Definitions of `Uniplate`

and `Biplate`

classes, along with all the standard operations.

Import this module directly only if you are defining new Uniplate operations, otherwise import one of Data.Generics.Uniplate.Direct, Data.Generics.Uniplate.Typeable or Data.Generics.Uniplate.Data.

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

- 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. All definitions must
define `uniplate`

, while `descend`

and `descendM`

are optional.

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. This function can be defined explicitly,
or can be provided by automatically in terms of `uniplate`

.

For example, on the sample type, we could write:

descend f (Val i ) = Val i descend f (Neg a ) = Neg (f a) descend f (Add a b) = Add (f a) (f b)

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*. All instances must define `biplate`

, while
`descendBi`

and `descendBiM`

are optional.

biplate :: from -> (Str to, Str to -> from)Source

Return all the top most children of type `to`

within `from`

.

If `from == to`

then this function should return the root as the single
child.

descendBi :: (to -> to) -> from -> fromSource

Like `descend`

but with more general types. If `from == to`

then this
function *does not* descend. Therefore, when writing definitions it is
highly unlikely that this function should be used in the recursive case.
A common pattern is to first match the types using `descendBi`

, then continue
the recursion with `descend`

.

descendBiM :: Monad m => (to -> m to) -> from -> m fromSource

# 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.

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

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

The one depth version of `contexts`

children x == map fst (holes 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