diff --git a/LICENSE b/LICENSE
--- a/LICENSE
+++ b/LICENSE
@@ -1,4 +1,4 @@
-Copyright Tony Day (c) 2016
+Copyright (c) 2016, Tony Day
 
 All rights reserved.
 
diff --git a/numhask.cabal b/numhask.cabal
--- a/numhask.cabal
+++ b/numhask.cabal
@@ -1,141 +1,138 @@
-cabal-version:      3.0
-name:               numhask
-version:            0.11.0.2
-synopsis:           A numeric class hierarchy.
+cabal-version: 3.0
+name: numhask
+version: 0.11.1.0
+license: BSD-3-Clause
+license-file: LICENSE
+copyright: Tony Day (c) 2016
+category: math
+author: Tony Day
+maintainer: tonyday567@gmail.com
+homepage: https://github.com/tonyday567/numhask#readme
+bug-reports: https://github.com/tonyday567/numhask/issues
+synopsis: A numeric class hierarchy.
 description:
-  This package provides alternative numeric classes over Prelude.
+    This package provides alternative numeric classes over Prelude.
 
-  The numeric class constellation looks somewhat like:
+    The numeric class constellation looks somewhat like:
 
-  ![nh](docs/other/nh.svg)
+    ![nh](docs/other/nh.svg)
 
-  == Usage
+    == Usage
 
-  >>> {-# LANGUAGE GHC2021 #-}
-  >>> {-# LANGUAGE RebindableSyntax #-}
-  >>> import NumHask.Prelude
+    >>> {-# LANGUAGE GHC2021 #-}
+    >>> {-# LANGUAGE RebindableSyntax #-}
+    >>> import NumHask.Prelude
 
-  See "NumHask" for a detailed overview.
+    See "NumHask" for a detailed overview.
 
-category:           mathematics
-homepage:           https://github.com/tonyday567/numhask#readme
-bug-reports:        https://github.com/tonyday567/numhask/issues
-author:             Tony Day
-maintainer:         tonyday567@gmail.com
-copyright:          Tony Day
-license:            BSD-3-Clause
-license-file:       LICENSE
-build-type:         Simple
+build-type: Simple
 tested-with:
-  GHC ==8.6.5 || ==8.8.4 || ==8.10.7 || ==9.0.2 || ==9.2.8 || ==9.4.5 || ==9.6.2
-
-extra-doc-files:    other/*.svg,
-                    ChangeLog.md
+    GHC ==8.6.5 || ==8.8.4 || ==8.10.7 || ==9.0.2 || ==9.2.8 || ==9.4.5 || ==9.6.2
+extra-doc-files:
+    ChangeLog.md
+    other/*.svg
 
 source-repository head
-  type:     git
-  location: https://github.com/tonyday567/numhask
-  subdir:   numhask
-
-common ghc2021-stanza
-  if impl(ghc >=9.2)
-    default-language:
-      GHC2021
-  if impl(ghc <9.2)
-    default-language:
-      Haskell2010
-    default-extensions:
-      BangPatterns
-      BinaryLiterals
-      ConstrainedClassMethods
-      ConstraintKinds
-      DeriveDataTypeable
-      DeriveFoldable
-      DeriveFunctor
-      DeriveGeneric
-      DeriveLift
-      DeriveTraversable
-      DoAndIfThenElse
-      EmptyCase
-      EmptyDataDecls
-      EmptyDataDeriving
-      ExistentialQuantification
-      ExplicitForAll
-      FlexibleContexts
-      FlexibleInstances
-      ForeignFunctionInterface
-      GADTSyntax
-      GeneralisedNewtypeDeriving
-      HexFloatLiterals
-      ImplicitPrelude
-      InstanceSigs
-      KindSignatures
-      MonomorphismRestriction
-      MultiParamTypeClasses
-      NamedFieldPuns
-      NamedWildCards
-      NumericUnderscores
-      PatternGuards
-      PolyKinds
-      PostfixOperators
-      RankNTypes
-      RelaxedPolyRec
-      ScopedTypeVariables
-      StandaloneDeriving
-      StarIsType
-      TraditionalRecordSyntax
-      TupleSections
-      TypeApplications
-      TypeOperators
-      TypeSynonymInstances
-  if impl(ghc <9.2) && impl(ghc >=8.10)
-    default-extensions:
-      ImportQualifiedPost
-      StandaloneKindSignatures
+    type: git
+    location: https://github.com/tonyday567/numhask
 
 common ghc-options-stanza
-  ghc-options:
-    -Wall
-    -Wcompat
-    -Wincomplete-record-updates
-    -Wincomplete-uni-patterns
-    -Wredundant-constraints
-    -Widentities
-    -Wpartial-fields
-  if impl(ghc >=8.8)
     ghc-options:
-      -fwrite-ide-info
-      -hiedir=.hie
+        -Wall
+        -Wcompat
+        -Widentities
+        -Wincomplete-record-updates
+        -Wincomplete-uni-patterns
+        -Wpartial-fields
+        -Wredundant-constraints
 
-library
-  import: ghc2021-stanza
-  import: ghc-options-stanza
-  hs-source-dirs: src
-  default-extensions:
-    RebindableSyntax
-  -- keeping ormolu happy
-  if impl(ghc >=8.10)
-    default-extensions:
-      NoImportQualifiedPost
-  build-depends:
-    base >=4.7 && <5,
-    -- keeping cabal-docspec happy
-    QuickCheck >=2.14 && <3
-  exposed-modules:
-    NumHask
-    NumHask.Algebra.Additive
-    NumHask.Algebra.Field
-    NumHask.Algebra.Group
-    NumHask.Algebra.Lattice
-    NumHask.Algebra.Metric
-    NumHask.Algebra.Action
-    NumHask.Algebra.Multiplicative
-    NumHask.Algebra.Ring
-    NumHask.Data.Complex
-    NumHask.Data.Integral
-    NumHask.Data.Rational
-    NumHask.Exception
-    NumHask.Prelude
+    if impl ( ghc >= 8.8 )
+        ghc-options:
+            -fwrite-ide-info
+            -hiedir=.hie
 
-  other-modules:
+common ghc2021-stanza
+    if impl ( ghc >= 9.2 )
+        default-language: GHC2021
 
+    if impl ( ghc < 9.2 )
+        default-language: Haskell2010
+        default-extensions:
+            BangPatterns
+            BinaryLiterals
+            ConstrainedClassMethods
+            ConstraintKinds
+            DeriveDataTypeable
+            DeriveFoldable
+            DeriveFunctor
+            DeriveGeneric
+            DeriveLift
+            DeriveTraversable
+            DoAndIfThenElse
+            EmptyCase
+            EmptyDataDecls
+            EmptyDataDeriving
+            ExistentialQuantification
+            ExplicitForAll
+            FlexibleContexts
+            FlexibleInstances
+            ForeignFunctionInterface
+            GADTSyntax
+            GeneralisedNewtypeDeriving
+            HexFloatLiterals
+            ImplicitPrelude
+            InstanceSigs
+            KindSignatures
+            MonomorphismRestriction
+            MultiParamTypeClasses
+            NamedFieldPuns
+            NamedWildCards
+            NumericUnderscores
+            PatternGuards
+            PolyKinds
+            PostfixOperators
+            RankNTypes
+            RelaxedPolyRec
+            ScopedTypeVariables
+            StandaloneDeriving
+            StarIsType
+            TraditionalRecordSyntax
+            TupleSections
+            TypeApplications
+            TypeOperators
+            TypeSynonymInstances
+
+    if impl ( ghc < 9.2 ) && impl ( ghc >= 8.10 )
+        default-extensions:
+            ImportQualifiedPost
+            StandaloneKindSignatures
+
+library
+    import: ghc-options-stanza
+    import: ghc2021-stanza
+    hs-source-dirs: src
+    build-depends:
+        -- keeping cabal-docspec happy
+        , QuickCheck >=2.14 && <3
+        , base       >=4.7 && <5
+    exposed-modules:
+        NumHask
+        NumHask.Algebra.Action
+        NumHask.Algebra.Additive
+        NumHask.Algebra.Field
+        NumHask.Algebra.Group
+        NumHask.Algebra.Lattice
+        NumHask.Algebra.Metric
+        NumHask.Algebra.Multiplicative
+        NumHask.Algebra.Ring
+        NumHask.Data.Complex
+        NumHask.Data.Integral
+        NumHask.Data.Rational
+        NumHask.Exception
+        NumHask.Prelude
+    other-modules:
+    default-extensions: RebindableSyntax
+
+    -- keeping ormolu happy
+    if impl ( ghc >= 8.10 )
+        default-extensions: NoImportQualifiedPost
diff --git a/src/NumHask.hs b/src/NumHask.hs
--- a/src/NumHask.hs
+++ b/src/NumHask.hs
@@ -266,7 +266,8 @@
 -- numhask is largely a set of classes that can replace the 'GHC.Num.Num' class and it's descendents.
 -- Principles that have guided design include:
 --
--- - __/balanced class density/__. The numeric heirarchy begins with addition and multiplication rather than from a Monoidal or Magma base. Whilst not being as principled as other approaches, this circumvents the instance explosion problems of Haskell whilst maintaining clarity of class purpose.
+-- - __/balanced class density/__. The numeric hierarchy begins with addition and multiplication,
+--   choosing not to build from a Magma base. Whilst not being as principled as other approaches, this circumvents the instance explosion problems of Haskell whilst maintaining clarity of class purpose.
 --
 -- - __/operator-first/__. In all cases, a class exists to define useful operators.
 --   Major class groupings, such as 'Distributive', 'Ring' and 'Field' are type synonyms.
@@ -290,7 +291,7 @@
 
 -- $mapping
 --
--- 'GHC.Num' is a very old part of haskell, and is virtually unchanged since it's specification in
+-- 'GHC.Num' is a very old part of haskell, and is virtually unchanged since its specification in
 -- [haskell98](https://www.haskell.org/onlinereport/standard-prelude.html).
 --
 -- A deconstruction of 'GHC.Num.Num' and mapping to numhask.
@@ -309,7 +310,7 @@
 --
 -- '(*)' is an operator of the 'Multiplicative' class.
 --
--- 'zero' and 'one' are also introduced to the numeric heirarchy.
+-- 'zero' and 'one' are also introduced to the numeric hierarchy.
 --
 -- >    -- | Absolute value.
 -- >    abs                 :: a -> a
diff --git a/src/NumHask/Algebra/Additive.hs b/src/NumHask/Algebra/Additive.hs
--- a/src/NumHask/Algebra/Additive.hs
+++ b/src/NumHask/Algebra/Additive.hs
@@ -1,18 +1,19 @@
 -- | Additive classes
 module NumHask.Algebra.Additive
   ( Additive (..),
+    Sum (..),
     sum,
     accsum,
     Subtractive (..),
   )
 where
 
-import Data.Foldable (foldl')
 import Data.Int (Int16, Int32, Int64, Int8)
+import Data.Semigroup (Semigroup (..))
 import Data.Traversable (mapAccumL)
 import Data.Word (Word, Word16, Word32, Word64, Word8)
 import GHC.Natural (Natural (..))
-import Prelude (Bool, Double, Float, Int, Integer, fromInteger)
+import Prelude (Bool, Double, Eq, Float, Int, Integer, Ord, Show, fromInteger)
 import qualified Prelude as P
 
 -- $setup
@@ -42,12 +43,26 @@
 
   zero :: a
 
+-- | A wrapper for an Additive which distinguishes the additive structure
+newtype Sum a = Sum
+  { getSum :: a
+  }
+  deriving (Eq, Ord, Show)
+
+instance (Additive a) => P.Semigroup (Sum a) where
+  Sum a <> Sum b = Sum (a + b)
+
+instance (Additive a) => P.Monoid (Sum a) where
+  mempty = Sum zero
+
+deriving instance (Additive a) => Additive (Sum a)
+
 -- | Compute the sum of a 'Data.Foldable.Foldable'.
 --
 -- >>> sum [0..10]
 -- 55
 sum :: (Additive a, P.Foldable f) => f a -> a
-sum = foldl' (+) zero
+sum = getSum P.. P.foldMap Sum
 
 -- | Compute the accumulating sum of a 'Data.Traversable.Traversable'.
 --
diff --git a/src/NumHask/Algebra/Multiplicative.hs b/src/NumHask/Algebra/Multiplicative.hs
--- a/src/NumHask/Algebra/Multiplicative.hs
+++ b/src/NumHask/Algebra/Multiplicative.hs
@@ -1,6 +1,7 @@
 -- | Multiplicative classes
 module NumHask.Algebra.Multiplicative
   ( Multiplicative (..),
+    Product (..),
     product,
     accproduct,
     Divisive (..),
@@ -11,7 +12,7 @@
 import Data.Traversable (mapAccumL)
 import Data.Word (Word, Word16, Word32, Word64, Word8)
 import GHC.Natural (Natural (..))
-import Prelude (Double, Float, Int, Integer, fromInteger, fromRational)
+import Prelude (Double, Eq, Float, Int, Integer, Ord, Show, fromInteger, fromRational)
 import qualified Prelude as P
 
 -- $setup
@@ -41,12 +42,24 @@
 
   one :: a
 
+-- | A wrapper for an Multiplicative which distinguishes the multiplicative structure
+newtype Product a = Product
+  { getProduct :: a
+  }
+  deriving (Eq, Ord, Show)
+
+instance (Multiplicative a) => P.Semigroup (Product a) where
+  Product a <> Product b = Product (a * b)
+
+instance (Multiplicative a) => P.Monoid (Product a) where
+  mempty = Product one
+
 -- | Compute the product of a 'Data.Foldable.Foldable'.
 --
 -- >>> product [1..5]
 -- 120
 product :: (Multiplicative a, P.Foldable f) => f a -> a
-product = P.foldr (*) one
+product = getProduct P.. P.foldMap Product
 
 -- | Compute the accumulating product of a 'Data.Traversable.Traversable'.
 --
diff --git a/src/NumHask/Prelude.hs b/src/NumHask/Prelude.hs
--- a/src/NumHask/Prelude.hs
+++ b/src/NumHask/Prelude.hs
@@ -57,7 +57,7 @@
 import Data.Function hiding (id, (.))
 import Data.Kind
 import Data.Maybe
-import Data.Semigroup
+import Data.Semigroup hiding (Product (..), Sum (..))
 import Data.Traversable
 import GHC.Exts
 import GHC.Generics