{- | 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 -} module Data.Generics.UniplateStr( module Data.Generics.UniplateStr, module Data.Generics.Str ) where import Control.Monad hiding (mapM) import Data.List(inits,tails) import Control.Monad.State hiding (mapM) import Data.Traversable import Prelude hiding (mapM) import Data.Generics.PlateInternal import Data.Generics.Str -- * The Class -- | 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. type UniplateType on = on -> (Str on, Str on -> on) -- | The standard Uniplate class, all operations require this. class Uniplate on where -- | The underlying method in the class. -- -- 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) uniplate :: UniplateType on -- | Compatibility method, for direct users of the old list-based 'uniplate' function uniplateList :: Uniplate on => on -> ([on], [on] -> on) uniplateList x = (c, b . d) where (a,b) = uniplate x (c,d) = strStructure a -- * The Operations -- ** Queries -- | 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] universe :: Uniplate on => on -> [on] universe x = builder f where f cons nil = g cons nil (One x) nil g cons nil Zero res = res g cons nil (One x) res = x `cons` g cons nil (fst $ uniplate x) res g cons nil (Two x y) res = g cons nil x (g cons nil y res) -- | Get the direct children of a node. Usually using 'universe' is more appropriate. -- -- @children = fst . 'uniplate'@ children :: Uniplate on => on -> [on] children x = builder f where f cons nil = g cons nil (fst $ uniplate x) nil g cons nil Zero res = res g cons nil (One x) res = x `cons` res g cons nil (Two x y) res = g cons nil x (g cons nil y res) -- ** Transformations -- | 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 transform :: Uniplate on => (on -> on) -> on -> on transform f = f . descend (transform f) -- | Monadic variant of 'transform' transformM :: (Monad m, Uniplate on) => (on -> m on) -> on -> m on transformM f x = f =<< descendM (transformM f) 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. rewrite :: Uniplate on => (on -> Maybe on) -> on -> on rewrite f = transform g where g x = maybe x (rewrite f) (f x) -- | Monadic variant of 'rewrite' rewriteM :: (Monad m, Uniplate on) => (on -> m (Maybe on)) -> on -> m on rewriteM f = transformM g where g x = f x >>= maybe (return x) (rewriteM f) -- | 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. descend :: Uniplate on => (on -> on) -> on -> on descend f x = generate $ fmap f current where (current, generate) = uniplate x -- | Monadic variant of 'descend' descendM :: (Monad m, Uniplate on) => (on -> m on) -> on -> m on descendM f x = liftM generate $ mapM f current where (current, generate) = uniplate x -- ** Others -- | Return all the contexts and holes. -- -- > propUniverse x = universe x == map fst (contexts x) -- > propId x = all (== x) [b a | (a,b) <- contexts x] contexts :: Uniplate on => on -> [(on, on -> on)] contexts x = (x,id) : f (holes x) where f xs = [ (y, ctx . context) | (child, ctx) <- xs , (y, context) <- contexts child] -- | The one depth version of 'contexts' -- -- > propChildren x = children x == map fst (holes x) -- > propId x = all (== x) [b a | (a,b) <- holes x] holes :: Uniplate on => on -> [(on, on -> on)] holes x = uncurry f (uniplate x) where f Zero _ = [] f (One i) generate = [(i, generate . One)] f (Two l r) gen = f l (gen . (\i -> Two i r)) ++ f r (gen . (\i -> Two l i)) -- | Perform a fold-like computation on each value, -- technically a paramorphism para :: Uniplate on => (on -> [r] -> r) -> on -> r para op x = op x $ map (para op) $ children x