{-# LANGUAGE UndecidableInstances , FlexibleContexts , MultiParamTypeClasses , FlexibleInstances , GeneralizedNewtypeDeriving, TypeOperators, ScopedTypeVariables, CPP #-} ----------------------------------------------------------------------------- -- | -- Module : Data.Semigroup.Reducer -- Copyright : (c) Edward Kmett 2009 -- License : BSD3 -- Maintainer : ekmett@gmail.com -- Stability : experimental -- Portability : non-portable (MPTCs) -- -- A @c@-'Reducer' is a 'Semigroup' with a canonical mapping from @c@ to the Semigroup. -- ----------------------------------------------------------------------------- module Data.Semigroup.Reducer ( Reducer(..) , foldMapReduce, foldMapReduce1 , foldReduce, foldReduce1 , pureUnit , returnUnit , Count(..) ) where import Control.Applicative import qualified Data.Monoid as Monoid import Data.Semigroup as Semigroup import Data.Semigroup.Foldable import Data.Semigroup.Instances () import Data.Hashable import Data.Foldable import Data.FingerTree import qualified Data.Sequence as Seq import Data.Sequence (Seq) import qualified Data.Set as Set import Data.Set (Set) import qualified Data.IntSet as IntSet import Data.IntSet (IntSet) import qualified Data.IntMap as IntMap import Data.IntMap (IntMap) import qualified Data.Map as Map import Data.Map (Map) #ifdef LANGUAGE_DeriveDataTypeable import Data.Data #endif --import Text.Parsec.Prim -- | This type may be best read infix. A @c `Reducer` m@ is a 'Semigroup' @m@ that maps -- values of type @c@ through @unit@ to values of type @m@. A @c@-'Reducer' may also -- supply operations which tack-on another @c@ to an existing 'Monoid' @m@ on the left -- or right. These specialized reductions may be more efficient in some scenarios -- and are used when appropriate by a 'Generator'. The names 'cons' and 'snoc' work -- by analogy to the synonymous operations in the list monoid. -- -- This class deliberately avoids functional-dependencies, so that () can be a @c@-Reducer -- for all @c@, and so many common reducers can work over multiple types, for instance, -- First and Last may reduce both @a@ and 'Maybe' @a@. Since a 'Generator' has a fixed element -- type, the input to the reducer is generally known and extracting from the monoid usually -- is sufficient to fix the result type. Combinators are available for most scenarios where -- this is not the case, and the few remaining cases can be handled by using an explicit -- type annotation. -- -- Minimal definition: 'unit' or 'snoc' class Semigroup m => Reducer c m where -- | Convert a value into a 'Semigroup' unit :: c -> m -- | Append a value to a 'Semigroup' for use in left-to-right reduction snoc :: m -> c -> m -- | Prepend a value onto a 'Semigroup' for use during right-to-left reduction cons :: c -> m -> m snoc m = (<>) m . unit cons = (<>) . unit -- | Apply a 'Reducer' to a 'Foldable' container, after mapping the contents into a suitable form for reduction. foldMapReduce :: (Foldable f, Monoid m, Reducer e m) => (a -> e) -> f a -> m foldMapReduce f = foldMap (unit . f) foldMapReduce1 :: (Foldable1 f, Reducer e m) => (a -> e) -> f a -> m foldMapReduce1 f = foldMap1 (unit . f) -- | Apply a 'Reducer' to a 'Foldable' mapping each element through 'unit' foldReduce :: (Foldable f, Monoid m, Reducer e m) => f e -> m foldReduce = foldMap unit -- | Apply a 'Reducer' to a 'Foldable1' mapping each element through 'unit' foldReduce1 :: (Foldable1 f, Reducer e m) => f e -> m foldReduce1 = foldMap1 unit returnUnit :: (Monad m, Reducer c n) => c -> m n returnUnit = return . unit pureUnit :: (Applicative f, Reducer c n) => c -> f n pureUnit = pure . unit newtype Count = Count { getCount :: Int } deriving ( Eq, Ord, Show, Read #ifdef LANGUAGE_DeriveDataTypeable , Data, Typeable #endif ) instance Hashable Count where hash = hash . getCount hashWithSalt n = hashWithSalt n . getCount instance Semigroup Count where Count a <> Count b = Count (a + b) times1p n (Count a) = Count $ (fromIntegral n + 1) * a instance Monoid Count where mempty = Count 0 Count a `mappend` Count b = Count (a + b) instance Reducer a Count where unit _ = Count 1 Count n `snoc` _ = Count (n + 1) _ `cons` Count n = Count (n + 1) instance (Reducer c m, Reducer c n) => Reducer c (m,n) where unit x = (unit x,unit x) (m,n) `snoc` x = (m `snoc` x, n `snoc` x) x `cons` (m,n) = (x `cons` m, x `cons` n) instance (Reducer c m, Reducer c n, Reducer c o) => Reducer c (m,n,o) where unit x = (unit x,unit x, unit x) (m,n,o) `snoc` x = (m `snoc` x, n `snoc` x, o `snoc` x) x `cons` (m,n,o) = (x `cons` m, x `cons` n, x `cons` o) instance (Reducer c m, Reducer c n, Reducer c o, Reducer c p) => Reducer c (m,n,o,p) where unit x = (unit x,unit x, unit x, unit x) (m,n,o,p) `snoc` x = (m `snoc` x, n `snoc` x, o `snoc` x, p `snoc` x) x `cons` (m,n,o,p) = (x `cons` m, x `cons` n, x `cons` o, x `cons` p) instance Reducer c [c] where unit = return cons = (:) xs `snoc` x = xs ++ [x] instance Reducer c () where unit _ = () _ `snoc` _ = () _ `cons` _ = () instance Reducer Bool Any where unit = Any instance Reducer Bool All where unit = All instance Reducer (a -> a) (Endo a) where unit = Endo instance Semigroup a => Reducer a (Dual a) where unit = Dual instance Num a => Reducer a (Sum a) where unit = Sum instance Num a => Reducer a (Product a) where unit = Product instance Ord a => Reducer a (Min a) where unit = Min instance Ord a => Reducer a (Max a) where unit = Max instance Reducer (Maybe a) (Monoid.First a) where unit = Monoid.First instance Reducer a (Semigroup.First a) where unit = Semigroup.First instance Reducer (Maybe a) (Monoid.Last a) where unit = Monoid.Last instance Reducer a (Semigroup.Last a) where unit = Semigroup.Last instance Measured v a => Reducer a (FingerTree v a) where unit = singleton cons = (<|) snoc = (|>) --instance (Stream s m t, Reducer c a) => Reducer c (ParsecT s u m a) where -- unit = return . unit instance Reducer a (Seq a) where unit = Seq.singleton cons = (Seq.<|) snoc = (Seq.|>) instance Reducer Int IntSet where unit = IntSet.singleton cons = IntSet.insert snoc = flip IntSet.insert -- left bias irrelevant instance Ord a => Reducer a (Set a) where unit = Set.singleton cons = Set.insert -- pedantic about order in case 'Eq' doesn't implement structural equality snoc s m | Set.member m s = s | otherwise = Set.insert m s instance Reducer (Int, v) (IntMap v) where unit = uncurry IntMap.singleton cons = uncurry IntMap.insert snoc = flip . uncurry . IntMap.insertWith $ const id instance Ord k => Reducer (k, v) (Map k v) where unit = uncurry Map.singleton cons = uncurry Map.insert snoc = flip . uncurry . Map.insertWith $ const id instance Monoid m => Reducer m (WrappedMonoid m) where unit = WrapMonoid