diff --git a/CHANGELOG.md b/CHANGELOG.md
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -1,3 +1,8 @@
+## [v1.3.0.8](https://github.com/diagrams/diagrams-core/tree/v1.3.0.8) (2016-06-05)
+
+- allow `base-4.9`
+- build warning-free on GHC 8.0.1
+
 ## [v1.3.0.7](https://github.com/diagrams/diagrams-core/tree/v1.3.0.7) (2016-05-01)
 
 - allow `lens-4.14`
diff --git a/diagrams-core.cabal b/diagrams-core.cabal
--- a/diagrams-core.cabal
+++ b/diagrams-core.cabal
@@ -1,5 +1,5 @@
 Name:                diagrams-core
-Version:             1.3.0.7
+Version:             1.3.0.8
 Synopsis:            Core libraries for diagrams EDSL
 Description:         The core modules underlying diagrams,
                      an embedded domain-specific language
@@ -15,7 +15,7 @@
 Cabal-version:       >=1.10
 Extra-source-files:  CHANGELOG.md, README.markdown, diagrams/*.svg
 extra-doc-files:     diagrams/*.svg
-Tested-with:         GHC == 7.4.2, GHC == 7.6.3, GHC == 7.8.4, GHC == 7.10.1
+Tested-with:         GHC == 7.6.3, GHC == 7.8.4, GHC == 7.10.1, GHC == 8.0.1
 Source-repository head
   type:     git
   location: git://github.com/diagrams/diagrams-core.git
@@ -36,7 +36,7 @@
                        Diagrams.Core.Types,
                        Diagrams.Core.V
 
-  Build-depends:       base >= 4.2 && < 4.9,
+  Build-depends:       base >= 4.2 && < 4.10,
                        containers >= 0.4.2 && < 0.6,
                        unordered-containers >= 0.2 && < 0.3,
                        semigroups >= 0.8.4 && < 0.19,
diff --git a/src/Diagrams/Core/Compile.hs b/src/Diagrams/Core/Compile.hs
--- a/src/Diagrams/Core/Compile.hs
+++ b/src/Diagrams/Core/Compile.hs
@@ -34,7 +34,6 @@
   )
   where
 
-import           Data.Typeable
 import qualified Data.List.NonEmpty        as NEL
 import           Data.Maybe                (fromMaybe)
 import           Data.Monoid.Coproduct
@@ -43,13 +42,14 @@
 import           Data.Semigroup
 import           Data.Tree
 import           Data.Tree.DUAL
+import           Data.Typeable
 
 import           Diagrams.Core.Envelope    (OrderedField, diameter)
+import           Diagrams.Core.Style
 import           Diagrams.Core.Transform
 import           Diagrams.Core.Types
-import           Diagrams.Core.Style
 
-import           Linear.Metric hiding (qd)
+import           Linear.Metric             hiding (qd)
 
 -- Typeable1 is a depreciated synonym in ghc > 707
 #if __GLASGOW_HASKELL__ >= 707
@@ -117,7 +117,7 @@
           => DTree b v n Annotation -> RTree b v n Annotation
 fromDTree = fromDTree' mempty
   where
-    fromDTree' :: HasLinearMap v => Transformation v n -> DTree b v n Annotation -> RTree b v n Annotation
+    fromDTree' :: Transformation v n -> DTree b v n Annotation -> RTree b v n Annotation
     -- We put the accumulated transformation (accTr) and the prim
     -- into an RPrim node.
     fromDTree' accTr (Node (DPrim p) _)
@@ -151,7 +151,7 @@
 --   transformation used to convert the diagram from local to output
 --   units.
 toRTree
-  :: (HasLinearMap v, Metric v, Typeable1 v, Typeable n,
+  :: (HasLinearMap v, Metric v, Typeable n,
       OrderedField n, Monoid m, Semigroup m)
   => Transformation v n -> QDiagram b v n m -> RTree b v n Annotation
 toRTree globalToOutput d
@@ -183,7 +183,7 @@
 --   transformation can be used, for example, to convert output/screen
 --   coordinates back into diagram coordinates.  See also 'adjustDia'.
 renderDiaT
-  :: (Backend b v n , HasLinearMap v, Metric v, Typeable1 v,
+  :: (Backend b v n , HasLinearMap v, Metric v,
       Typeable n, OrderedField n, Monoid' m)
   => b -> Options b v n -> QDiagram b v n m -> (Transformation v n, Result b v n)
 renderDiaT b opts d = (g2o, renderRTree b opts' . toRTree g2o $ d')
@@ -191,7 +191,7 @@
 
 -- | Render a diagram.
 renderDia
-  :: (Backend b v n , HasLinearMap v, Metric v, Typeable1 v,
+  :: (Backend b v n , HasLinearMap v, Metric v,
       Typeable n, OrderedField n, Monoid' m)
   => b -> Options b v n -> QDiagram b v n m -> Result b v n
 renderDia b opts d = snd (renderDiaT b opts d)
diff --git a/src/Diagrams/Core/Envelope.hs b/src/Diagrams/Core/Envelope.hs
--- a/src/Diagrams/Core/Envelope.hs
+++ b/src/Diagrams/Core/Envelope.hs
@@ -257,7 +257,7 @@
 --   Note that the 'envelopeV' / 'envelopeP' functions above should be
 --   preferred, as this requires a call to norm. However, it is more
 --   efficient than calling norm on the results of those functions.
-envelopeS :: (V a ~ v, N a ~ n, Enveloped a, Num n) => v n -> a -> n
+envelopeS :: (V a ~ v, N a ~ n, Enveloped a) => v n -> a -> n
 envelopeS v = fromMaybe 0 . envelopeSMay v
 
 -- | Compute the diameter of a enveloped object along a particular
diff --git a/src/Diagrams/Core/HasOrigin.hs b/src/Diagrams/Core/HasOrigin.hs
--- a/src/Diagrams/Core/HasOrigin.hs
+++ b/src/Diagrams/Core/HasOrigin.hs
@@ -23,11 +23,11 @@
        ( HasOrigin(..), moveOriginBy, moveTo, place
        ) where
 
-import qualified Data.Map             as M
-import qualified Data.Set             as S
+import qualified Data.Map              as M
+import qualified Data.Set              as S
 
 import           Diagrams.Core.Measure
-import           Diagrams.Core.Points ()
+import           Diagrams.Core.Points  ()
 import           Diagrams.Core.V
 
 import           Linear.Affine
@@ -59,7 +59,7 @@
   moveOriginTo :: Point (V t) (N t) -> t -> t
 
 -- | Move the local origin by a relative vector.
-moveOriginBy :: (V t ~ v, N t ~ n, Num n, HasOrigin t) => v n -> t -> t
+moveOriginBy :: (V t ~ v, N t ~ n, HasOrigin t) => v n -> t -> t
 moveOriginBy = moveOriginTo . P
 
 -- | Translate the object by the translation that sends the origin to
diff --git a/src/Diagrams/Core/Measure.hs b/src/Diagrams/Core/Measure.hs
--- a/src/Diagrams/Core/Measure.hs
+++ b/src/Diagrams/Core/Measure.hs
@@ -49,7 +49,7 @@
 fromMeasured g n (Measured m) = m (1,g,n)
 
 -- | Output units don't change.
-output :: Num n => n -> Measure n
+output :: n -> Measure n
 output = pure
 
 -- | Local units are scaled by the average scale of a transform.
diff --git a/src/Diagrams/Core/Style.hs b/src/Diagrams/Core/Style.hs
--- a/src/Diagrams/Core/Style.hs
+++ b/src/Diagrams/Core/Style.hs
@@ -139,7 +139,7 @@
 
 -- | Shows the kind of attribute and the type contained in the
 --   attribute.
-instance Typeable n => Show (Attribute v n) where
+instance Show (Attribute v n) where
   showsPrec d attr = showParen (d > 10) $ case attr of
     Attribute a  -> showString "Attribute "  . showsPrec 11 (typeOf a)
     MAttribute a -> showString "MAttribute " . showsPrec 11 (mType a)
@@ -178,7 +178,7 @@
 
 -- | Turn an 'MAttribute' into an 'Attribute' using the given 'global'
 --   and 'normalized' scale.
-unmeasureAttribute :: (Num n, Typeable n)
+unmeasureAttribute :: (Num n)
                    => n -> n -> Attribute v n -> Attribute v n
 unmeasureAttribute g n (MAttribute m) = Attribute (fromMeasured g n m)
 unmeasureAttribute _ _ a              = a
@@ -257,7 +257,7 @@
 instance A.Action (Style v n) m
 
 -- | Show the attributes in the style.
-instance Typeable n => Show (Style v n) where
+instance Show (Style v n) where
   showsPrec d sty = showParen (d > 10) $
     showString "Style " . showsPrec d (sty ^.. each)
 
@@ -289,7 +289,7 @@
 
 -- | Replace all 'MAttribute's with 'Attribute's using the 'global' and
 --   'normalized' scales.
-unmeasureAttrs :: (Num n, Typeable n) => n -> n -> Style v n -> Style v n
+unmeasureAttrs :: (Num n) => n -> n -> Style v n -> Style v n
 unmeasureAttrs g n = over each (unmeasureAttribute g n)
 
 -- style lenses --------------------------------------------------------
@@ -361,7 +361,7 @@
 --   diagram or a style). If the object already has an attribute of
 --   the same type, the new attribute is combined on the left with the
 --   existing attribute, according to their semigroup structure.
-applyMAttr :: (AttributeClass a, N d ~ n, HasStyle d, Typeable n) => Measured n a -> d -> d
+applyMAttr :: (AttributeClass a, N d ~ n, HasStyle d) => Measured n a -> d -> d
 applyMAttr = applyStyle . attributeToStyle . MAttribute
 
 -- | Apply a transformable attribute to an instance of 'HasStyle'
diff --git a/src/Diagrams/Core/Transform.hs b/src/Diagrams/Core/Transform.hs
--- a/src/Diagrams/Core/Transform.hs
+++ b/src/Diagrams/Core/Transform.hs
@@ -219,8 +219,8 @@
 
 -- | Get the dimension of an object whose vector space is an instance of
 --   @HasLinearMap@, e.g. transformations, paths, diagrams, etc.
-dimension :: forall a v. (V a ~ v, Additive v, Traversable v) => a -> Int
-dimension _ = length (basis :: [v Int])
+dimension :: forall a. (Additive (V a), Traversable (V a)) => a -> Int
+dimension _ = length (basis :: [V a Int])
 
 -- | Get the matrix equivalent of the linear transform,
 --   (as a list of columns) and the translation vector.  This
@@ -404,7 +404,7 @@
 translation = Transformation mempty mempty
 
 -- | Translate by a vector.
-translate :: (Num (N t), Transformable t) => Vn t -> t -> t
+translate :: (Transformable t) => Vn t -> t -> t
 translate = transform . translation
 
 -- | Create a uniform scaling transformation.
diff --git a/src/Diagrams/Core/Types.hs b/src/Diagrams/Core/Types.hs
--- a/src/Diagrams/Core/Types.hs
+++ b/src/Diagrams/Core/Types.hs
@@ -627,7 +627,7 @@
 --   @mkSubdiagram . pointDiagram@, which would result in a subdiagram
 --   with local origin at the parent origin, rather than at the given
 --   point.
-subPoint :: (Metric v, OrderedField n, Semigroup m)
+subPoint :: (Metric v, OrderedField n)
          => Point v n -> Subdiagram b v n m
 subPoint p = Subdiagram
                (pointDiagram origin)
@@ -648,8 +648,7 @@
       => HasOrigin (Subdiagram b v n m) where
   moveOriginTo = translate . (origin .-.)
 
-instance (Metric v, Floating n)
-    => Transformable (Subdiagram b v n m) where
+instance Transformable (Subdiagram b v n m) where
   transform t (Subdiagram d a) = Subdiagram d (transfToAnnot t <> a)
 
 -- | Get the location of a subdiagram; that is, the location of its
@@ -716,8 +715,7 @@
       => HasOrigin (SubMap b v n m) where
   moveOriginTo = over _Wrapped' . moveOriginTo
 
-instance (Metric v, Floating n)
-  => Transformable (SubMap b v n m) where
+instance Transformable (SubMap b v n m) where
   transform = over _Wrapped' . transform
 
 -- | 'SubMap's are qualifiable: if @ns@ is a 'SubMap', then @a |>
@@ -777,7 +775,7 @@
 data Prim b v n where
   Prim :: (Transformable p, Typeable p, Renderable p b) => p -> Prim b (V p) (N p)
 
-_Prim :: (Transformable p, Typeable p, Renderable p b) => Prism' (Prim b (V p) (N p)) p
+_Prim :: (Typeable p, Renderable p b) => Prism' (Prim b (V p) (N p)) p
 _Prim = prism' Prim (\(Prim p) -> cast p)
 
 type instance V (Prim b v n) = v