This module functions identically to Data.Generics.Uniplate.Data, but instead of
using the standard `Uniplate`

/ `Biplate`

classes defined in
Data.Generics.Uniplate.Operations it uses a local copy.

Only use this module if you are using both `Data`

and `Direct`

instances in
the same project and they are conflicting.

- class Uniplate on where
- class Uniplate to => Biplate from to where
- universe :: Uniplate on => on -> [on]
- children :: Uniplate on => on -> [on]
- transform :: Uniplate on => (on -> on) -> on -> on
- transformM :: (Monad m, Uniplate on) => (on -> m on) -> on -> m on
- rewrite :: Uniplate on => (on -> Maybe on) -> on -> on
- rewriteM :: (Monad m, Uniplate on) => (on -> m (Maybe on)) -> on -> m on
- contexts :: Uniplate on => on -> [(on, on -> on)]
- holes :: Uniplate on => on -> [(on, on -> on)]
- para :: Uniplate on => (on -> [r] -> r) -> on -> r
- universeBi :: Biplate from to => from -> [to]
- childrenBi :: Biplate from to => from -> [to]
- transformBi :: Biplate from to => (to -> to) -> from -> from
- transformBiM :: (Monad m, Biplate from to) => (to -> m to) -> from -> m from
- rewriteBi :: Biplate from to => (to -> Maybe to) -> from -> from
- rewriteBiM :: (Monad m, Biplate from to) => (to -> m (Maybe to)) -> from -> m from
- contextsBi :: Biplate from to => from -> [(to, to -> from)]
- holesBi :: Biplate from to => from -> [(to, to -> from)]

# The Classes

The standard Uniplate class, all operations require this.

uniplate :: on -> (Str on, Str on -> on)Source

The underlying method in the class. Taking a value, the function should return all the immediate children of the same type, and a function to replace them.

Given `uniplate x = (cs, gen)`

`cs`

should be a `Str on`

, constructed of `Zero`

, `One`

and `Two`

,
containing all `x`

's direct children of the same type as `x`

. `gen`

should take a `Str on`

with exactly the same structure as `cs`

,
and generate a new element with the children replaced.

Example instance:

instance Uniplate Expr where uniplate (Val i ) = (Zero , \Zero -> Val i ) uniplate (Neg a ) = (One a , \(One a) -> Neg a ) uniplate (Add a b) = (Two (One a) (One b), \(Two (One a) (One b)) -> Add a b)

descend :: (on -> on) -> on -> onSource

Perform a transformation on all the immediate children, then combine them back. This operation allows additional information to be passed downwards, and can be used to provide a top-down transformation.

descendM :: Monad m => (on -> m on) -> on -> m onSource

Monadic variant of `descend`

class Uniplate to => Biplate from to whereSource

Children are defined as the top-most items of type to
*starting at the root*.

# Single Type Operations

## Queries

universe :: Uniplate on => on -> [on]Source

Get all the children of a node, including itself and all children.

universe (Add (Val 1) (Neg (Val 2))) = [Add (Val 1) (Neg (Val 2)), Val 1, Neg (Val 2), Val 2]

This method is often combined with a list comprehension, for example:

vals x = [i | Val i <- universe x]

children :: Uniplate on => on -> [on]Source

Get the direct children of a node. Usually using `universe`

is more appropriate.

## Transformations

transform :: Uniplate on => (on -> on) -> on -> onSource

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

For example, replacing negative literals with literals:

negLits = transform f where f (Neg (Lit i)) = Lit (negate i) f x = x

transformM :: (Monad m, Uniplate on) => (on -> m on) -> on -> m onSource

Monadic variant of `transform`

rewrite :: Uniplate on => (on -> Maybe on) -> on -> onSource

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 `f `

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

g

rewriteM :: (Monad m, Uniplate on) => (on -> m (Maybe on)) -> on -> m onSource

Monadic variant of `rewrite`

## Others

contexts :: Uniplate on => on -> [(on, on -> on)]Source

Return all the contexts and holes.

propUniverse x = universe x == map fst (contexts x) propId x = all (== x) [b a | (a,b) <- contexts x]

holes :: Uniplate on => on -> [(on, on -> on)]Source

The one depth version of `contexts`

propChildren x = children x == map fst (holes x) propId x = all (== x) [b a | (a,b) <- holes x]

para :: Uniplate on => (on -> [r] -> r) -> on -> rSource

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

# Multiple Type Operations

## Queries

universeBi :: Biplate from to => from -> [to]Source

childrenBi :: Biplate from to => from -> [to]Source

Return the children of a type. If `to == from`

then it returns the
original element (in contrast to `children`

)

## Transformations

transformBi :: Biplate from to => (to -> to) -> from -> fromSource

transformBiM :: (Monad m, Biplate from to) => (to -> m to) -> from -> m fromSource

rewriteBiM :: (Monad m, Biplate from to) => (to -> m (Maybe to)) -> from -> m fromSource

## Others

contextsBi :: Biplate from to => from -> [(to, to -> from)]Source