-- Hoogle documentation, generated by Haddock
-- See Hoogle, http://www.haskell.org/hoogle/


-- | Data structure supporting partial orders
--   
--   Please see README.md
@package partialord
@version 0.0.2


-- | Partial orders
module Data.PartialOrd

-- | A data type representing relationships between two objects in a poset:
--   they can be related (by EQ', LT' or GT'; like EQ, LT or GT), or
--   unrelated (NT').
data PartialOrdering
EQ' :: PartialOrdering
LT' :: PartialOrdering
GT' :: PartialOrdering
NT' :: PartialOrdering

-- | Convert an ordering into a partial ordering
fromOrd :: Ordering -> PartialOrdering

-- | Convert a partial ordering to an ordering
toMaybeOrd :: PartialOrdering -> Maybe Ordering

-- | Convert an ordering into a partial ordering
fromMaybeOrd :: Maybe Ordering -> PartialOrdering

-- | Convert from <a>leq</a> and <a>geq</a> to a partial ordering
fromLeqGeq :: Bool -> Bool -> PartialOrdering

-- | Lift a <a>compare</a> to a <a>compare</a>`
fromCompare :: Ord a => a -> a -> PartialOrdering

-- | A typeclass expressing partially ordered types: any two elements are
--   related by a <a>PartialOrdering</a>.
class PartialOrd a
compare' :: PartialOrd a => a -> a -> PartialOrdering
leq :: PartialOrd a => a -> a -> Bool
geq :: PartialOrd a => a -> a -> Bool

-- | Are they LT', EQ', GT'
comparable :: PartialOrd a => a -> a -> Bool

-- | A helper type for constructing partial orderings from total orderings
--   (using deriving via)
newtype FullyOrd a
FullyOrd :: a -> FullyOrd a
[getOrd] :: FullyOrd a -> a

-- | A helper type for constructing partial orderings where everything is
--   equal or incomparable.
newtype Discrete a
Discrete :: a -> Discrete a
[getDiscrete] :: Discrete a -> a

-- | Sets of incomparable elements, with a monoidal structure obtained by
--   taking the maximal ones.
--   
--   Unfortunately, we need a full ordering for these to work (since they
--   use sets), though we don't assume this ordering has any compatibility
--   with the partial order. The monoid structures are most efficient with
--   pre-reduced sets as the left-hand argument.
newtype Maxima a
Maxima :: Set a -> Maxima a
[maxSet] :: Maxima a -> Set a

-- | Find the maxima of a list (passing it through the machinery above)
maxima :: (Ord a, PartialOrd a) => [a] -> [a]

-- | As above, but with minima
newtype Minima a
Minima :: Set a -> Minima a
[minSet] :: Minima a -> Set a

-- | Find the minima of a list (passing it through the machinery above)
minima :: (Ord a, PartialOrd a) => [a] -> [a]

-- | Lists partially ordered by infix inclusion
newtype Infix a
Infix :: [a] -> Infix a
[unInfix] :: Infix a -> [a]

-- | Lists partially ordered by prefix inclusion
newtype Prefix a
Prefix :: [a] -> Prefix a
[unPrefix] :: Prefix a -> [a]

-- | Lists partially ordered by suffix inclusion
newtype Suffix a
Suffix :: [a] -> Suffix a
[unSuffix] :: Suffix a -> [a]

-- | Lists partially ordered by the subsequence relation
newtype Subseq a
Subseq :: [a] -> Subseq a
[unSubseq] :: Subseq a -> [a]
instance GHC.Show.Show Data.PartialOrd.PartialOrdering
instance GHC.Classes.Eq Data.PartialOrd.PartialOrdering
instance GHC.Show.Show a => GHC.Show.Show (Data.PartialOrd.FullyOrd a)
instance GHC.Classes.Ord a => GHC.Classes.Ord (Data.PartialOrd.FullyOrd a)
instance GHC.Classes.Eq a => GHC.Classes.Eq (Data.PartialOrd.FullyOrd a)
instance GHC.Show.Show a => GHC.Show.Show (Data.PartialOrd.Discrete a)
instance GHC.Classes.Eq a => GHC.Classes.Eq (Data.PartialOrd.Discrete a)
instance GHC.Show.Show a => GHC.Show.Show (Data.PartialOrd.Infix a)
instance GHC.Classes.Eq a => GHC.Classes.Eq (Data.PartialOrd.Infix a)
instance GHC.Show.Show a => GHC.Show.Show (Data.PartialOrd.Prefix a)
instance GHC.Classes.Eq a => GHC.Classes.Eq (Data.PartialOrd.Prefix a)
instance GHC.Show.Show a => GHC.Show.Show (Data.PartialOrd.Suffix a)
instance GHC.Classes.Eq a => GHC.Classes.Eq (Data.PartialOrd.Suffix a)
instance GHC.Show.Show a => GHC.Show.Show (Data.PartialOrd.Subseq a)
instance GHC.Classes.Eq a => GHC.Classes.Eq (Data.PartialOrd.Subseq a)
instance Data.PartialOrd.PartialOrd GHC.Types.Int
instance Data.PartialOrd.PartialOrd GHC.Num.Integer.Integer
instance (GHC.Classes.Ord a, Data.PartialOrd.PartialOrd a) => GHC.Base.Semigroup (Data.PartialOrd.Minima a)
instance (GHC.Classes.Ord a, Data.PartialOrd.PartialOrd a) => GHC.Base.Monoid (Data.PartialOrd.Minima a)
instance (GHC.Classes.Ord a, Data.PartialOrd.PartialOrd a) => GHC.Base.Semigroup (Data.PartialOrd.Maxima a)
instance (GHC.Classes.Ord a, Data.PartialOrd.PartialOrd a) => GHC.Base.Monoid (Data.PartialOrd.Maxima a)
instance GHC.Classes.Eq a => Data.PartialOrd.PartialOrd (Data.PartialOrd.Subseq a)
instance GHC.Classes.Eq a => Data.PartialOrd.PartialOrd (Data.PartialOrd.Suffix a)
instance GHC.Classes.Eq a => Data.PartialOrd.PartialOrd (Data.PartialOrd.Prefix a)
instance GHC.Classes.Eq a => Data.PartialOrd.PartialOrd (Data.PartialOrd.Infix a)
instance GHC.Classes.Ord a => Data.PartialOrd.PartialOrd (Data.PartialOrd.FullyOrd a)
instance GHC.Classes.Eq a => Data.PartialOrd.PartialOrd (Data.PartialOrd.Discrete a)
instance Data.PartialOrd.PartialOrd ()
instance (Data.PartialOrd.PartialOrd a, Data.PartialOrd.PartialOrd b) => Data.PartialOrd.PartialOrd (a, b)
instance (Data.PartialOrd.PartialOrd a, Data.PartialOrd.PartialOrd b, Data.PartialOrd.PartialOrd c) => Data.PartialOrd.PartialOrd (a, b, c)
instance (Data.PartialOrd.PartialOrd a, Data.PartialOrd.PartialOrd b, Data.PartialOrd.PartialOrd c, Data.PartialOrd.PartialOrd d) => Data.PartialOrd.PartialOrd (a, b, c, d)
instance (Data.PartialOrd.PartialOrd a, Data.PartialOrd.PartialOrd b, Data.PartialOrd.PartialOrd c, Data.PartialOrd.PartialOrd d, Data.PartialOrd.PartialOrd e) => Data.PartialOrd.PartialOrd (a, b, c, d, e)
instance GHC.Classes.Ord a => Data.PartialOrd.PartialOrd (Data.Set.Internal.Set a)
instance Data.PartialOrd.PartialOrd Data.IntSet.Internal.IntSet
instance GHC.Base.Semigroup Data.PartialOrd.PartialOrdering
instance GHC.Base.Monoid Data.PartialOrd.PartialOrdering