these-0.4.2: An either-or-both data type, with corresponding hybrid error/writer monad transformer.

Safe HaskellNone




These-based zipping and unzipping of functors with non-uniform shapes, plus traversal of (bi)foldable (bi)functors through said functors.



class Functor f => Align f whereSource

Functors supporting a zip operation that takes the union of non-uniform shapes.

If your functor is actually a functor from Kleisli Maybe to Hask (so it supports maybeMap :: (a -> Maybe b) -> f a -> f b), then an Align instance is making your functor lax monoidal w.r.t. the cartesian monoidal structure on Kleisli Maybe, because These is the cartesian product in that category (a -> Maybe (These b c) ~ (a -> Maybe b, a -> Maybe c)). This insight is due to rwbarton.

Minimal definition: nil and either align or alignWith.


 (`align` nil) = fmap This
 (nil `align`) = fmap That
 join align = fmap (join These)
 align (f <$> x) (g <$> y) = bimap f g <$> align x y
 alignWith f a b = f <$> align a b


nil :: f aSource

align :: f a -> f b -> f (These a b)Source

alignWith :: (These a b -> c) -> f a -> f b -> f cSource


Align [] 
Align ZipList 
Align Maybe 
Align Seq 
Align IntMap 
Ord k => Align (Map k) 
Monad m => Align (Stream m) 
(Align f, Align g) => Align (Product f g) 

Specialized aligns

malign :: (Align f, Monoid a) => f a -> f a -> f aSource

Align two structures and combine with mappend.

padZip :: Align f => f a -> f b -> f (Maybe a, Maybe b)Source

Align two structures as in zip, but filling in blanks with Nothing.

padZipWith :: Align f => (Maybe a -> Maybe b -> c) -> f a -> f b -> f cSource

Align two structures as in zipWith, but filling in blanks with Nothing.

lpadZip :: [a] -> [b] -> [(Maybe a, b)]Source

Left-padded zip.

lpadZipWith :: (Maybe a -> b -> c) -> [a] -> [b] -> [c]Source

Left-padded zipWith.

rpadZip :: [a] -> [b] -> [(a, Maybe b)]Source

Right-padded zip.

rpadZipWith :: (a -> Maybe b -> c) -> [a] -> [b] -> [c]Source

Right-padded zipWith.

alignVectorWith :: (Vector v a, Vector v b, Vector v c) => (These a b -> c) -> v a -> v b -> v cSource


class Align f => Unalign f whereSource

Alignable functors supporting an "inverse" to align: splitting a union shape into its component parts.

Minimal definition: nothing; a default definition is provided, but it may not have the desired definition for all functors. See the source for more information.


 unalign nil                 = (nil,           nil)
 unalign (This        <$> x) = (Just    <$> x, Nothing <$  x)
 unalign (That        <$> y) = (Nothing <$  y, Just    <$> y)
 unalign (join These  <$> x) = (Just    <$> x, Just    <$> x)
 unalign ((x `These`) <$> y) = (Just x  <$  y, Just    <$> y)
 unalign ((`These` y) <$> x) = (Just    <$> x, Just y  <$  x)


unalign :: f (These a b) -> (f (Maybe a), f (Maybe b))Source



class (Functor t, Foldable t) => Crosswalk t whereSource

Foldable functors supporting traversal through an alignable functor.

Minimal definition: crosswalk or sequenceL.


 crosswalk (const nil) = const nil
 crosswalk f = sequenceL . fmap f


crosswalk :: Align f => (a -> f b) -> t a -> f (t b)Source

sequenceL :: Align f => t (f a) -> f (t a)Source


class (Bifunctor t, Bifoldable t) => Bicrosswalk t whereSource

Bifoldable bifunctors supporting traversal through an alignable functor.

Minimal definition: bicrosswalk or bisequenceL.


 bicrosswalk (const empty) (const empty) = const empty
 bicrosswalk f g = bisequenceL . bimap f g


bicrosswalk :: Align f => (a -> f c) -> (b -> f d) -> t a b -> f (t c d)Source

bisequenceL :: Align f => t (f a) (f b) -> f (t a b)Source