| Safe Haskell | Safe |
|---|---|
| Language | Haskell2010 |
Data.Generics.Fixplate.Morphisms
Description
Recursion schemes, also known as scary named folds...
- cata :: Functor f => (f a -> a) -> Mu f -> a
- para :: Functor f => (f (Mu f, a) -> a) -> Mu f -> a
- para' :: Functor f => (Mu f -> f a -> a) -> Mu f -> a
- paraList :: (Functor f, Foldable f) => (Mu f -> [a] -> a) -> Mu f -> a
- ana :: Functor f => (a -> f a) -> a -> Mu f
- apo :: Functor f => (a -> f (Either (Mu f) a)) -> a -> Mu f
- hylo :: Functor f => (f a -> a) -> (b -> f b) -> b -> a
- zygo_ :: Functor f => (f b -> b) -> (f (b, a) -> a) -> Mu f -> a
- zygo :: Functor f => (f b -> b) -> (f (b, a) -> a) -> Mu f -> (b, a)
- histo :: Functor f => (f (Attr f a) -> a) -> Mu f -> a
- futu :: Functor f => (a -> f (CoAttr f a)) -> a -> Mu f
- cataM :: (Monad m, Traversable f) => (f a -> m a) -> Mu f -> m a
- cataM_ :: (Monad m, Traversable f) => (f a -> m a) -> Mu f -> m ()
- paraM :: (Monad m, Traversable f) => (f (Mu f, a) -> m a) -> Mu f -> m a
- paraM_ :: (Monad m, Traversable f) => (f (Mu f, a) -> m a) -> Mu f -> m ()
- paraM' :: (Monad m, Traversable f) => (Mu f -> f a -> m a) -> Mu f -> m a
Classic ana/cata/para/hylo-morphisms
cata :: Functor f => (f a -> a) -> Mu f -> a Source #
A catamorphism is the generalization of right fold from lists to trees.
para :: Functor f => (f (Mu f, a) -> a) -> Mu f -> a Source #
A paramorphism is a more general version of the catamorphism.
para' :: Functor f => (Mu f -> f a -> a) -> Mu f -> a Source #
Another version of para (a bit less natural in some sense).
paraList :: (Functor f, Foldable f) => (Mu f -> [a] -> a) -> Mu f -> a Source #
A list version of para (compare with Uniplate)
ana :: Functor f => (a -> f a) -> a -> Mu f Source #
An anamorphism is simply an unfold. Probably not very useful in this context.
apo :: Functor f => (a -> f (Either (Mu f) a)) -> a -> Mu f Source #
An apomorphism is a generalization of the anamorphism.
hylo :: Functor f => (f a -> a) -> (b -> f b) -> b -> a Source #
A hylomorphism is the composition of a catamorphism and an anamorphism.
Zygomorphisms
zygo_ :: Functor f => (f b -> b) -> (f (b, a) -> a) -> Mu f -> a Source #
A zygomorphism is a basically a catamorphism inside another catamorphism.
It could be implemented (somewhat wastefully) by first annotating each subtree
with the corresponding values of the inner catamorphism (synthCata), then running
a paramorphims on the annotated tree:
zygo_ g h == para u . synthCata g
where
u = h . fmap (first attribute) . unAnn
first f (x,y) = (f x, y)Futu- and histomorphisms
histo :: Functor f => (f (Attr f a) -> a) -> Mu f -> a Source #
Histomorphism. This is a kind of glorified cata/paramorphism, after all:
cata f == histo (f . fmap attribute) para f == histo (f . fmap (\t -> (forget t, attribute t)))
futu :: Functor f => (a -> f (CoAttr f a)) -> a -> Mu f Source #
Futumorphism. This is a more interesting unfold.