{-# LANGUAGE DeriveDataTypeable    #-}
{-# LANGUAGE DeriveFoldable        #-}
{-# LANGUAGE DeriveFunctor         #-}
{-# LANGUAGE DeriveTraversable     #-}
{-# LANGUAGE FlexibleInstances     #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# OPTIONS_GHC -fno-warn-unused-imports       #-}
-----------------------------------------------------------------------------
-- |
-- Module      :  Data.Monoid.Split
-- Copyright   :  (c) 2011-2015 diagrams-core team (see LICENSE)
-- License     :  BSD-style (see LICENSE)
-- Maintainer  :  diagrams-discuss@googlegroups.com
--
-- Sometimes we want to accumulate values from some monoid, but have
-- the ability to introduce a \"split\" which separates values on
-- either side.  Only the rightmost split is kept.  For example,
--
-- > a b c | d e | f g h == a b c d e | f g h
--
-- In the diagrams graphics framework this is used when accumulating
-- transformations to be applied to primitive diagrams: the 'freeze'
-- operation introduces a split, since only transformations occurring
-- outside the freeze should be applied to attributes.
--
-----------------------------------------------------------------------------

module Data.Monoid.Split
       ( Split(..)
       , split
       , unsplit

       ) where

import Data.Data
import Data.Foldable
import Data.Semigroup
import Data.Traversable

import Data.Monoid.Action

infix 5 :|

-- | A value of type @Split m@ is either a single @m@, or a pair of
--   @m@'s separated by a divider.  Single @m@'s combine as usual;
--   single @m@'s combine with split values by combining with the
--   value on the appropriate side; when two split values meet only
--   the rightmost split is kept, with both the values from the left
--   split combining with the left-hand value of the right split.
--
--   "Data.Monoid.Cut" is similar, but uses a different scheme for
--   composition.  @Split@ uses the asymmetric constructor @:|@, and
--   @Cut@ the symmetric constructor @:||:@, to emphasize the inherent
--   asymmetry of @Split@ and symmetry of @Cut@.  @Split@ keeps only
--   the rightmost split and combines everything on the left; @Cut@
--   keeps the outermost splits and throws away everything in between.
data Split m = M m
             | m :| m
  deriving (Typeable (Split m)
DataType
Constr
Typeable (Split m)
-> (forall (c :: * -> *).
    (forall d b. Data d => c (d -> b) -> d -> c b)
    -> (forall g. g -> c g) -> Split m -> c (Split m))
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    (forall b r. Data b => c (b -> r) -> c r)
    -> (forall r. r -> c r) -> Constr -> c (Split m))
-> (Split m -> Constr)
-> (Split m -> DataType)
-> (forall (t :: * -> *) (c :: * -> *).
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-> (forall (t :: * -> * -> *) (c :: * -> *).
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-> ((forall b. Data b => b -> b) -> Split m -> Split m)
-> (forall r r'.
    (r -> r' -> r)
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-> (forall r r'.
    (r' -> r -> r)
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-> (forall (m :: * -> *).
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-> Data (Split m)
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-> (forall a. t a -> Int)
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-> (forall a. Ord a => t a -> a)
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-> Foldable t
product :: Split a -> a
$cproduct :: forall a. Num a => Split a -> a
sum :: Split a -> a
$csum :: forall a. Num a => Split a -> a
minimum :: Split a -> a
$cminimum :: forall a. Ord a => Split a -> a
maximum :: Split a -> a
$cmaximum :: forall a. Ord a => Split a -> a
elem :: a -> Split a -> Bool
$celem :: forall a. Eq a => a -> Split a -> Bool
length :: Split a -> Int
$clength :: forall a. Split a -> Int
null :: Split a -> Bool
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toList :: Split a -> [a]
$ctoList :: forall a. Split a -> [a]
foldl1 :: (a -> a -> a) -> Split a -> a
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foldr1 :: (a -> a -> a) -> Split a -> a
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foldl' :: (b -> a -> b) -> b -> Split a -> b
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$cfoldr' :: forall a b. (a -> b -> b) -> b -> Split a -> b
foldr :: (a -> b -> b) -> b -> Split a -> b
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    (a -> f b) -> Split a -> f (Split b))
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    Split (f a) -> f (Split a))
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    Monad m =>
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    (a -> f b) -> t a -> f (t b))
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    (a -> m b) -> t a -> m (t b))
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traverse :: (a -> f b) -> Split a -> f (Split b)
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Traversable)

-- | If @m@ is a @Semigroup@, then @Split m@ is a semigroup which
--   combines values on either side of a split, keeping only the
--   rightmost split.
instance Semigroup m => Semigroup (Split m) where
  (M m
m1)       <> :: Split m -> Split m -> Split m
<> (M m
m2)       = m -> Split m
forall m. m -> Split m
M (m
m1 m -> m -> m
forall a. Semigroup a => a -> a -> a
<> m
m2)
  (M m
m1)       <> (m
m1' :| m
m2)  = m
m1 m -> m -> m
forall a. Semigroup a => a -> a -> a
<> m
m1'         m -> m -> Split m
forall m. m -> m -> Split m
:| m
m2
  (m
m1  :| m
m2)  <> (M m
m2')      = m
m1                m -> m -> Split m
forall m. m -> m -> Split m
:| m
m2 m -> m -> m
forall a. Semigroup a => a -> a -> a
<> m
m2'
  (m
m11 :| m
m12) <> (m
m21 :| m
m22) = m
m11 m -> m -> m
forall a. Semigroup a => a -> a -> a
<> m
m12 m -> m -> m
forall a. Semigroup a => a -> a -> a
<> m
m21 m -> m -> Split m
forall m. m -> m -> Split m
:| m
m22

instance (Semigroup m, Monoid m) => Monoid (Split m) where
  mempty :: Split m
mempty  = m -> Split m
forall m. m -> Split m
M m
forall a. Monoid a => a
mempty
  mappend :: Split m -> Split m -> Split m
mappend = Split m -> Split m -> Split m
forall a. Semigroup a => a -> a -> a
(<>)

-- | A convenient name for @mempty :| mempty@, so @M a \<\> split \<\>
--   M b == a :| b@.
split :: Monoid m => Split m
split :: Split m
split = m
forall a. Monoid a => a
mempty m -> m -> Split m
forall m. m -> m -> Split m
:| m
forall a. Monoid a => a
mempty

-- | \"Unsplit\" a split monoid value, combining the two values into
--   one (or returning the single value if there is no split).
unsplit :: Semigroup m => Split m -> m
unsplit :: Split m -> m
unsplit (M m
m)      = m
m
unsplit (m
m1 :| m
m2) = m
m1 m -> m -> m
forall a. Semigroup a => a -> a -> a
<> m
m2

-- | By default, the action of a split monoid is the same as for
--   the underlying monoid, as if the split were removed.
instance Action m n => Action (Split m) n where
  act :: Split m -> n -> n
act (M m
m) n
n      = m -> n -> n
forall m s. Action m s => m -> s -> s
act m
m n
n
  act (m
m1 :| m
m2) n
n = m -> n -> n
forall m s. Action m s => m -> s -> s
act m
m1 (m -> n -> n
forall m s. Action m s => m -> s -> s
act m
m2 n
n)