A Plated type is one where we know how to extract its immediate self-similar children.

Example 1 :

import Control.Applicative
import Control.Lens
import Control.Lens.Plated
import Data.Data
import Data.Data.Lens (uniplate)

data Expr
  = Val Int
  | Neg Expr
  | Add Expr Expr
  deriving (Eq,Ord,Show,Read,Data,Typeable)

instance Plated Expr where
  plate f (Neg e) = Neg <$> f e
  plate f (Add a b) = Add <$> f a <*> f b
  plate _ a = pure a

or

instance Plated Expr where
  plate = uniplate

Example 2 :

import Control.Applicative
import Control.Lens
import Control.Lens.Plated
import Data.Data
import Data.Data.Lens (uniplate)

data Tree a
  = Bin (Tree a) (Tree a)
  | Tip a
  deriving (Eq,Ord,Show,Read,Data,Typeable)

instance Plated (Tree a) where
  plate f (Bin l r) = Bin <$> f l <*> f r
  plate _ t = pure t

or

instance Data a => Plated (Tree a) where
  plate = uniplate

Note the big distinction between these two implementations.

The former will only treat children directly in this tree as descendents, the latter will treat trees contained in the values under the tips also as descendants!

When in doubt, pick a Traversal and just use the various ...Of combinators rather than pollute Plated with orphan instances!

If you want to find something unplated and non-recursive with biplate use the ...OnOf variant with ignored , though those usecases are much better served in most cases by using the existing Lens combinators! e.g.

toListOf biplate ≡ universeOnOf biplate ignored

This same ability to explicitly pass the Traversal in question is why there is no analogue to uniplate's Biplate .

Moreover, since we can allow custom traversals, we implement reasonable defaults for polymorphic data types, that only traverse into themselves, and not their polymorphic arguments.

Extract the immediate descendants of a Plated container.

children ≡ toListOf plate

Rewrite by applying a rule everywhere you can. Ensures that the rule cannot be applied anywhere in the result:

propRewrite r x = all (isNothing . r) (universe (rewrite r x))

Usually transform is more appropriate, but rewrite can give better compositionality. Given two single transformations f and g , you can construct \a -> f a <|> g a which performs both rewrites until a fixed point.

Rewrite by applying a rule everywhere you can. Ensures that the rule cannot be applied anywhere in the result:

propRewriteOf l r x = all (isNothing . r) (universeOf l (rewriteOf l r x))

Usually transformOf is more appropriate, but rewriteOf can give better compositionality. Given two single transformations f and g , you can construct \a -> f a <|> g a which performs both rewrites until a fixed point.

rewriteOf :: Iso' a a       -> (a -> Maybe a) -> a -> a
rewriteOf :: Lens' a a      -> (a -> Maybe a) -> a -> a
rewriteOf :: Traversal' a a -> (a -> Maybe a) -> a -> a
rewriteOf :: Setter' a a    -> (a -> Maybe a) -> a -> a

Rewrite recursively over part of a larger structure.

rewriteOn :: Plated a => Iso' s a       -> (a -> Maybe a) -> s -> s
rewriteOn :: Plated a => Lens' s a      -> (a -> Maybe a) -> s -> s
rewriteOn :: Plated a => Traversal' s a -> (a -> Maybe a) -> s -> s
rewriteOn :: Plated a => ASetter' s a   -> (a -> Maybe a) -> s -> s

Rewrite recursively over part of a larger structure using a specified Setter .

rewriteOnOf :: Iso' s a       -> Iso' a a       -> (a -> Maybe a) -> s -> s
rewriteOnOf :: Lens' s a      -> Lens' a a      -> (a -> Maybe a) -> s -> s
rewriteOnOf :: Traversal' s a -> Traversal' a a -> (a -> Maybe a) -> s -> s
rewriteOnOf :: Setter' s a    -> Setter' a a    -> (a -> Maybe a) -> s -> s

Rewrite by applying a monadic rule everywhere you can. Ensures that the rule cannot be applied anywhere in the result.

Rewrite by applying a monadic rule everywhere you recursing with a user-specified Traversal . Ensures that the rule cannot be applied anywhere in the result.

Rewrite by applying a monadic rule everywhere inside of a structure located by a user-specified Traversal . Ensures that the rule cannot be applied anywhere in the result.

Rewrite by applying a monadic rule everywhere inside of a structure located by a user-specified Traversal , using a user-specified Traversal for recursion. Ensures that the rule cannot be applied anywhere in the result.

Retrieve all of the transitive descendants of a Plated container, including itself.

Given a Fold that knows how to locate immediate children, retrieve all of the transitive descendants of a node, including itself.

universeOf :: Fold a a -> a -> [a]

Given a Fold that knows how to find Plated parts of a container retrieve them and all of their descendants, recursively.

Given a Fold that knows how to locate immediate children, retrieve all of the transitive descendants of a node, including itself that lie in a region indicated by another Fold .

toListOf l ≡ universeOnOf l ignored

Fold over all transitive descendants of a Plated container, including itself.

Given a Fold that knows how to locate immediate children, fold all of the transitive descendants of a node, including itself.

cosmosOf :: Fold a a -> Fold a a

Given a Fold that knows how to find Plated parts of a container fold them and all of their descendants, recursively.

cosmosOn :: Plated a => Fold s a -> Fold s a

Given a Fold that knows how to locate immediate children, fold all of the transitive descendants of a node, including itself that lie in a region indicated by another Fold .

cosmosOnOf :: Fold s a -> Fold a a -> Fold s a

Transform every element in the tree, in a bottom-up manner.

For example, replacing negative literals with literals:

negLits = transform $ \x -> case x of
  Neg (Lit i) -> Lit (negate i)
  _           -> x

Transform every element by recursively applying a given Setter in a bottom-up manner.

transformOf :: Traversal' a a -> (a -> a) -> a -> a
transformOf :: Setter' a a    -> (a -> a) -> a -> a

Transform every element in the tree in a bottom-up manner over a region indicated by a Setter .

transformOn :: Plated a => Traversal' s a -> (a -> a) -> s -> s
transformOn :: Plated a => Setter' s a    -> (a -> a) -> s -> s

Transform every element in a region indicated by a Setter by recursively applying another Setter in a bottom-up manner.

transformOnOf :: Setter' s a -> Traversal' a a -> (a -> a) -> s -> s
transformOnOf :: Setter' s a -> Setter' a a    -> (a -> a) -> s -> s

Transform every element in the tree, in a bottom-up manner, monadically.

Transform every element in a tree using a user supplied Traversal in a bottom-up manner with a monadic effect.

transformMOf :: Monad m => Traversal' a a -> (a -> m a) -> a -> m a

Transform every element in the tree in a region indicated by a supplied Traversal , in a bottom-up manner, monadically.

transformMOn :: (Monad m, Plated a) => Traversal' s a -> (a -> m a) -> s -> m s

Transform every element in a tree that lies in a region indicated by a supplied Traversal , walking with a user supplied Traversal in a bottom-up manner with a monadic effect.

transformMOnOf :: Monad m => Traversal' s a -> Traversal' a a -> (a -> m a) -> s -> m s

Return a list of all of the editable contexts for every location in the structure, recursively.

propUniverse x = universe x == map pos (contexts x)
propId x = all (== x) [extract w | w <- contexts x]

contexts ≡ contextsOf plate

Return a list of all of the editable contexts for every location in the structure, recursively, using a user-specified Traversal to walk each layer.

propUniverse l x = universeOf l x == map pos (contextsOf l x)
propId l x = all (== x) [extract w | w <- contextsOf l x]

contextsOf :: Traversal' a a -> a -> [Context a a a]

Return a list of all of the editable contexts for every location in the structure in an areas indicated by a user supplied Traversal , recursively using plate .

contextsOn b ≡ contextsOnOf b plate

contextsOn :: Plated a => Traversal' s a -> s -> [Context a a s]

Return a list of all of the editable contexts for every location in the structure in an areas indicated by a user supplied Traversal , recursively using another user-supplied Traversal to walk each layer.

contextsOnOf :: Traversal' s a -> Traversal' a a -> s -> [Context a a s]

The one-level version of context . This extracts a list of the immediate children as editable contexts.

Given a context you can use pos to see the values, peek at what the structure would be like with an edited result, or simply extract the original structure.

propChildren x = children l x == map pos (holes l x)
propId x = all (== x) [extract w | w <- holes l x]

holes = holesOf plate

An alias for holesOf , provided for consistency with the other combinators.

holesOn ≡ holesOf

holesOn :: Iso' s a                -> s -> [Pretext (->) a a s]
holesOn :: Lens' s a               -> s -> [Pretext (->) a a s]
holesOn :: Traversal' s a          -> s -> [Pretext (->) a a s]
holesOn :: IndexedLens' i s a      -> s -> [Pretext (Indexed i) a a s]
holesOn :: IndexedTraversal' i s a -> s -> [Pretext (Indexed i) a a s]

Extract one level of holes from a container in a region specified by one Traversal , using another.

holesOnOf b l ≡ holesOf (b . l)

holesOnOf :: Iso' s a       -> Iso' a a                -> s -> [Pretext (->) a a s]
holesOnOf :: Lens' s a      -> Lens' a a               -> s -> [Pretext (->) a a s]
holesOnOf :: Traversal' s a -> Traversal' a a          -> s -> [Pretext (->) a a s]
holesOnOf :: Lens' s a      -> IndexedLens' i a a      -> s -> [Pretext (Indexed i) a a s]
holesOnOf :: Traversal' s a -> IndexedTraversal' i a a -> s -> [Pretext (Indexed i) a a s]

Perform a fold-like computation on each value, technically a paramorphism.

para ≡ paraOf plate

Perform a fold-like computation on each value, technically a paramorphism.

paraOf :: Fold a a -> (a -> [r] -> r) -> a -> r

Compose through a plate

Try to apply a traversal to all transitive descendants of a Plated container, but do not recurse through matching descendants.

deep :: Plated s => Fold s a                 -> Fold s a
deep :: Plated s => IndexedFold s a          -> IndexedFold s a
deep :: Plated s => Traversal s s a b        -> Traversal s s a b
deep :: Plated s => IndexedTraversal s s a b -> IndexedTraversal s s a b

Fold the immediate children of a Plated container.

composOpFold z c f = foldrOf plate (c . f) z

The original uniplate combinator, implemented in terms of Plated as a Lens .

parts ≡ partsOf plate

The resulting Lens is safer to use as it ignores 'over-application' and deals gracefully with under-application, but it is only a proper Lens if you don't change the list length !

Implement plate operation for a type using its Generic instance.

Note: the behavior may be different than with uniplate in some special cases. gplate doesn't look through other types in a group of mutually recursive types.

For example consider mutually recursive even and odd natural numbers:

>>> data Even = Z | E Odd deriving (Show, Generic, Typeable, Data); data Odd = O Even deriving (Show, Generic, Typeable, Data)

Then uniplate , which is based on Data , finds all even numbers less or equal than four:

>>> import Data.Data.Lens (uniplate)
>>> universeOf uniplate (E (O (E (O Z))))
[E (O (E (O Z))),E (O Z),Z]

but gplate doesn't see through Odd .

>>> universeOf gplate (E (O (E (O Z))))
[E (O (E (O Z)))]

If using Data is not an option, you can still write the traversal manually. It is sometimes useful to use helper traversals

>>> :{
let oddeven :: Traversal' Odd Even
    oddeven f (O n) = O <$> f n
    evenplate :: Traversal' Even Even
    evenplate f Z     = pure Z
    evenplate f (E n) = E <$> oddeven f n
:}

>>> universeOf evenplate (E (O (E (O Z))))
[E (O (E (O Z))),E (O Z),Z]

Implement plate operation for a type using its Generic1 instance.