Data.Bitraversable

class (Bifunctor t, Bifoldable t) <= Bitraversable t  where

Bitraversable represents data structures with two type arguments which can be traversed.

A traversal for such a structure requires two functions, one for each type argument. Type class instances should choose the appropriate function based on the type of the element encountered at each point of the traversal.

Default implementations are provided by the following functions:

• bitraverseDefault
• bisequenceDefault

Members

• bitraverse :: forall d c b a f. Applicative f => (a -> f c) -> (b -> f d) -> t a b -> f (t c d)
• bisequence :: forall b a f. Applicative f => t (f a) (f b) -> f (t a b)

Instances

• (Traversable f) => Bitraversable (Clown f)
• (Traversable f) => Bitraversable (Joker f)
• (Bitraversable p) => Bitraversable (Flip p)
• (Bitraversable f, Bitraversable g) => Bitraversable (Product f g)
• (Bitraversable p) => Bitraversable (Wrap p)

bitraverseDefault :: forall d c b a f t. Bitraversable t => Applicative f => (a -> f c) -> (b -> f d) -> t a b -> f (t c d)

A default implementation of bitraverse using bisequence and bimap.

bisequenceDefault :: forall b a f t. Bitraversable t => Applicative f => t (f a) (f b) -> f (t a b)

A default implementation of bisequence using bitraverse.

ltraverse :: forall f a c b t. Bitraversable t => Applicative f => (a -> f c) -> t a b -> f (t c b)

rtraverse :: forall f a c b t. Bitraversable t => Applicative f => (b -> f c) -> t a b -> f (t a c)

bifor :: forall d c b a f t. Bitraversable t => Applicative f => t a b -> (a -> f c) -> (b -> f d) -> f (t c d)

Traverse a data structure, accumulating effects and results using an Applicative functor.

lfor :: forall f a c b t. Bitraversable t => Applicative f => t a b -> (a -> f c) -> f (t c b)

rfor :: forall f a c b t. Bitraversable t => Applicative f => t a b -> (b -> f c) -> f (t a c)

class Bifoldable p  where

Bifoldable represents data structures with two type arguments which can be folded.

A fold for such a structure requires two step functions, one for each type argument. Type class instances should choose the appropriate step function based on the type of the element encountered at each point of the fold.

Default implementations are provided by the following functions:

• bifoldrDefault
• bifoldlDefault
• bifoldMapDefaultR
• bifoldMapDefaultL

Note: some combinations of the default implementations are unsafe to use together - causing a non-terminating mutually recursive cycle. These combinations are documented per function.

Members

• bifoldr :: forall c b a. (a -> c -> c) -> (b -> c -> c) -> c -> p a b -> c
• bifoldl :: forall c b a. (c -> a -> c) -> (c -> b -> c) -> c -> p a b -> c
• bifoldMap :: forall b a m. Monoid m => (a -> m) -> (b -> m) -> p a b -> m

Instances

• (Foldable f) => Bifoldable (Clown f)
• (Foldable f) => Bifoldable (Joker f)
• (Bifoldable p) => Bifoldable (Flip p)
• (Bifoldable f, Bifoldable g) => Bifoldable (Product f g)
• (Bifoldable p) => Bifoldable (Wrap p)

bitraverse_ :: forall d c b a f t. Bifoldable t => Applicative f => (a -> f c) -> (b -> f d) -> t a b -> f Unit

Traverse a data structure, accumulating effects using an Applicative functor, ignoring the final result.

bisequence_ :: forall b a f t. Bifoldable t => Applicative f => t (f a) (f b) -> f Unit

Collapse a data structure, collecting effects using an Applicative functor, ignoring the final result.

bifor_ :: forall d c b a f t. Bifoldable t => Applicative f => t a b -> (a -> f c) -> (b -> f d) -> f Unit

A version of bitraverse_ with the data structure as the first argument.

bifoldrDefault :: forall c b a p. Bifoldable p => (a -> c -> c) -> (b -> c -> c) -> c -> p a b -> c

A default implementation of bifoldr using bifoldMap.

Note: when defining a Bifoldable instance, this function is unsafe to use in combination with bifoldMapDefaultR.

bifoldlDefault :: forall c b a p. Bifoldable p => (c -> a -> c) -> (c -> b -> c) -> c -> p a b -> c

A default implementation of bifoldl using bifoldMap.

Note: when defining a Bifoldable instance, this function is unsafe to use in combination with bifoldMapDefaultL.

bifoldMapDefaultR :: forall b a m p. Bifoldable p => Monoid m => (a -> m) -> (b -> m) -> p a b -> m

A default implementation of bifoldMap using bifoldr.

Note: when defining a Bifoldable instance, this function is unsafe to use in combination with bifoldrDefault.

bifoldMapDefaultL :: forall b a m p. Bifoldable p => Monoid m => (a -> m) -> (b -> m) -> p a b -> m

A default implementation of bifoldMap using bifoldl.

Note: when defining a Bifoldable instance, this function is unsafe to use in combination with bifoldlDefault.

bifold :: forall m t. Bifoldable t => Monoid m => t m m -> m

Fold a data structure, accumulating values in a monoidal type.

biany :: forall c b a t. Bifoldable t => BooleanAlgebra c => (a -> c) -> (b -> c) -> t a b -> c

Test whether a predicate holds at any position in a data structure.

biall :: forall c b a t. Bifoldable t => BooleanAlgebra c => (a -> c) -> (b -> c) -> t a b -> c

Test whether a predicate holds at all positions in a data structure.