Control.Arrow

Definitions

interface Arrow : (Type -> Type -> Type) -> Type

Parameters: arr
Constraints: Category arr
Methods:

arrow : (a -> b) -> arr a b

  Converts a function from input to output into a arrow computation.

first : arr a b -> arr (a, c) (b, c)

  Converts an arrow from `a` to `b` into an arrow on pairs, that applies
  its argument to the first component and leaves the second component
  untouched, thus saving its value across a computation.

second : arr a b -> arr (c, a) (c, b)

  Converts an arrow from `a` to `b` into an arrow on pairs, that applies
  its argument to the second component and leaves the first component
  untouched, thus saving its value across a computation.

(***) : arr a b -> arr a' b' -> arr (a, a') (b, b')

  A combinator which processes both components of a pair.

Fixity Declaration: infixr operator, level 3

(&&&) : arr a b -> arr a b' -> arr a (b, b')

  A combinator which builds a pair from the results of two arrows.

Fixity Declaration: infixr operator, level 3

Implementations:

Arrow Morphism

Monad m => Arrow (Kleislimorphism m)

arrow : Arrow arr => (a -> b) -> arr a b

  Converts a function from input to output into a arrow computation.

Visibility: public export

first : Arrow arr => arr a b -> arr (a, c) (b, c)

  Converts an arrow from `a` to `b` into an arrow on pairs, that applies
  its argument to the first component and leaves the second component
  untouched, thus saving its value across a computation.

Visibility: public export

second : Arrow arr => arr a b -> arr (c, a) (c, b)

  Converts an arrow from `a` to `b` into an arrow on pairs, that applies
  its argument to the second component and leaves the first component
  untouched, thus saving its value across a computation.

Visibility: public export

(***) : Arrow arr => arr a b -> arr a' b' -> arr (a, a') (b, b')

  A combinator which processes both components of a pair.

Visibility: public export
Fixity Declaration: infixr operator, level 3

(&&&) : Arrow arr => arr a b -> arr a b' -> arr a (b, b')

  A combinator which builds a pair from the results of two arrows.

Visibility: public export
Fixity Declaration: infixr operator, level 3

interface ArrowZero : (Type -> Type -> Type) -> Type

Parameters: arr
Constraints: Arrow arr
Methods:

zeroArrow : arr a b

Implementation: 

ArrowPlus arr -> ArrowZero arr

zeroArrow : ArrowZero arr => arr a b

Visibility: public export

interface ArrowPlus : (Type -> Type -> Type) -> Type

Parameters: arr
Constraints: ArrowZero arr
Methods:

(<++>) : arr a b -> arr a b -> arr a b

Fixity Declaration: infixr operator, level 5

(<++>) : ArrowPlus arr => arr a b -> arr a b -> arr a b

Visibility: public export
Fixity Declaration: infixr operator, level 5

interface ArrowChoice : (Type -> Type -> Type) -> Type

Parameters: arr
Constraints: Arrow arr
Methods:

left : arr a b -> arr (Either a c) (Either b c)

right : arr a b -> arr (Either c a) (Either c b)

(+++) : arr a b -> arr c d -> arr (Either a c) (Either b d)

Fixity Declaration: infixr operator, level 2

(\|/) : arr a b -> arr c b -> arr (Either a c) b

Fixity Declaration: infixr operator, level 2

Implementation: 

Monad m => ArrowChoice (Kleislimorphism m)

left : ArrowChoice arr => arr a b -> arr (Either a c) (Either b c)

Visibility: public export

right : ArrowChoice arr => arr a b -> arr (Either c a) (Either c b)

Visibility: public export

(+++) : ArrowChoice arr => arr a b -> arr c d -> arr (Either a c) (Either b d)

Visibility: public export
Fixity Declaration: infixr operator, level 2

(\|/) : ArrowChoice arr => arr a b -> arr c b -> arr (Either a c) b

Visibility: public export
Fixity Declaration: infixr operator, level 2

interface ArrowApply : (Type -> Type -> Type) -> Type

Parameters: arr
Constraints: Arrow arr
Methods:

app : arr (arr a b, a) b

Implementation: 

Monad m => ArrowApply (Kleislimorphism m)

app : ArrowApply arr => arr (arr a b, a) b

Visibility: public export

data ArrowMonad : (Type -> Type -> Type) -> Type -> Type

Totality: total
Visibility: public export
Constructor: 

MkArrowMonad : arr () a -> ArrowMonad arr a

Hints:

Arrow a => Applicative (ArrowMonad a)

Arrow a => Functor (ArrowMonad a)

ArrowApply a => Monad (ArrowMonad a)

runArrowMonad : ArrowMonad arr a -> arr () a

Visibility: public export

interface ArrowLoop : (Type -> Type -> Type) -> Type

Parameters: arr
Constraints: Arrow arr
Methods:

loop : arr (a, c) (b, c) -> arr a b

loop : ArrowLoop arr => arr (a, c) (b, c) -> arr a b

Visibility: public export

liftA2 : Arrow arr => (a -> b -> c) -> arr d a -> arr d b -> arr d c

  Applying a binary operator to the results of two arrow computations.

Visibility: public export