*RECOMMENDATION* Use Data.Generics.UniplateStr instead.

This is the main Uniplate module, which defines all the essential operations in a Haskell 98 compatible manner.

Most functions have an example of a possible use for the function.
To illustate, I have used the `Expr`

type as below:

data Expr = Val Int | Neg Expr | Add Expr Expr

- type UniplateType on = on -> ([on], [on] -> on)
- class Uniplate on where
- uniplate :: UniplateType on

- 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
- descend :: Uniplate on => (on -> on) -> on -> on
- descendM :: (Monad m, Uniplate on) => (on -> m 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

# The Class

type UniplateType on = on -> ([on], [on] -> on)Source

The type of replacing all the children of a node

Taking a value, the function should return all the immediate children of the same type, and a function to replace them.

The standard Uniplate class, all operations require this

uniplate :: UniplateType onSource

The underlying method in the class

uniplate (Add (Val 1) (Neg (Val 2))) = ([Val 1, Neg (Val 2)], \[a,b] -> Add a b) uniplate (Val 1) = ([] , \[] -> Val 1 )

# The 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 = [Val i | i <- universe x]

## 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`

descend :: Uniplate on => (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.

## 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]