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

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.

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]

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

children = fst . uniplate

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

For example, replacing negative literals with literals:

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

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.

Return all the contexts and holes. This operation is only occasionally useful.

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