From 89f95cbcb82c8112c4c75f07f7a4c58b762ea472 Mon Sep 17 00:00:00 2001
From: Henning Thielemann <git@henning-thielemann.de>
Date: Sat, 11 Mar 2017 18:56:05 +0100
Subject: [PATCH 1/9] PQueue.Prio: unification of MinPQueue and MaxPQueue

It is based on the implementation of MaxPQueue
but uses new data type (Wrap top) instead of Down.

PQueue.Top: generalization of Down data type.

Bump version to 1.3.3
---
 Data/PQueue/Prio.hs | 478 ++++++++++++++++++++++++++++++++++++++++++++
 Data/PQueue/Top.hs  |  34 ++++
 pqueue.cabal        |   4 +-
 3 files changed, 515 insertions(+), 1 deletion(-)
 create mode 100644 Data/PQueue/Prio.hs
 create mode 100644 Data/PQueue/Top.hs

diff --git a/Data/PQueue/Prio.hs b/Data/PQueue/Prio.hs
new file mode 100644
index 0000000..70690ea
--- /dev/null
+++ b/Data/PQueue/Prio.hs
@@ -0,0 +1,478 @@
+{-# LANGUAGE CPP #-}
+{-# OPTIONS_GHC -fno-warn-orphans #-}
+
+-----------------------------------------------------------------------------
+-- |
+-- Module      :  Data.PQueue.Prio
+-- Copyright   :  (c) Henning Thielemann 2017
+--                (c) Louis Wasserman 2010
+-- License     :  BSD-style
+-- Maintainer  :  libraries@haskell.org
+-- Stability   :  experimental
+-- Portability :  portable
+--
+-- General purpose priority queue.
+-- Each element is associated with a /key/, and the priority queue supports
+-- viewing and extracting the element with the top key.
+--
+-- A worst-case bound is given for each operation.  In some cases, an amortized
+-- bound is also specified; these bounds do not hold in a persistent context.
+--
+-- This implementation is based on a binomial heap augmented with a global root.
+-- The spine of the heap is maintained lazily.  To force the spine of the heap,
+-- use 'seqSpine'.
+--
+-- We do not guarantee stable behavior.
+-- Ties are broken arbitrarily -- that is, if @k1 <= k2@ and @k2 <= k1@, then there
+-- are no guarantees about the relative order in which @k1@, @k2@, and their associated
+-- elements are returned.  (Unlike Data.Map, we allow multiple elements with the
+-- same key.)
+--
+-- This implementation offers a number of methods of the form @xxxU@, where @U@ stands for
+-- unordered.  No guarantees whatsoever are made on the execution or traversal order of
+-- these functions.
+-----------------------------------------------------------------------------
+module Data.PQueue.Prio (
+  PQueue,
+  MinPQueue,
+  MaxPQueue,
+  -- * Construction
+  empty,
+  singleton,
+  insert,
+  insertBehind,
+  union,
+  unions,
+  -- * Query
+  null,
+  size,
+  -- ** Top view
+  findTop,
+  getTop,
+  deleteTop,
+  deleteFindTop,
+  adjustTop,
+  adjustTopWithKey,
+  updateTop,
+  updateTopWithKey,
+  topView,
+  topViewWithKey,
+  -- * Traversal
+  -- ** Map
+  map,
+  mapWithKey,
+  mapKeys,
+  mapKeysMonotonic,
+  -- ** Fold
+  foldrWithKey,
+  foldlWithKey,
+  -- ** Traverse
+  traverseWithKey,
+  -- * Subsets
+  -- ** Indexed
+  take,
+  drop,
+  splitAt,
+  -- ** Predicates
+  takeWhile,
+  takeWhileWithKey,
+  dropWhile,
+  dropWhileWithKey,
+  span,
+  spanWithKey,
+  break,
+  breakWithKey,
+  -- *** Filter
+  filter,
+  filterWithKey,
+  partition,
+  partitionWithKey,
+  mapMaybe,
+  mapMaybeWithKey,
+  mapEither,
+  mapEitherWithKey,
+  -- * List operations
+  -- ** Conversion from lists
+  fromList,
+  fromOrderedList,
+  -- ** Conversion to lists
+  keys,
+  elems,
+  assocs,
+  toList,
+  -- * Unordered operations
+  foldrU,
+  foldrWithKeyU,
+  foldlU,
+  foldlWithKeyU,
+  traverseU,
+  traverseWithKeyU,
+  keysU,
+  elemsU,
+  assocsU,
+  toListU,
+  -- * Helper methods
+  seqSpine
+  )
+  where
+
+import qualified Data.PQueue.Prio.Min as Q
+import qualified Data.PQueue.Top as Top
+import Data.PQueue.Top (Top, Wrap(Wrap, unwrap))
+
+import Control.DeepSeq (NFData (rnf))
+import Control.Applicative (Applicative, (<$>))
+import Data.Monoid (Monoid(mempty, mappend, mconcat))
+import Data.Traversable (Traversable(traverse))
+import Data.Foldable (Foldable, foldr, foldl)
+import Data.Maybe (fromMaybe)
+
+import Prelude hiding (map, filter, break, span, takeWhile, dropWhile, splitAt, take, drop, (!!), null, foldr, foldl)
+
+
+#ifdef __GLASGOW_HASKELL__
+import Data.Data (Data, Typeable)
+import Text.Read (Lexeme(Ident), lexP, parens, prec,
+  readPrec, readListPrec, readListPrecDefault)
+#else
+build :: ((a -> [a] -> [a]) -> [a] -> [a]) -> [a]
+build f = f (:) []
+#endif
+
+first' :: (a -> b) -> (a, c) -> (b, c)
+first' f (a, c) = (f a, c)
+
+
+-- | A priority queue where values of type @a@ are annotated with keys of type @k@.
+-- The queue supports extracting the element with top key.
+newtype PQueue top k a = PQ (Q.MinPQueue (Wrap top k) a)
+# if __GLASGOW_HASKELL__
+  deriving (Eq, Ord, Data, Typeable)
+# else
+  deriving (Eq, Ord)
+# endif
+
+instance (NFData k, NFData a) => NFData (PQueue top k a) where
+  rnf (PQ q) = rnf q
+
+
+type MinPQueue = PQueue Top.Min
+type MaxPQueue = PQueue Top.Max
+
+instance (Top top, Ord k) => Monoid (PQueue top k a) where
+  mempty = empty
+  mappend = union
+  mconcat = unions
+
+instance (Top top, Ord k, Show k, Show a) => Show (PQueue top k a) where
+  showsPrec p xs = showParen (p > 10) $
+    showString "fromOrderedList " . shows (toList xs)
+
+instance (Read k, Read a) => Read (PQueue top k a) where
+#ifdef __GLASGOW_HASKELL__
+  readPrec = parens $ prec 10 $ do
+    Ident "fromOrderedList" <- lexP
+    xs <- readPrec
+    return (fromOrderedList xs)
+
+  readListPrec = readListPrecDefault
+#else
+  readsPrec p = readParen (p > 10) $ \ r -> do
+    ("fromOrderedList",s) <- lex r
+    (xs,t) <- reads s
+    return (fromOrderedList xs,t)
+#endif
+
+instance Functor (PQueue top k) where
+  fmap f (PQ q) = PQ (fmap f q)
+
+instance (Top top, Ord k) => Foldable (PQueue top k) where
+  foldr f z (PQ q) = foldr f z q
+  foldl f z (PQ q) = foldl f z q
+
+instance (Top top, Ord k) => Traversable (PQueue top k) where
+  traverse f (PQ q) = PQ <$> traverse f q
+
+-- | /O(1)/.  Returns the empty priority queue.
+empty :: PQueue top k a
+empty = PQ Q.empty
+
+-- | /O(1)/.  Constructs a singleton priority queue.
+singleton :: k -> a -> PQueue top k a
+singleton k a = PQ (Q.singleton (Wrap k) a)
+
+-- | Amortized /O(1)/, worst-case /O(log n)/.  Inserts
+-- an element with the specified key into the queue.
+insert :: (Top top, Ord k) => k -> a -> PQueue top k a -> PQueue top k a
+insert k a (PQ q) = PQ (Q.insert (Wrap k) a q)
+
+-- | Amortized /O(1)/, worst-case /O(log n)/.  Insert an element into the priority queue,
+--   putting it behind elements that compare equal to the inserted one.
+insertBehind :: (Top top, Ord k) => k -> a -> PQueue top k a -> PQueue top k a
+insertBehind k a (PQ q) = PQ (Q.insertBehind (Wrap k) a q)
+
+-- | Amortized /O(log(min(n1, n2)))/, worst-case /O(log(max(n1, n2)))/.  Returns the union
+-- of the two specified queues.
+union :: (Top top, Ord k) => PQueue top k a -> PQueue top k a -> PQueue top k a
+PQ q1 `union` PQ q2 = PQ (q1 `Q.union` q2)
+
+-- | The union of a list of queues: (@'unions' == 'List.foldl' 'union' 'empty'@).
+unions :: (Top top, Ord k) => [PQueue top k a] -> PQueue top k a
+unions qs = PQ (Q.unions [q | PQ q <- qs])
+
+-- | /O(1)/.  Checks if this priority queue is empty.
+null :: PQueue top k a -> Bool
+null (PQ q) = Q.null q
+
+-- | /O(1)/.  Returns the size of this priority queue.
+size :: PQueue top k a -> Int
+size (PQ q) = Q.size q
+
+-- | /O(1)/.  The top (key, element) in the queue.  Calls 'error' if empty.
+findTop :: PQueue top k a -> (k, a)
+findTop = fromMaybe (error "Error: findTop called on an empty queue") . getTop
+
+-- | /O(1)/.  The top (key, element) in the queue, if the queue is nonempty.
+getTop :: PQueue top k a -> Maybe (k, a)
+getTop (PQ q) = do
+  (Wrap k, a) <- Q.getMin q
+  return (k, a)
+
+-- | /O(log n)/.  Delete and find the element with the top key.  Calls 'error' if empty.
+deleteTop :: (Top top, Ord k) => PQueue top k a -> PQueue top k a
+deleteTop (PQ q) = PQ (Q.deleteMin q)
+
+-- | /O(log n)/.  Delete and find the element with the top key.  Calls 'error' if empty.
+deleteFindTop :: (Top top, Ord k) => PQueue top k a -> ((k, a), PQueue top k a)
+deleteFindTop = fromMaybe (error "Error: deleteFindTop called on an empty queue") . topViewWithKey
+
+-- | /O(1)/.  Alter the value at the top key.  If the queue is empty, does nothing.
+adjustTop :: (a -> a) -> PQueue top k a -> PQueue top k a
+adjustTop = adjustTopWithKey . const
+
+-- | /O(1)/.  Alter the value at the top key.  If the queue is empty, does nothing.
+adjustTopWithKey :: (k -> a -> a) -> PQueue top k a -> PQueue top k a
+adjustTopWithKey f (PQ q) = PQ (Q.adjustMinWithKey (f . unwrap) q)
+
+-- | /O(log n)/.  (Actually /O(1)/ if there's no deletion.)  Update the value at the top key.
+-- If the queue is empty, does nothing.
+updateTop :: (Top top, Ord k) => (a -> Maybe a) -> PQueue top k a -> PQueue top k a
+updateTop = updateTopWithKey . const
+
+-- | /O(log n)/.  (Actually /O(1)/ if there's no deletion.)  Update the value at the top key.
+-- If the queue is empty, does nothing.
+updateTopWithKey :: (Top top, Ord k) => (k -> a -> Maybe a) -> PQueue top k a -> PQueue top k a
+updateTopWithKey f (PQ q) = PQ (Q.updateMinWithKey (f . unwrap) q)
+
+-- | /O(log n)/.  Retrieves the value associated with the top key of the queue, and the queue
+-- stripped of that element, or 'Nothing' if passed an empty queue.
+topView :: (Top top, Ord k) => PQueue top k a -> Maybe (a, PQueue top k a)
+topView q = do
+  ((_, a), q') <- topViewWithKey q
+  return (a, q')
+
+-- | /O(log n)/.  Retrieves the top (key, value) pair of the map, and the map stripped of that
+-- element, or 'Nothing' if passed an empty map.
+topViewWithKey :: (Top top, Ord k) => PQueue top k a -> Maybe ((k, a), PQueue top k a)
+topViewWithKey (PQ q) = do
+  ((Wrap k, a), q') <- Q.minViewWithKey q
+  return ((k, a), PQ q')
+
+-- | /O(n)/.  Map a function over all values in the queue.
+map :: (a -> b) -> PQueue top k a -> PQueue top k b
+map = mapWithKey . const
+
+-- | /O(n)/.  Map a function over all values in the queue.
+mapWithKey :: (k -> a -> b) -> PQueue top k a -> PQueue top k b
+mapWithKey f (PQ q) = PQ (Q.mapWithKey (f . unwrap) q)
+
+-- | /O(n)/.  Map a function over all values in the queue.
+mapKeys :: (Top top, Ord k') => (k -> k') -> PQueue top k a -> PQueue top k' a
+mapKeys f (PQ q) = PQ (Q.mapKeys (fmap f) q)
+
+-- | /O(n)/.  @'mapKeysMonotonic' f q == 'mapKeys' f q@, but only works when @f@ is strictly
+-- monotonic.  /The precondition is not checked./  This function has better performance than
+-- 'mapKeys'.
+mapKeysMonotonic :: (k -> k') -> PQueue top k a -> PQueue top k' a
+mapKeysMonotonic f (PQ q) = PQ (Q.mapKeysMonotonic (fmap f) q)
+
+-- | /O(n log n)/.  Fold the keys and values in the map, such that
+-- @'foldrWithKey' f z q == 'List.foldr' ('uncurry' f) z ('toList' q)@.
+--
+-- If you do not care about the traversal order, consider using 'foldrWithKeyU'.
+foldrWithKey :: (Top top, Ord k) => (k -> a -> b -> b) -> b -> PQueue top k a -> b
+foldrWithKey f z (PQ q) = Q.foldrWithKey (f . unwrap) z q
+
+-- | /O(n log n)/.  Fold the keys and values in the map, such that
+-- @'foldlWithKey' f z q == 'List.foldl' ('uncurry' . f) z ('toList' q)@.
+--
+-- If you do not care about the traversal order, consider using 'foldlWithKeyU'.
+foldlWithKey :: (Top top, Ord k) => (b -> k -> a -> b) -> b -> PQueue top k a -> b
+foldlWithKey f z0 (PQ q) = Q.foldlWithKey (\ z -> f z . unwrap) z0 q
+
+-- | /O(n log n)/.  Traverses the elements of the queue in natural order by key.
+-- (@'traverseWithKey' f q == 'fromOrderedList' <$> 'traverse' ('uncurry' f) ('toList' q)@)
+--
+-- If you do not care about the /order/ of the traversal, consider using 'traverseWithKeyU'.
+traverseWithKey :: (Top top, Ord k, Applicative f) => (k -> a -> f b) -> PQueue top k a -> f (PQueue top k b)
+traverseWithKey f (PQ q) = PQ <$> Q.traverseWithKey (f . unwrap) q
+
+-- | /O(k log n)/.  Takes the first @k@ (key, value) pairs in the queue, or the first @n@ if @k >= n@.
+-- (@'take' k q == 'List.take' k ('toList' q)@)
+take :: (Top top, Ord k) => Int -> PQueue top k a -> [(k, a)]
+take k (PQ q) = fmap (first' unwrap) (Q.take k q)
+
+-- | /O(k log n)/.  Deletes the first @k@ (key, value) pairs in the queue, or returns an empty queue if @k >= n@.
+drop :: (Top top, Ord k) => Int -> PQueue top k a -> PQueue top k a
+drop k (PQ q) = PQ (Q.drop k q)
+
+-- | /O(k log n)/.  Equivalent to @('take' k q, 'drop' k q)@.
+splitAt :: (Top top, Ord k) => Int -> PQueue top k a -> ([(k, a)], PQueue top k a)
+splitAt k (PQ q) = case Q.splitAt k q of
+  (xs, q') -> (fmap (first' unwrap) xs, PQ q')
+
+-- | Takes the longest possible prefix of elements satisfying the predicate.
+-- (@'takeWhile' p q == 'List.takeWhile' (p . 'snd') ('toList' q)@)
+takeWhile :: (Top top, Ord k) => (a -> Bool) -> PQueue top k a -> [(k, a)]
+takeWhile = takeWhileWithKey . const
+
+-- | Takes the longest possible prefix of elements satisfying the predicate.
+-- (@'takeWhile' p q == 'List.takeWhile' (uncurry p) ('toList' q)@)
+takeWhileWithKey :: (Top top, Ord k) => (k -> a -> Bool) -> PQueue top k a -> [(k, a)]
+takeWhileWithKey p (PQ q) = fmap (first' unwrap) (Q.takeWhileWithKey (p . unwrap) q)
+
+-- | Removes the longest possible prefix of elements satisfying the predicate.
+dropWhile :: (Top top, Ord k) => (a -> Bool) -> PQueue top k a -> PQueue top k a
+dropWhile = dropWhileWithKey . const
+
+-- | Removes the longest possible prefix of elements satisfying the predicate.
+dropWhileWithKey :: (Top top, Ord k) => (k -> a -> Bool) -> PQueue top k a -> PQueue top k a
+dropWhileWithKey p (PQ q) = PQ (Q.dropWhileWithKey (p . unwrap) q)
+
+-- | Equivalent to @('takeWhile' p q, 'dropWhile' p q)@.
+span :: (Top top, Ord k) => (a -> Bool) -> PQueue top k a -> ([(k, a)], PQueue top k a)
+span = spanWithKey . const
+
+-- | Equivalent to @'span' ('not' . p)@.
+break :: (Top top, Ord k) => (a -> Bool) -> PQueue top k a -> ([(k, a)], PQueue top k a)
+break = breakWithKey . const
+
+-- | Equivalent to @'spanWithKey' (\ k a -> 'not' (p k a)) q@.
+spanWithKey :: (Top top, Ord k) => (k -> a -> Bool) -> PQueue top k a -> ([(k, a)], PQueue top k a)
+spanWithKey p (PQ q) = case Q.spanWithKey (p . unwrap) q of
+  (xs, q') -> (fmap (first' unwrap) xs, PQ q')
+
+-- | Equivalent to @'spanWithKey' (\ k a -> 'not' (p k a)) q@.
+breakWithKey :: (Top top, Ord k) => (k -> a -> Bool) -> PQueue top k a -> ([(k, a)], PQueue top k a)
+breakWithKey p (PQ q) = case Q.breakWithKey (p . unwrap) q of
+  (xs, q') -> (fmap (first' unwrap) xs, PQ q')
+
+-- | /O(n)/.  Filter all values that satisfy the predicate.
+filter :: (Top top, Ord k) => (a -> Bool) -> PQueue top k a -> PQueue top k a
+filter = filterWithKey . const
+
+-- | /O(n)/.  Filter all values that satisfy the predicate.
+filterWithKey :: (Top top, Ord k) => (k -> a -> Bool) -> PQueue top k a -> PQueue top k a
+filterWithKey p (PQ q) = PQ (Q.filterWithKey (p . unwrap) q)
+
+-- | /O(n)/.  Partition the queue according to a predicate.  The first queue contains all elements
+-- which satisfy the predicate, the second all elements that fail the predicate.
+partition :: (Top top, Ord k) => (a -> Bool) -> PQueue top k a -> (PQueue top k a, PQueue top k a)
+partition = partitionWithKey . const
+
+-- | /O(n)/.  Partition the queue according to a predicate.  The first queue contains all elements
+-- which satisfy the predicate, the second all elements that fail the predicate.
+partitionWithKey :: (Top top, Ord k) => (k -> a -> Bool) -> PQueue top k a -> (PQueue top k a, PQueue top k a)
+partitionWithKey p (PQ q) = case Q.partitionWithKey (p . unwrap) q of
+  (q1, q0) -> (PQ q1, PQ q0)
+
+-- | /O(n)/.  Map values and collect the 'Just' results.
+mapMaybe :: (Top top, Ord k) => (a -> Maybe b) -> PQueue top k a -> PQueue top k b
+mapMaybe = mapMaybeWithKey . const
+
+-- | /O(n)/.  Map values and collect the 'Just' results.
+mapMaybeWithKey :: (Top top, Ord k) => (k -> a -> Maybe b) -> PQueue top k a -> PQueue top k b
+mapMaybeWithKey f (PQ q) = PQ (Q.mapMaybeWithKey (f . unwrap) q)
+
+-- | /O(n)/.  Map values and separate the 'Left' and 'Right' results.
+mapEither :: (Top top, Ord k) => (a -> Either b c) -> PQueue top k a -> (PQueue top k b, PQueue top k c)
+mapEither = mapEitherWithKey . const
+
+-- | /O(n)/.  Map values and separate the 'Left' and 'Right' results.
+mapEitherWithKey :: (Top top, Ord k) => (k -> a -> Either b c) -> PQueue top k a -> (PQueue top k b, PQueue top k c)
+mapEitherWithKey f (PQ q) = case Q.mapEitherWithKey (f . unwrap) q of
+  (qL, qR) -> (PQ qL, PQ qR)
+
+-- | /O(n)/.  Build a priority queue from the list of (key, value) pairs.
+fromList :: (Top top, Ord k) => [(k, a)] -> PQueue top k a
+fromList = PQ . Q.fromList . fmap (first' Wrap)
+
+-- | /O(n)/.  Build a priority queue from a list of (key, value) pairs where every suffix contains the top element at the list head.  /The precondition is not checked./
+fromOrderedList :: [(k, a)] -> PQueue top k a
+fromOrderedList = PQ . Q.fromAscList . fmap (first' Wrap)
+
+-- | /O(n log n)/.  Return all keys of the queue in natural order, that is, top keys first.
+keys :: (Top top, Ord k) => PQueue top k a -> [k]
+keys = fmap fst . toList
+
+-- | /O(n log n)/.  Return all elements of the queue in natural order by key.
+elems :: (Top top, Ord k) => PQueue top k a -> [a]
+elems = fmap snd . toList
+
+-- | /O(n log n)/.  Equivalent to 'toList'.
+assocs :: (Top top, Ord k) => PQueue top k a -> [(k, a)]
+assocs = toList
+
+-- | /O(n log n)/.  Return all (key, value) pairs in natural order by key.
+--
+-- If the traversal order is irrelevant, consider using 'toListU'.
+toList :: (Top top, Ord k) => PQueue top k a -> [(k, a)]
+toList (PQ q) = fmap (first' unwrap) (Q.toAscList q)
+
+-- | /O(n)/.  An unordered right fold over the elements of the queue, in no particular order.
+foldrU :: (a -> b -> b) -> b -> PQueue top k a -> b
+foldrU = foldrWithKeyU . const
+
+-- | /O(n)/.  An unordered right fold over the elements of the queue, in no particular order.
+foldrWithKeyU :: (k -> a -> b -> b) -> b -> PQueue top k a -> b
+foldrWithKeyU f z (PQ q) = Q.foldrWithKeyU (f . unwrap) z q
+
+-- | /O(n)/.  An unordered left fold over the elements of the queue, in no particular order.
+foldlU :: (b -> a -> b) -> b -> PQueue top k a -> b
+foldlU f = foldlWithKeyU (const . f)
+
+-- | /O(n)/.  An unordered left fold over the elements of the queue, in no particular order.
+foldlWithKeyU :: (b -> k -> a -> b) -> b -> PQueue top k a -> b
+foldlWithKeyU f z0 (PQ q) = Q.foldlWithKeyU (\ z -> f z . unwrap) z0 q
+
+-- | /O(n)/.  An unordered traversal over a priority queue, in no particular order.
+-- While there is no guarantee in which order the elements are traversed, the resulting
+-- priority queue will be perfectly valid.
+traverseU :: (Applicative f) => (a -> f b) -> PQueue top k a -> f (PQueue top k b)
+traverseU = traverseWithKeyU . const
+
+-- | /O(n)/.  An unordered traversal over a priority queue, in no particular order.
+-- While there is no guarantee in which order the elements are traversed, the resulting
+-- priority queue will be perfectly valid.
+traverseWithKeyU :: (Applicative f) => (k -> a -> f b) -> PQueue top k a -> f (PQueue top k b)
+traverseWithKeyU f (PQ q) = PQ <$> Q.traverseWithKeyU (f . unwrap) q
+
+-- | /O(n)/.  Return all keys of the queue in no particular order.
+keysU :: PQueue top k a -> [k]
+keysU = fmap fst . toListU
+
+-- | /O(n)/.  Return all elements of the queue in no particular order.
+elemsU :: PQueue top k a -> [a]
+elemsU = fmap snd . toListU
+
+-- | /O(n)/.  Equivalent to 'toListU'.
+assocsU :: PQueue top k a -> [(k, a)]
+assocsU = toListU
+
+-- | /O(n)/.  Returns all (key, value) pairs in the queue in no particular order.
+toListU :: PQueue top k a -> [(k, a)]
+toListU (PQ q) = fmap (first' unwrap) (Q.toListU q)
+
+-- | /O(log n)/.  Analogous to @deepseq@ in the @deepseq@ package, but only forces the spine of the binomial heap.
+seqSpine :: PQueue top k a -> b -> b
+seqSpine (PQ q) = Q.seqSpine q
diff --git a/Data/PQueue/Top.hs b/Data/PQueue/Top.hs
new file mode 100644
index 0000000..43cbb33
--- /dev/null
+++ b/Data/PQueue/Top.hs
@@ -0,0 +1,34 @@
+{-# LANGUAGE CPP #-}
+module Data.PQueue.Top where
+
+import Control.DeepSeq (NFData(rnf))
+import qualified Data.Ord as Ord
+import Prelude hiding (compare)
+
+#ifdef __GLASGOW_HASKELL__
+import Data.Data (Data, Typeable)
+#endif
+
+class Top top where
+  compare :: (Ord a) => Wrap top a -> Wrap top a -> Ordering
+
+newtype Wrap top a = Wrap {unwrap :: a}
+  deriving (Data, Typeable)
+
+data Min = Min
+data Max = Max
+
+instance Top Min where compare (Wrap x) (Wrap y) = Ord.compare x y
+instance Top Max where compare (Wrap x) (Wrap y) = Ord.compare y x
+
+instance (Top top, Eq a) => Eq (Wrap top a) where
+  Wrap x == Wrap y  =  x==y
+
+instance (Top top, Ord a) => Ord (Wrap top a) where
+  compare = compare
+
+instance NFData a => NFData (Wrap top a) where
+  rnf (Wrap a) = rnf a
+
+instance Functor (Wrap top) where
+  fmap f (Wrap a) = Wrap (f a)
diff --git a/pqueue.cabal b/pqueue.cabal
index b6ddd9f..71e151d 100644
--- a/pqueue.cabal
+++ b/pqueue.cabal
@@ -1,5 +1,5 @@
 Name:               pqueue
-Version:            1.3.2.2
+Version:            1.3.3
 Category:           Data Structures
 Author:             Louis Wasserman
 License:            BSD3
@@ -30,6 +30,7 @@ Library {
   , deepseq >= 1.3 && < 1.5
   }
   exposed-modules:
+    Data.PQueue.Prio
     Data.PQueue.Prio.Min
     Data.PQueue.Prio.Max
     Data.PQueue.Min
@@ -38,6 +39,7 @@ Library {
     Data.PQueue.Prio.Internals
     Data.PQueue.Internals
     Data.PQueue.Prio.Max.Internals
+    Data.PQueue.Top
     Control.Applicative.Identity
   if impl(ghc) {
     default-extensions: DeriveDataTypeable

From 63291863913790e77a2db528cbbdff982c1cff9d Mon Sep 17 00:00:00 2001
From: Henning Thielemann <git@henning-thielemann.de>
Date: Sat, 11 Mar 2017 19:33:54 +0100
Subject: [PATCH 2/9] PQueue.Top: turn into closed-world class

---
 Data/PQueue/Top.hs | 18 ++++++++++++------
 1 file changed, 12 insertions(+), 6 deletions(-)

diff --git a/Data/PQueue/Top.hs b/Data/PQueue/Top.hs
index 43cbb33..b82ee96 100644
--- a/Data/PQueue/Top.hs
+++ b/Data/PQueue/Top.hs
@@ -2,15 +2,13 @@
 module Data.PQueue.Top where
 
 import Control.DeepSeq (NFData(rnf))
-import qualified Data.Ord as Ord
-import Prelude hiding (compare)
 
 #ifdef __GLASGOW_HASKELL__
 import Data.Data (Data, Typeable)
 #endif
 
 class Top top where
-  compare :: (Ord a) => Wrap top a -> Wrap top a -> Ordering
+  switch :: f Min -> f Max -> f top
 
 newtype Wrap top a = Wrap {unwrap :: a}
   deriving (Data, Typeable)
@@ -18,14 +16,22 @@ newtype Wrap top a = Wrap {unwrap :: a}
 data Min = Min
 data Max = Max
 
-instance Top Min where compare (Wrap x) (Wrap y) = Ord.compare x y
-instance Top Max where compare (Wrap x) (Wrap y) = Ord.compare y x
+instance Top Min where switch f _ = f
+instance Top Max where switch _ f = f
+
 
 instance (Top top, Eq a) => Eq (Wrap top a) where
   Wrap x == Wrap y  =  x==y
 
+newtype
+  Compare a top = Compare {runCompare :: Wrap top a -> Wrap top a -> Ordering}
+
 instance (Top top, Ord a) => Ord (Wrap top a) where
-  compare = compare
+  compare =
+    runCompare $
+    switch
+      (Compare $ \(Wrap x) (Wrap y) -> compare x y)
+      (Compare $ \(Wrap x) (Wrap y) -> compare y x)
 
 instance NFData a => NFData (Wrap top a) where
   rnf (Wrap a) = rnf a

From 2329991358d842b88069c9d11f64983bde092138 Mon Sep 17 00:00:00 2001
From: Henning Thielemann <git@henning-thielemann.de>
Date: Sat, 11 Mar 2017 19:42:35 +0100
Subject: [PATCH 3/9] PQueue.Prio.fromAscList, fromDescList, toAscList,
 toDescList: implement using Top.switch

---
 Data/PQueue/Prio.hs | 38 ++++++++++++++++++++++++++++++++++++++
 1 file changed, 38 insertions(+)

diff --git a/Data/PQueue/Prio.hs b/Data/PQueue/Prio.hs
index 70690ea..253a7c5 100644
--- a/Data/PQueue/Prio.hs
+++ b/Data/PQueue/Prio.hs
@@ -94,11 +94,15 @@ module Data.PQueue.Prio (
   -- * List operations
   -- ** Conversion from lists
   fromList,
+  fromAscList,
+  fromDescList,
   fromOrderedList,
   -- ** Conversion to lists
   keys,
   elems,
   assocs,
+  toAscList,
+  toDescList,
   toList,
   -- * Unordered operations
   foldrU,
@@ -407,6 +411,24 @@ mapEitherWithKey f (PQ q) = case Q.mapEitherWithKey (f . unwrap) q of
 fromList :: (Top top, Ord k) => [(k, a)] -> PQueue top k a
 fromList = PQ . Q.fromList . fmap (first' Wrap)
 
+newtype
+  FromList k a top =
+    FromList {runFromList :: [(Wrap top k, a)] -> Q.MinPQueue (Wrap top k) a}
+
+-- | /O(n)/.  Build a priority queue from an ascending list of (key, value) pairs.  /The precondition is not checked./
+fromAscList :: (Top top) => [(k, a)] -> PQueue top k a
+fromAscList =
+  PQ .
+  runFromList (Top.switch (FromList Q.fromAscList) (FromList Q.fromDescList)) .
+  fmap (first' Wrap)
+
+-- | /O(n)/.  Build a priority queue from a descending list of (key, value) pairs.  /The precondition is not checked./
+fromDescList :: (Top top) => [(k, a)] -> PQueue top k a
+fromDescList =
+  PQ .
+  runFromList (Top.switch (FromList Q.fromDescList) (FromList Q.fromAscList)) .
+  fmap (first' Wrap)
+
 -- | /O(n)/.  Build a priority queue from a list of (key, value) pairs where every suffix contains the top element at the list head.  /The precondition is not checked./
 fromOrderedList :: [(k, a)] -> PQueue top k a
 fromOrderedList = PQ . Q.fromAscList . fmap (first' Wrap)
@@ -423,6 +445,22 @@ elems = fmap snd . toList
 assocs :: (Top top, Ord k) => PQueue top k a -> [(k, a)]
 assocs = toList
 
+newtype
+  ToList k a top =
+    ToList {runToList :: Q.MinPQueue (Wrap top k) a -> [(Wrap top k, a)]}
+
+-- | /O(n log n)/.  Return all (key, value) pairs in ascending order by key.
+toAscList :: (Top top, Ord k) => PQueue top k a -> [(k, a)]
+toAscList (PQ q) =
+  fmap (first' unwrap) $
+  runToList (Top.switch (ToList Q.toAscList) (ToList Q.toDescList)) q
+
+-- | /O(n log n)/.  Return all (key, value) pairs in descending order by key.
+toDescList :: (Top top, Ord k) => PQueue top k a -> [(k, a)]
+toDescList (PQ q) =
+  fmap (first' unwrap) $
+  runToList (Top.switch (ToList Q.toDescList) (ToList Q.toAscList)) q
+
 -- | /O(n log n)/.  Return all (key, value) pairs in natural order by key.
 --
 -- If the traversal order is irrelevant, consider using 'toListU'.

From 8aa38d45f6ee735ada24c8817ba205c43ca49469 Mon Sep 17 00:00:00 2001
From: Henning Thielemann <git@henning-thielemann.de>
Date: Sat, 11 Mar 2017 21:18:35 +0100
Subject: [PATCH 4/9] PQueue.Top: instance Foldable Wrap

---
 Data/PQueue/Top.hs | 7 +++++++
 1 file changed, 7 insertions(+)

diff --git a/Data/PQueue/Top.hs b/Data/PQueue/Top.hs
index b82ee96..d73b892 100644
--- a/Data/PQueue/Top.hs
+++ b/Data/PQueue/Top.hs
@@ -3,6 +3,8 @@ module Data.PQueue.Top where
 
 import Control.DeepSeq (NFData(rnf))
 
+import qualified Data.Foldable as Fold
+
 #ifdef __GLASGOW_HASKELL__
 import Data.Data (Data, Typeable)
 #endif
@@ -38,3 +40,8 @@ instance NFData a => NFData (Wrap top a) where
 
 instance Functor (Wrap top) where
   fmap f (Wrap a) = Wrap (f a)
+
+instance Fold.Foldable (Wrap top) where
+  foldMap f (Wrap a) = f a
+  foldr f z (Wrap a) = a `f` z
+  foldl f z (Wrap a) = z `f` a

From 063c81e17a1208072a291fede3b1aea6af410bbe Mon Sep 17 00:00:00 2001
From: Henning Thielemann <git@henning-thielemann.de>
Date: Sat, 11 Mar 2017 21:26:10 +0100
Subject: [PATCH 5/9] PQueue: unification of MinQueue and MaxQueue

PQueue.Prio.PQ: export data constructor temporarily

It is based on the implementation of MaxQueue but uses Wrap instead of Down.
---
 Data/PQueue.hs      | 394 ++++++++++++++++++++++++++++++++++++++++++++
 Data/PQueue/Prio.hs |   2 +-
 pqueue.cabal        |   1 +
 3 files changed, 396 insertions(+), 1 deletion(-)
 create mode 100644 Data/PQueue.hs

diff --git a/Data/PQueue.hs b/Data/PQueue.hs
new file mode 100644
index 0000000..85492d3
--- /dev/null
+++ b/Data/PQueue.hs
@@ -0,0 +1,394 @@
+{-# LANGUAGE CPP #-}
+
+-----------------------------------------------------------------------------
+-- |
+-- Module      :  Data.PQueue
+-- Copyright   :  (c) Henning Thielemann 2017
+--                (c) Louis Wasserman 2010
+-- License     :  BSD-style
+-- Maintainer  :  libraries@haskell.org
+-- Stability   :  experimental
+-- Portability :  portable
+--
+-- General purpose priority queue, supporting view-top operations.
+--
+-- An amortized running time is given for each operation, with /n/ referring
+-- to the length of the sequence and /k/ being the integral index used by
+-- some operations.  These bounds hold even in a persistent (shared) setting.
+--
+-- This implementation is based on a binomial heap augmented with a global root.
+-- The spine of the heap is maintained lazily.  To force the spine of the heap,
+-- use 'seqSpine'.
+--
+-- This implementation does not guarantee stable behavior.
+--
+-- This implementation offers a number of methods of the form @xxxU@, where @U@ stands for
+-- unordered.  No guarantees whatsoever are made on the execution or traversal order of
+-- these functions.
+-----------------------------------------------------------------------------
+module Data.PQueue (
+  Queue,
+  MinQueue,
+  MaxQueue,
+  -- * Basic operations
+  empty,
+  null,
+  size,
+  -- * Query operations
+  findTop,
+  getTop,
+  deleteTop,
+  deleteFindTop,
+  delete,
+  topView,
+  -- * Construction operations
+  singleton,
+  insert,
+  insertBehind,
+  union,
+  unions,
+  -- * Subsets
+  -- ** Extracting subsets
+  (!!),
+  take,
+  drop,
+  splitAt,
+  -- ** Predicates
+  takeWhile,
+  dropWhile,
+  span,
+  break,
+  -- * Filter/Map
+  filter,
+  partition,
+  mapMaybe,
+  mapEither,
+  -- * Fold\/Functor\/Traversable variations
+  map,
+  foldrAsc,
+  foldlAsc,
+  foldrDesc,
+  foldlDesc,
+  -- * List operations
+  toList,
+  toAscList,
+  toDescList,
+  fromList,
+  fromAscList,
+  fromDescList,
+  fromOrderedList,
+  -- * Unordered operations
+  mapU,
+  foldrU,
+  foldlU,
+  elemsU,
+  toListU,
+  -- * Miscellaneous operations
+  keysQueue,
+  seqSpine) where
+
+import qualified Data.PQueue.Min as Min
+import qualified Data.PQueue.Top as Top
+import qualified Data.PQueue.Prio as Prio
+import Data.PQueue.Top (Top, Wrap(Wrap, unwrap))
+
+import Control.DeepSeq (NFData(rnf))
+
+import Data.Functor ((<$>))
+import Data.Monoid (Monoid(mempty, mappend))
+import Data.Maybe (fromMaybe)
+import Data.Foldable (foldl, foldr)
+
+import Prelude hiding (null, foldr, foldl, take, drop, takeWhile, dropWhile, splitAt, span, break, (!!), filter)
+
+#ifdef __GLASGOW_HASKELL__
+import Text.Read (Lexeme(Ident), lexP, parens, prec,
+  readPrec, readListPrec, readListPrecDefault)
+import Data.Data
+#else
+build :: ((a -> [a] -> [a]) -> [a] -> [a]) -> [a]
+build f = f (:) []
+#endif
+
+-- | A priority queue with elements of type @a@.  Supports extracting the top element.
+-- Implemented as a wrapper around 'Min.MinQueue'.
+newtype Queue top a = Q (Min.MinQueue (Wrap top a))
+# if __GLASGOW_HASKELL__
+  deriving (Eq, Ord, Data, Typeable)
+# else
+  deriving (Eq, Ord)
+# endif
+
+type MinQueue = Queue Top.Min
+type MaxQueue = Queue Top.Max
+
+instance NFData a => NFData (Queue top a) where
+  rnf (Q q) = rnf q
+
+instance (Top top, Ord a, Show a) => Show (Queue top a) where
+  showsPrec p xs = showParen (p > 10) $
+    showString "fromOrderedList " . shows (toList xs)
+
+instance Read a => Read (Queue top a) where
+#ifdef __GLASGOW_HASKELL__
+  readPrec = parens $ prec 10 $ do
+    Ident "fromOrderedList" <- lexP
+    xs <- readPrec
+    return (fromOrderedList xs)
+
+  readListPrec = readListPrecDefault
+#else
+  readsPrec p = readParen (p > 10) $ \ r -> do
+    ("fromOrderedList",s) <- lex r
+    (xs,t) <- reads s
+    return (fromOrderedList xs,t)
+#endif
+
+instance (Top top, Ord a) => Monoid (Queue top a) where
+  mempty = empty
+  mappend = union
+
+-- | /O(1)/.  The empty priority queue.
+empty :: Queue top a
+empty = Q Min.empty
+
+-- | /O(1)/.  Is this the empty priority queue?
+null :: Queue top a -> Bool
+null (Q q) = Min.null q
+
+-- | /O(1)/.  The number of elements in the queue.
+size :: Queue top a -> Int
+size (Q q) = Min.size q
+
+-- | /O(1)/.  Returns the top element of the queue.  Throws an error on an empty queue.
+findTop :: Queue top a -> a
+findTop = fromMaybe (error "Error: findTop called on empty queue") . getTop
+
+-- | /O(1)/.  The top element of the queue, if there is one.
+getTop :: Queue top a -> Maybe a
+getTop (Q q) = unwrap <$> Min.getMin q
+
+-- | /O(log n)/.  Deletes the top element of the queue.  Does nothing on an empty queue.
+deleteTop :: (Top top, Ord a) => Queue top a -> Queue top a
+deleteTop (Q q) = Q (Min.deleteMin q)
+
+-- | /O(log n)/.  Extracts the top element of the queue.  Throws an error on an empty queue.
+deleteFindTop :: (Top top, Ord a) => Queue top a -> (a, Queue top a)
+deleteFindTop = fromMaybe (error "Error: deleteFindTop called on empty queue") . topView
+
+-- | /O(log n)/.  Extract the top element of the sequence, if there is one.
+topView :: (Top top, Ord a) => Queue top a -> Maybe (a, Queue top a)
+topView (Q q) = case Min.minView q of
+  Nothing -> Nothing
+  Just (Wrap x, q')
+          -> Just (x, Q q')
+
+-- | /O(log n)/.  Delete the top element of the sequence, if there is one.
+delete :: (Top top, Ord a) => Queue top a -> Maybe (Queue top a)
+delete = fmap snd . topView
+
+-- | /O(1)/.  Construct a priority queue with a single element.
+singleton :: a -> Queue top a
+singleton = Q . Min.singleton . Wrap
+
+-- | /O(1)/.  Insert an element into the priority queue.
+insert :: (Top top, Ord a) => a -> Queue top a -> Queue top a
+x `insert` Q q = Q (Wrap x `Min.insert` q)
+
+-- | Amortized /O(1)/, worst-case /O(log n)/.  Insert an element into the priority queue,
+--   putting it behind elements that compare equal to the inserted one.
+insertBehind :: (Top top, Ord a) => a -> Queue top a -> Queue top a
+x `insertBehind` Q q = Q (Wrap x `Min.insertBehind` q)
+
+-- | /O(log (min(n1,n2)))/.  Take the union of two priority queues.
+union :: (Top top, Ord a) => Queue top a -> Queue top a -> Queue top a
+Q q1 `union` Q q2 = Q (q1 `Min.union` q2)
+
+-- | Takes the union of a list of priority queues.  Equivalent to @'foldl' 'union' 'empty'@.
+unions :: (Top top, Ord a) => [Queue top a] -> Queue top a
+unions qs = Q (Min.unions [q | Q q <- qs])
+
+-- | /O(k log n)/.  Returns the @(k+1)@th top element of the queue.
+(!!) :: (Top top, Ord a) => Queue top a -> Int -> a
+Q q !! n = unwrap ((Min.!!) q n)
+
+{-# INLINE take #-}
+-- | /O(k log n)/.  Returns the list of the @k@ top elements of the queue, in natural order, or
+-- all elements of the queue, if @k >= n@.
+take :: (Top top, Ord a) => Int -> Queue top a -> [a]
+take k (Q q) = [a | Wrap a <- Min.take k q]
+
+-- | /O(k log n)/.  Returns the queue with the @k@ top elements deleted, or the empty queue if @k >= n@.
+drop :: (Top top, Ord a) => Int -> Queue top a -> Queue top a
+drop k (Q q) = Q (Min.drop k q)
+
+-- | /O(k log n)/.  Equivalent to @(take k queue, drop k queue)@.
+splitAt :: (Top top, Ord a) => Int -> Queue top a -> ([a], Queue top a)
+splitAt k (Q q) = (map unwrap xs, Q q') where
+  (xs, q') = Min.splitAt k q
+
+-- | 'takeWhile', applied to a predicate @p@ and a queue @queue@, returns the
+-- longest prefix (possibly empty) of @queue@ of elements that satisfy @p@.
+takeWhile :: (Top top, Ord a) => (a -> Bool) -> Queue top a -> [a]
+takeWhile p (Q q) = map unwrap (Min.takeWhile (p . unwrap) q)
+
+-- | 'dropWhile' @p queue@ returns the queue remaining after 'takeWhile' @p queue@.
+dropWhile :: (Top top, Ord a) => (a -> Bool) -> Queue top a -> Queue top a
+dropWhile p (Q q) = Q (Min.dropWhile (p . unwrap) q)
+
+-- | 'span', applied to a predicate @p@ and a queue @queue@, returns a tuple where
+-- first element is longest prefix (possibly empty) of @queue@ of elements that
+-- satisfy @p@ and second element is the remainder of the queue.
+--
+span :: (Top top, Ord a) => (a -> Bool) -> Queue top a -> ([a], Queue top a)
+span p (Q q) = (map unwrap xs, Q q') where
+  (xs, q') = Min.span (p . unwrap) q
+
+-- | 'break', applied to a predicate @p@ and a queue @queue@, returns a tuple where
+-- first element is longest prefix (possibly empty) of @queue@ of elements that
+-- /do not satisfy/ @p@ and second element is the remainder of the queue.
+break :: (Top top, Ord a) => (a -> Bool) -> Queue top a -> ([a], Queue top a)
+break p = span (not . p)
+
+-- | /O(n)/.  Returns a queue of those elements which satisfy the predicate.
+filter :: (Top top, Ord a) => (a -> Bool) -> Queue top a -> Queue top a
+filter p (Q q) = Q (Min.filter (p . unwrap) q)
+
+-- | /O(n)/.  Returns a pair of queues, where the left queue contains those elements that satisfy the predicate,
+-- and the right queue contains those that do not.
+partition :: (Top top, Ord a) => (a -> Bool) -> Queue top a -> (Queue top a, Queue top a)
+partition p (Q q) = (Q q0, Q q1)
+  where  (q0, q1) = Min.partition (p . unwrap) q
+
+-- | /O(n)/.  Maps a function over the elements of the queue, and collects the 'Just' values.
+mapMaybe :: (Top top, Ord b) => (a -> Maybe b) -> Queue top a -> Queue top b
+mapMaybe f (Q q) = Q (Min.mapMaybe (\ (Wrap x) -> Wrap <$> f x) q)
+
+-- | /O(n)/.  Maps a function over the elements of the queue, and separates the 'Left' and 'Right' values.
+mapEither :: (Top top, Ord b, Ord c) => (a -> Either b c) -> Queue top a -> (Queue top b, Queue top c)
+mapEither f (Q q) = (Q q0, Q q1)
+  where  (q0, q1) = Min.mapEither (either (Left . Wrap) (Right . Wrap) . f . unwrap) q
+
+-- | /O(n)/.  Assumes that the function it is given is monotonic, and applies this function to every element of the priority queue.
+-- /Does not check the precondition/.
+mapU :: (a -> b) -> Queue top a -> Queue top b
+mapU f (Q q) = Q (Min.mapU (\ (Wrap a) -> Wrap (f a)) q)
+
+-- | /O(n)/.  Unordered right fold on a priority queue.
+foldrU :: (a -> b -> b) -> b -> Queue top a -> b
+foldrU f z (Q q) = Min.foldrU (flip (foldr f)) z q
+
+-- | /O(n)/.  Unordered left fold on a priority queue.
+foldlU :: (b -> a -> b) -> b -> Queue top a -> b
+foldlU f z (Q q) = Min.foldlU (foldl f) z q
+
+{-# INLINE elemsU #-}
+-- | Equivalent to 'toListU'.
+elemsU :: Queue top a -> [a]
+elemsU = toListU
+
+{-# INLINE toListU #-}
+-- | /O(n)/.  Returns a list of the elements of the priority queue, in no particular order.
+toListU :: Queue top a -> [a]
+toListU (Q q) = map unwrap (Min.toListU q)
+
+-- | /O(n log n)/.  Performs a right-fold on the elements of a priority queue in ascending order.
+-- @'foldrAsc' f z q == 'foldlDesc' (flip f) z q@.
+foldrAsc :: (Top top, Ord a) => (a -> b -> b) -> b -> Queue top a -> b
+foldrAsc = foldlDesc . flip
+
+-- | /O(n log n)/.  Performs a left-fold on the elements of a priority queue in descending order.
+-- @'foldlAsc' f z q == 'foldrDesc' (flip f) z q@.
+foldlAsc :: (Top top, Ord a) => (b -> a -> b) -> b -> Queue top a -> b
+foldlAsc = foldrDesc . flip
+
+newtype
+  Foldr b a top =
+    Foldr {
+      runFoldr :: (Wrap top a -> b -> b) -> b -> Min.MinQueue (Wrap top a) -> b
+    }
+
+-- | /O(n log n)/.  Performs a right-fold on the elements of a priority queue in descending order.
+foldrDesc :: (Top top, Ord a) => (a -> b -> b) -> b -> Queue top a -> b
+foldrDesc f z (Q q) =
+  runFoldr
+    (Top.switch (Foldr Min.foldrDesc) (Foldr Min.foldrAsc))
+    (flip (foldr f)) z q
+
+newtype
+  Foldl b a top =
+    Foldl {
+      runFoldl :: (b -> Wrap top a -> b) -> b -> Min.MinQueue (Wrap top a) -> b
+    }
+
+-- | /O(n log n)/.  Performs a left-fold on the elements of a priority queue in descending order.
+foldlDesc :: (Top top, Ord a) => (b -> a -> b) -> b -> Queue top a -> b
+foldlDesc f z (Q q) =
+  runFoldl
+    (Top.switch (Foldl Min.foldlDesc) (Foldl Min.foldlAsc))
+    (foldl f) z q
+
+newtype
+  ToList a top =
+    ToList {runToList :: Min.MinQueue (Wrap top a) -> [Wrap top a]}
+
+{-# INLINE toAscList #-}
+-- | /O(n log n)/.  Extracts the elements of the priority queue in ascending order.
+toAscList :: (Top top, Ord a) => Queue top a -> [a]
+toAscList (Q q) =
+  fmap unwrap $
+  runToList (Top.switch (ToList Min.toAscList) (ToList Min.toDescList)) q
+
+{-# INLINE toDescList #-}
+-- | /O(n log n)/.  Extracts the elements of the priority queue in descending order.
+toDescList :: (Top top, Ord a) => Queue top a -> [a]
+toDescList (Q q) =
+  fmap unwrap $
+  runToList (Top.switch (ToList Min.toDescList) (ToList Min.toAscList)) q
+
+{-# INLINE toList #-}
+-- | /O(n log n)/.  Returns the elements of the priority queue with top keys first.
+--
+-- If the order of the elements is irrelevant, consider using 'toListU'.
+toList :: (Top top, Ord a) => Queue top a -> [a]
+toList (Q q) = map unwrap (Min.toList q)
+
+newtype
+  FromList a top =
+    FromList {runFromList :: [Wrap top a] -> Min.MinQueue (Wrap top a)}
+
+{-# INLINE fromAscList #-}
+-- | /O(n)/.  Constructs a priority queue from an ascending list.  /Warning/: Does not check the precondition.
+fromAscList :: (Top top) => [a] -> Queue top a
+fromAscList =
+  Q .
+  runFromList
+    (Top.switch (FromList Min.fromAscList) (FromList Min.fromDescList)) .
+  map Wrap
+
+{-# INLINE fromDescList #-}
+-- | /O(n)/.  Constructs a priority queue from a descending list.  /Warning/: Does not check the precondition.
+fromDescList :: (Top top) => [a] -> Queue top a
+fromDescList =
+  Q .
+  runFromList
+    (Top.switch (FromList Min.fromDescList) (FromList Min.fromAscList)) .
+  map Wrap
+
+{-# INLINE fromOrderedList #-}
+-- | /O(n)/.  Constructs a priority queue from a list with top keys first.  /Warning/: Does not check the precondition.
+fromOrderedList :: [a] -> Queue top a
+fromOrderedList = Q . Min.fromAscList . map Wrap
+
+{-# INLINE fromList #-}
+-- | /O(n log n)/.  Constructs a priority queue from an unordered list.
+fromList :: (Top top, Ord a) => [a] -> Queue top a
+fromList = foldr insert empty
+
+-- | /O(n)/.  Constructs a priority queue from the keys of a 'Prio.PQueue'.
+keysQueue :: Prio.PQueue top k a -> Queue top k
+keysQueue (Prio.PQ q) = Q (Min.keysQueue q)
+
+-- | /O(log n)/.  Forces the spine of the heap.
+seqSpine :: Queue top a -> b -> b
+seqSpine (Q q) = Min.seqSpine q
diff --git a/Data/PQueue/Prio.hs b/Data/PQueue/Prio.hs
index 253a7c5..edfb929 100644
--- a/Data/PQueue/Prio.hs
+++ b/Data/PQueue/Prio.hs
@@ -33,7 +33,7 @@
 -- these functions.
 -----------------------------------------------------------------------------
 module Data.PQueue.Prio (
-  PQueue,
+  PQueue(PQ),
   MinPQueue,
   MaxPQueue,
   -- * Construction
diff --git a/pqueue.cabal b/pqueue.cabal
index 71e151d..f938465 100644
--- a/pqueue.cabal
+++ b/pqueue.cabal
@@ -33,6 +33,7 @@ Library {
     Data.PQueue.Prio
     Data.PQueue.Prio.Min
     Data.PQueue.Prio.Max
+    Data.PQueue
     Data.PQueue.Min
     Data.PQueue.Max
   other-modules:

From dc6187bb83c2a46bf3fd9faee44c910afc69f2e0 Mon Sep 17 00:00:00 2001
From: Henning Thielemann <git@henning-thielemann.de>
Date: Sat, 11 Mar 2017 21:34:45 +0100
Subject: [PATCH 6/9] PQueue.mapU: simplify using fmap on Wrap

---
 Data/PQueue.hs | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Data/PQueue.hs b/Data/PQueue.hs
index 85492d3..a70e3c3 100644
--- a/Data/PQueue.hs
+++ b/Data/PQueue.hs
@@ -272,7 +272,7 @@ mapEither f (Q q) = (Q q0, Q q1)
 -- | /O(n)/.  Assumes that the function it is given is monotonic, and applies this function to every element of the priority queue.
 -- /Does not check the precondition/.
 mapU :: (a -> b) -> Queue top a -> Queue top b
-mapU f (Q q) = Q (Min.mapU (\ (Wrap a) -> Wrap (f a)) q)
+mapU f (Q q) = Q (Min.mapU (fmap f) q)
 
 -- | /O(n)/.  Unordered right fold on a priority queue.
 foldrU :: (a -> b -> b) -> b -> Queue top a -> b

From a18fbcd981084e0e5a82fd7118eb5e190f676a20 Mon Sep 17 00:00:00 2001
From: Henning Thielemann <git@henning-thielemann.de>
Date: Sat, 11 Mar 2017 21:35:20 +0100
Subject: [PATCH 7/9] PQueue.take: simplify using 'unwrap'

---
 Data/PQueue.hs | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Data/PQueue.hs b/Data/PQueue.hs
index a70e3c3..d692013 100644
--- a/Data/PQueue.hs
+++ b/Data/PQueue.hs
@@ -216,7 +216,7 @@ Q q !! n = unwrap ((Min.!!) q n)
 -- | /O(k log n)/.  Returns the list of the @k@ top elements of the queue, in natural order, or
 -- all elements of the queue, if @k >= n@.
 take :: (Top top, Ord a) => Int -> Queue top a -> [a]
-take k (Q q) = [a | Wrap a <- Min.take k q]
+take k (Q q) = map unwrap $ Min.take k q
 
 -- | /O(k log n)/.  Returns the queue with the @k@ top elements deleted, or the empty queue if @k >= n@.
 drop :: (Top top, Ord a) => Int -> Queue top a -> Queue top a

From 1276837628a010d357f3f9b5326a95bd76e7f2d4 Mon Sep 17 00:00:00 2001
From: Henning Thielemann <git@henning-thielemann.de>
Date: Sat, 11 Mar 2017 21:42:16 +0100
Subject: [PATCH 8/9] PQueue.Top: instance Traversable Wrap PQueue.mapMaybe:
 use it here

---
 Data/PQueue.hs     | 3 ++-
 Data/PQueue/Top.hs | 4 ++++
 2 files changed, 6 insertions(+), 1 deletion(-)

diff --git a/Data/PQueue.hs b/Data/PQueue.hs
index d692013..81eec63 100644
--- a/Data/PQueue.hs
+++ b/Data/PQueue.hs
@@ -97,6 +97,7 @@ import Control.DeepSeq (NFData(rnf))
 import Data.Functor ((<$>))
 import Data.Monoid (Monoid(mempty, mappend))
 import Data.Maybe (fromMaybe)
+import Data.Traversable (traverse)
 import Data.Foldable (foldl, foldr)
 
 import Prelude hiding (null, foldr, foldl, take, drop, takeWhile, dropWhile, splitAt, span, break, (!!), filter)
@@ -262,7 +263,7 @@ partition p (Q q) = (Q q0, Q q1)
 
 -- | /O(n)/.  Maps a function over the elements of the queue, and collects the 'Just' values.
 mapMaybe :: (Top top, Ord b) => (a -> Maybe b) -> Queue top a -> Queue top b
-mapMaybe f (Q q) = Q (Min.mapMaybe (\ (Wrap x) -> Wrap <$> f x) q)
+mapMaybe f (Q q) = Q (Min.mapMaybe (traverse f) q)
 
 -- | /O(n)/.  Maps a function over the elements of the queue, and separates the 'Left' and 'Right' values.
 mapEither :: (Top top, Ord b, Ord c) => (a -> Either b c) -> Queue top a -> (Queue top b, Queue top c)
diff --git a/Data/PQueue/Top.hs b/Data/PQueue/Top.hs
index d73b892..7b72b3b 100644
--- a/Data/PQueue/Top.hs
+++ b/Data/PQueue/Top.hs
@@ -3,6 +3,7 @@ module Data.PQueue.Top where
 
 import Control.DeepSeq (NFData(rnf))
 
+import qualified Data.Traversable as Trav
 import qualified Data.Foldable as Fold
 
 #ifdef __GLASGOW_HASKELL__
@@ -45,3 +46,6 @@ instance Fold.Foldable (Wrap top) where
   foldMap f (Wrap a) = f a
   foldr f z (Wrap a) = a `f` z
   foldl f z (Wrap a) = z `f` a
+
+instance Trav.Traversable (Wrap top) where
+  traverse f (Wrap a) = fmap Wrap $ f a

From 6258cf9210fe8a856c2e2cc941efa9f4eea5123a Mon Sep 17 00:00:00 2001
From: Henning Thielemann <git@henning-thielemann.de>
Date: Sat, 11 Mar 2017 22:01:41 +0100
Subject: [PATCH 9/9] PQueue.Prio.Private: extracted data type and instance
 definitions from PQueue.Prio

This way, we do no longer need to expose the PQ constructor.
---
 Data/PQueue.hs              |  6 +--
 Data/PQueue/Prio.hs         | 89 ++-------------------------------
 Data/PQueue/Prio/Private.hs | 99 +++++++++++++++++++++++++++++++++++++
 pqueue.cabal                |  3 +-
 4 files changed, 107 insertions(+), 90 deletions(-)
 create mode 100644 Data/PQueue/Prio/Private.hs

diff --git a/Data/PQueue.hs b/Data/PQueue.hs
index 81eec63..e4ed1bb 100644
--- a/Data/PQueue.hs
+++ b/Data/PQueue.hs
@@ -89,7 +89,7 @@ module Data.PQueue (
 
 import qualified Data.PQueue.Min as Min
 import qualified Data.PQueue.Top as Top
-import qualified Data.PQueue.Prio as Prio
+import Data.PQueue.Prio.Private (PQueue(PQ))
 import Data.PQueue.Top (Top, Wrap(Wrap, unwrap))
 
 import Control.DeepSeq (NFData(rnf))
@@ -387,8 +387,8 @@ fromList :: (Top top, Ord a) => [a] -> Queue top a
 fromList = foldr insert empty
 
 -- | /O(n)/.  Constructs a priority queue from the keys of a 'Prio.PQueue'.
-keysQueue :: Prio.PQueue top k a -> Queue top k
-keysQueue (Prio.PQ q) = Q (Min.keysQueue q)
+keysQueue :: PQueue top k a -> Queue top k
+keysQueue (PQ q) = Q (Min.keysQueue q)
 
 -- | /O(log n)/.  Forces the spine of the heap.
 seqSpine :: Queue top a -> b -> b
diff --git a/Data/PQueue/Prio.hs b/Data/PQueue/Prio.hs
index edfb929..7c6ed8a 100644
--- a/Data/PQueue/Prio.hs
+++ b/Data/PQueue/Prio.hs
@@ -1,6 +1,3 @@
-{-# LANGUAGE CPP #-}
-{-# OPTIONS_GHC -fno-warn-orphans #-}
-
 -----------------------------------------------------------------------------
 -- |
 -- Module      :  Data.PQueue.Prio
@@ -33,7 +30,7 @@
 -- these functions.
 -----------------------------------------------------------------------------
 module Data.PQueue.Prio (
-  PQueue(PQ),
+  PQueue,
   MinPQueue,
   MaxPQueue,
   -- * Construction
@@ -122,84 +119,23 @@ module Data.PQueue.Prio (
 
 import qualified Data.PQueue.Prio.Min as Q
 import qualified Data.PQueue.Top as Top
+import Data.PQueue.Prio.Private
+        (PQueue(PQ), toList, fromOrderedList, empty, union, unions)
 import Data.PQueue.Top (Top, Wrap(Wrap, unwrap))
 
-import Control.DeepSeq (NFData (rnf))
 import Control.Applicative (Applicative, (<$>))
-import Data.Monoid (Monoid(mempty, mappend, mconcat))
-import Data.Traversable (Traversable(traverse))
-import Data.Foldable (Foldable, foldr, foldl)
 import Data.Maybe (fromMaybe)
 
 import Prelude hiding (map, filter, break, span, takeWhile, dropWhile, splitAt, take, drop, (!!), null, foldr, foldl)
 
 
-#ifdef __GLASGOW_HASKELL__
-import Data.Data (Data, Typeable)
-import Text.Read (Lexeme(Ident), lexP, parens, prec,
-  readPrec, readListPrec, readListPrecDefault)
-#else
-build :: ((a -> [a] -> [a]) -> [a] -> [a]) -> [a]
-build f = f (:) []
-#endif
-
 first' :: (a -> b) -> (a, c) -> (b, c)
 first' f (a, c) = (f a, c)
 
 
--- | A priority queue where values of type @a@ are annotated with keys of type @k@.
--- The queue supports extracting the element with top key.
-newtype PQueue top k a = PQ (Q.MinPQueue (Wrap top k) a)
-# if __GLASGOW_HASKELL__
-  deriving (Eq, Ord, Data, Typeable)
-# else
-  deriving (Eq, Ord)
-# endif
-
-instance (NFData k, NFData a) => NFData (PQueue top k a) where
-  rnf (PQ q) = rnf q
-
-
 type MinPQueue = PQueue Top.Min
 type MaxPQueue = PQueue Top.Max
 
-instance (Top top, Ord k) => Monoid (PQueue top k a) where
-  mempty = empty
-  mappend = union
-  mconcat = unions
-
-instance (Top top, Ord k, Show k, Show a) => Show (PQueue top k a) where
-  showsPrec p xs = showParen (p > 10) $
-    showString "fromOrderedList " . shows (toList xs)
-
-instance (Read k, Read a) => Read (PQueue top k a) where
-#ifdef __GLASGOW_HASKELL__
-  readPrec = parens $ prec 10 $ do
-    Ident "fromOrderedList" <- lexP
-    xs <- readPrec
-    return (fromOrderedList xs)
-
-  readListPrec = readListPrecDefault
-#else
-  readsPrec p = readParen (p > 10) $ \ r -> do
-    ("fromOrderedList",s) <- lex r
-    (xs,t) <- reads s
-    return (fromOrderedList xs,t)
-#endif
-
-instance Functor (PQueue top k) where
-  fmap f (PQ q) = PQ (fmap f q)
-
-instance (Top top, Ord k) => Foldable (PQueue top k) where
-  foldr f z (PQ q) = foldr f z q
-  foldl f z (PQ q) = foldl f z q
-
-instance (Top top, Ord k) => Traversable (PQueue top k) where
-  traverse f (PQ q) = PQ <$> traverse f q
-
--- | /O(1)/.  Returns the empty priority queue.
-empty :: PQueue top k a
-empty = PQ Q.empty
 
 -- | /O(1)/.  Constructs a singleton priority queue.
 singleton :: k -> a -> PQueue top k a
@@ -215,15 +151,6 @@ insert k a (PQ q) = PQ (Q.insert (Wrap k) a q)
 insertBehind :: (Top top, Ord k) => k -> a -> PQueue top k a -> PQueue top k a
 insertBehind k a (PQ q) = PQ (Q.insertBehind (Wrap k) a q)
 
--- | Amortized /O(log(min(n1, n2)))/, worst-case /O(log(max(n1, n2)))/.  Returns the union
--- of the two specified queues.
-union :: (Top top, Ord k) => PQueue top k a -> PQueue top k a -> PQueue top k a
-PQ q1 `union` PQ q2 = PQ (q1 `Q.union` q2)
-
--- | The union of a list of queues: (@'unions' == 'List.foldl' 'union' 'empty'@).
-unions :: (Top top, Ord k) => [PQueue top k a] -> PQueue top k a
-unions qs = PQ (Q.unions [q | PQ q <- qs])
-
 -- | /O(1)/.  Checks if this priority queue is empty.
 null :: PQueue top k a -> Bool
 null (PQ q) = Q.null q
@@ -429,10 +356,6 @@ fromDescList =
   runFromList (Top.switch (FromList Q.fromDescList) (FromList Q.fromAscList)) .
   fmap (first' Wrap)
 
--- | /O(n)/.  Build a priority queue from a list of (key, value) pairs where every suffix contains the top element at the list head.  /The precondition is not checked./
-fromOrderedList :: [(k, a)] -> PQueue top k a
-fromOrderedList = PQ . Q.fromAscList . fmap (first' Wrap)
-
 -- | /O(n log n)/.  Return all keys of the queue in natural order, that is, top keys first.
 keys :: (Top top, Ord k) => PQueue top k a -> [k]
 keys = fmap fst . toList
@@ -461,12 +384,6 @@ toDescList (PQ q) =
   fmap (first' unwrap) $
   runToList (Top.switch (ToList Q.toDescList) (ToList Q.toAscList)) q
 
--- | /O(n log n)/.  Return all (key, value) pairs in natural order by key.
---
--- If the traversal order is irrelevant, consider using 'toListU'.
-toList :: (Top top, Ord k) => PQueue top k a -> [(k, a)]
-toList (PQ q) = fmap (first' unwrap) (Q.toAscList q)
-
 -- | /O(n)/.  An unordered right fold over the elements of the queue, in no particular order.
 foldrU :: (a -> b -> b) -> b -> PQueue top k a -> b
 foldrU = foldrWithKeyU . const
diff --git a/Data/PQueue/Prio/Private.hs b/Data/PQueue/Prio/Private.hs
new file mode 100644
index 0000000..94a6162
--- /dev/null
+++ b/Data/PQueue/Prio/Private.hs
@@ -0,0 +1,99 @@
+{-# LANGUAGE CPP #-}
+module Data.PQueue.Prio.Private (
+  PQueue(PQ), toList, fromOrderedList, empty, union, unions,
+  ) where
+
+import qualified Data.PQueue.Prio.Min as Q
+import Data.PQueue.Top (Top, Wrap(Wrap, unwrap))
+
+import Control.DeepSeq (NFData (rnf))
+import Control.Applicative ((<$>))
+import Data.Monoid (Monoid(mempty, mappend, mconcat))
+import Data.Traversable (Traversable(traverse))
+import Data.Foldable (Foldable, foldr, foldl)
+
+import Prelude hiding (map, filter, break, span, takeWhile, dropWhile, splitAt, take, drop, (!!), null, foldr, foldl)
+
+
+#ifdef __GLASGOW_HASKELL__
+import Data.Data (Data, Typeable)
+import Text.Read (Lexeme(Ident), lexP, parens, prec,
+  readPrec, readListPrec, readListPrecDefault)
+#else
+build :: ((a -> [a] -> [a]) -> [a] -> [a]) -> [a]
+build f = f (:) []
+#endif
+
+first' :: (a -> b) -> (a, c) -> (b, c)
+first' f (a, c) = (f a, c)
+
+
+-- | A priority queue where values of type @a@ are annotated with keys of type @k@.
+-- The queue supports extracting the element with top key.
+newtype PQueue top k a = PQ (Q.MinPQueue (Wrap top k) a)
+# if __GLASGOW_HASKELL__
+  deriving (Eq, Ord, Data, Typeable)
+# else
+  deriving (Eq, Ord)
+# endif
+
+instance (NFData k, NFData a) => NFData (PQueue top k a) where
+  rnf (PQ q) = rnf q
+
+
+instance (Top top, Ord k) => Monoid (PQueue top k a) where
+  mempty = empty
+  mappend = union
+  mconcat = unions
+
+instance (Top top, Ord k, Show k, Show a) => Show (PQueue top k a) where
+  showsPrec p xs = showParen (p > 10) $
+    showString "fromOrderedList " . shows (toList xs)
+
+instance (Read k, Read a) => Read (PQueue top k a) where
+#ifdef __GLASGOW_HASKELL__
+  readPrec = parens $ prec 10 $ do
+    Ident "fromOrderedList" <- lexP
+    xs <- readPrec
+    return (fromOrderedList xs)
+
+  readListPrec = readListPrecDefault
+#else
+  readsPrec p = readParen (p > 10) $ \ r -> do
+    ("fromOrderedList",s) <- lex r
+    (xs,t) <- reads s
+    return (fromOrderedList xs,t)
+#endif
+
+instance Functor (PQueue top k) where
+  fmap f (PQ q) = PQ (fmap f q)
+
+instance (Top top, Ord k) => Foldable (PQueue top k) where
+  foldr f z (PQ q) = foldr f z q
+  foldl f z (PQ q) = foldl f z q
+
+instance (Top top, Ord k) => Traversable (PQueue top k) where
+  traverse f (PQ q) = PQ <$> traverse f q
+
+-- | /O(1)/.  Returns the empty priority queue.
+empty :: PQueue top k a
+empty = PQ Q.empty
+
+-- | Amortized /O(log(min(n1, n2)))/, worst-case /O(log(max(n1, n2)))/.  Returns the union
+-- of the two specified queues.
+union :: (Top top, Ord k) => PQueue top k a -> PQueue top k a -> PQueue top k a
+PQ q1 `union` PQ q2 = PQ (q1 `Q.union` q2)
+
+-- | The union of a list of queues: (@'unions' == 'List.foldl' 'union' 'empty'@).
+unions :: (Top top, Ord k) => [PQueue top k a] -> PQueue top k a
+unions qs = PQ (Q.unions [q | PQ q <- qs])
+
+-- | /O(n)/.  Build a priority queue from a list of (key, value) pairs where every suffix contains the top element at the list head.  /The precondition is not checked./
+fromOrderedList :: [(k, a)] -> PQueue top k a
+fromOrderedList = PQ . Q.fromAscList . fmap (first' Wrap)
+
+-- | /O(n log n)/.  Return all (key, value) pairs in natural order by key.
+--
+-- If the traversal order is irrelevant, consider using 'toListU'.
+toList :: (Top top, Ord k) => PQueue top k a -> [(k, a)]
+toList (PQ q) = fmap (first' unwrap) (Q.toAscList q)
diff --git a/pqueue.cabal b/pqueue.cabal
index f938465..afebfdd 100644
--- a/pqueue.cabal
+++ b/pqueue.cabal
@@ -37,8 +37,9 @@ Library {
     Data.PQueue.Min
     Data.PQueue.Max
   other-modules:
-    Data.PQueue.Prio.Internals
     Data.PQueue.Internals
+    Data.PQueue.Prio.Private
+    Data.PQueue.Prio.Internals
     Data.PQueue.Prio.Max.Internals
     Data.PQueue.Top
     Control.Applicative.Identity