: ArrowMonad a a0 -> ArrowMonad a a0 -> ArrowMonad a a0 Source #some :: ArrowMonad a a0 -> ArrowMonad a [a0] Source #many :: ArrowMonad a a0 -> ArrowMonad a [a0] Source # Arrow a => Applicative (ArrowMonad a) Source # @since base-4.6.0.0 Instance detailsDefined in GHC.Internal.Control.Arrow Methodspure :: a0 -> ArrowMonad a a0 Source #(<*>) :: ArrowMonad a (a0 -> b) -> ArrowMonad a a0 -> ArrowMonad a b Source #liftA2 :: (a0 -> b -> c) -> ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a c Source #(*>) :: ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a b Source #(<*) :: ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a a0 Source # Arrow a => Functor (ArrowMonad a) Source # @since base-4.6.0.0 Instance detailsDefined in GHC.Internal.Control.Arrow Methodsfmap :: (a0 -> b) -> ArrowMonad a a0 -> ArrowMonad a b Source #(<$) :: a0 -> ArrowMonad a b -> ArrowMonad a a0 Source # ArrowApply a => Monad (ArrowMonad a) Source # @since base-2.01 Instance detailsDefined in GHC.Internal.Control.Arrow Methods(>>=) :: ArrowMonad a a0 -> (a0 -> ArrowMonad a b) -> ArrowMonad a b Source #(>>) :: ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a b Source #return :: a0 -> ArrowMonad a a0 Source # (ArrowApply a, ArrowPlus a) => MonadPlus (ArrowMonad a) Source # @since base-4.6.0.0 Instance detailsDefined in GHC.Internal.Control.Arrow Methodsmzero :: ArrowMonad a a0 Source #mplus :: ArrowMonad a a0 -> ArrowMonad a a0 -> ArrowMonad a a0 Source #

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 :: Type -> Type -> Type) where Source #

The loop operator expresses computations in which an output value is fed back as input, although the computation occurs only once. It underlies the rec value recursion construct in arrow notation. loop should satisfy the following laws:

extension
loop (arr f) = arr (\ b -> fst (fix (\ (c,d) -> f (b,d))))
left tightening
loop (first h >>> f) = h >>> loop f
right tightening
loop (f >>> first h) = loop f >>> h
sliding
loop (f >>> arr (id *** k)) = loop (arr (id *** k) >>> f)
vanishing
loop (loop f) = loop (arr unassoc >>> f >>> arr assoc)
superposing
second (loop f) = loop (arr assoc >>> second f >>> arr unassoc)

where

assoc ((a,b),c) = (a,(b,c))
unassoc (a,(b,c)) = ((a,b),c)

Methods

loop :: a (b, d) (c, d) -> a b c Source #

#### Instances

Instances details
 MonadFix m => ArrowLoop (Kleisli m) Source # Beware that for many monads (those for which the >>= operation is strict) this instance will not satisfy the right-tightening law required by the ArrowLoop class.@since base-2.01 Instance detailsDefined in GHC.Internal.Control.Arrow Methodsloop :: Kleisli m (b, d) (c, d) -> Kleisli m b c Source # ArrowLoop (->) Source # @since base-2.01 Instance detailsDefined in GHC.Internal.Control.Arrow Methodsloop :: ((b, d) -> (c, d)) -> b -> c Source #