Haskell's Scrap Your Boilerplate (SYB) - applying transformation only once instead of everywhere

Question

What's the best way to apply a transformation to a tree only once instead of everywhere using SYB? For instance, in the following simplified expression, there are several instances of Var "x", and I want to replace the first instance with Var "y" only.

data Exp = Var String | Val Int | Plus Exp Exp |...

myExp = Val 5 `Plus` Var "x" `Plus` Val 5 `Plus` Var "x" ...

This can't be done using the everywhere combinator since it will try to transform all instances of Var "x" to Var "y".

EDIT (after posting): Looks like somewhere is what I am looking for.

Answer 1

Being a SYB beginner myself, my answer is more like a guess, but seems to work.

Combinator somewhere recommended by Neil Brown probably doesn't do exactly what you want. It's defined as

-- | Apply a monadic transformation at least somewhere
somewhere :: MonadPlus m => GenericM m -> GenericM m

-- We try "f" in top-down manner, but descent into "x" when we fail
-- at the root of the term. The transformation fails if "f" fails
-- everywhere, say succeeds nowhere.
-- 
somewhere f x = f x `mplus` gmapMp (somewhere f) x

where

-- | Transformation of at least one immediate subterm does not fail 
gmapMp :: forall m. MonadPlus m => (forall d. Data d => d -> m d) -> a -> m a

But we need to transform at most once. For this it seems that gmapMo will be better:

-- | Transformation of one immediate subterm with success 
gmapMo :: forall m. MonadPlus m => (forall d. Data d => d -> m d) -> a -> m a

So I made my own combinator:

{-# LANGUAGE DeriveDataTypeable, RankNTypes #-}
import Control.Monad
import Data.Maybe (fromMaybe)
import Data.Data
import Data.Typeable (Typeable)
import Data.Generics.Schemes
import Data.Generics.Aliases

-- | Apply a monadic transformation once.
once :: MonadPlus m => GenericM m -> GenericM m
once f x = f x `mplus` gmapMo (once f) x

If the substitution fails, it returns mzero, otherwise it returns the substituted result. If you don't care if the substitution fails (no matches), you could use something like

once' :: (forall a. Data a => a -> Maybe a) -> (forall a. Data a => a -> a)
once' f x = fromMaybe x (once f x)

With these, we can do some replacements:

data Exp = Var String | Val Int | Plus Exp Exp
  deriving (Show, Typeable, Data)

myExp = Val 5 `Plus` Var "x" `Plus` Val 5 `Plus` Var "x"

replM :: (MonadPlus m) => Exp -> m Exp
replM (Var "x") = return $ Var "y"
replM t         = mzero

main = do
    -- `somewhere` doesn't do what we want:
    print $ (somewhere (mkMp replM) myExp :: Maybe Exp)

    -- returns `Just ..` if the substitution succeeds once,
    -- Nothing otherwise.
    print $ (once (mkMp replM) myExp :: Maybe Exp)
    -- performs the substitution once, if possible.
    print $ (once' (mkMp replM) myExp :: Exp)

    -- Just for kicks, this returns all possible substitutions
    -- where one `Var "x"` is replaced by `Var "y"`.
    print $ (once (mkMp replM) myExp :: [Exp])