Copyright | (C) 2012-13 Edward Kmett |
---|---|

License | BSD-style (see the file LICENSE) |

Maintainer | Edward Kmett <ekmett@gmail.com> |

Stability | provisional |

Portability | Rank2Types |

Safe Haskell | Trustworthy |

Language | Haskell98 |

The name "plate" stems originally from "boilerplate", which was the term used by the "Scrap Your Boilerplate" papers, and later inherited by Neil Mitchell's "Uniplate".

http://community.haskell.org/~ndm/uniplate/

The combinators in here are designed to be compatible with and subsume the
`uniplate`

API with the notion of a `Traversal`

replacing
a `uniplate`

or `biplate`

.

By implementing these combinators in terms of `plate`

instead of
`uniplate`

additional type safety is gained, as the user is
no longer responsible for maintaining invariants such as the number of
children they received.

Note: The `Biplate`

is *deliberately* excluded from the API here, with the
intention that you replace them with either explicit traversals, or by using the
`On`

variants of the combinators below with `biplate`

from
`Data.Data.Lens`

. As a design, it forced the user into too many situations where
they had to choose between correctness and ease of use, and it was brittle in the
face of competing imports.

The sensible use of these combinators makes some simple assumptions. Notably, any
of the `On`

combinators are expecting a `Traversal`

, `Setter`

or `Fold`

to play the role of the `biplate`

combinator, and so when the
types of the contents and the container match, they should be the `id`

`Traversal`

,
`Setter`

or `Fold`

.

It is often beneficial to use the combinators in this module with the combinators
from `Data.Data.Lens`

or `GHC.Generics.Lens`

to make it easier to automatically
derive definitions for `plate`

, or to derive custom traversals.

- class Plated a where
- plate :: Traversal' a a

- children :: Plated a => a -> [a]
- rewrite :: Plated a => (a -> Maybe a) -> a -> a
- rewriteOf :: ASetter' a a -> (a -> Maybe a) -> a -> a
- rewriteOn :: Plated a => ASetter s t a a -> (a -> Maybe a) -> s -> t
- rewriteOnOf :: ASetter s t a a -> ASetter' a a -> (a -> Maybe a) -> s -> t
- rewriteM :: (Monad m, Plated a) => (a -> m (Maybe a)) -> a -> m a
- rewriteMOf :: Monad m => LensLike' (WrappedMonad m) a a -> (a -> m (Maybe a)) -> a -> m a
- rewriteMOn :: (Monad m, Plated a) => LensLike (WrappedMonad m) s t a a -> (a -> m (Maybe a)) -> s -> m t
- rewriteMOnOf :: Monad m => LensLike (WrappedMonad m) s t a a -> LensLike' (WrappedMonad m) a a -> (a -> m (Maybe a)) -> s -> m t
- universe :: Plated a => a -> [a]
- universeOf :: Getting [a] a a -> a -> [a]
- universeOn :: Plated a => Getting [a] s a -> s -> [a]
- universeOnOf :: Getting [a] s a -> Getting [a] a a -> s -> [a]
- transform :: Plated a => (a -> a) -> a -> a
- transformOf :: ASetter' a a -> (a -> a) -> a -> a
- transformOn :: Plated a => ASetter s t a a -> (a -> a) -> s -> t
- transformOnOf :: ASetter s t a a -> ASetter' a a -> (a -> a) -> s -> t
- transformM :: (Monad m, Plated a) => (a -> m a) -> a -> m a
- transformMOf :: Monad m => LensLike' (WrappedMonad m) a a -> (a -> m a) -> a -> m a
- transformMOn :: (Monad m, Plated a) => LensLike (WrappedMonad m) s t a a -> (a -> m a) -> s -> m t
- transformMOnOf :: Monad m => LensLike (WrappedMonad m) s t a a -> LensLike' (WrappedMonad m) a a -> (a -> m a) -> s -> m t
- contexts :: Plated a => a -> [Context a a a]
- contextsOf :: ATraversal' a a -> a -> [Context a a a]
- contextsOn :: Plated a => ATraversal s t a a -> s -> [Context a a t]
- contextsOnOf :: ATraversal s t a a -> ATraversal' a a -> s -> [Context a a t]
- holes :: Plated a => a -> [Pretext (->) a a a]
- holesOn :: Conjoined p => Optical p (->) (Bazaar p a a) s t a a -> s -> [Pretext p a a t]
- holesOnOf :: Conjoined p => LensLike (Bazaar p r r) s t a b -> Optical p (->) (Bazaar p r r) a b r r -> s -> [Pretext p r r t]
- para :: Plated a => (a -> [r] -> r) -> a -> r
- paraOf :: Getting (Endo [a]) a a -> (a -> [r] -> r) -> a -> r
- (...) :: (Applicative f, Plated c) => LensLike f s t c c -> Over p f c c a b -> Over p f s t a b
- deep :: (Conjoined p, Applicative f, Plated s) => Traversing p f s s a b -> Over p f s s a b
- composOpFold :: Plated a => b -> (b -> b -> b) -> (a -> b) -> a -> b
- parts :: Plated a => Lens' a [a]

# Uniplate

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.

Nothing

plate :: Traversal' a a Source

# Uniplate Combinators

rewrite :: Plated a => (a -> Maybe a) -> a -> a Source

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 `

which performs both rewrites until a fixed point.`mplus`

g a

rewriteOf :: ASetter' a a -> (a -> Maybe a) -> a -> a Source

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 `

which performs both rewrites until a fixed point.`mplus`

g a

`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

rewriteOn :: Plated a => ASetter s t a a -> (a -> Maybe a) -> s -> t Source

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

rewriteOnOf :: ASetter s t a a -> ASetter' a a -> (a -> Maybe a) -> s -> t Source

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

.

`rewriteOnOf`

::`Plated`

a =>`Iso'`

s a ->`Iso'`

a a -> (a ->`Maybe`

a) -> s -> s`rewriteOnOf`

::`Plated`

a =>`Lens'`

s a ->`Lens'`

a a -> (a ->`Maybe`

a) -> s -> s`rewriteOnOf`

::`Plated`

a =>`Traversal'`

s a ->`Traversal'`

a a -> (a ->`Maybe`

a) -> s -> s`rewriteOnOf`

::`Plated`

a =>`Setter'`

s a ->`Setter'`

a a -> (a ->`Maybe`

a) -> s -> s

rewriteM :: (Monad m, Plated a) => (a -> m (Maybe a)) -> a -> m a Source

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

rewriteMOf :: Monad m => LensLike' (WrappedMonad m) a a -> (a -> m (Maybe a)) -> a -> m a Source

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.

rewriteMOn :: (Monad m, Plated a) => LensLike (WrappedMonad m) s t a a -> (a -> m (Maybe a)) -> s -> m t Source

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.

rewriteMOnOf :: Monad m => LensLike (WrappedMonad m) s t a a -> LensLike' (WrappedMonad m) a a -> (a -> m (Maybe a)) -> s -> m t Source

universe :: Plated a => a -> [a] Source

Retrieve all of the transitive descendants of a `Plated`

container, including itself.

universeOf :: Getting [a] a a -> a -> [a] Source

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]

universeOn :: Plated a => Getting [a] s a -> s -> [a] Source

universeOnOf :: Getting [a] s a -> Getting [a] a a -> s -> [a] Source

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`

transformOf :: ASetter' a a -> (a -> a) -> a -> a Source

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

transformOn :: Plated a => ASetter s t a a -> (a -> a) -> s -> t Source

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

transformOnOf :: ASetter s t a a -> ASetter' a a -> (a -> a) -> s -> t Source

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

transformM :: (Monad m, Plated a) => (a -> m a) -> a -> m a Source

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

transformMOf :: Monad m => LensLike' (WrappedMonad m) a a -> (a -> m a) -> a -> m a Source

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

transformMOn :: (Monad m, Plated a) => LensLike (WrappedMonad m) s t a a -> (a -> m a) -> s -> m t Source

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

transformMOnOf :: Monad m => LensLike (WrappedMonad m) s t a a -> LensLike' (WrappedMonad m) a a -> (a -> m a) -> s -> m t Source

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

contextsOf :: ATraversal' a a -> a -> [Context a a a] Source

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]

contextsOn :: Plated a => ATraversal s t a a -> s -> [Context a a t] Source

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]

contextsOnOf :: ATraversal s t a a -> ATraversal' a a -> s -> [Context a a t] Source

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]

holes :: Plated a => a -> [Pretext (->) a a a] Source

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`

holesOn :: Conjoined p => Optical p (->) (Bazaar p a a) s t a a -> s -> [Pretext p a a t] Source

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]

holesOnOf :: Conjoined p => LensLike (Bazaar p r r) s t a b -> Optical p (->) (Bazaar p r r) a b r r -> s -> [Pretext p r r t] Source

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]

(...) :: (Applicative f, Plated c) => LensLike f s t c c -> Over p f c c a b -> Over p f s t a b infixr 9 Source

Compose through a plate

deep :: (Conjoined p, Applicative f, Plated s) => Traversing p f s s a b -> Over p f s s a b Source

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

# Compos

Provided for compatibility with Björn Bringert's `compos`

library.

Note: Other operations from compos that were inherited by `uniplate`

are *not* included
to avoid having even more redundant names for the same operators. For comparison:

`composOpMonoid`

≡`foldMapOf`

`plate`

`composOpMPlus`

f ≡`msumOf`

(`plate`

`.`

`to`

f)`composOp`

≡`descend`

≡`over`

`plate`

`composOpM`

≡`descendM`

≡`mapMOf`

`plate`

`composOpM_`

≡`descendM_`

≡`mapMOf_`

`plate`

composOpFold :: Plated a => b -> (b -> b -> b) -> (a -> b) -> a -> b Source

Fold the immediate children of a `Plated`

container.

`composOpFold`

z c f =`foldrOf`

`plate`

(c`.`

f) z