diff --git a/numhask.cabal b/numhask.cabal
--- a/numhask.cabal
+++ b/numhask.cabal
@@ -1,14 +1,14 @@
 cabal-version: 2.4
 name: numhask
-version: 0.7.0.0
+version: 0.7.1.0
 synopsis:
-  A numeric class heirarchy.
+  A numeric class hierarchy.
 description:
     This package provides numeric classes alternate to the prelude specified in [haskell98](https://www.haskell.org/onlinereport/standard-prelude.html).
     .
     The numeric class constellation looks somewhat like:
     .
-    ![nh](other/nh.svg)
+    ![nh](docs/other/nh.svg)
     .
     == Usage
     .
@@ -63,6 +63,8 @@
     -Wincomplete-record-updates
     -Wincomplete-uni-patterns
     -Wredundant-constraints
+    -fwrite-ide-info
+    -hiedir=.hie
   build-depends:
     base >=4.7 && <5,
     protolude >=0.3 && <0.4,
diff --git a/src/NumHask/Algebra/Field.hs b/src/NumHask/Algebra/Field.hs
--- a/src/NumHask/Algebra/Field.hs
+++ b/src/NumHask/Algebra/Field.hs
@@ -76,7 +76,8 @@
 -- > for +ive b, a != 0,1: a ** logBase a b ≈ b
 class
   (Field a) =>
-  ExpField a where
+  ExpField a
+  where
   exp :: a -> a
   log :: a -> a
   logBase :: a -> a -> a
@@ -176,7 +177,8 @@
 -- Note the tricky law that, although nan is assigned to zero/zero, they are never-the-less not equal. A committee decided this.
 class
   (Field a) =>
-  UpperBoundedField a where
+  UpperBoundedField a
+  where
   infinity :: a
   infinity = one / zero
 
@@ -194,7 +196,8 @@
 -- | Negative infinity.
 class
   (Subtractive a, Field a) =>
-  LowerBoundedField a where
+  LowerBoundedField a
+  where
   negInfinity :: a
   negInfinity = negate (one / zero)
 
@@ -208,7 +211,8 @@
 -- | Trigonometric Field
 class
   (Field a) =>
-  TrigField a where
+  TrigField a
+  where
   pi :: a
   sin :: a -> a
   cos :: a -> a
diff --git a/src/NumHask/Algebra/Group.hs b/src/NumHask/Algebra/Group.hs
--- a/src/NumHask/Algebra/Group.hs
+++ b/src/NumHask/Algebra/Group.hs
@@ -52,7 +52,8 @@
 -- > a ⊕ unit = a
 class
   Magma a =>
-  Unital a where
+  Unital a
+  where
   unit :: a
 
 instance Unital b => Unital (a -> b) where
@@ -83,7 +84,8 @@
 -- > ∀ a,b ∈ T: inv a ⊕ (a ⊕ b) = b = (b ⊕ a) ⊕ inv a
 class
   Magma a =>
-  Invertible a where
+  Invertible a
+  where
   inv :: a -> a
 
 instance Invertible b => Invertible (a -> b) where
@@ -102,7 +104,8 @@
 -- > a ⊕ absorb = absorb
 class
   Magma a =>
-  Absorbing a where
+  Absorbing a
+  where
   absorb :: a
 
 instance Absorbing b => Absorbing (a -> b) where
diff --git a/src/NumHask/Algebra/Module.hs b/src/NumHask/Algebra/Module.hs
--- a/src/NumHask/Algebra/Module.hs
+++ b/src/NumHask/Algebra/Module.hs
@@ -32,7 +32,8 @@
 class
   (Additive a) =>
   AdditiveAction m a
-    | m -> a where
+    | m -> a
+  where
   infixl 6 .+
   (.+) :: a -> m -> m
 
@@ -43,7 +44,8 @@
 class
   (Subtractive a) =>
   SubtractiveAction m a
-    | m -> a where
+    | m -> a
+  where
   infixl 6 .-
   (.-) :: a -> m -> m
 
@@ -54,7 +56,8 @@
 class
   (Multiplicative a) =>
   MultiplicativeAction m a
-    | m -> a where
+    | m -> a
+  where
   infixl 7 .*
   (.*) :: a -> m -> m
   infixl 7 *.
@@ -64,7 +67,8 @@
 class
   (Divisive a) =>
   DivisiveAction m a
-    | m -> a where
+    | m -> a
+  where
   infixl 7 ./
   (./) :: a -> m -> m
   infixl 7 /.
diff --git a/src/NumHask/Analysis/Metric.hs b/src/NumHask/Analysis/Metric.hs
--- a/src/NumHask/Analysis/Metric.hs
+++ b/src/NumHask/Analysis/Metric.hs
@@ -18,6 +18,7 @@
   )
 where
 
+import Data.Bool (bool)
 import Data.Int (Int16, Int32, Int64, Int8)
 import Data.Word (Word16, Word32, Word64, Word8)
 import GHC.Generics (Generic)
@@ -27,11 +28,11 @@
 import NumHask.Algebra.Module
 import NumHask.Algebra.Multiplicative
 import Prelude hiding
-  ( (*),
-    (-),
-    Bounded (..),
+  ( Bounded (..),
     Integral (..),
     negate,
+    (*),
+    (-),
   )
 import qualified Prelude as P
 
@@ -40,100 +41,101 @@
 -- > abs a * sign a == a
 class
   (Additive a, Multiplicative a) =>
-  Signed a where
+  Signed a
+  where
   sign :: a -> a
   abs :: a -> a
 
 instance Signed Double where
-  sign a
-    | a == zero = zero
-    | a > zero = one
-    | otherwise = negate one
+  sign a =
+    case compare a zero of
+      EQ -> zero
+      GT -> one
+      LT -> negate one
   abs = P.abs
 
 instance Signed Float where
-  sign a
-    | a == zero = zero
-    | a > zero = one
-    | otherwise = negate one
+  sign a =
+    case compare a zero of
+      EQ -> zero
+      GT -> one
+      LT -> negate one
   abs = P.abs
 
 instance Signed Int where
-  sign a
-    | a == zero = zero
-    | a > zero = one
-    | otherwise = negate one
+  sign a =
+    case compare a zero of
+      EQ -> zero
+      GT -> one
+      LT -> negate one
   abs = P.abs
 
 instance Signed Integer where
-  sign a
-    | a == zero = zero
-    | a > zero = one
-    | otherwise = negate one
+  sign a =
+    case compare a zero of
+      EQ -> zero
+      GT -> one
+      LT -> negate one
   abs = P.abs
 
 instance Signed Natural where
-  sign a
-    | a == zero = zero
-    | otherwise = one
+  sign a =
+    case compare a zero of
+      EQ -> zero
+      GT -> one
+      LT -> negate one
   abs = id
 
 instance Signed Int8 where
-  sign a
-    | a == zero = zero
-    | a > zero = one
-    | otherwise = negate one
+  sign a =
+    case compare a zero of
+      EQ -> zero
+      GT -> one
+      LT -> negate one
   abs = P.abs
 
 instance Signed Int16 where
-  sign a
-    | a == zero = zero
-    | a > zero = one
-    | otherwise = negate one
+  sign a =
+    case compare a zero of
+      EQ -> zero
+      GT -> one
+      LT -> negate one
   abs = P.abs
 
 instance Signed Int32 where
-  sign a
-    | a == zero = zero
-    | a > zero = one
-    | otherwise = negate one
+  sign a =
+    case compare a zero of
+      EQ -> zero
+      GT -> one
+      LT -> negate one
   abs = P.abs
 
 instance Signed Int64 where
-  sign a
-    | a == zero = zero
-    | a > zero = one
-    | otherwise = negate one
+  sign a =
+    case compare a zero of
+      EQ -> zero
+      GT -> one
+      LT -> negate one
   abs = P.abs
 
 instance Signed Word where
-  sign a
-    | a == zero = zero
-    | otherwise = one
+  sign a = bool one zero (a == zero)
   abs = P.abs
 
 instance Signed Word8 where
-  sign a
-    | a == zero = zero
-    | otherwise = one
+  sign a = bool one zero (a == zero)
   abs = P.abs
 
 instance Signed Word16 where
-  sign a
-    | a == zero = zero
-    | otherwise = one
+  sign a = bool one zero (a == zero)
   abs = P.abs
 
 instance Signed Word32 where
-  sign a
-    | a == zero = zero
-    | otherwise = one
+  sign a = bool one zero (a == zero)
   abs = P.abs
 
 instance Signed Word64 where
-  sign a
-    | a == zero = zero
-    | otherwise = one
+  sign a = bool one zero (a == zero)
   abs = P.abs
 
 -- | Norm is a slight generalisation of Signed. The class has the same shape but allows the codomain to be different to the domain.
@@ -221,8 +223,7 @@
   ray :: dir -> coord
 
 -- | Something that has a magnitude and a direction.
-data Polar mag dir
-  = Polar {magnitude :: mag, direction :: dir}
+data Polar mag dir = Polar {magnitude :: !mag, direction :: !dir}
   deriving (Eq, Show, Generic)
 
 -- | Convert from a number to a Polar.
@@ -236,7 +237,8 @@
 -- | A small number, especially useful for approximate equality.
 class
   (Eq a, Additive a, Subtractive a, MeetSemiLattice a) =>
-  Epsilon a where
+  Epsilon a
+  where
   epsilon :: a
   epsilon = zero
 
diff --git a/src/NumHask/Data/Complex.hs b/src/NumHask/Data/Complex.hs
--- a/src/NumHask/Data/Complex.hs
+++ b/src/NumHask/Data/Complex.hs
@@ -1,6 +1,4 @@
 {-# LANGUAGE DeriveDataTypeable #-}
-{-# LANGUAGE DeriveFoldable #-}
-{-# LANGUAGE DeriveFunctor #-}
 {-# LANGUAGE DeriveGeneric #-}
 {-# LANGUAGE DeriveTraversable #-}
 {-# LANGUAGE FlexibleInstances #-}
@@ -26,8 +24,7 @@
 import NumHask.Analysis.Metric
 import NumHask.Data.Integral
 import Prelude hiding
-  ( (/),
-    Num (..),
+  ( Num (..),
     atan,
     atan2,
     cos,
@@ -39,8 +36,9 @@
     recip,
     sin,
     sqrt,
+    (/),
   )
-import qualified Prelude as P ((&&), (<), (<=), (==), (>), Ord (..), otherwise)
+import qualified Prelude as P (Ord (..), otherwise, (&&), (<), (<=), (==), (>))
 
 -- -----------------------------------------------------------------------------
 -- The Complex type
diff --git a/src/NumHask/Data/Integral.hs b/src/NumHask/Data/Integral.hs
--- a/src/NumHask/Data/Integral.hs
+++ b/src/NumHask/Data/Integral.hs
@@ -21,12 +21,14 @@
 where
 
 import Data.Int (Int16, Int32, Int64, Int8)
+import Data.Ord
 import Data.Word (Word, Word16, Word32, Word64, Word8)
 import GHC.Natural (Natural (..))
+import GHC.Num (naturalFromInteger)
 import NumHask.Algebra.Additive
 import NumHask.Algebra.Multiplicative
 import NumHask.Algebra.Ring
-import Prelude ((.), Double, Float, Int, Integer, fst, snd)
+import Prelude (Double, Float, Int, Integer, fst, snd, (.))
 import qualified Prelude as P
 
 -- | An Integral is anything that satisfies the law:
@@ -34,7 +36,8 @@
 -- > b == zero || b * (a `div` b) + (a `mod` b) == a
 class
   (Distributive a) =>
-  Integral a where
+  Integral a
+  where
   infixl 7 `div`, `mod`
   div :: a -> a -> a
   div a1 a2 = fst (divMod a1 a2)
@@ -244,7 +247,7 @@
   fromIntegral = P.id
 
 instance FromIntegral Natural Integer where
-  fromIntegral = P.fromInteger
+  fromIntegral = naturalFromInteger
 
 instance FromIntegral Int8 Integer where
   fromIntegral = P.fromInteger
@@ -368,7 +371,7 @@
   fromInteger = P.id
 
 instance FromInteger Natural where
-  fromInteger = P.fromInteger
+  fromInteger = naturalFromInteger
 
 instance FromInteger Int8 where
   fromInteger = P.fromInteger
@@ -409,16 +412,19 @@
 odd :: (P.Eq a, Integral a) => a -> P.Bool
 odd = P.not . even
 
+infixr 8 ^^
+
 -- | raise a number to an 'Integral' power
 (^^) ::
   (P.Ord b, Divisive a, Subtractive b, Integral b) =>
   a ->
   b ->
   a
-x0 ^^ y0
-  | y0 P.< zero = recip (x0 ^^ negate y0)
-  | y0 P.== zero = one
-  | P.otherwise = f x0 y0
+x0 ^^ y0 =
+  case compare y0 zero of
+    EQ -> one
+    GT -> f x0 y0
+    LT -> recip (x0 ^^ negate y0)
   where
     f x y
       | even y = f (x * x) (y `quot` two)
@@ -428,6 +434,8 @@
       | even y = g (x * x) (y `quot` two) z
       | y P.== one = x * z
       | P.otherwise = g (x * x) (y `quot` two) (x * z)
+
+infixr 8 ^
 
 -- | raise a number to an 'Int' power
 --
diff --git a/src/NumHask/Data/LogField.hs b/src/NumHask/Data/LogField.hs
--- a/src/NumHask/Data/LogField.hs
+++ b/src/NumHask/Data/LogField.hs
@@ -1,6 +1,4 @@
 {-# LANGUAGE DeriveDataTypeable #-}
-{-# LANGUAGE DeriveFoldable #-}
-{-# LANGUAGE DeriveFunctor #-}
 {-# LANGUAGE DeriveGeneric #-}
 {-# LANGUAGE DeriveTraversable #-}
 {-# LANGUAGE FlexibleInstances #-}
diff --git a/src/NumHask/Data/Rational.hs b/src/NumHask/Data/Rational.hs
--- a/src/NumHask/Data/Rational.hs
+++ b/src/NumHask/Data/Rational.hs
@@ -33,7 +33,7 @@
 import NumHask.Algebra.Ring
 import NumHask.Analysis.Metric
 import NumHask.Data.Integral
-import Prelude ((.), Int, Integer, Rational)
+import Prelude (Int, Integer, Ord (..), Ordering (..), Rational, (.))
 import qualified Prelude as P
 
 -- $setup
@@ -102,10 +102,11 @@
 instance (P.Ord a, Signed a, Integral a, Field a) => LowerBoundedField (Ratio a)
 
 instance (P.Ord a, Signed a, Integral a, Ring a) => Signed (Ratio a) where
-  sign (n :% _)
-    | n P.== zero = zero
-    | n P.> zero = one
-    | P.otherwise = negate one
+  sign (n :% _) =
+    case compare n zero of
+      EQ -> zero
+      GT -> one
+      LT -> negate one
   abs (n :% d) = abs n :% abs d
 
 instance (P.Ord a, Signed a, Integral a, Ring a) => Norm (Ratio a) (Ratio a) where