diff --git a/CHANGELOG.md b/CHANGELOG.md
index 827bdaa8..fd1f5eb0 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -1,5 +1,11 @@
 # Change Log
 
+# Circa 2022.10.03 (pre release)
+
+- Added `Semigroup` and `Monoid` instances for `STM` and `WrappedSTM` monads
+- Added `MArray` instance for `WrappedSTM` monad
+- Added `MonadFix` instance for `STM`
+
 # Circa 2022.09.27 (pre release)
 
 - Module structure of `MonadSTM` changed to follow `stm` package structure.
diff --git a/io-classes/src/Control/Monad/Class/MonadSTM/Internal.hs b/io-classes/src/Control/Monad/Class/MonadSTM/Internal.hs
index 61b4a611..1dfffdd0 100644
--- a/io-classes/src/Control/Monad/Class/MonadSTM/Internal.hs
+++ b/io-classes/src/Control/Monad/Class/MonadSTM/Internal.hs
@@ -1319,6 +1319,18 @@ deriving instance MonadSTM m => Monad       (WrappedSTM t r m)
 deriving instance MonadSTM m => Alternative (WrappedSTM t r m)
 deriving instance MonadSTM m => MonadPlus   (WrappedSTM t r m)
 
+instance ( Semigroup a, MonadSTM m ) => Semigroup (WrappedSTM t r m a) where
+    a <> b = (<>) <$> a <*> b
+instance ( Monoid a, MonadSTM m )    => Monoid (WrappedSTM t r m a) where
+    mempty = pure mempty
+
+instance ( MonadSTM m, MArray e a (STM m) ) => MArray e a (WrappedSTM t r m) where
+    getBounds         = WrappedSTM . getBounds
+    getNumElements    = WrappedSTM . getNumElements
+    unsafeRead arr    = WrappedSTM . unsafeRead arr
+    unsafeWrite arr i = WrappedSTM . unsafeWrite arr i
+
+
 -- note: this (and the following) instance requires 'UndecidableInstances'
 -- extension because it violates 3rd Paterson condition, however `STM m` will
 -- resolve to a concrete type of kind (Type -> Type), and thus no larger than
diff --git a/io-sim/src/Control/Monad/IOSim/Internal.hs b/io-sim/src/Control/Monad/IOSim/Internal.hs
index 71f8f87d..9dc62d97 100644
--- a/io-sim/src/Control/Monad/IOSim/Internal.hs
+++ b/io-sim/src/Control/Monad/IOSim/Internal.hs
@@ -1008,6 +1008,19 @@ execAtomically !time !tid !tlbl !nextVid0 action0 k0 =
         trace <- go ctl read written writtenSeq createdSeq nextVid k
         return $ SimTrace time tid tlbl (EventLog x) trace
 
+      LiftSTStm st k ->
+        {-# SCC "schedule.LiftSTStm" #-} do
+        x <- strictToLazyST st
+        go ctl read written writtenSeq createdSeq nextVid (k x)
+
+      FixStm f k ->
+        {-# SCC "execAtomically.go.FixStm" #-} do
+        r <- newSTRef (throw NonTermination)
+        x <- unsafeInterleaveST $ readSTRef r
+        let k' = unSTM (f x) $ \x' ->
+                    LiftSTStm (lazyToStrictST (writeSTRef r x')) (\() -> k x')
+        go ctl read written writtenSeq createdSeq nextVid k'
+
       where
         localInvariant =
             Map.keysSet written
diff --git a/io-sim/src/Control/Monad/IOSim/Types.hs b/io-sim/src/Control/Monad/IOSim/Types.hs
index f56539db..0e1c0e89 100644
--- a/io-sim/src/Control/Monad/IOSim/Types.hs
+++ b/io-sim/src/Control/Monad/IOSim/Types.hs
@@ -178,6 +178,12 @@ data SimA s a where
 
 newtype STM s a = STM { unSTM :: forall r. (a -> StmA s r) -> StmA s r }
 
+instance Semigroup a => Semigroup (STM s a) where
+    a <> b = (<>) <$> a <*> b
+
+instance Monoid a => Monoid (STM s a) where
+    mempty = pure mempty
+
 runSTM :: STM s a -> StmA s a
 runSTM (STM k) = k ReturnStm
 
@@ -199,6 +205,9 @@ data StmA s a where
                -> (Maybe a -> a -> ST s TraceValue)
                -> StmA s b -> StmA s b
 
+  LiftSTStm    :: StrictST.ST s a -> (a -> StmA s b) -> StmA s b
+  FixStm       :: (x -> STM s x) -> (x -> StmA s r) -> StmA s r
+
 -- Exported type
 type STMSim = STM
 
@@ -291,6 +300,9 @@ instance Alternative (STM s) where
 
 instance MonadPlus (STM s) where
 
+instance MonadFix (STM s) where
+    mfix f = STM $ oneShot $ \k -> FixStm f k
+
 instance MonadSay (IOSim s) where
   say msg = IOSim $ oneShot $ \k -> Say msg (k ())
 
diff --git a/io-sim/src/Control/Monad/IOSimPOR/Internal.hs b/io-sim/src/Control/Monad/IOSimPOR/Internal.hs
index 7f244371..62e55ec7 100644
--- a/io-sim/src/Control/Monad/IOSimPOR/Internal.hs
+++ b/io-sim/src/Control/Monad/IOSimPOR/Internal.hs
@@ -1261,6 +1261,19 @@ execAtomically time tid tlbl nextVid0 action0 k0 =
         -- TODO: step
         return $ SimPORTrace time tid (-1) tlbl (EventLog x) trace
 
+      LiftSTStm st k ->
+        {-# SCC "schedule.LiftSTStm" #-} do
+        x <- strictToLazyST st
+        go ctl read written writtenSeq createdSeq nextVid (k x)
+
+      FixStm f k ->
+        {-# SCC "execAtomically.go.FixStm" #-} do
+        r <- newSTRef (throw NonTermination)
+        x <- unsafeInterleaveST $ readSTRef r
+        let k' = unSTM (f x) $ \x' ->
+                    LiftSTStm (lazyToStrictST (writeSTRef r x')) (\() -> k x')
+        go ctl read written writtenSeq createdSeq nextVid k'
+
       where
         localInvariant =
             Map.keysSet written
diff --git a/io-sim/test/Test/IOSim.hs b/io-sim/test/Test/IOSim.hs
index 4ae7658a..fc0316fc 100644
--- a/io-sim/test/Test/IOSim.hs
+++ b/io-sim/test/Test/IOSim.hs
@@ -139,12 +139,18 @@ tests =
     [ testProperty "Reference vs IO"    prop_stm_referenceIO
     , testProperty "Reference vs Sim"   prop_stm_referenceSim
     ]
-  , testGroup "MonadFix instance"
-    [ testProperty "purity"     prop_mfix_purity
-    , testProperty "purity2"    prop_mfix_purity_2
-    , testProperty "tightening" prop_mfix_left_shrinking
-    , testProperty "lazy"       prop_mfix_lazy
-    , testProperty "recdata"    prop_mfix_recdata
+  , testGroup "MonadFix instances"
+    [ testGroup "IOSim"
+      [ testProperty "purity"     prop_mfix_purity_IOSim
+      , testProperty "purity2"    prop_mfix_purity_2
+      , testProperty "tightening" prop_mfix_left_shrinking_IOSim
+      , testProperty "lazy"       prop_mfix_lazy
+      , testProperty "recdata"    prop_mfix_recdata
+      ]
+    , testGroup "STM"
+      [ testProperty "purity"     prop_mfix_purity_STM
+      , testProperty "tightening" prop_mfix_left_shrinking_STM
+      ]
     ]
   -- NOTE: Most of the tests below only work because the io-sim
   -- scheduler works the way it does.
@@ -592,15 +598,18 @@ test_wakeup_order = do
 
 -- | Purity demands that @mfix (return . f) = return (fix f)@.
 --
-prop_mfix_purity :: Positive Int -> Bool
-prop_mfix_purity (Positive n) =
-       runSimOrThrow
-         (mfix (return . factorial)) n
-    == fix factorial n
+prop_mfix_purity_m :: forall m. MonadFix m => Positive Int -> m Bool
+prop_mfix_purity_m (Positive n) =
+    (== fix factorial n) . ($ n) <$> mfix (return . factorial)
   where
     factorial :: (Int -> Int) -> Int -> Int
     factorial = \rec_ k -> if k <= 1 then 1 else k * rec_ (k - 1)
 
+prop_mfix_purity_IOSim :: Positive Int -> Bool
+prop_mfix_purity_IOSim a = runSimOrThrow $ prop_mfix_purity_m a
+
+prop_mfix_purity_STM:: Positive Int -> Bool
+prop_mfix_purity_STM a = runSimOrThrow $ atomically $ prop_mfix_purity_m a
 
 prop_mfix_purity_2 :: [Positive Int] -> Bool
 prop_mfix_purity_2 as =
@@ -634,12 +643,12 @@ prop_mfix_purity_2 as =
                       (realToFrac `map` as')
 
 
-prop_mfix_left_shrinking
+prop_mfix_left_shrinking_IOSim
     :: Int
     -> NonNegative Int
     -> Positive Int
     -> Bool
-prop_mfix_left_shrinking n (NonNegative d) (Positive i) =
+prop_mfix_left_shrinking_IOSim n (NonNegative d) (Positive i) =
    let mn :: IOSim s Int
        mn = do say ""
                threadDelay (realToFrac d)
@@ -657,6 +666,25 @@ prop_mfix_left_shrinking n (NonNegative d) (Positive i) =
               threadDelay (realToFrac d) $> a : rec_)))
 
 
+prop_mfix_left_shrinking_STM
+    :: Int
+    -> Positive Int
+    -> Bool
+prop_mfix_left_shrinking_STM n (Positive i) =
+   let mn :: STMSim s Int
+       mn = do say ""
+               return n
+   in
+        take i
+        (runSimOrThrow $ atomically $
+          mfix (\rec_ -> mn >>= \a -> return $ a : rec_))
+      ==
+        take i
+        (runSimOrThrow $ atomically $
+          mn >>= \a ->
+            (mfix (\rec_ -> return $ a : rec_)))
+
+
 
 -- | 'Example 8.2.1' in 'Value Recursion in Monadic Computations'
 -- <https://leventerkok.github.io/papers/erkok-thesis.pdf>
@@ -756,7 +784,7 @@ probeOutput probe x = atomically (modifyTVar probe (x:))
 
 
 --
--- Syncronous exceptions
+-- Synchronous exceptions
 --
 
 unit_catch_0, unit_catch_1, unit_catch_2, unit_catch_3, unit_catch_4,