diff --git a/changelog.md b/changelog.md
--- a/changelog.md
+++ b/changelog.md
@@ -1,3 +1,7 @@
+0.3.0.3
+
+* added some more functions.
+
 0.3.0.2
 
 * fix bug in `zero` and `one` prisms.
diff --git a/natural.cabal b/natural.cabal
--- a/natural.cabal
+++ b/natural.cabal
@@ -1,7 +1,7 @@
 -- documentation, see http://haskell.org/cabal/users-guide/
 
 name:                natural
-version:             0.3.0.2
+version:             0.3.0.3
 synopsis:            Natural number
 description:       
   <<http://i.imgur.com/uZnp9ke.png>>
@@ -18,7 +18,7 @@
 cabal-version:       >=1.10
 homepage:            https://github.com/qfpl/natural
 bug-reports:         https://github.com/qfpl/natural/issues
-tested-with:         GHC == 7.10.3, GHC == 8.0.2, GHC == 8.2.2, GHC == 8.4.3
+tested-with:         GHC == 7.10.3, GHC == 8.0.2, GHC == 8.2.2, GHC == 8.4.3, GHC == 8.6.1
 
 source-repository   head
   type:             git
@@ -26,7 +26,7 @@
 
 library
   exposed-modules:     Natural
-  build-depends:       base >=4.8 && <4.12
+  build-depends:       base >=4.8 && <4.13
                      , lens >=4.15 && < 4.18
                      , semigroupoids >= 5 && < 6
   hs-source-dirs:      src
@@ -36,8 +36,8 @@
     build-depends:     semigroups >= 0.9 && < 0.19
 
 test-suite             tests
-  build-depends:       QuickCheck >=2.9.2 && <2.12
-                     , base >=4.8 && <4.12
+  build-depends:       QuickCheck >=2.9.2 && <2.13
+                     , base >=4.8 && <4.13
                      , checkers >=0.4.6 && <0.5
                      , natural
                      , hedgehog >=0.5 && <0.7
diff --git a/src/Natural.hs b/src/Natural.hs
--- a/src/Natural.hs
+++ b/src/Natural.hs
@@ -14,6 +14,10 @@
 , zero'
 , successor
 , successor'
+, plus
+, multiply
+, square
+, zeroOr
 , length
 , replicate
 , take
@@ -37,6 +41,10 @@
 , successor1
 , successor1'
 , successorW
+, plus1
+, multiply1
+, square1
+, oneOr
 , notZero
 , length1
 , replicate1
@@ -50,6 +58,8 @@
 , elemIndex1
 , minus1
 , list1
+, plusone
+, minusone
 ) where
 
 import Control.Applicative(Const)
@@ -65,14 +75,14 @@
 import Data.List(iterate, zip, filter, map, repeat)
 import Data.List.NonEmpty(NonEmpty((:|)))
 import qualified Data.List.NonEmpty as NonEmpty(iterate, zip, filter)
-import Data.Maybe(listToMaybe, Maybe(Just, Nothing))
+import Data.Maybe(listToMaybe, Maybe(Just, Nothing), fromMaybe)
 import Data.Monoid(Monoid(mappend, mempty))
 import Data.Ord(Ord((<)), min, max)
 import Data.Semigroup(Semigroup((<>)))
 import Data.Semigroup.Foldable(Foldable1(foldMap1))
 import Data.Tuple(fst, snd)
 import Data.Word(Word)
-import Prelude(Show, Integral, Integer, (-), (+), (*), fromIntegral)
+import Prelude(Show, Integral, Integer, (-), (+), (*), (^), fromIntegral)
 
 newtype Natural =
   Natural
@@ -255,6 +265,34 @@
 successor' =
   (successor #)
 
+plus ::
+  Natural
+  -> Natural
+  -> Natural
+plus =
+  (<>)
+
+multiply ::
+  Natural
+  -> Natural
+  -> Natural
+multiply x y =
+  (_Wrapped # x <> (_Wrapped # y :: ProductNatural)) ^. _Wrapped
+
+square ::
+  Natural
+  -> Natural
+  -> Natural
+square (Natural x) (Natural y) =
+  Natural (x ^ y)
+
+zeroOr ::
+  AsNatural a =>
+  a
+  -> Natural
+zeroOr n =
+  fromMaybe zero' (n ^? _Natural)
+
 length ::
   Foldable f =>
   f a
@@ -543,6 +581,34 @@
     (\(Natural n) -> Positive (n + 1))
     (\(Positive n) -> Natural (n - 1))
 
+plus1 ::
+  Positive
+  -> Positive
+  -> Positive
+plus1 x y =
+  (_Wrapped # x <> (_Wrapped # y :: SumPositive)) ^. _Wrapped
+
+multiply1 ::
+  Positive
+  -> Positive
+  -> Positive
+multiply1 =
+  (<>)
+
+square1 ::
+  Positive
+  -> Positive
+  -> Positive
+square1 (Positive x) (Positive y) =
+  Positive (x ^ y)
+
+oneOr ::
+  AsPositive a =>
+  a
+  -> Positive
+oneOr n =
+  fromMaybe one' (n ^? _Positive)
+
 notZero ::
   Prism'
     Natural
@@ -639,3 +705,15 @@
   iso
     (\n -> replicate1 n ())
     length1
+
+plusone ::
+  Natural
+  -> Positive
+plusone =
+  (^. successorW)
+
+minusone ::
+  Positive
+  -> Natural
+minusone =
+  (successorW #)