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


-- | Combinators for creating bijections from some type to the natural numbers.
--   
--   Combinators for creating bijections from a subset of an arbitrary type
--   to a range of <a>Int</a>s, , e.g. for using libraries that require
--   <a>Int</a> IDs.
@package numbering
@version 0.2

module Data.Numbering

-- | Invariant: For all <tt>i</tt> in <tt>[ 0 .. <a>nuLength</a> - 1
--   ]</tt>, <tt><a>toInt</a> (<a>fromInt</a> i) == i</tt>.
--   
--   This implies that for all <tt>a</tt> of the form <tt><a>fromInt</a>
--   i</tt> (with <tt>i</tt> in <tt>[ 0 .. <a>nuLength</a> - 1 ]</tt>),
--   <tt><a>fromInt</a> (<a>toInt</a> a) = a</tt>.
--   
--   The behaviour of <tt>fromInt</tt> for out-of-bounds indices and that
--   of <tt>toInt</tt> for elements not occuring in the numbering is
--   undefined.
data Numbering a
UnsafeMkNumbering :: (a -> Int) -> (Int -> a) -> Int -> Numbering a
toInt :: Numbering a -> a -> Int
fromInt :: Numbering a -> Int -> a
nuLength :: Numbering a -> Int

-- | <tt>enumNu a b</tt> creates a numbering of the elements <tt>[a ..
--   b]</tt> (inclusively).
enumNu :: Enum a => a -> a -> Numbering a

-- | <tt>enumNu' i j</tt> creates a numbering of the elements <tt>[toEnum i
--   .. toEnum j]</tt> (inclusively).
enumNu' :: Enum a => Int -> Int -> Numbering a

-- | (Uses a <a>Map</a> because <a>Data.Set</a> doesn't expose the
--   necessary index-based API)
nuFromSet :: Map Int ignored -> Numbering Int

-- | The distinctness precondition is checked (we have to create a map
--   anyway).
nuFromDistinctVector :: (Ord a, Show a, Vector v a) => v a -> Numbering a

-- | Allows customization of the map type used.
nuFromDistinctVectorG :: (Show a, Vector v a) => map -> ((a -> Int -> Int -> t) -> a -> Int -> map -> map) -> (a -> map -> Maybe Int) -> v a -> Numbering a

-- | See <a>nuFromDistinctVector</a>.
nuFromDistinctList :: (Ord a, Show a) => [a] -> Numbering a
nuFromDistinctUnboxList :: (Ord a, Show a, Unbox a) => [a] -> Numbering a
nuFromDistinctIntList :: [Int] -> Numbering Int

-- | Uniquifies the input first (resulting in an unspecified order).
nuFromList :: (Ord a, Show a) => [a] -> Numbering a

-- | Uniquifies the input first (resulting in an unspecified order).
nuFromUnboxList :: (Ord a, Show a, Unbox a) => [a] -> Numbering a

-- | Uniquifies the input first (resulting in an unspecified order).
nuFromIntList :: [Int] -> Numbering Int
finiteTypeNu :: (Enum a, Bounded a) => Numbering a

-- | Identity numbering
idNu :: Int -> Numbering Int

-- | Creates a numbering for an <a>Either</a>-like type, given numberings
--   for the summand types.
sumNu :: (a1 -> a) -> (a2 -> a) -> ((a1 -> Int) -> (a2 -> Int) -> a -> Int) -> Numbering a1 -> Numbering a2 -> Numbering a
eitherNu :: Numbering a -> Numbering b -> Numbering (Either a b)

-- | Creates a numbering for an pair-like type, given numberings for the
--   component types.
prodNu :: (a -> a2) -> (a -> a1) -> (a2 -> a1 -> a) -> Numbering a2 -> Numbering a1 -> Numbering a
pairNu :: Numbering a -> Numbering b -> Numbering (a, b)
nuIndices :: Numbering a -> [Int]
nuElements :: Numbering a -> [a]
data NumberingBrokenInvariantException a
NumberingBrokenInvariantException :: Int -> a -> Int -> NumberingBrokenInvariantException a
nbie_index :: NumberingBrokenInvariantException a -> Int
nbie_fromIntOfIndex :: NumberingBrokenInvariantException a -> a
nbie_toIntOfFromIntOfIndex :: NumberingBrokenInvariantException a -> Int
checkNu :: Numbering a -> Either (NumberingBrokenInvariantException a) ()
instance Typeable1 NumberingBrokenInvariantException
instance Show a => Show (NumberingBrokenInvariantException a)
instance (Show a, Typeable a) => Exception (NumberingBrokenInvariantException a)
instance Show a => Show (Numbering a)