    --------------------------------------------------------------------------------
    --  See end of this file for licence information.
    --------------------------------------------------------------------------------
    -- |
    --  Module      :  Partial
    --  Copyright   :  (c) 2003, Graham Klyne, 2009 Vasili I Galchin, 2011, 2012 Douglas Burke
    --  License     :  GPL V2
    --
    --  Maintainer  :  Douglas Burke
    --  Stability   :  experimental
    --  Portability :  H98
    --
    --  This module provides methods to support operations on partially ordered
    --  collections.  The partial ordering relationship is represented by
    --  'Maybe' 'Ordering'.
    --
    --  Thanks to members of the haskell-cafe mailing list -
    --    Robert (rvollmert-lists\@gmx.net) and
    --    Tom Pledger (Tom.Pledger\@peace.com) -
    --  who suggested key ideas on which some of the code in this module is based.
    --
    --------------------------------------------------------------------------------

    -- at present the only user of this module is Swish.RDF.ClassRestrictionRule

    module Data.Ord.Partial
        ( PartCompare
          -- * Finding the range of a part-ordered list
        , minima
        , maxima
          -- * Comparing part-ordered containers
        , partCompareEq
        , partComparePair
        , partCompareListMaybe
        , partCompareListSubset
        )
        where

    import Data.List (foldl')

    ------------------------------------------------------------
    --  Type of partial compare function
    ------------------------------------------------------------

    -- | Partial comparison function.
    type PartCompare a = a -> a -> Maybe Ordering

    ------------------------------------------------------------
    --  Functions for minima and maxima of a part-ordered list
    ------------------------------------------------------------

    -- |This function finds the maxima in a list of partially
    --  ordered values, preserving the sequence of retained
    --  values from the supplied list.
    --
    --  It returns all those values in the supplied list
    --  for which there is no larger element in the list.
    --
    maxima :: PartCompare a -> [a] -> [a]
    maxima cmp = foldl' add []
        where
            add []     e = [e]
            add ms@(m:mr) e = case cmp m e of
                Nothing -> m : add mr e
                Just GT -> ms
                Just EQ -> ms
                Just LT -> add mr e

    -- |This function finds the minima in a list of partially
    --  ordered values, preserving the sequence of retained
    --  values from the supplied list.
    --
    --  It returns all those values in the supplied list
    --  for which there is no smaller element in the list.
    --
    minima :: PartCompare a -> [a] -> [a]
    minima cmp = maxima (flip cmp)

    ------------------------------------------------------------
    --  Partial ordering comparison functions
    ------------------------------------------------------------

    -- |Partial ordering for Eq values
    partCompareEq :: (Eq a) => PartCompare a
    partCompareEq a1 a2 = if a1 == a2 then Just EQ else Nothing

    -- |Part-ordering comparison on pairs of values,
    --  where each has a part-ordering relationship
    partComparePair ::
        PartCompare a
        -> PartCompare b
        -> (a,b)
        -> (a,b)
        -> Maybe Ordering
    partComparePair cmpa cmpb (a1,b1) (a2,b2) = case (cmpa a1 a2,cmpb b1 b2) of
        (_,Nothing)       -> Nothing
        (jc1,Just EQ)     -> jc1
        (Nothing,_)       -> Nothing
        (Just EQ,jc2)     -> jc2
        (Just c1,Just c2) -> if c1 == c2 then Just c1 else Nothing

    -- |Part-ordering comparison on lists of partially ordered values, where:
    --
    --  [@as==bs@]  if members of as are all equal to corresponding members of bs
    --
    --  [@as<=bs@]  if members of as are all less than or equal to corresponding
    --          members of bs
    --
    --  [@as>=bs@]  if members of as are all greater than or equal to corresponding
    --          members of bs
    --
    --  [otherwise] as and bs are unrelated
    --
    --  The comparison is restricted to the common elements in the two lists.
    --
    partCompareListPartOrd :: PartCompare a -> [a] -> [a] -> Maybe Ordering
    partCompareListPartOrd cmp a1s b1s = pcomp a1s b1s EQ
        where
            pcomp (a:as) (b:bs) ordp = case cmp a b of
                Just rel  -> pcomp1 as bs rel ordp
                _         -> Nothing
            pcomp _      _      ordp = Just ordp
            -- pcomp []     []     ordp = Just ordp

            pcomp1 as bs ordn EQ   = pcomp as bs ordn
            pcomp1 as bs EQ   ordp = pcomp as bs ordp
            pcomp1 as bs ordn ordp =
                if ordn == ordp then pcomp as bs ordp else Nothing

    -- |Part-ordering comparison for Maybe values.
    partCompareMaybe :: (Eq a) => Maybe a -> Maybe a -> Maybe Ordering
    partCompareMaybe Nothing  Nothing  = Just EQ
    partCompareMaybe (Just _) Nothing  = Just GT
    partCompareMaybe Nothing  (Just _) = Just LT
    partCompareMaybe (Just a) (Just b) = if a == b then Just EQ else Nothing

    -- |Part-ordering comparison on lists of Maybe values.
    partCompareListMaybe :: (Eq a) => [Maybe a] -> [Maybe a] -> Maybe Ordering
    partCompareListMaybe = partCompareListPartOrd partCompareMaybe

    -- |Part-ordering comparison on lists based on subset relationship
    partCompareListSubset :: (Eq a) => [a] -> [a] -> Maybe Ordering
    partCompareListSubset a b
        | aeqvb     = Just EQ
        | asubb     = Just LT
        | bsuba     = Just GT
        | otherwise = Nothing
        where
            asubb = a `subset` b
            bsuba = b `subset` a
            aeqvb = asubb && bsuba
            x `subset` y = and [ ma `elem` y | ma <- x ]

    ------------------------------------------------------------
    --  Test cases
    ------------------------------------------------------------

    {-

    notTrueFalse  = Nothing :: Maybe Bool

    -- partCompareListOrd
    test01 = partCompareListOrd [1,2,3] [1,2,3] == Just EQ
    test02 = partCompareListOrd [1,2,3] [2,3,4] == Just LT
    test03 = partCompareListOrd [1,2,4] [1,2,3] == Just GT
    test04 = partCompareListOrd [1,2,3] [2,1,3] == Nothing

    -- partCompareMaybe
    test11 = partCompareMaybe (Just True)  (Just True)  == Just EQ
    test12 = partCompareMaybe (Just True)  (Just False) == Nothing
    test13 = partCompareMaybe notTrueFalse (Just False) == Just LT
    test14 = partCompareMaybe (Just True)  notTrueFalse == Just GT
    test15 = partCompareMaybe notTrueFalse notTrueFalse == Just EQ

    -- partCompareListMaybe
    test21 = partCompareListMaybe [Just True,Just False]
                                  [Just True,Just False]
                == Just EQ
    test22 = partCompareListMaybe [Just True,Just False]
                                  [Just True,Just True]
                == Nothing
    test23 = partCompareListMaybe [Just False,Just True]
                                  [Just False,Just True]
                == Just EQ
    test24 = partCompareListMaybe [Nothing,   Just True]
                                  [Just False,Just True]
                == Just LT
    test25 = partCompareListMaybe [Just False,Just True]
                                  [Just False,Nothing]
                == Just GT
    test26 = partCompareListMaybe [Nothing,   Just True]
                                  [Just False,Nothing]
                == Nothing
    test27 = partCompareListMaybe [Nothing,Just True]
                                  [Nothing,Nothing]
                == Just GT
    test28 = partCompareListMaybe [notTrueFalse,notTrueFalse]
                                  [notTrueFalse,notTrueFalse]
                == Just EQ

    --  minima, maxima
    test31a = maxima partCompareListMaybe ds1a == ds1b
    test31b = minima partCompareListMaybe ds1a == ds1c
    ds1a =
        [ [Just 'a',Just 'b',Just 'c']
        , [Just 'a',Just 'b',Nothing ]
        , [Just 'a',Nothing ,Just 'c']
        , [Just 'a',Nothing ,Nothing ]
        , [Nothing ,Just 'b',Just 'c']
        , [Nothing ,Just 'b',Nothing ]
        , [Nothing ,Nothing ,Just 'c']
        , [Nothing ,Nothing ,Nothing ]
        ]
    ds1b =
        [ [Just 'a',Just 'b',Just 'c']
        ]
    ds1c =
        [ [Nothing ,Nothing ,Nothing ]
        ]

    test32a = maxima partCompareListMaybe ds2a == ds2b
    test32b = minima partCompareListMaybe ds2a == ds2c
    ds2a =
        [ [Just 'a',Just 'b',Nothing ]
        , [Just 'a',Nothing ,Just 'c']
        , [Just 'a',Nothing ,Nothing ]
        , [Nothing ,Just 'b',Just 'c']
        , [Nothing ,Just 'b',Nothing ]
        , [Nothing ,Nothing ,Just 'c']
        ]
    ds2b =
        [ [Just 'a',Just 'b',Nothing ]
        , [Just 'a',Nothing ,Just 'c']
        , [Nothing ,Just 'b',Just 'c']
        ]
    ds2c =
        [ [Just 'a',Nothing ,Nothing ]
        , [Nothing ,Just 'b',Nothing ]
        , [Nothing ,Nothing ,Just 'c']
        ]

    test33a = maxima partCompareListMaybe ds3a == ds3b
    test33b = minima partCompareListMaybe ds3a == ds3c
    ds3a =
        [ [Just "a1",Just "b1",Just "c1"]
        , [Just "a2",Just "b2",Nothing  ]
        , [Just "a3",Nothing  ,Just "c3"]
        , [Just "a4",Nothing  ,Nothing  ]
        , [Nothing  ,Just "b5",Just "c5"]
        , [Nothing  ,Just "b6",Nothing  ]
        , [Nothing  ,Nothing  ,Just "c7"]
        ]
    ds3b =
        [ [Just "a1",Just "b1",Just "c1"]
        , [Just "a2",Just "b2",Nothing  ]
        , [Just "a3",Nothing  ,Just "c3"]
        , [Just "a4",Nothing  ,Nothing  ]
        , [Nothing  ,Just "b5",Just "c5"]
        , [Nothing  ,Just "b6",Nothing  ]
        , [Nothing  ,Nothing  ,Just "c7"]
        ]
    ds3c =
        [ [Just "a1",Just "b1",Just "c1"]
        , [Just "a2",Just "b2",Nothing  ]
        , [Just "a3",Nothing  ,Just "c3"]
        , [Just "a4",Nothing  ,Nothing  ]
        , [Nothing  ,Just "b5",Just "c5"]
        , [Nothing  ,Just "b6",Nothing  ]
        , [Nothing  ,Nothing  ,Just "c7"]
        ]

    test34a = maxima partCompareListMaybe ds4a == ds4b
    test34b = minima partCompareListMaybe ds4a == ds4c
    ds4a =
        [ [Just 1, Just 1 ]
        , [Just 2, Nothing]
        , [Nothing,Just 3 ]
        , [Nothing,Nothing]
        ]
    ds4b =
        [ [Just 1, Just 1 ]
        , [Just 2, Nothing]
        , [Nothing,Just 3 ]
        ]
    ds4c =
        [ [Nothing,Nothing]
        ]

    -- Check handling of equal values
    test35a = maxima partCompareListMaybe ds5a == ds5b
    test35b = minima partCompareListMaybe ds5a == ds5c
    ds5a =
        [ [Just 1, Just 1 ]
        , [Just 2, Nothing]
        , [Nothing,Just 3 ]
        , [Nothing,Nothing]
        , [Just 1, Just 1 ]
        , [Just 2, Nothing]
        , [Nothing,Just 3 ]
        , [Nothing,Nothing]
        ]
    ds5b =
        [ [Just 1, Just 1 ]
        , [Just 2, Nothing]
        , [Nothing,Just 3 ]
        ]
    ds5c =
        [ [Nothing,Nothing]
        ]

    -- test case 32 with different ordering of values
    test36a = maxima partCompareListMaybe ds6a == ds6b
    test36b = minima partCompareListMaybe ds6a == ds6c
    ds6a =
        [ [Just 'a',Just 'b',Nothing ]
        , [Nothing ,Nothing ,Just 'c']
        , [Nothing ,Just 'b',Nothing ]
        , [Nothing ,Just 'b',Just 'c']
        , [Just 'a',Nothing ,Nothing ]
        , [Just 'a',Nothing ,Just 'c']
        ]
    ds6b =
        [ [Just 'a',Just 'b',Nothing ]
        , [Nothing ,Just 'b',Just 'c']
        , [Just 'a',Nothing ,Just 'c']
        ]
    ds6c =
        [ [Nothing ,Nothing ,Just 'c']
        , [Nothing ,Just 'b',Nothing ]
        , [Just 'a',Nothing ,Nothing ]
        ]

    test = and
        [ test01, test02, test03, test04
        , test11, test12, test13, test14, test15
        , test21, test22, test23, test24, test25, test26, test27, test28
        , test31a, test31b, test32a, test32b, test33a, test33b
        , test34a, test34b, test35a, test35b, test36a, test36b
        ]

    -}

    --------------------------------------------------------------------------------
    --
    --  Copyright (c) 2003, Graham Klyne, 2009 Vasili I Galchin,
    --    2011, 2012 Douglas Burke
    --  All rights reserved.
    --
    --  This file is part of Swish.
    --
    --  Swish is free software; you can redistribute it and/or modify
    --  it under the terms of the GNU General Public License as published by
    --  the Free Software Foundation; either version 2 of the License, or
    --  (at your option) any later version.
    --
    --  Swish is distributed in the hope that it will be useful,
    --  but WITHOUT ANY WARRANTY; without even the implied warranty of
    --  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    --  GNU General Public License for more details.
    --
    --  You should have received a copy of the GNU General Public License
    --  along with Swish; if not, write to:
    --    The Free Software Foundation, Inc.,
    --    59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
    --
    --------------------------------------------------------------------------------