diff --git a/ChangeLog.md b/ChangeLog.md
--- a/ChangeLog.md
+++ b/ChangeLog.md
@@ -1,3 +1,12 @@
+0.9.0
+===
+* added emptyHistogram
+* fixes for numhask-0.9
+
+0.8.2
+===
+* replaced space1 partial with unsafeSpace1 + total space1
+
 0.8.1
 ===
 * GHC 9.0.1 support
diff --git a/numhask-space.cabal b/numhask-space.cabal
--- a/numhask-space.cabal
+++ b/numhask-space.cabal
@@ -1,81 +1,62 @@
-cabal-version: 2.4
-name: numhask-space
-version: 0.8.1.0
-synopsis:
-  Numerical spaces.
+cabal-version:      2.4
+name:               numhask-space
+version:            0.9.0.0
+synopsis:           Numerical spaces.
 description:
-    @numhask-space@ provides support for spaces where [space](https://en.wikipedia.org/wiki/Space_(mathematics\)) is defined as a set of numbers with a lower and upper bound.
-    .
-    == Usage
-    .
-    >>> {-# LANGUAGE RebindableSyntax #-}
-    >>> import NumHask.Prelude
-    >>> import NumHask.Space
-    .
+  @numhask-space@ provides support for spaces where [space](https://en.wikipedia.org/wiki/Space_(mathematics\)) is defined as a set of numbers with a lower and upper bound.
+  .
+  == Usage
+  .
+  >>> {-# LANGUAGE RebindableSyntax #-}
+  >>> import NumHask.Prelude
+  >>> import NumHask.Space
+  .
 
-category:
-  mathematics
-homepage:
-  https://github.com/tonyday567/numhask-space#readme
-bug-reports:
-  https://github.com/tonyday567/numhask-space/issues
-author:
-  Tony Day
-maintainer:
-  tonyday567@gmail.com
-copyright:
-  Tony Day
-license:
-  BSD-3-Clause
-license-file:
-  LICENSE
-build-type:
-  Simple
-tested-with:
-  GHC ==8.8.4
-   || ==8.10.4
-   || ==9.0.1
-   || ==9.2.0.20210821
-extra-source-files:
-  ChangeLog.md
+category:           mathematics
+homepage:           https://github.com/tonyday567/numhask-space#readme
+bug-reports:        https://github.com/tonyday567/numhask-space/issues
+author:             Tony Day
+maintainer:         tonyday567@gmail.com
+copyright:          Tony Day
+license:            BSD-3-Clause
+license-file:       LICENSE
+build-type:         Simple
+tested-with:        GHC ==8.8.4 || ==8.10.7 || ==9.2.1
+extra-source-files: ChangeLog.md
+
 source-repository head
-  type:
-    git
-  location:
-    https://github.com/tonyday567/numhask-space
+  type:     git
+  location: https://github.com/tonyday567/numhask-space
 
 library
-  hs-source-dirs:
-    src
+  hs-source-dirs:     src
   ghc-options:
-    -Wall
-    -Wcompat
-    -Wincomplete-record-updates
-    -Wincomplete-uni-patterns
-    -Wredundant-constraints
-    -fwrite-ide-info
+    -Wall -Wcompat -Wincomplete-record-updates
+    -Wincomplete-uni-patterns -Wredundant-constraints -fwrite-ide-info
     -hiedir=.hie
+
   default-extensions:
   build-depends:
-    adjunctions >=4.0 && <5,
-    base >=4.7 && <5,
-    containers >= 0.6 && < 0.7,
-    distributive >=0.2.2 && <1,
-    numhask >= 0.8.1 && < 0.9,
-    random >= 1.2 && < 1.3,
-    semigroupoids >=5 && <5.4,
-    tdigest >= 0.2.1 && < 0.3,
-    text >= 1.2.3.1 && <2,
-    time >= 1.9.1 && <1.12,
-    vector >= 0.12 && < 0.13,
+    , adjunctions    >=4.0     && <5
+    , base           >=4.7     && <5
+    , containers     ^>=0.6
+    , distributive   >=0.2.2   && <1
+    , numhask        ^>=0.9.0
+    , random         ^>=1.2
+    , semigroupoids  >=5       && <5.4
+    , tdigest        ^>=0.2.1
+    , text           >=1.2.3.1 && <2
+    , time           >=1.9.1   && <1.12
+    , vector         ^>=0.12
+
   exposed-modules:
     NumHask.Space
-    NumHask.Space.Types
+    NumHask.Space.Histogram
+    NumHask.Space.Point
     NumHask.Space.Range
     NumHask.Space.Rect
-    NumHask.Space.Point
     NumHask.Space.Time
-    NumHask.Space.Histogram
-    NumHask.Space.XY
+    NumHask.Space.Types
+
   other-modules:
-  default-language: Haskell2010
+  default-language:   Haskell2010
diff --git a/src/NumHask/Space.hs b/src/NumHask/Space.hs
--- a/src/NumHask/Space.hs
+++ b/src/NumHask/Space.hs
@@ -30,7 +30,6 @@
     module NumHask.Space.Rect,
     module NumHask.Space.Time,
     module NumHask.Space.Histogram,
-    module NumHask.Space.XY,
   )
 where
 
@@ -40,7 +39,6 @@
 import NumHask.Space.Rect hiding ()
 import NumHask.Space.Time hiding ()
 import NumHask.Space.Types hiding ()
-import NumHask.Space.XY hiding ()
 
 -- $setup
 --
diff --git a/src/NumHask/Space/Histogram.hs b/src/NumHask/Space/Histogram.hs
--- a/src/NumHask/Space/Histogram.hs
+++ b/src/NumHask/Space/Histogram.hs
@@ -7,6 +7,7 @@
 -- | A histogram, if you squint, is a series of contiguous 'Range's, annotated with values.
 module NumHask.Space.Histogram
   ( Histogram (..),
+    emptyHistogram,
     DealOvers (..),
     fill,
     cutI,
@@ -43,6 +44,10 @@
   }
   deriving (Show, Eq)
 
+-- | A histogram with no cuts nor data.
+emptyHistogram :: Histogram
+emptyHistogram = Histogram V.empty Map.empty
+
 -- | Whether or not to ignore unders and overs.  If overs and unders are dealt with, IncludeOvers supplies an assumed width for the outer buckets.
 data DealOvers = IgnoreOvers | IncludeOvers Double
 
@@ -80,9 +85,10 @@
 -- >>> regular 4 [0..100]
 -- Histogram {cuts = [0.0,25.0,50.0,75.0,100.0], values = fromList [(1,25.0),(2,25.0),(3,25.0),(4,25.0),(5,1.0)]}
 regular :: Int -> [Double] -> Histogram
+regular _ [] = emptyHistogram
 regular n xs = fill cs xs
   where
-    cs = grid OuterPos (space1 xs :: Range Double) n
+    cs = grid OuterPos (unsafeSpace1 xs :: Range Double) n
 
 -- | Transform a Histogram to Rects
 --
diff --git a/src/NumHask/Space/Point.hs b/src/NumHask/Space/Point.hs
--- a/src/NumHask/Space/Point.hs
+++ b/src/NumHask/Space/Point.hs
@@ -61,7 +61,7 @@
 --
 -- This is used extensively in [chart-svg](https://hackage.haskell.org/package/chart-svg) to ergonomically obtain chart areas.
 --
--- > space1 [Point 1 0, Point 0 1] :: Rect Double
+-- > unsafeSpace1 [Point 1 0, Point 0 1] :: Rect Double
 -- Rect 0.0 1.0 0.0 1.0
 data Point a = Point
   { _x :: a,
@@ -141,19 +141,15 @@
 
 instance (Additive a) => AdditiveAction (Point a) a where
   (.+) a (Point x y) = Point (a + x) (a + y)
-  (+.) (Point x y) a = Point (a + x) (a + y)
 
 instance (Subtractive a) => SubtractiveAction (Point a) a where
   (.-) a (Point x y) = Point (a - x) (a - y)
-  (-.) (Point x y) a = Point (x - a) (y - a)
 
 instance (Multiplicative a) => MultiplicativeAction (Point a) a where
   (.*) a (Point x y) = Point (a * x) (a * y)
-  (*.) (Point x y) a = Point (a * x) (a * y)
 
 instance (Divisive a) => DivisiveAction (Point a) a where
   (./) a (Point x y) = Point (a / x) (a / y)
-  (/.) (Point x y) a = Point (x / a) (y / a)
 
 instance Representable Point where
   type Rep Point = Bool
diff --git a/src/NumHask/Space/Range.hs b/src/NumHask/Space/Range.hs
--- a/src/NumHask/Space/Range.hs
+++ b/src/NumHask/Space/Range.hs
@@ -147,7 +147,7 @@
   (<>) a b = getUnion (Union a <> Union b)
 
 instance (Additive a, Eq a, Ord a) => Additive (Range a) where
-  (Range l u) + (Range l' u') = space1 [l + l', u + u']
+  (Range l u) + (Range l' u') = unsafeSpace1 [l + l', u + u']
   zero = Range zero zero
 
 instance (Subtractive a, Eq a, Ord a) => Subtractive (Range a) where
diff --git a/src/NumHask/Space/Rect.hs b/src/NumHask/Space/Rect.hs
--- a/src/NumHask/Space/Rect.hs
+++ b/src/NumHask/Space/Rect.hs
@@ -270,7 +270,7 @@
 -- >>> rotationBound (pi/4) one
 -- Rect -0.7071067811865475 0.7071067811865475 -0.7071067811865475 0.7071067811865475
 rotationBound :: (TrigField a, Ord a) => a -> Rect a -> Rect a
-rotationBound d = space1 . fmap (rotate d |.) . corners4
+rotationBound d = unsafeSpace1 . fmap (rotate d |.) . corners4
 
 -- | Create Rects for a formulae y = f(x) across an x range where the y range is Range 0 y
 --
diff --git a/src/NumHask/Space/Time.hs b/src/NumHask/Space/Time.hs
--- a/src/NumHask/Space/Time.hs
+++ b/src/NumHask/Space/Time.hs
@@ -238,9 +238,10 @@
 -- >>> placedTimeLabelDiscontinuous PosIncludeBoundaries (Just (pack "%d %b")) 2 [UTCTime (fromGregorian 2017 12 6) (toDiffTime 0), UTCTime (fromGregorian 2017 12 29) (toDiffTime 0), UTCTime (fromGregorian 2018 1 31) (toDiffTime 0), UTCTime (fromGregorian 2018 3 3) (toDiffTime 0)]
 -- ([(0,"06 Dec"),(1,"31 Dec"),(2,"28 Feb"),(3,"03 Mar")],[])
 placedTimeLabelDiscontinuous :: PosDiscontinuous -> Maybe Text -> Int -> [UTCTime] -> ([(Int, Text)], [UTCTime])
+placedTimeLabelDiscontinuous _ _ _ [] = ([], [])
 placedTimeLabelDiscontinuous posd format n ts = (zip (fst <$> inds') labels, rem')
   where
-    r@(Range l u) = space1 ts
+    r@(Range l u) = unsafeSpace1 ts
     (grain, tps) = sensibleTimeGrid InnerPos n r
     tps' = case posd of
       PosInnerOnly -> tps
@@ -296,7 +297,7 @@
       Just f -> unpack f
       Nothing -> autoFormat grain
     labels = pack . formatTime defaultTimeLocale fmt <$> tps'
-    (Range l' u') = space1 tps'
+    (Range l' u') = unsafeSpace1 tps'
     r' = fromNominalDiffTime $ diffUTCTime u' l'
     tpsd = (/ r') . fromNominalDiffTime . flip diffUTCTime l <$> tps'
 
diff --git a/src/NumHask/Space/Types.hs b/src/NumHask/Space/Types.hs
--- a/src/NumHask/Space/Types.hs
+++ b/src/NumHask/Space/Types.hs
@@ -18,6 +18,7 @@
     project,
     Pos (..),
     space1,
+    unsafeSpace1,
     randomS,
     randomSM,
     randomSs,
@@ -199,7 +200,7 @@
 
 -- | a space that can be divided neatly
 --
--- > space1 (grid OuterPos s g) == s
+-- > unsafeSpace1 (grid OuterPos s g) == s
 -- > getUnion (sconcat (Union <$> (gridSpace s g))) == s
 class (Space s, Field (Element s)) => FieldSpace s where
   type Grid s :: Type
@@ -244,15 +245,21 @@
 project s0 s1 p =
   ((p - lower s0) / (upper s0 - lower s0)) * (upper s1 - lower s1) + lower s1
 
--- | the containing space of a non-empty Traversable
+-- | the containing space of a non-empty Traversable.
 --
--- > all $ space1 a `contains` <$> a
-space1 :: (Space s, Traversable f) => f (Element s) -> s
-space1 = P.foldr1 union . fmap singleton
+-- partial function.
+--
+-- > all $ unsafeSpace1 a `contains` <$> a
+unsafeSpace1 :: (Space s, Traversable f) => f (Element s) -> s
+unsafeSpace1 = P.foldr1 union . fmap singleton
 
+-- | Maybe containing space of a traversable.
+space1 :: (Space s, Traversable f) => f (Element s) -> Maybe s
+space1 s = bool (Just $ unsafeSpace1 s) Nothing (null s)
+
 -- | lift a monotone function (increasing or decreasing) over a given space
 monotone :: (Space a, Space b) => (Element a -> Element b) -> a -> b
-monotone f s = space1 [f (lower s), f (upper s)]
+monotone f s = unsafeSpace1 [f (lower s), f (upper s)]
 
 -- | a small space
 eps ::
diff --git a/src/NumHask/Space/XY.hs b/src/NumHask/Space/XY.hs
deleted file mode 100644
--- a/src/NumHask/Space/XY.hs
+++ /dev/null
@@ -1,101 +0,0 @@
-{-# LANGUAGE DeriveFunctor #-}
-{-# LANGUAGE PatternSynonyms #-}
-{-# LANGUAGE RebindableSyntax #-}
-{-# LANGUAGE StrictData #-}
-
--- | Unification of 'Point' and 'Rect'.
-module NumHask.Space.XY
-  ( XY (..),
-    pattern P,
-    pattern R,
-    toRect,
-    toPoint,
-    projectOn,
-    projectTo,
-  )
-where
-
-import qualified Data.List.NonEmpty as NonEmpty
-import GHC.Show (show)
-import NumHask.Prelude hiding (show)
-import NumHask.Space.Point
-import NumHask.Space.Rect
-import NumHask.Space.Types
-
--- $setup
--- >>> import NumHask.Prelude
--- >>> import NumHask.Space
-
--- | unification of a point and rect on the plane
-data XY a
-  = PointXY (Point a)
-  | RectXY (Rect a)
-  deriving (Eq, Functor)
-
-instance (Show a) => Show (XY a) where
-  show (PointXY (Point x y)) = "P " <> show x <> " " <> show y
-  show (RectXY (Rect x z y w)) = "R " <> show x <> " " <> show z <> " " <> show y <> " " <> show w
-
--- | make an XY from a point
-pattern P :: a -> a -> XY a
-pattern P x y = PointXY (Point x y)
-
-{-# COMPLETE P #-}
-
--- | make an XY from a rectangle
-pattern R :: a -> a -> a -> a -> XY a
-pattern R x z y w = RectXY (Rect x z y w)
-
-{-# COMPLETE R #-}
-
-instance (Additive a) => Additive (XY a) where
-  PointXY (Point x y) + PointXY (Point x' y') = PointXY (Point (x + x') (y + y'))
-  PointXY (Point x' y') + RectXY (Rect x z y w) = RectXY $ Rect (x + x') (z + x') (y + y') (w + y')
-  RectXY (Rect x z y w) + PointXY (Point x' y') = RectXY $ Rect (x + x') (z + x') (y + y') (w + y')
-  RectXY (Rect x z y w) + RectXY (Rect x' z' y' w') =
-    RectXY $ Rect (x + x') (z + z') (y + y') (w + w')
-  zero = PointXY (Point zero zero)
-
-instance (Ord a, Field a) => Multiplicative (XY a) where
-  x * y = RectXY $ toRect x * toRect y
-  one = RectXY one
-
-instance (Ord a, Subtractive a) => Subtractive (XY a) where
-  negate (PointXY (Point x y)) = PointXY (Point (negate x) (negate y))
-  negate (RectXY (Rect x z y w)) = RectXY (Rect (negate x) (negate z) (negate y) (negate w))
-
-instance (Ord a, Field a, Signed a) => Signed (XY a) where
-  abs x = PointXY $ abs <$> toPoint x
-  sign x = PointXY $ sign <$> toPoint x
-
--- * Natural transformations
-
--- | Convert an XY to a Rect
-toRect :: XY a -> Rect a
-toRect (PointXY (Point x y)) = Rect x x y y
-toRect (RectXY a) = a
-
--- | Convert an XY to a Point
-toPoint :: (Ord a, Field a) => XY a -> Point a
-toPoint (PointXY (Point x y)) = Point x y
-toPoint (RectXY (Ranges x y)) = Point (mid x) (mid y)
-
-instance (Ord a) => Semigroup (XY a) where
-  (<>) a b = RectXY (toRect a `union` toRect b)
-
--- | project an XY from one Rect to another, preserving relative position.
---
--- >>> projectOn one (Rect 0 1 0 1) zero
--- P -0.5 -0.5
-projectOn :: Rect Double -> Rect Double -> XY Double -> XY Double
-projectOn new old (PointXY p) = PointXY $ projectOnP new old p
-projectOn new old (RectXY r) = RectXY $ projectOnR new old r
-
--- | project an [XY a] from it's enclosing space to the given space
---
--- >>> projectTo one (zipWith P [0..2] [0..2])
--- [P -0.5 -0.5,P 0.0 0.0,P 0.5 0.5]
-projectTo :: Rect Double -> [XY Double] -> [XY Double]
-projectTo _ [] = []
-projectTo vb (x : xs) =
-  projectOn vb (toRect $ sconcat (x NonEmpty.:| xs)) <$> (x : xs)