Data.Generics.Uniplate

uniplate-1.6.13: Help writing simple, concise and fast generic operations.

Safe Haskell | None
Language | Haskell2010

Data.Generics.Uniplate

Contents

- The Class
- The Operations
  - Queries
  - Transformations
  - Others

Description

DEPRECATED Use Data.Generics.Uniplate.Operations 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

Synopsis

- 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) #

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.

class Uniplate on where #

The standard Uniplate class, all operations require this

Methods

uniplate :: UniplateType on #

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] #

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] #

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

    children = fst . uniplate

## Transformations

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

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 on #

Monadic variant of `transform`

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

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

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

Monadic variant of `rewrite`

descend :: Uniplate on => (on -> on) -> on -> on #

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, Uniplate on) => (on -> m on) -> on -> m on #

Monadic variant of `descend`

## Others

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

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)] #

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 -> r #

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