diff --git a/Data/Semigroup.hs b/Data/Semigroup.hs
--- a/Data/Semigroup.hs
+++ b/Data/Semigroup.hs
@@ -41,6 +41,7 @@
 import Data.Traversable
 import Data.List.NonEmpty
 
+import Numeric.Natural.Internal
 import Data.Sequence (Seq, (><))
 import Data.Set (Set)
 import Data.IntSet (IntSet)
@@ -61,12 +62,29 @@
     go b (c:cs) = b <> go c cs
     go b []     = b
 
+  -- replicate1p n r = replicate (1 + n) r
+  replicate1p :: Whole n => n -> a -> a
+  replicate1p y0 x0 = f x0 (1 Prelude.+ y0)
+    where
+      f x y
+        | even y = f (x <> x) (y `quot` 2)
+        | y == 1 = x
+        | otherwise = g (x <> x) (unsafePred y  `quot` 2) x
+      g x y z
+        | even y = g (x <> x) (y `quot` 2) z
+        | y == 1 = x <> z
+        | otherwise = g (x <> x) (unsafePred y `quot` 2) (x <> z)
+  {-# INLINE replicate1p #-}
+
+
 instance Semigroup () where
   _ <> _ = ()
   sconcat _ = ()
+  replicate1p _ _ = ()
 
 instance Semigroup b => Semigroup (a -> b) where
   f <> g = \a -> f a <> g a
+  replicate1p n f e = replicate1p n (f e)
 
 instance Semigroup [a] where
   (<>) = (++)
@@ -82,27 +100,34 @@
 
 instance (Semigroup a, Semigroup b) => Semigroup (a, b) where
   (a,b) <> (a',b') = (a<>a',b<>b')
+  replicate1p n (a,b) = (replicate1p n a, replicate1p n b)
   
 instance (Semigroup a, Semigroup b, Semigroup c) => Semigroup (a, b, c) where
   (a,b,c) <> (a',b',c') = (a<>a',b<>b',c<>c')
+  replicate1p n (a,b,c) = (replicate1p n a, replicate1p n b, replicate1p n c)
 
 instance (Semigroup a, Semigroup b, Semigroup c, Semigroup d) => Semigroup (a, b, c, d) where
   (a,b,c,d) <> (a',b',c',d') = (a<>a',b<>b',c<>c',d<>d')
+  replicate1p n (a,b,c,d) = (replicate1p n a, replicate1p n b, replicate1p n c, replicate1p n d)
 
 instance (Semigroup a, Semigroup b, Semigroup c, Semigroup d, Semigroup e) => Semigroup (a, b, c, d, e) where
   (a,b,c,d,e) <> (a',b',c',d',e') = (a<>a',b<>b',c<>c',d<>d',e<>e')
+  replicate1p n (a,b,c,d,e) = (replicate1p n a, replicate1p n b, replicate1p n c, replicate1p n d, replicate1p n e)
 
 instance Semigroup a => Semigroup (Dual a) where
   Dual a <> Dual b = Dual (b <> a)
+  replicate1p n (Dual a) = Dual (replicate1p n a)
 
 instance Semigroup (Endo a) where
   Endo f <> Endo g = Endo (f . g) 
 
 instance Semigroup All where
   All a <> All b = All (a && b)
+  replicate1p _ a = a 
 
 instance Semigroup Any where
   Any a <> Any b = Any (a || b)
+  replicate1p _ a = a 
 
 instance Num a => Semigroup (Sum a) where
   Sum a <> Sum b = Sum (a + b)
@@ -113,10 +138,12 @@
 instance Semigroup (Monoid.First a) where
   Monoid.First Nothing <> b = b
   a                    <> _ = a
+  replicate1p _ a = a 
 
 instance Semigroup (Monoid.Last a) where
   a <> Monoid.Last Nothing = a
   _ <> b                   = b
+  replicate1p _ a = a 
 
 instance Semigroup (NonEmpty a) where
   (a :| as) <> ~(b :| bs) = a :| (as ++ b : bs)
@@ -130,6 +157,7 @@
 
 instance Ord a => Semigroup (Min a) where
   Min a <> Min b = Min (a `min` b)
+  replicate1p _ a = a 
 
 instance (Ord a, Bounded a) => Monoid (Min a) where
   mempty = maxBound
@@ -144,6 +172,7 @@
 
 instance Ord a => Semigroup (Max a) where
   Max a <> Max b = Max (a `max` b)
+  replicate1p _ a = a 
 
 instance (Ord a, Bounded a) => Monoid (Max a) where
   mempty = minBound
@@ -160,6 +189,7 @@
 
 instance Semigroup (First a) where
   a <> _ = a
+  replicate1p _ a = a 
 
 -- | Use @'Option' ('Last' a)@ -- to get the behavior of 'Data.Monoid.Last'
 newtype Last a = Last { getLast :: a } deriving 
@@ -171,6 +201,7 @@
 
 instance Semigroup (Last a) where
   _ <> b = b
+  replicate1p _ a = a 
 
 -- (==)/XNOR on Bool forms a 'Semigroup', but has no good name
 
@@ -255,12 +286,16 @@
 
 instance Semigroup IntSet where
   (<>) = mappend
+  replicate1p _ a = a 
 
 instance Ord a => Semigroup (Set a) where
   (<>) = mappend
+  replicate1p _ a = a 
 
 instance Semigroup (IntMap v) where
   (<>) = mappend
+  replicate1p _ a = a 
 
 instance Ord k => Semigroup (Map k v) where
   (<>) = mappend
+  replicate1p _ a = a 
diff --git a/Numeric/Natural.hs b/Numeric/Natural.hs
new file mode 100644
--- /dev/null
+++ b/Numeric/Natural.hs
@@ -0,0 +1,6 @@
+module Numeric.Natural 
+  ( Natural
+  , Whole(toNatural)
+  ) where
+
+import Numeric.Natural.Internal
diff --git a/Numeric/Natural/Internal.hs b/Numeric/Natural/Internal.hs
new file mode 100644
--- /dev/null
+++ b/Numeric/Natural/Internal.hs
@@ -0,0 +1,96 @@
+module Numeric.Natural.Internal
+  ( Natural(..)
+  , Whole(..)
+  ) where
+
+import Data.Word
+import Data.Bits
+import Text.Read
+import Data.Ix
+
+newtype Natural = Natural { runNatural :: Integer } deriving (Eq,Ord,Ix)
+
+instance Show Natural where
+  showsPrec d (Natural n) = showsPrec d n
+
+instance Read Natural where
+  readPrec = fmap Natural $ step readPrec
+
+instance Num Natural where
+  Natural n + Natural m = Natural (n + m)
+  Natural n * Natural m = Natural (n * m)
+  Natural n - Natural m | result < 0 = error "Natural.(-): negative result"
+                        | otherwise  = Natural result
+	where result = n - m
+  abs (Natural n) = Natural n
+  signum (Natural n) = Natural (signum n)
+  fromInteger n 
+    | n >= 0 = Natural n
+    | otherwise = error "Natural.fromInteger: negative"
+
+instance Bits Natural where
+  Natural n .&. Natural m = Natural (n .&. m)
+  Natural n .|. Natural m = Natural (n .|. m)
+  xor (Natural n) (Natural m) = Natural (xor n m)
+  complement _ = error "Bits.complement: Natural complement undefined"
+  shift (Natural n) = Natural . shift n
+  rotate (Natural n) = Natural . rotate n
+  bit = Natural . bit
+  setBit (Natural n) = Natural . setBit n
+  clearBit (Natural n) = Natural . clearBit n
+  complementBit (Natural n) = Natural . complementBit n
+  testBit = testBit . runNatural 
+  bitSize = bitSize . runNatural
+  isSigned _ = False
+  shiftL (Natural n) = Natural . shiftL n
+  shiftR (Natural n) = Natural . shiftR n
+  rotateL (Natural n) = Natural . rotateL n
+  rotateR (Natural n) = Natural . rotateR n
+
+instance Real Natural where
+  toRational (Natural a) = toRational a
+
+instance Enum Natural where
+  pred (Natural 0) = error "Natural.pred: 0"
+  pred (Natural n) = Natural (pred n)
+  succ (Natural n) = Natural (succ n)
+  fromEnum (Natural n) = fromEnum n
+  toEnum n | n < 0     = error "Natural.toEnum: negative"
+           | otherwise = Natural (toEnum n)
+
+instance Integral Natural where
+  quot (Natural a) (Natural b) = Natural (quot a b)
+  rem (Natural a) (Natural b) = Natural (rem a b)
+  div (Natural a) (Natural b) = Natural (div a b)
+  mod (Natural a) (Natural b) = Natural (mod a b)
+  divMod (Natural a) (Natural b) = (Natural q, Natural r) where (q,r) = divMod a b
+  quotRem (Natural a) (Natural b) = (Natural q, Natural r) where (q,r) = quotRem a b
+  toInteger = runNatural
+
+class Integral n => Whole n where
+  toNatural :: n -> Natural
+  unsafePred :: n -> n
+
+instance Whole Word where
+  toNatural = Natural . toInteger
+  unsafePred n = n - 1
+
+instance Whole Word8 where
+  toNatural = Natural . toInteger
+  unsafePred n = n - 1
+
+instance Whole Word16 where
+  toNatural = Natural . toInteger
+  unsafePred n = n - 1
+
+instance Whole Word32 where
+  toNatural = Natural . toInteger
+  unsafePred n = n - 1
+
+instance Whole Word64 where
+  toNatural = Natural . toInteger
+  unsafePred n = n - 1
+
+instance Whole Natural where
+  toNatural = id
+  unsafePred (Natural n) = Natural (n - 1)
diff --git a/semigroups.cabal b/semigroups.cabal
--- a/semigroups.cabal
+++ b/semigroups.cabal
@@ -1,6 +1,6 @@
 name:          semigroups
 category:      Algebra, Data, Data Structures, Math
-version:       0.6.1
+version:       0.7.0
 license:       BSD3
 cabal-version: >= 1.6
 license-file:  LICENSE
@@ -36,3 +36,5 @@
   exposed-modules:
     Data.Semigroup
     Data.List.NonEmpty
+    Numeric.Natural
+    Numeric.Natural.Internal