diff --git a/Changelog.md b/Changelog.md
index bb38351d..6b785d6d 100644
--- a/Changelog.md
+++ b/Changelog.md
@@ -1,6 +1,15 @@
 ## Unreleased
 
 ### Breaking changes
+* Change the semantics of the Semigroup instance for `InterleavedT`, `AsyncT`
+  and `ParallelT`. Now the `<>` operation interleaves two streams for
+  `InterleavedT` (just like the now deprecated `<=>` operation which has been
+  renamed to `interleave`). For `AsyncT` `<>` now concurrently merges two
+  streams (just like the now deprecated `<|` operation which has been renamed
+  to `asyncmerge`). For `ParallelT` the `<>` operation now behaves like the
+  earlier `Alternative` operator `<|>`.
+* Change the semantics of `Alternative` instance. The `<|>` operator now has a
+  different behavior for each type. See the documentation for more details.
 * Change the type of `foldrM` to make it consistent with `foldrM` in base
 
 ### Deprecations
@@ -11,6 +20,8 @@
     * `runZipStream` to `runZipSerial`
     * `Streaming` to `IsStream`
     * `runStreaming` to `runStream`
+    * `<=>` to `interleave`
+    * `<|` to `asyncmerge`
     * `each` to `fromFoldable`
     * `scan` to `scanx`
     * `foldl` to `foldx`
diff --git a/src/Streamly.hs b/src/Streamly.hs
index 7004d5b9..be3bfe40 100644
--- a/src/Streamly.hs
+++ b/src/Streamly.hs
@@ -18,22 +18,24 @@ module Streamly
       MonadAsync
     , IsStream
 
-    -- * Product Style Composition
+    -- * General Stream Styles
     -- $product
     , SerialT
     , InterleavedT
     , AsyncT
     , ParallelT
 
-    -- * Zip Style Composition
+    -- * Zip Style Streams
     -- $zipping
     , ZipSerial
     , ZipAsync
 
-    -- * Sum Style Composition
+    -- * Type Independent Sum Operations
     -- $sum
-    , (<=>)
-    , (<|)
+    , append
+    , interleave
+    , asyncmerge
+    , parmerge
 
     -- * Transformation
     , async
@@ -78,6 +80,8 @@ module Streamly
     , runZipStream
     , StreamT
     , ZipStream
+    , (<=>)
+    , (<|)
     )
 where
 
@@ -146,18 +150,14 @@ import Control.Monad.Trans.Class (MonadTrans (..))
 -- being zipped serially whereas 'ZipAsync' produces both the elements being
 -- zipped concurrently.
 --
--- Two streams of the same type can be combined using a sum style composition
--- to generate a stream of the same type where the output stream would contain
--- all elements of both the streams. However, the sequence in which the
--- elements in the resulting stream are produced depends on the combining
--- operator. Four distinct sum style operators, '<>', '<=>', '<|' and '<|>'
--- combine two streams in different ways, each corresponding to the one of the
--- four ways of combining monadically. See the respective section below for
--- more details.
+-- Two streams of the same type can be merged using a sum style composition to
+-- generate a stream of the same type where the output stream would contain all
+-- elements of both the streams. However, the sequence or the manner
+-- (concurrent or serial) in which the elements in the resulting stream are
+-- produced depends on the type of the stream.
 --
--- Concurrent composition types 'AsyncT', 'ParallelT', 'ZipAsync' and
--- concurrent composition operators '<|' and '<|>' require the underlying monad
--- of the streaming monad transformer to be 'MonadAsync'.
+-- Concurrent composition types 'AsyncT', 'ParallelT', 'ZipAsync' require the
+-- underlying monad of the streaming monad transformer to be 'MonadAsync'.
 --
 -- For more details please see the "Streamly.Tutorial" and "Streamly.Examples"
 -- (the latter is available only when built with the 'examples' build flag).
@@ -179,37 +179,11 @@ import Control.Monad.Trans.Class (MonadTrans (..))
 -- not monads.
 
 -- $sum
---
--- Just like product style composition there are four distinct ways to combine
--- streams in sum style each directly corresponding to one of the product style
--- composition.
---
--- The standard semigroup append '<>' operator appends two streams serially,
--- this style corresponds to the 'SerialT' style of monadic composition.
---
--- @
--- main = ('toList' . 'serially' $ (return 1 <> return 2) <> (return 3 <> return 4)) >>= print
--- @
--- @
--- [1,2,3,4]
--- @
---
--- The standard 'Alternative' operator '<|>'  fairly interleaves two streams in
--- parallel, this operator corresponds to the 'ParallelT' style.
---
--- @
--- main = ('toList' . 'serially' $ (return 1 <> return 2) \<|\> (return 3 <> return 4)) >>= print
--- @
--- @
--- [1,3,2,4]
--- @
---
--- Unlike '<|', this operator cannot be used to fold infinite containers since
--- that might accumulate too many partially drained streams.  To be clear, it
--- can combine infinite streams but not infinite number of streams.
---
--- Two additional sum style composition operators that streamly introduces are
--- described below.
+-- Each stream style provides its own way of merging streams. The 'Semigroup'
+-- '<>' operation can be used to merge streams in the style of the current
+-- type. In case you want to merge streams in a particular style you can either
+-- use a type adapter to force that type of composition or alternatively use
+-- the type independent merge operations described in this section.
 
 -- $adapters
 --
diff --git a/src/Streamly/Core.hs b/src/Streamly/Core.hs
index 2f97d9ac..728b3ed0 100644
--- a/src/Streamly/Core.hs
+++ b/src/Streamly/Core.hs
@@ -24,12 +24,18 @@ module Streamly.Core
     , Stream (..)
 
     -- * Construction
-    , scons
-    , srepeat
-    , snil
+    , cons
+    , repeat
+    , nil
 
-    -- * Composition
+    -- * Semigroup Style Composition
+    , append
     , interleave
+    , asyncmerge
+    , parmerge
+
+    -- * Alternative
+    , alt
 
     -- * Concurrent Stream Vars (SVars)
     , SVar
@@ -42,10 +48,6 @@ module Streamly.Core
     , joinStreamVar2
     , fromStreamVar
     , toStreamVar
-
-    -- * Concurrent Streams
-    , parAlt
-    , parLeft
     )
 where
 
@@ -76,6 +78,7 @@ import           Data.Maybe                  (isNothing)
 import           Data.Semigroup              (Semigroup(..))
 import           Data.Set                    (Set)
 import qualified Data.Set                    as S
+import           Prelude                     hiding (repeat)
 
 ------------------------------------------------------------------------------
 -- Parent child thread communication type
@@ -215,14 +218,14 @@ newtype Stream m a =
 -- 'MonadAsync'.
 type MonadAsync m = (MonadIO m, MonadBaseControl IO m, MonadThrow m)
 
-scons :: a -> Maybe (Stream m a) -> Stream m a
-scons a r = Stream $ \_ _ yld -> yld a r
+cons :: a -> Maybe (Stream m a) -> Stream m a
+cons a r = Stream $ \_ _ yld -> yld a r
 
-srepeat :: a -> Stream m a
-srepeat a = let x = scons a (Just x) in x
+repeat :: a -> Stream m a
+repeat a = let x = cons a (Just x) in x
 
-snil :: Stream m a
-snil = Stream $ \_ stp _ -> stp
+nil :: Stream m a
+nil = Stream $ \_ stp _ -> stp
 
 ------------------------------------------------------------------------------
 -- Composing streams
@@ -237,30 +240,32 @@ snil = Stream $ \_ stp _ -> stp
 -- Semigroup
 ------------------------------------------------------------------------------
 
--- | '<>' concatenates two streams sequentially i.e. the first stream is
+-- | Concatenates two streams sequentially i.e. the first stream is
 -- exhausted completely before yielding any element from the second stream.
+append :: Stream m a -> Stream m a -> Stream m a
+append m1 m2 = go m1
+    where
+    go (Stream m) = Stream $ \_ stp yld ->
+            let stop = (runStream m2) Nothing stp yld
+                yield a Nothing  = yld a (Just m2)
+                yield a (Just r) = yld a (Just (go r))
+            in m Nothing stop yield
+
 instance Semigroup (Stream m a) where
-    m1 <> m2 = go m1
-        where
-        go (Stream m) = Stream $ \_ stp yld ->
-                let stop = (runStream m2) Nothing stp yld
-                    yield a Nothing  = yld a (Just m2)
-                    yield a (Just r) = yld a (Just (go r))
-                in m Nothing stop yield
+    (<>) = append
 
 ------------------------------------------------------------------------------
 -- Monoid
 ------------------------------------------------------------------------------
 
 instance Monoid (Stream m a) where
-    mempty = Stream $ \_ stp _ -> stp
+    mempty = nil
     mappend = (<>)
 
 ------------------------------------------------------------------------------
 -- Interleave
 ------------------------------------------------------------------------------
 
--- | Same as '<=>'.
 interleave :: Stream m a -> Stream m a -> Stream m a
 interleave m1 m2 = Stream $ \_ stp yld -> do
     let stop = (runStream m2) Nothing stp yld
@@ -603,32 +608,13 @@ joinStreamVar2 style m1 m2 = Stream $ \st stp yld ->
 -- Semigroup and Monoid style compositions for parallel actions
 ------------------------------------------------------------------------------
 
-{-
--- | Same as '<>|'.
-parAhead :: Stream m a -> Stream m a -> Stream m a
-parAhead = undefined
+{-# INLINE asyncmerge #-}
+asyncmerge :: MonadAsync m => Stream m a -> Stream m a -> Stream m a
+asyncmerge = joinStreamVar2 (SVarStyle Disjunction LIFO)
 
--- | Sequential composition similar to '<>' except that it can execute the
--- action on the right in parallel ahead of time. Returns the results in
--- sequential order like '<>' from left to right.
-(<>|) :: Stream m a -> Stream m a -> Stream m a
-(<>|) = parAhead
--}
-
--- | Same as '<|>'. Since this schedules all the composed streams fairly you
--- cannot fold infinite number of streams using this operation.
-{-# INLINE parAlt #-}
-parAlt :: MonadAsync m => Stream m a -> Stream m a -> Stream m a
-parAlt = joinStreamVar2 (SVarStyle Disjunction FIFO)
-
--- | Same as '<|'. Since this schedules the left side computation first you can
--- right fold an infinite container using this operator. However a left fold
--- will not work well as it first unpeels the whole structure before scheduling
--- a computation requiring an amount of memory proportional to the size of the
--- structure.
-{-# INLINE parLeft #-}
-parLeft :: MonadAsync m => Stream m a -> Stream m a -> Stream m a
-parLeft = joinStreamVar2 (SVarStyle Disjunction LIFO)
+{-# INLINE parmerge #-}
+parmerge :: MonadAsync m => Stream m a -> Stream m a -> Stream m a
+parmerge = joinStreamVar2 (SVarStyle Disjunction FIFO)
 
 -------------------------------------------------------------------------------
 -- Instances (only used for deriving newtype instances)
@@ -655,17 +641,18 @@ instance Monad m => Monad (Stream m) where
 -- Alternative & MonadPlus
 ------------------------------------------------------------------------------
 
--- | `empty` represents an action that takes non-zero time to complete.  Since
--- all actions take non-zero time, an `Alternative` composition ('<|>') is a
--- monoidal composition executing all actions in parallel, it is similar to
--- '<>' except that it runs all the actions in parallel and interleaves their
--- results fairly.
+alt :: Stream m a -> Stream m a -> Stream m a
+alt m1 m2 = Stream $ \_ stp yld ->
+    let stop  = runStream m2 Nothing stp yld
+        yield = yld
+    in runStream m1 Nothing stop yield
+
 instance MonadAsync m => Alternative (Stream m) where
-    empty = mempty
-    (<|>) = parAlt
+    empty = nil
+    (<|>) = alt
 
 instance MonadAsync m => MonadPlus (Stream m) where
-    mzero = empty
+    mzero = nil
     mplus = (<|>)
 
 -------------------------------------------------------------------------------
diff --git a/src/Streamly/Prelude.hs b/src/Streamly/Prelude.hs
index a453b8a5..59f0ada4 100644
--- a/src/Streamly/Prelude.hs
+++ b/src/Streamly/Prelude.hs
@@ -100,8 +100,9 @@ import           Prelude hiding              (filter, drop, dropWhile, take,
 import qualified Prelude
 import qualified System.IO as IO
 
-import           Streamly.Core
-import           Streamly.Streams hiding (runStream)
+import qualified Streamly.Core as S
+import           Streamly.Core (Stream(Stream))
+import           Streamly.Streams
 
 ------------------------------------------------------------------------------
 -- Construction
@@ -141,7 +142,7 @@ each = fromFoldable
 iterate :: IsStream t => (a -> a) -> a -> t m a
 iterate step = fromStream . go
     where
-    go s = scons s (Just (go (step s)))
+    go s = S.cons s (Just (go (step s)))
 
 -- | Iterate a monadic function from a seed value, streaming the results forever
 iterateM :: (IsStream t, Monad m) => (a -> m a) -> a -> t m a
@@ -180,7 +181,7 @@ foldr step acc m = go (toStream m)
         let stop = return acc
             yield a Nothing  = return (step a acc)
             yield a (Just x) = go x >>= \b -> return (step a b)
-        in (runStream m1) Nothing stop yield
+        in (S.runStream m1) Nothing stop yield
 
 -- | Lazy right fold with a monadic step function. For example, to fold a
 -- stream into a list:
@@ -197,7 +198,7 @@ foldrM step acc m = go (toStream m)
         let stop = return acc
             yield a Nothing  = step a acc
             yield a (Just x) = (go x) >>= (step a)
-        in (runStream m1) Nothing stop yield
+        in (S.runStream m1) Nothing stop yield
 
 -- | Strict left scan with an extraction function. Like 'scanl'', but applies a
 -- user supplied extraction function (the third argument) at each step. This is
@@ -213,7 +214,7 @@ scanx step begin done m = cons (done begin) $ fromStream $ go (toStream m) begin
             yield a (Just x) =
                 let s = step acc a
                 in yld (done s) (Just (go x s))
-        in runStream m1 Nothing stop yield
+        in S.runStream m1 Nothing stop yield
 
 {-# DEPRECATED scan "Please use scanx instead." #-}
 scan :: IsStream t => (x -> a -> x) -> x -> (x -> b) -> t m a -> t m b
@@ -240,7 +241,7 @@ foldx step begin done m = get $ go (toStream m) begin
     get m1 =
         let yield a Nothing  = return $ done a
             yield _ _ = undefined
-         in (runStream m1) Nothing undefined yield
+         in (S.runStream m1) Nothing undefined yield
 
     -- Note, this can be implemented by making a recursive call to "go",
     -- however that is more expensive because of unnecessary recursion
@@ -252,8 +253,8 @@ foldx step begin done m = get $ go (toStream m) begin
                 let s = step acc a
                 in case r of
                     Nothing -> yld s Nothing
-                    Just x -> (runStream (go x s)) Nothing undefined yld
-        in (runStream m1) Nothing stop yield
+                    Just x -> (S.runStream (go x s)) Nothing undefined yld
+        in (S.runStream m1) Nothing stop yield
 
 {-# DEPRECATED foldl "Please use foldx instead." #-}
 foldl :: (IsStream t, Monad m)
@@ -275,7 +276,7 @@ foldxM step begin done m = go begin (toStream m)
         let stop = acc >>= done
             yield a Nothing  = acc >>= \b -> step b a >>= done
             yield a (Just x) = acc >>= \b -> go (step b a) x
-         in (runStream m1) Nothing stop yield
+         in (S.runStream m1) Nothing stop yield
 
 {-# DEPRECATED foldlM "Please use foldxM instead." #-}
 foldlM :: (IsStream t, Monad m)
@@ -294,7 +295,7 @@ uncons m =
     let stop = return Nothing
         yield a Nothing  = return (Just (a, nil))
         yield a (Just x) = return (Just (a, fromStream x))
-    in (runStream (toStream m)) Nothing stop yield
+    in (S.runStream (toStream m)) Nothing stop yield
 
 -- | Write a stream of Strings to an IO Handle.
 toHandle :: (IsStream t, MonadIO m) => IO.Handle -> t m String -> m ()
@@ -304,7 +305,7 @@ toHandle h m = go (toStream m)
         let stop = return ()
             yield a Nothing  = liftIO (IO.hPutStrLn h a)
             yield a (Just x) = liftIO (IO.hPutStrLn h a) >> go x
-        in (runStream m1) Nothing stop yield
+        in (S.runStream m1) Nothing stop yield
 
 ------------------------------------------------------------------------------
 -- Special folds
@@ -323,7 +324,7 @@ take n m = fromStream $ go n (toStream m)
     go n1 m1 = Stream $ \ctx stp yld ->
         let yield a Nothing  = yld a Nothing
             yield a (Just x) = yld a (Just (go (n1 - 1) x))
-        in if n1 <= 0 then stp else (runStream m1) ctx stp yield
+        in if n1 <= 0 then stp else (S.runStream m1) ctx stp yield
 
 -- | Include only those elements that pass a predicate.
 {-# INLINE filter #-}
@@ -334,8 +335,8 @@ filter p m = fromStream $ go (toStream m)
         let yield a Nothing  | p a       = yld a Nothing
                              | otherwise = stp
             yield a (Just x) | p a       = yld a (Just (go x))
-                             | otherwise = (runStream x) ctx stp yield
-         in (runStream m1) ctx stp yield
+                             | otherwise = (S.runStream x) ctx stp yield
+         in (S.runStream m1) ctx stp yield
 
 -- | End the stream as soon as the predicate fails on an element.
 {-# INLINE takeWhile #-}
@@ -347,7 +348,7 @@ takeWhile p m = fromStream $ go (toStream m)
                              | otherwise = stp
             yield a (Just x) | p a       = yld a (Just (go x))
                              | otherwise = stp
-         in (runStream m1) ctx stp yield
+         in (S.runStream m1) ctx stp yield
 
 -- | Discard first 'n' elements from the stream and take the rest.
 drop :: IsStream t => Int -> t m a -> t m a
@@ -355,11 +356,11 @@ drop n m = fromStream $ go n (toStream m)
     where
     go n1 m1 = Stream $ \ctx stp yld ->
         let yield _ Nothing  = stp
-            yield _ (Just x) = (runStream $ go (n1 - 1) x) ctx stp yld
+            yield _ (Just x) = (S.runStream $ go (n1 - 1) x) ctx stp yld
         -- Somehow "<=" check performs better than a ">"
         in if n1 <= 0
-           then (runStream m1) ctx stp yld
-           else (runStream m1) ctx stp yield
+           then (S.runStream m1) ctx stp yld
+           else (S.runStream m1) ctx stp yield
 
 -- | Drop elements in the stream as long as the predicate succeeds and then
 -- take the rest of the stream.
@@ -370,9 +371,9 @@ dropWhile p m = fromStream $ go (toStream m)
     go m1 = Stream $ \ctx stp yld ->
         let yield a Nothing  | p a       = stp
                              | otherwise = yld a Nothing
-            yield a (Just x) | p a       = (runStream x) ctx stp yield
+            yield a (Just x) | p a       = (S.runStream x) ctx stp yield
                              | otherwise = yld a (Just x)
-         in (runStream m1) ctx stp yield
+         in (S.runStream m1) ctx stp yield
 
 -- | Determine whether all elements of a stream satisfy a predicate.
 all :: (IsStream t, Monad m) => (a -> Bool) -> t m a -> m Bool
@@ -383,7 +384,7 @@ all p m = go (toStream m)
                              | otherwise = return False
             yield a (Just x) | p a       = go x
                              | otherwise = return False
-         in (runStream m1) Nothing (return True) yield
+         in (S.runStream m1) Nothing (return True) yield
 
 -- | Determine whether any of the elements of a stream satisfy a predicate.
 any :: (IsStream t, Monad m) => (a -> Bool) -> t m a -> m Bool
@@ -394,7 +395,7 @@ any p m = go (toStream m)
                              | otherwise = return False
             yield a (Just x) | p a       = return True
                              | otherwise = go x
-         in (runStream m1) Nothing (return False) yield
+         in (S.runStream m1) Nothing (return False) yield
 
 -- | Determine the sum of all elements of a stream of numbers
 sum :: (IsStream t, Monad m, Num a) => t m a -> m a
@@ -409,7 +410,7 @@ head :: (IsStream t, Monad m) => t m a -> m (Maybe a)
 head m =
     let stop      = return Nothing
         yield a _ = return (Just a)
-    in (runStream (toStream m)) Nothing stop yield
+    in (S.runStream (toStream m)) Nothing stop yield
 
 -- | Extract all but the first element of the stream, if any.
 tail :: (IsStream t, Monad m) => t m a -> m (Maybe (t m a))
@@ -417,7 +418,7 @@ tail m =
     let stop             = return Nothing
         yield _ Nothing  = return $ Just nil
         yield _ (Just t) = return $ Just $ fromStream t
-    in (runStream (toStream m)) Nothing stop yield
+    in (S.runStream (toStream m)) Nothing stop yield
 
 -- | Extract the last element of the stream, if any.
 {-# INLINE last #-}
@@ -429,7 +430,7 @@ null :: (IsStream t, Monad m) => t m a -> m Bool
 null m =
     let stop      = return True
         yield _ _ = return False
-    in (runStream (toStream m)) Nothing stop yield
+    in (S.runStream (toStream m)) Nothing stop yield
 
 -- | Determine whether an element is present in the stream.
 elem :: (IsStream t, Monad m, Eq a) => a -> t m a -> m Bool
@@ -439,7 +440,7 @@ elem e m = go (toStream m)
         let stop            = return False
             yield a Nothing = return (a == e)
             yield a (Just x) = if a == e then return True else go x
-        in (runStream m1) Nothing stop yield
+        in (S.runStream m1) Nothing stop yield
 
 -- | Determine whether an element is not present in the stream.
 notElem :: (IsStream t, Monad m, Eq a) => a -> t m a -> m Bool
@@ -449,7 +450,7 @@ notElem e m = go (toStream m)
         let stop            = return True
             yield a Nothing = return (a /= e)
             yield a (Just x) = if a == e then return False else go x
-        in (runStream m1) Nothing stop yield
+        in (S.runStream m1) Nothing stop yield
 
 -- | Determine the length of the stream.
 length :: (IsStream t, Monad m) => t m a -> m Int
@@ -463,10 +464,10 @@ reverse m = fromStream $ go Nothing (toStream m)
     go rev rest = Stream $ \svr stp yld ->
         let stop = case rev of
                 Nothing ->  stp
-                Just str -> runStream str svr stp yld
-            yield a Nothing  = runStream (a `scons` rev) svr stp yld
-            yield a (Just x) = runStream (go (Just $ a `scons` rev) x) svr stp yld
-         in runStream rest svr stop yield
+                Just str -> S.runStream str svr stp yld
+            yield a Nothing  = S.runStream (a `S.cons` rev) svr stp yld
+            yield a (Just x) = S.runStream (go (Just $ a `S.cons` rev) x) svr stp yld
+         in S.runStream rest svr stop yield
 
 -- XXX replace the recursive "go" with continuation
 -- | Determine the minimum element in a stream.
@@ -477,7 +478,7 @@ minimum m = go Nothing (toStream m)
         let stop            = return r
             yield a Nothing = return $ min_ a r
             yield a (Just x) = go (min_ a r) x
-        in (runStream m1) Nothing stop yield
+        in (S.runStream m1) Nothing stop yield
 
     min_ a r = case r of
         Nothing -> Just a
@@ -492,7 +493,7 @@ maximum m = go Nothing (toStream m)
         let stop            = return r
             yield a Nothing = return $ max_ a r
             yield a (Just x) = go (max_ a r) x
-        in (runStream m1) Nothing stop yield
+        in (S.runStream m1) Nothing stop yield
 
     max_ a r = case r of
         Nothing -> Just a
@@ -514,7 +515,7 @@ mapM f m = fromStream $ go (toStream m)
         let stop = stp
             yield a Nothing  = f a >>= \b -> yld b Nothing
             yield a (Just x) = f a >>= \b -> yld b (Just (go x))
-         in (runStream m1) Nothing stop yield
+         in (S.runStream m1) Nothing stop yield
 
 -- | Apply a monadic action to each element of the stream and discard the
 -- output of the action.
@@ -525,7 +526,7 @@ mapM_ f m = go (toStream m)
         let stop = return ()
             yield a Nothing  = void (f a)
             yield a (Just x) = f a >> go x
-         in (runStream m1) Nothing stop yield
+         in (S.runStream m1) Nothing stop yield
 
 -- | Reduce a stream of monadic actions to a stream of the output of those
 -- actions.
@@ -536,7 +537,7 @@ sequence m = fromStream $ go (toStream m)
         let stop = stp
             yield a Nothing  = a >>= \b -> yld b Nothing
             yield a (Just x) = a >>= \b -> yld b (Just (go x))
-         in (runStream m1) Nothing stop yield
+         in (S.runStream m1) Nothing stop yield
 
 -- | Generate a stream by performing an action @n@ times.
 replicateM :: (IsStream t, Monad m) => Int -> m a -> t m a
@@ -557,13 +558,13 @@ zipWithM f m1 m2 = fromStream $ go (toStream m1) (toStream m2)
     where
     go mx my = Stream $ \_ stp yld -> do
         let merge a ra =
-                let yield2 b Nothing   = (runStream (g a b)) Nothing stp yld
+                let yield2 b Nothing   = (S.runStream (g a b)) Nothing stp yld
                     yield2 b (Just rb) =
-                        (runStream (g a b <> go ra rb)) Nothing stp yld
-                 in (runStream my) Nothing stp yield2
-        let yield1 a Nothing   = merge a snil
+                        (S.runStream (g a b <> go ra rb)) Nothing stp yld
+                 in (S.runStream my) Nothing stp yield2
+        let yield1 a Nothing   = merge a S.nil
             yield1 a (Just ra) = merge a ra
-        (runStream mx) Nothing stp yield1
+        (S.runStream mx) Nothing stp yield1
     g a b = toStream $ f a b
 
 ------------------------------------------------------------------------------
@@ -577,4 +578,4 @@ zipAsyncWithM :: (IsStream t, MonadAsync m)
 zipAsyncWithM f m1 m2 = fromStream $ Stream $ \_ stp yld -> do
     ma <- async m1
     mb <- async m2
-    (runStream (toStream (zipWithM f ma mb))) Nothing stp yld
+    (S.runStream (toStream (zipWithM f ma mb))) Nothing stp yld
diff --git a/src/Streamly/Streams.hs b/src/Streamly/Streams.hs
index 8f699acc..d05d8b62 100644
--- a/src/Streamly/Streams.hs
+++ b/src/Streamly/Streams.hs
@@ -28,7 +28,7 @@ module Streamly.Streams
     , SVarTag (..)
     , SVarStyle (..)
     , SVar
-    , newEmptySVar
+    , S.newEmptySVar
 
     -- * Construction
     , nil
@@ -47,6 +47,14 @@ module Streamly.Streams
     -- * Transformation
     , async
 
+    -- * Merging Streams
+    , append
+    , interleave
+    , asyncmerge
+    , parmerge
+    , (<=>)            --deprecated
+    , (<|)             --deprecated
+
     -- * Stream Styles
     , SerialT
     , StreamT           -- deprecated
@@ -80,10 +88,6 @@ module Streamly.Streams
     , zipWith
     , zipAsyncWith
 
-    -- * Sum Style Composition
-    , (<=>)
-    , (<|)
-
     -- * Fold Utilities
     -- $foldutils
     , foldWith
@@ -103,8 +107,10 @@ import           Control.Monad.State.Class   (MonadState(..))
 import           Control.Monad.Trans.Class   (MonadTrans)
 import           Data.Semigroup              (Semigroup(..))
 import           Prelude hiding              (zipWith)
-import           Streamly.Core hiding        (runStream)
-import qualified Streamly.Core as SC
+import           Streamly.Core               ( MonadAsync, Stream(Stream)
+                                             , SVar, SVarStyle(..)
+                                             , SVarTag(..), SVarSched(..))
+import qualified Streamly.Core as S
 
 ------------------------------------------------------------------------------
 -- Types that can behave as a Stream
@@ -126,7 +132,7 @@ type Streaming = IsStream
 
 -- | Represesnts an empty stream just like @[]@ represents an empty list.
 nil :: IsStream t => t m a
-nil = fromStream snil
+nil = fromStream S.nil
 
 infixr 5 `cons`
 
@@ -139,7 +145,7 @@ infixr 5 `cons`
 -- [1,2,3]
 -- @
 cons :: IsStream t => a -> t m a -> t m a
-cons a r = fromStream $ scons a (Just (toStream r))
+cons a r = fromStream $ S.cons a (Just (toStream r))
 
 infixr 5 .:
 
@@ -194,7 +200,7 @@ fromCallback k = fromStream $ Stream $ \_ _ yld -> k (\a -> yld a Nothing)
 
 -- | Read an SVar to get a stream.
 fromSVar :: (MonadAsync m, IsStream t) => SVar m a -> t m a
-fromSVar sv = fromStream $ fromStreamVar sv
+fromSVar sv = fromStream $ S.fromStreamVar sv
 
 ------------------------------------------------------------------------------
 -- Destroying a stream
@@ -208,7 +214,7 @@ streamFold :: IsStream t
 streamFold sv step blank m =
     let yield a Nothing = step a Nothing
         yield a (Just x) = step a (Just (fromStream x))
-     in (SC.runStream (toStream m)) sv blank yield
+     in (S.runStream (toStream m)) sv blank yield
 
 -- | Run a streaming composition, discard the results.
 runStream :: (Monad m, IsStream t) => t m a -> m ()
@@ -218,7 +224,7 @@ runStream m = go (toStream m)
         let stop = return ()
             yield _ Nothing  = stop
             yield _ (Just x) = go x
-         in (SC.runStream m1) Nothing stop yield
+         in (S.runStream m1) Nothing stop yield
 
 -- | Same as 'runStream'
 {-# Deprecated runStreaming "Please use runStream instead." #-}
@@ -228,7 +234,7 @@ runStreaming = runStream
 -- | Write a stream to an 'SVar' in a non-blocking manner. The stream can then
 -- be read back from the SVar using 'fromSVar'.
 toSVar :: (IsStream t, MonadAsync m) => SVar m a -> t m a -> m ()
-toSVar sv m = toStreamVar sv (toStream m)
+toSVar sv m = S.toStreamVar sv (toStream m)
 
 ------------------------------------------------------------------------------
 -- Transformation
@@ -243,14 +249,25 @@ toSVar sv m = toStreamVar sv (toStream m)
 
 async :: (IsStream t, MonadAsync m) => t m a -> m (t m a)
 async m = do
-    sv <- newStreamVar1 (SVarStyle Disjunction LIFO) (toStream m)
+    sv <- S.newStreamVar1 (SVarStyle Disjunction LIFO) (toStream m)
     return $ fromSVar sv
 
 ------------------------------------------------------------------------------
 -- SerialT
 ------------------------------------------------------------------------------
 
--- | The 'Monad' instance of 'SerialT' runs the /monadic continuation/ for each
+-- | The 'Semigroup' instance of 'SerialT' appends two streams sequentially,
+-- yielding all elements from the first stream, and then all elements from the
+-- second stream.
+--
+-- @
+-- main = ('toList' . 'serially' $ (fromFoldable [1,2]) \<\> (fromFoldable [3,4])) >>= print
+-- @
+-- @
+-- [1,2,3,4]
+-- @
+--
+-- The 'Monad' instance runs the /monadic continuation/ for each
 -- element of the stream, serially.
 --
 -- @
@@ -278,11 +295,14 @@ async m = do
 -- (2,4)
 -- @
 --
--- This behavior is exactly like a list transformer. We call the monadic code
--- being run for each element of the stream a monadic continuation. In
--- imperative paradigm we can think of this composition as nested @for@ loops
--- and the monadic continuation is the body of the loop. The loop iterates for
--- all elements of the stream.
+-- This behavior of 'SerialT' is exactly like a list transformer. We call the
+-- monadic code being run for each element of the stream a monadic
+-- continuation. In imperative paradigm we can think of this composition as
+-- nested @for@ loops and the monadic continuation is the body of the loop. The
+-- loop iterates for all elements of the stream.
+--
+-- Note that serial composition can be used to combine an infinite number of
+-- streams as it explores only one stream at a time.
 --
 newtype SerialT m a = SerialT {getSerialT :: Stream m a}
     deriving (Semigroup, Monoid, MonadTrans, MonadIO, MonadThrow)
@@ -307,6 +327,17 @@ type StreamT = SerialT
 -- from a single base type because they depend on the Monad instance which is
 -- different for each type.
 
+------------------------------------------------------------------------------
+-- Semigroup
+------------------------------------------------------------------------------
+
+-- | Same as the 'Semigroup' instance of 'SerialT'. Appends two streams
+-- sequentially, yielding all elements from the first stream, and then all
+-- elements from the second stream.
+{-# INLINE append #-}
+append :: IsStream t => t m a -> t m a -> t m a
+append m1 m2 = fromStream $ S.append (toStream m1) (toStream m2)
+
 ------------------------------------------------------------------------------
 -- Monad
 ------------------------------------------------------------------------------
@@ -314,10 +345,9 @@ type StreamT = SerialT
 instance Monad m => Monad (SerialT m) where
     return = pure
     (SerialT (Stream m)) >>= f = SerialT $ Stream $ \_ stp yld ->
-        let run x = (SC.runStream x) Nothing stp yld
-            yield a Nothing  = run $ getSerialT (f a)
-            yield a (Just r) = run $ getSerialT (f a)
-                                  <> getSerialT (SerialT r >>= f)
+        let run x = (S.runStream x) Nothing stp yld
+            yield a Nothing  = run $ toStream (f a)
+            yield a (Just r) = run $ toStream $ f a <> (fromStream r >>= f)
         in m Nothing stp yield
 
 ------------------------------------------------------------------------------
@@ -325,7 +355,7 @@ instance Monad m => Monad (SerialT m) where
 ------------------------------------------------------------------------------
 
 instance Monad m => Applicative (SerialT m) where
-    pure a = SerialT $ scons a Nothing
+    pure a = SerialT $ S.cons a Nothing
     (<*>) = ap
 
 ------------------------------------------------------------------------------
@@ -387,9 +417,18 @@ instance (Monad m, Floating a) => Floating (SerialT m a) where
 -- InterleavedT
 ------------------------------------------------------------------------------
 
--- | Like 'SerialT' but different in nesting behavior. It fairly interleaves
--- the iterations of the inner and the outer loop, nesting loops in a breadth
--- first manner.
+-- | The 'Semigroup' instance of 'InterleavedT' interleaves two streams,
+-- yielding one element from each stream alternately.
+--
+-- @
+-- main = ('toList' . 'interleaving $ (fromFoldable [1,2]) \<\> (fromFoldable [3,4])) >>= print
+-- @
+-- @
+-- [1,3,2,4]
+-- @
+--
+-- Similarly, the 'Monad' instance fairly interleaves the iterations of the
+-- inner and the outer loop, nesting loops in a breadth first manner.
 --
 --
 -- @
@@ -405,8 +444,11 @@ instance (Monad m, Floating a) => Floating (SerialT m a) where
 -- (2,4)
 -- @
 --
+-- Note that interleaving composition can only combine a finite number of
+-- streams as it needs to retain state for each unfinished stream.
+--
 newtype InterleavedT m a = InterleavedT {getInterleavedT :: Stream m a}
-    deriving (Semigroup, Monoid, MonadTrans, MonadIO, MonadThrow)
+    deriving (Monoid, MonadTrans, MonadIO, MonadThrow)
 
 deriving instance MonadAsync m => Alternative (InterleavedT m)
 deriving instance MonadAsync m => MonadPlus (InterleavedT m)
@@ -419,14 +461,37 @@ instance IsStream InterleavedT where
     toStream = getInterleavedT
     fromStream = InterleavedT
 
+------------------------------------------------------------------------------
+-- Semigroup
+------------------------------------------------------------------------------
+
+-- | Same as the 'Semigroup' instance of 'InterleavedT'.  Interleaves two
+-- streams, yielding one element from each stream alternately.
+{-# INLINE interleave #-}
+interleave :: IsStream t => t m a -> t m a -> t m a
+interleave m1 m2 = fromStream $ S.interleave (toStream m1) (toStream m2)
+
+instance Semigroup (InterleavedT m a) where
+    (<>) = interleave
+
+infixr 5 <=>
+
+-- | Same as 'interleave'.
+{-# Deprecated (<=>) "Please use '<>' of InterleavedT or 'interleave' instead." #-}
+{-# INLINE (<=>) #-}
+(<=>) :: IsStream t => t m a -> t m a -> t m a
+(<=>) = interleave
+
+------------------------------------------------------------------------------
+-- Monad
+------------------------------------------------------------------------------
+
 instance Monad m => Monad (InterleavedT m) where
     return = pure
     (InterleavedT (Stream m)) >>= f = InterleavedT $ Stream $ \_ stp yld ->
-        let run x = (SC.runStream x) Nothing stp yld
-            yield a Nothing  = run $ getInterleavedT (f a)
-            yield a (Just r) = run $ getInterleavedT (f a)
-                                     `interleave`
-                                     getInterleavedT (InterleavedT r >>= f)
+        let run x = (S.runStream x) Nothing stp yld
+            yield a Nothing  = run $ toStream (f a)
+            yield a (Just r) = run $ toStream $ f a <> (fromStream r >>= f)
         in m Nothing stp yield
 
 ------------------------------------------------------------------------------
@@ -434,7 +499,7 @@ instance Monad m => Monad (InterleavedT m) where
 ------------------------------------------------------------------------------
 
 instance Monad m => Applicative (InterleavedT m) where
-    pure a = InterleavedT $ scons a Nothing
+    pure a = InterleavedT $ S.cons a Nothing
     (<*>) = ap
 
 ------------------------------------------------------------------------------
@@ -496,9 +561,24 @@ instance (Monad m, Floating a) => Floating (InterleavedT m a) where
 -- AsyncT
 ------------------------------------------------------------------------------
 
--- | Like 'SerialT' but /may/ run each iteration concurrently using demand
--- driven concurrency.  More concurrent iterations are started only if the
--- previous iterations are not able to produce enough output for the consumer.
+-- | Left biased concurrent composition.
+--
+-- The Semigroup instance of 'AsyncT' concurrently /merges/ streams in a left
+-- biased manner.  It keeps yielding elements from the left stream as long as
+-- it can. If the left stream blocks or cannot keep up with the pace of the
+-- consumer it can concurrently yield from the stream on the right as well.
+--
+-- @
+-- main = ('toList' . 'asyncly' $ (fromFoldable [1,2]) \<> (fromFoldable [3,4])) >>= print
+-- @
+-- @
+-- [1,2,3,4]
+-- @
+--
+-- Similarly, the monad instance of 'AsyncT' /may/ run each iteration
+-- concurrently using demand driven concurrency.  More concurrent iterations
+-- are started only if the previous iterations are not able to produce enough
+-- output for the consumer.
 --
 -- @
 -- import "Streamly"
@@ -517,8 +597,12 @@ instance (Monad m, Floating a) => Floating (InterleavedT m a) where
 -- @
 --
 -- All iterations may run in the same thread if they do not block.
+--
+-- Note that this composition can be used to combine infinite number of streams
+-- as it explores only a bounded number of streams at a time.
+--
 newtype AsyncT m a = AsyncT {getAsyncT :: Stream m a}
-    deriving (Semigroup, Monoid, MonadTrans)
+    deriving (Monoid, MonadTrans)
 
 deriving instance MonadAsync m => Alternative (AsyncT m)
 deriving instance MonadAsync m => MonadPlus (AsyncT m)
@@ -533,6 +617,29 @@ instance IsStream AsyncT where
     toStream = getAsyncT
     fromStream = AsyncT
 
+------------------------------------------------------------------------------
+-- Semigroup
+------------------------------------------------------------------------------
+
+-- | Same as the 'Semigroup' instance of 'AsyncT'.  Merges two streams
+-- concurrently, preferring the elements from the left one when available.
+{-# INLINE asyncmerge #-}
+asyncmerge :: (IsStream t, MonadAsync m) => t m a -> t m a -> t m a
+asyncmerge m1 m2 = fromStream $ S.asyncmerge (toStream m1) (toStream m2)
+
+instance MonadAsync m => Semigroup (AsyncT m a) where
+    (<>) = asyncmerge
+
+-- | Same as 'asyncmerge'.
+{-# DEPRECATED (<|) "Please use '<>' of AsyncT or 'asyncmerge' instead." #-}
+{-# INLINE (<|) #-}
+(<|) :: (IsStream t, MonadAsync m) => t m a -> t m a -> t m a
+(<|) = asyncmerge
+
+------------------------------------------------------------------------------
+-- Monad
+------------------------------------------------------------------------------
+
 {-# INLINE parbind #-}
 parbind
     :: (forall c. Stream m c -> Stream m c -> Stream m c)
@@ -543,7 +650,7 @@ parbind par m f = go m
     where
         go (Stream g) =
             Stream $ \ctx stp yld ->
-            let run x = (SC.runStream x) ctx stp yld
+            let run x = (S.runStream x) ctx stp yld
                 yield a Nothing  = run $ f a
                 yield a (Just r) = run $ f a `par` go r
             in g Nothing stp yield
@@ -552,14 +659,14 @@ instance MonadAsync m => Monad (AsyncT m) where
     return = pure
     (AsyncT m) >>= f = AsyncT $ parbind par m g
         where g x = getAsyncT (f x)
-              par = joinStreamVar2 (SVarStyle Conjunction LIFO)
+              par = S.joinStreamVar2 (SVarStyle Conjunction LIFO)
 
 ------------------------------------------------------------------------------
 -- Applicative
 ------------------------------------------------------------------------------
 
 instance MonadAsync m => Applicative (AsyncT m) where
-    pure a = AsyncT $ scons a Nothing
+    pure a = AsyncT $ S.cons a Nothing
     (<*>) = ap
 
 ------------------------------------------------------------------------------
@@ -620,8 +727,20 @@ instance (MonadAsync m, Floating a) => Floating (AsyncT m a) where
 -- ParallelT
 ------------------------------------------------------------------------------
 
--- | Like 'SerialT' but runs /all/ iterations fairly concurrently using a round
--- robin scheduling.
+-- | Round robin concurrent composition.
+--
+-- The Semigroup instance of 'ParallelT' concurrently /merges/ streams in a
+-- round robin fashion, yielding elements from both streams alternately.
+--
+-- @
+-- main = ('toList' . 'parallely' $ (fromFoldable [1,2]) \<> (fromFoldable [3,4])) >>= print
+-- @
+-- @
+-- [1,3,2,4]
+-- @
+--
+-- Similarly, the 'Monad' instance of 'ParallelT' runs /all/ iterations fairly
+-- concurrently using a round robin scheduling.
 --
 -- @
 -- import "Streamly"
@@ -641,8 +760,12 @@ instance (MonadAsync m, Floating a) => Floating (AsyncT m a) where
 --
 -- Unlike 'AsyncT' all iterations are guaranteed to run fairly concurrently,
 -- unconditionally.
+--
+-- Note that round robin composition can only combine a finite number of
+-- streams as it needs to retain state for each unfinished stream.
+--
 newtype ParallelT m a = ParallelT {getParallelT :: Stream m a}
-    deriving (Semigroup, Monoid, MonadTrans)
+    deriving (Monoid, MonadTrans)
 
 deriving instance MonadAsync m => Alternative (ParallelT m)
 deriving instance MonadAsync m => MonadPlus (ParallelT m)
@@ -657,18 +780,35 @@ instance IsStream ParallelT where
     toStream = getParallelT
     fromStream = ParallelT
 
+------------------------------------------------------------------------------
+-- Semigroup
+------------------------------------------------------------------------------
+
+-- | Same as the 'Semigroup' instance of 'ParallelT'.  Merges two streams
+-- concurrently choosing elements from both fairly.
+{-# INLINE parmerge #-}
+parmerge :: (IsStream t, MonadAsync m) => t m a -> t m a -> t m a
+parmerge m1 m2 = fromStream $ S.parmerge (toStream m1) (toStream m2)
+
+instance MonadAsync m => Semigroup (ParallelT m a) where
+    (<>) = parmerge
+
+------------------------------------------------------------------------------
+-- Monad
+------------------------------------------------------------------------------
+
 instance MonadAsync m => Monad (ParallelT m) where
     return = pure
     (ParallelT m) >>= f = ParallelT $ parbind par m g
         where g x = getParallelT (f x)
-              par = joinStreamVar2 (SVarStyle Conjunction FIFO)
+              par = S.joinStreamVar2 (SVarStyle Conjunction FIFO)
 
 ------------------------------------------------------------------------------
 -- Applicative
 ------------------------------------------------------------------------------
 
 instance MonadAsync m => Applicative (ParallelT m) where
-    pure a = ParallelT $ scons a Nothing
+    pure a = ParallelT $ S.cons a Nothing
     (<*>) = ap
 
 ------------------------------------------------------------------------------
@@ -738,10 +878,10 @@ zipWith f m1 m2 = fromStream $ go (toStream m1) (toStream m2)
         let merge a ra =
                 let yield2 b Nothing   = yld (f a b) Nothing
                     yield2 b (Just rb) = yld (f a b) (Just (go ra rb))
-                 in (SC.runStream my) Nothing stp yield2
-        let yield1 a Nothing   = merge a snil
+                 in (S.runStream my) Nothing stp yield2
+        let yield1 a Nothing   = merge a S.nil
             yield1 a (Just ra) = merge a ra
-        (SC.runStream mx) Nothing stp yield1
+        (S.runStream mx) Nothing stp yield1
 
 -- | The applicative instance of 'ZipSerial' zips a number of streams serially
 -- i.e. it produces one element from each stream serially and then zips all
@@ -758,8 +898,9 @@ zipWith f m1 m2 = fromStream $ go (toStream m1) (toStream m2)
 -- [(1,3,5),(2,4,6)]
 -- @
 --
--- This applicative operation can be seen as the zipping equivalent of
--- interleaving with '<=>'.
+-- The 'Semigroup' instance of this type works the same way as that of
+-- 'SerialT'.
+--
 newtype ZipSerial m a = ZipSerial {getZipSerial :: Stream m a}
         deriving (Semigroup, Monoid)
 
@@ -777,7 +918,7 @@ instance Monad m => Functor (ZipSerial m) where
         in m Nothing stp yield
 
 instance Monad m => Applicative (ZipSerial m) where
-    pure = ZipSerial . srepeat
+    pure = ZipSerial . S.repeat
     (<*>) = zipWith id
 
 instance IsStream ZipSerial where
@@ -835,7 +976,7 @@ zipAsyncWith :: (IsStream t, MonadAsync m)
 zipAsyncWith f m1 m2 = fromStream $ Stream $ \_ stp yld -> do
     ma <- async m1
     mb <- async m2
-    (SC.runStream (toStream (zipWith f ma mb))) Nothing stp yld
+    (S.runStream (toStream (zipWith f ma mb))) Nothing stp yld
 
 -- | Like 'ZipSerial' but zips in parallel, it generates all the elements to
 -- be zipped concurrently.
@@ -850,8 +991,9 @@ zipAsyncWith f m1 m2 = fromStream $ Stream $ \_ stp yld -> do
 -- [(1,3,5),(2,4,6)]
 -- @
 --
--- This applicative operation can be seen as the zipping equivalent of
--- parallel composition with '<|>'.
+-- The 'Semigroup' instance of this type works the same way as that of
+-- 'SerialT'.
+--
 newtype ZipAsync m a = ZipAsync {getZipAsync :: Stream m a}
         deriving (Semigroup, Monoid)
 
@@ -865,7 +1007,7 @@ instance Monad m => Functor (ZipAsync m) where
         in m Nothing stp yield
 
 instance MonadAsync m => Applicative (ZipAsync m) where
-    pure = ZipAsync . srepeat
+    pure = ZipAsync . S.repeat
     (<*>) = zipAsyncWith id
 
 instance IsStream ZipAsync where
@@ -982,51 +1124,6 @@ runZipStream = runZipSerial
 runZipAsync :: Monad m => ZipAsync m a -> m ()
 runZipAsync = runStream
 
-------------------------------------------------------------------------------
--- Sum Style Composition
-------------------------------------------------------------------------------
-
-infixr 5 <=>
-
--- | Sequential interleaved composition, in contrast to '<>' this operator
--- fairly interleaves two streams instead of appending them; yielding one
--- element from each stream alternately.
---
--- @
--- main = ('toList' . 'serially' $ (return 1 <> return 2) \<=\> (return 3 <> return 4)) >>= print
--- @
--- @
--- [1,3,2,4]
--- @
---
--- This operator corresponds to the 'InterleavedT' style. Unlike '<>', this
--- operator cannot be used to fold infinite containers since that might
--- accumulate too many partially drained streams.  To be clear, it can combine
--- infinite streams but not infinite number of streams.
-{-# INLINE (<=>) #-}
-(<=>) :: IsStream t => t m a -> t m a -> t m a
-m1 <=> m2 = fromStream $ interleave (toStream m1) (toStream m2)
-
--- | Demand driven concurrent composition. In contrast to '<|>' this operator
--- concurrently "merges" streams in a left biased manner rather than fairly
--- interleaving them.  It keeps yielding from the stream on the left as long as
--- it can. If the left stream blocks or cannot keep up with the pace of the
--- consumer it can concurrently yield from the stream on the right in parallel.
---
--- @
--- main = ('toList' . 'serially' $ (return 1 <> return 2) \<| (return 3 <> return 4)) >>= print
--- @
--- @
--- [1,2,3,4]
--- @
---
--- Unlike '<|>' it can be used to fold infinite containers of streams. This
--- operator corresponds to the 'AsyncT' type for product style composition.
---
-{-# INLINE (<|) #-}
-(<|) :: (IsStream t, MonadAsync m) => t m a -> t m a -> t m a
-m1 <| m2 = fromStream $ parLeft (toStream m1) (toStream m2)
-
 ------------------------------------------------------------------------------
 -- Fold Utilities
 ------------------------------------------------------------------------------
diff --git a/test/Main.hs b/test/Main.hs
index be130f18..cad50db5 100644
--- a/test/Main.hs
+++ b/test/Main.hs
@@ -9,8 +9,12 @@ import Data.List (sort)
 import Test.Hspec
 
 import Streamly
+import Streamly.Prelude ((.:), nil)
 import qualified Streamly.Prelude as A
 
+singleton :: IsStream t => a -> t m a
+singleton a = a .: nil
+
 toListSerial :: SerialT IO a -> IO [a]
 toListSerial = A.toList . serially
 
@@ -20,8 +24,8 @@ toListInterleaved = A.toList . interleaving
 toListAsync :: AsyncT IO a -> IO [a]
 toListAsync = A.toList . asyncly
 
-toListParallel :: Ord a => ParallelT IO a -> IO [a]
-toListParallel = fmap sort . A.toList . parallely
+toListParallel :: ParallelT IO a -> IO [a]
+toListParallel = A.toList . parallely
 
 main :: IO ()
 main = hspec $ do
@@ -50,8 +54,9 @@ main = hspec $ do
         it "fmap on composed (<>)" $
             (toListSerial $ fmap (+1) (return 1 <> return 2))
                 `shouldReturn` ([2,3] :: [Int])
-        it "fmap on composed (<|>)" $
-            (toListSerial $ fmap (+1) (return 1 <|> return 2))
+
+        it "fmap on composed (<>)" $
+            ((toListParallel $ fmap (+1) (return 1 <> return 2)) >>= return .  sort)
                 `shouldReturn` ([2,3] :: [Int])
 
     ---------------------------------------------------------------------------
@@ -70,43 +75,43 @@ main = hspec $ do
                 `shouldReturn` ([(1,2),(1,3)] :: [(Int, Int)])
 
         it "Apply - parallel composed first argument" $
-            (toListSerial $ (,) <$> (return 1 <|> return 2) <*> (return 3))
+            (toListParallel ((,) <$> (return 1 <> return 2) <*> (return 3)) >>= return . sort)
                 `shouldReturn` ([(1,3),(2,3)] :: [(Int, Int)])
 
         it "Apply - parallel composed second argument" $
-            (toListSerial $ (,) <$> (return 1) <*> (return 2 <|> return 3))
+            (toListParallel ((,) <$> (return 1) <*> (return 2 <> return 3)) >>= return . sort)
                 `shouldReturn` ([(1,2),(1,3)] :: [(Int, Int)])
 
     ---------------------------------------------------------------------------
     -- Monoidal Compositions
     ---------------------------------------------------------------------------
 
-    describe "Serial Composition (<>)" $ compose (<>) id
-    describe "Serial Composition (mappend)" $ compose mappend id
-    describe "Interleaved Composition (<>)" $ compose (<=>) sort
-    describe "Left biased parallel Composition (<|)" $ compose (<|) sort
-    describe "Fair parallel Composition (<|>)" $ compose (<|>) sort
-    describe "Fair parallel Composition (mplus)" $ compose mplus sort
-
+    describe "Serial Composition" $ compose serially mempty id
+    describe "Interleaved Composition" $ compose interleaving mempty sort
+    describe "Left biased parallel Composition" $ compose asyncly mempty sort
+    describe "Fair parallel Composition" $ compose parallely mempty sort
+    describe "Semigroup Composition for ZipSerial" $ compose zipping mempty id
+    describe "Semigroup Composition for ZipAsync" $ compose zippingAsync mempty id
+    -- XXX need to check alternative compositions as well
     ---------------------------------------------------------------------------
     -- Monoidal Composition ordering checks
     ---------------------------------------------------------------------------
 
-    describe "Serial interleaved ordering check (<=>)" $ interleaveCheck (<=>)
-    describe "Parallel interleaved ordering check (<|>)" $ interleaveCheck (<|>)
-    describe "Left biased parallel time order check" $ parallelCheck (<|)
-    describe "Fair parallel time order check" $ parallelCheck (<|>)
+    describe "Serial interleaved ordering check" $ interleaveCheck interleaving
+    describe "Parallel interleaved ordering check" $ interleaveCheck parallely
+    describe "Left biased parallel time order check" $ parallelCheck asyncly
+    describe "Fair parallel time order check" $ parallelCheck parallely
 
     ---------------------------------------------------------------------------
     -- TBD Monoidal composition combinations
     ---------------------------------------------------------------------------
 
     -- TBD need more such combinations to be tested.
-    describe "<> and <>" $ composeAndComposeSimple (<>) (<>) (cycle [[1 .. 9]])
+    describe "<> and <>" $ composeAndComposeSimple serially serially (cycle [[1 .. 9]])
 
     describe "<> and <=>" $ composeAndComposeSimple
-      (<>)
-      (<=>)
+      serially
+      interleaving
       ([ [1 .. 9]
        , [1 .. 9]
        , [1, 3, 2, 4, 6, 5, 7, 9, 8]
@@ -114,8 +119,8 @@ main = hspec $ do
        ])
 
     describe "<=> and <=>" $ composeAndComposeSimple
-      (<=>)
-      (<=>)
+      interleaving
+      interleaving
       ([ [1, 4, 2, 7, 3, 5, 8, 6, 9]
        , [1, 7, 4, 8, 2, 9, 5, 3, 6]
        , [1, 4, 3, 7, 2, 6, 9, 5, 8]
@@ -123,8 +128,8 @@ main = hspec $ do
        ])
 
     describe "<=> and <>" $ composeAndComposeSimple
-      (<=>)
-      (<>)
+      interleaving
+      serially
       ([ [1, 4, 2, 7, 3, 5, 8, 6, 9]
        , [1, 7, 4, 8, 2, 9, 5, 3, 6]
        , [1, 4, 2, 7, 3, 5, 8, 6, 9]
@@ -132,6 +137,9 @@ main = hspec $ do
        ])
 
     describe "Nested parallel and serial compositions" $ do
+        let t = timed
+            p = adapt . parallely
+            s = adapt . serially
         {-
         -- This is not correct, the result can also be [4,4,8,0,8,0,2,2]
         -- because of parallelism of [8,0] and [8,0].
@@ -143,10 +151,9 @@ main = hspec $ do
             `shouldReturn` ([4,4,8,8,0,0,2,2])
         -}
         it "Nest <|>, <>, <|> (2)" $
-            let t = timed
-             in toListSerial (
-                    ((t 4 <|> t 8) <> (t 1 <|> t 2))
-                <|> ((t 4 <|> t 8) <> (t 1 <|> t 2)))
+            (A.toList . parallely) (
+                   s (p (t 4 <> t 8) <> p (t 1 <> t 2))
+                <> s (p (t 4 <> t 8) <> p (t 1 <> t 2)))
             `shouldReturn` ([4,4,8,8,1,1,2,2])
         -- FIXME: These two keep failing intermittently on Mac OS X
         -- Need to examine and fix the tests.
@@ -165,55 +172,82 @@ main = hspec $ do
             `shouldReturn` ([4,4,1,1,8,2,9,2])
         -}
         it "Nest <|>, <|>, <|>" $
-            let t = timed
-             in toListSerial (
-                    ((t 4 <|> t 8) <|> (t 0 <|> t 2))
-                <|> ((t 4 <|> t 8) <|> (t 0 <|> t 2)))
+            (A.toList . parallely) (
+                    ((t 4 <> t 8) <> (t 0 <> t 2))
+                <> ((t 4 <> t 8) <> (t 0 <> t 2)))
             `shouldReturn` ([0,0,2,2,4,4,8,8])
 
     ---------------------------------------------------------------------------
     -- Monoidal composition recursion loops
     ---------------------------------------------------------------------------
 
-    describe "Serial loops (<>)" $ loops (<>) id reverse
-    describe "Left biased parallel loops (<|)" $ loops (<|) sort sort
-    describe "Fair parallel loops (<|>)" $ loops (<|>) sort sort
+    describe "Serial loops (<>)" $ loops serially id reverse
+    describe "Left biased parallel loops (<|)" $ loops asyncly sort sort
+    describe "Fair parallel loops (<|>)" $ loops parallely sort sort
 
     ---------------------------------------------------------------------------
     -- Bind and monoidal composition combinations
     ---------------------------------------------------------------------------
 
-    forM_ [(<>), (<=>), (<|), (<|>)] $ \g ->
-        describe "Bind and compose" $ bindAndComposeSimple toListSerial g
+    describe "Bind and compose1" $ bindAndComposeSimple serially serially
+    describe "Bind and compose2" $ bindAndComposeSimple serially interleaving
+    describe "Bind and compose3" $ bindAndComposeSimple serially asyncly
+    describe "Bind and compose4" $ bindAndComposeSimple serially parallely
 
-    forM_ [(<>), (<=>), (<|), (<|>)] $ \g ->
-        describe "Bind and compose" $ bindAndComposeSimple toListInterleaved g
+    describe "Bind and compose1" $ bindAndComposeSimple interleaving serially
+    describe "Bind and compose2" $ bindAndComposeSimple interleaving interleaving
+    describe "Bind and compose3" $ bindAndComposeSimple interleaving asyncly
+    describe "Bind and compose4" $ bindAndComposeSimple interleaving parallely
 
-    forM_ [(<>), (<=>), (<|), (<|>)] $ \g ->
-        describe "Bind and compose" $ bindAndComposeSimple toListAsync g
+    describe "Bind and compose1" $ bindAndComposeSimple asyncly serially
+    describe "Bind and compose2" $ bindAndComposeSimple asyncly interleaving
+    describe "Bind and compose3" $ bindAndComposeSimple asyncly asyncly
+    describe "Bind and compose4" $ bindAndComposeSimple asyncly parallely
 
-    forM_ [(<>), (<=>), (<|), (<|>)] $ \g ->
-        describe "Bind and compose" $ bindAndComposeSimple toListParallel g
+    describe "Bind and compose1" $ bindAndComposeSimple parallely serially
+    describe "Bind and compose2" $ bindAndComposeSimple parallely interleaving
+    describe "Bind and compose3" $ bindAndComposeSimple parallely asyncly
+    describe "Bind and compose4" $ bindAndComposeSimple parallely parallely
 
-    let fldr f = foldr f empty
-        fldl f = foldl f empty
-     in do
-        forM_ [(<>), (<=>), (<|), (<|>)] $ \g ->
-            forM_ [fldr, fldl] $ \k ->
-                describe "Bind and compose" $
-                    bindAndComposeHierarchy toListSerial (k g)
-        forM_ [(<>), (<=>), (<|), (<|>)] $ \g ->
-            forM_ [fldr, fldl] $ \k ->
-                describe "Bind and compose" $
-                    bindAndComposeHierarchy toListInterleaved (k g)
-        forM_ [(<>), (<=>), (<|), (<|>)] $ \g ->
-            forM_ [fldr, fldl] $ \k ->
-                describe "Bind and compose" $
-                    bindAndComposeHierarchy toListAsync (k g)
-        forM_ [(<>), (<=>), (<|), (<|>)] $ \g ->
-            forM_ [fldr, fldl] $ \k ->
-                describe "Bind and compose" $
-                    bindAndComposeHierarchy toListParallel (k g)
+    let fldr, fldl :: (IsStream t, Semigroup (t IO Int)) => [t IO Int] -> t IO Int
+        fldr = foldr (<>) nil
+        fldl = foldl (<>) nil
+
+    forM_ [fldr, fldl] $ \k ->
+        describe "Bind and compose" $ bindAndComposeHierarchy serially serially k
+    forM_ [fldr, fldl] $ \k ->
+        describe "Bind and compose" $ bindAndComposeHierarchy serially interleaving k
+    forM_ [fldr, fldl] $ \k ->
+        describe "Bind and compose" $ bindAndComposeHierarchy serially asyncly k
+    forM_ [fldr, fldl] $ \k ->
+        describe "Bind and compose" $ bindAndComposeHierarchy serially parallely k
+
+    forM_ [fldr, fldl] $ \k ->
+        describe "Bind and compose" $ bindAndComposeHierarchy interleaving serially k
+    forM_ [fldr, fldl] $ \k ->
+        describe "Bind and compose" $ bindAndComposeHierarchy interleaving interleaving k
+    forM_ [fldr, fldl] $ \k ->
+        describe "Bind and compose" $ bindAndComposeHierarchy interleaving asyncly k
+    forM_ [fldr, fldl] $ \k ->
+        describe "Bind and compose" $ bindAndComposeHierarchy interleaving parallely k
+
+    forM_ [fldr, fldl] $ \k ->
+        describe "Bind and compose" $ bindAndComposeHierarchy asyncly serially k
+    forM_ [fldr, fldl] $ \k ->
+        describe "Bind and compose" $ bindAndComposeHierarchy asyncly interleaving k
+    forM_ [fldr, fldl] $ \k ->
+        describe "Bind and compose" $ bindAndComposeHierarchy asyncly asyncly k
+    forM_ [fldr, fldl] $ \k ->
+        describe "Bind and compose" $ bindAndComposeHierarchy asyncly parallely k
+
+    forM_ [fldr, fldl] $ \k ->
+        describe "Bind and compose" $ bindAndComposeHierarchy parallely serially k
+    forM_ [fldr, fldl] $ \k ->
+        describe "Bind and compose" $ bindAndComposeHierarchy parallely interleaving k
+    forM_ [fldr, fldl] $ \k ->
+        describe "Bind and compose" $ bindAndComposeHierarchy parallely asyncly k
+    forM_ [fldr, fldl] $ \k ->
+        describe "Bind and compose" $ bindAndComposeHierarchy parallely parallely k
 
     -- Nest two lists using different styles of product compositions
     it "Nests two streams using monadic serial composition" nestTwoSerial
@@ -229,8 +263,7 @@ main = hspec $ do
     it "Nests two streams using Num serial composition" nestTwoSerialNum
     it "Nests two streams using Num interleaved composition" nestTwoInterleavedNum
     it "Nests two streams using Num async composition" nestTwoAsyncNum
-    -- This test fails intermittently, need to investigate
-    -- it "Nests two streams using Num parallel composition" nestTwoParallelNum
+    it "Nests two streams using Num parallel composition" nestTwoParallelNum
 
     ---------------------------------------------------------------------------
     -- TBD Bind and Bind combinations
@@ -291,182 +324,183 @@ nestTwoAsync :: Expectation
 nestTwoAsync =
     let s1 = foldMapWith (<>) return [1..4]
         s2 = foldMapWith (<>) return [5..8]
-    in toListAsync (do
+    in (toListAsync (do
         x <- s1
         y <- s2
         return (x + y)
-        ) `shouldReturn` ([6,7,8,9,7,8,9,10,8,9,10,11,9,10,11,12] :: [Int])
+        ) >>= return . sort)
+    `shouldReturn` sort ([6,7,8,9,7,8,9,10,8,9,10,11,9,10,11,12] :: [Int])
 
 nestTwoAsyncApp :: Expectation
 nestTwoAsyncApp =
     let s1 = foldMapWith (<>) return [1..4]
         s2 = foldMapWith (<>) return [5..8]
-    in toListAsync ((+) <$> s1 <*> s2)
-        `shouldReturn` ([6,7,8,9,7,8,9,10,8,9,10,11,9,10,11,12] :: [Int])
+    in (toListAsync ((+) <$> s1 <*> s2) >>= return . sort)
+        `shouldReturn` sort ([6,7,8,9,7,8,9,10,8,9,10,11,9,10,11,12] :: [Int])
 
 nestTwoAsyncNum :: Expectation
 nestTwoAsyncNum =
     let s1 = foldMapWith (<>) return [1..4]
         s2 = foldMapWith (<>) return [5..8]
-    in toListAsync (s1 + s2)
-        `shouldReturn` ([6,7,8,9,7,8,9,10,8,9,10,11,9,10,11,12] :: [Int])
+    in (toListAsync (s1 + s2) >>= return . sort)
+        `shouldReturn` sort ([6,7,8,9,7,8,9,10,8,9,10,11,9,10,11,12] :: [Int])
 
 nestTwoParallel :: Expectation
 nestTwoParallel =
     let s1 = foldMapWith (<>) return [1..4]
         s2 = foldMapWith (<>) return [5..8]
-    in toListParallel (do
+    in (toListParallel (do
         x <- s1
         y <- s2
         return (x + y)
-        ) `shouldReturn` ([6,7,7,8,8,8,9,9,9,9,10,10,10,11,11,12] :: [Int])
+        ) >>= return . sort)
+    `shouldReturn` sort ([6,7,7,8,8,8,9,9,9,9,10,10,10,11,11,12] :: [Int])
 
 nestTwoParallelApp :: Expectation
 nestTwoParallelApp =
     let s1 = foldMapWith (<>) return [1..4]
         s2 = foldMapWith (<>) return [5..8]
-    in toListParallel ((+) <$> s1 <*> s2)
-        `shouldReturn` ([6,7,7,8,8,8,9,9,9,9,10,10,10,11,11,12] :: [Int])
+    in (toListParallel ((+) <$> s1 <*> s2) >>= return . sort)
+        `shouldReturn` sort ([6,7,7,8,8,8,9,9,9,9,10,10,10,11,11,12] :: [Int])
 
-{-
 nestTwoParallelNum :: Expectation
 nestTwoParallelNum =
     let s1 = foldMapWith (<>) return [1..4]
         s2 = foldMapWith (<>) return [5..8]
-    in toListParallel (s1 + s2)
-        `shouldReturn` ([6,7,7,8,8,8,9,9,9,9,10,10,10,11,11,12] :: [Int])
--}
+    in (toListParallel (s1 + s2) >>= return . sort)
+        `shouldReturn` sort ([6,7,7,8,8,8,9,9,9,9,10,10,10,11,11,12] :: [Int])
 
-timed :: Int -> SerialT IO Int
+timed :: MonadIO (t IO) => Int -> t IO Int
 timed x = liftIO (threadDelay (x * 100000)) >> return x
 
-interleaveCheck
-    :: (SerialT IO Int -> SerialT IO Int -> SerialT IO Int)
-    -> Spec
-interleaveCheck f =
+interleaveCheck :: (IsStream t, Semigroup (t IO Int))
+    => (t IO Int -> t IO Int) -> Spec
+interleaveCheck t =
     it "Interleave four" $
-        toListSerial ((return 0 <> return 1) `f` (return 100 <> return 101))
+        (A.toList . t) ((singleton 0 <> singleton 1) <> (singleton 100 <> singleton 101))
             `shouldReturn` ([0, 100, 1, 101])
 
-parallelCheck :: (SerialT IO Int -> SerialT IO Int -> SerialT IO Int) -> Spec
-parallelCheck f = do
+parallelCheck :: (IsStream t, Semigroup (t IO Int), MonadIO (t IO))
+    => (t IO Int -> t IO Int) -> Spec
+parallelCheck t = do
     it "Parallel ordering left associated" $
-        toListSerial (((event 4 `f` event 3) `f` event 2) `f` event 1)
+        (A.toList . t) (((event 4 <> event 3) <> event 2) <> event 1)
             `shouldReturn` ([1..4])
 
     it "Parallel ordering right associated" $
-        toListSerial (event 4 `f` (event 3 `f` (event 2 `f` event 1)))
+        (A.toList . t) (event 4 <> (event 3 <> (event 2 <> event 1)))
             `shouldReturn` ([1..4])
 
     where event n = (liftIO $ threadDelay (n * 100000)) >> (return n)
 
-compose
-    :: (SerialT IO Int -> SerialT IO Int -> SerialT IO Int)
-    -> ([Int] -> [Int])
-    -> Spec
-compose f srt = do
+compose :: (IsStream t, Semigroup (t IO Int))
+    => (t IO Int -> t IO Int) -> t IO Int -> ([Int] -> [Int]) -> Spec
+compose t z srt = do
+    -- XXX these should get covered by the property tests
     it "Compose mempty, mempty" $
-        (tl (mempty `f` mempty)) `shouldReturn` []
-    it "Compose empty, empty" $
-        (tl (empty `f` empty)) `shouldReturn` []
+        (tl (z <> z)) `shouldReturn` ([] :: [Int])
     it "Compose empty at the beginning" $
-        (tl $ (empty `f` return 1)) `shouldReturn` [1]
+        (tl $ (z <> singleton 1)) `shouldReturn` [1]
     it "Compose empty at the end" $
-        (tl $ (return 1 `f` empty)) `shouldReturn` [1]
+        (tl $ (singleton 1 <> z)) `shouldReturn` [1]
     it "Compose two" $
-        (tl (return 0 `f` return 1) >>= return . srt)
+        (tl (singleton 0 <> singleton 1) >>= return . srt)
             `shouldReturn` [0, 1]
+    it "Compose many" $
+        ((tl $ forEachWith (<>) [1..100] singleton) >>= return . srt)
+            `shouldReturn` [1..100]
+
+    -- These are not covered by the property tests
     it "Compose three - empty in the middle" $
-        ((tl $ (return 0 `f` empty `f` return 1)) >>= return . srt)
+        ((tl $ (singleton 0 <> z <> singleton 1)) >>= return . srt)
             `shouldReturn` [0, 1]
     it "Compose left associated" $
-        ((tl $ (((return 0 `f` return 1) `f` return 2) `f` return 3))
+        ((tl $ (((singleton 0 <> singleton 1) <> singleton 2) <> singleton 3))
             >>= return . srt) `shouldReturn` [0, 1, 2, 3]
     it "Compose right associated" $
-        ((tl $ (return 0 `f` (return 1 `f` (return 2 `f` return 3))))
+        ((tl $ (singleton 0 <> (singleton 1 <> (singleton 2 <> singleton 3))))
             >>= return . srt) `shouldReturn` [0, 1, 2, 3]
-    it "Compose many" $
-        ((tl $ forEachWith f [1..100] return) >>= return . srt)
-            `shouldReturn` [1..100]
     it "Compose hierarchical (multiple levels)" $
-        ((tl $ (((return 0 `f` return 1) `f` (return 2 `f` return 3))
-                `f` ((return 4 `f` return 5) `f` (return 6 `f` return 7)))
+        ((tl $ (((singleton 0 <> singleton 1) <> (singleton 2 <> singleton 3))
+                <> ((singleton 4 <> singleton 5) <> (singleton 6 <> singleton 7)))
             ) >>= return . srt) `shouldReturn` [0..7]
-    where tl = toListSerial
+    where tl = A.toList . t
 
 composeAndComposeSimple
-    :: (SerialT IO Int -> SerialT IO Int -> SerialT IO Int)
-    -> (SerialT IO Int -> SerialT IO Int -> SerialT IO Int)
-    -> [[Int]]
-    -> Spec
-composeAndComposeSimple f g answer = do
+    :: ( IsStream t1, Semigroup (t1 IO Int)
+       , IsStream t2, Semigroup (t2 IO Int), Monoid (t2 IO Int), Monad (t2 IO))
+    => (t1 IO Int -> t1 IO Int)
+    -> (t2 IO Int -> t2 IO Int)
+    -> [[Int]] -> Spec
+composeAndComposeSimple t1 t2 answer = do
+    let rfold = adapt . t2 . foldMapWith (<>) return
     it "Compose right associated outer expr, right folded inner" $
-        let fold = foldMapWith g return
-         in (toListSerial (fold [1,2,3] `f` (fold [4,5,6] `f` fold [7,8,9])))
+         ((A.toList. t1) (rfold [1,2,3] <> (rfold [4,5,6] <> rfold [7,8,9])))
             `shouldReturn` (answer !! 0)
 
     it "Compose left associated outer expr, right folded inner" $
-        let fold = foldMapWith g return
-         in (toListSerial ((fold [1,2,3] `f` fold [4,5,6]) `f` fold [7,8,9]))
+         ((A.toList . t1) ((rfold [1,2,3] <> rfold [4,5,6]) <> rfold [7,8,9]))
             `shouldReturn` (answer !! 1)
 
+    let lfold xs = adapt $ t2 $ foldl (<>) mempty $ map return xs
     it "Compose right associated outer expr, left folded inner" $
-        let fold xs = foldl g empty $ map return xs
-         in (toListSerial (fold [1,2,3] `f` (fold [4,5,6] `f` fold [7,8,9])))
+         ((A.toList . t1) (lfold [1,2,3] <> (lfold [4,5,6] <> lfold [7,8,9])))
             `shouldReturn` (answer !! 2)
 
     it "Compose left associated outer expr, left folded inner" $
-        let fold xs = foldl g empty $ map return xs
-         in (toListSerial ((fold [1,2,3] `f` fold [4,5,6]) `f` fold [7,8,9]))
+         ((A.toList . t1) ((lfold [1,2,3] <> lfold [4,5,6]) <> lfold [7,8,9]))
             `shouldReturn` (answer !! 3)
 
-
 loops
-    :: (SerialT IO Int -> SerialT IO Int -> SerialT IO Int)
+    :: (IsStream t, Semigroup (t IO Int), MonadIO (t IO))
+    => (t IO Int -> t IO Int)
     -> ([Int] -> [Int])
     -> ([Int] -> [Int])
     -> Spec
-loops f tsrt hsrt = do
-    it "Tail recursive loop" $ (toListSerial (loopTail 0) >>= return . tsrt)
+loops t tsrt hsrt = do
+    it "Tail recursive loop" $ (A.toList (loopTail 0) >>= return . tsrt)
             `shouldReturn` [0..3]
 
-    it "Head recursive loop" $ (toListSerial (loopHead 0) >>= return . hsrt)
+    it "Head recursive loop" $ (A.toList (loopHead 0) >>= return . hsrt)
             `shouldReturn` [0..3]
 
     where
         loopHead x = do
             -- this print line is important for the test (causes a bind)
             liftIO $ putStrLn "LoopHead..."
-            (if x < 3 then loopHead (x + 1) else empty) `f` return x
+            t $ (if x < 3 then loopHead (x + 1) else nil) <> return x
 
         loopTail x = do
             -- this print line is important for the test (causes a bind)
             liftIO $ putStrLn "LoopTail..."
-            return x `f` (if x < 3 then loopTail (x + 1) else empty)
+            t $ return x <> (if x < 3 then loopTail (x + 1) else nil)
 
 bindAndComposeSimple
-    :: (IsStream t, Alternative (t IO), Monad (t IO))
-    => (forall a. Ord a => t IO a -> IO [a])
-    -> (t IO Int -> t IO Int -> t IO Int)
+    :: ( IsStream t1, IsStream t2, Semigroup (t2 IO Int), Monad (t2 IO))
+    => (t1 IO Int -> t1 IO Int)
+    -> (t2 IO Int -> t2 IO Int)
     -> Spec
-bindAndComposeSimple tl g = do
+bindAndComposeSimple t1 t2 = do
+    -- XXX need a bind in the body of forEachWith instead of a simple return
     it "Compose many (right fold) with bind" $
-        (tl (forEachWith g [1..10 :: Int] $ \x -> return x `f` (return .  id))
+        ((A.toList . t1) (adapt . t2 $ forEachWith (<>) [1..10 :: Int] return)
             >>= return . sort) `shouldReturn` [1..10]
 
     it "Compose many (left fold) with bind" $
-        let forL xs k = foldl g empty $ map k xs
-         in (tl (forL [1..10 :: Int] $ \x -> return x `f` (return . id))
+        let forL xs k = foldl (<>) nil $ map k xs
+         in ((A.toList . t1) (adapt . t2 $ forL [1..10 :: Int] return)
                 >>= return . sort) `shouldReturn` [1..10]
-    where f = (>>=)
 
 bindAndComposeHierarchy
-    :: Monad (s IO) => (forall a. Ord a => s IO a -> IO [a])
-    -> ([s IO Int] -> s IO Int)
+    :: ( IsStream t1, Monad (t1 IO)
+       , IsStream t2, Monad (t2 IO))
+    => (t1 IO Int -> t1 IO Int)
+    -> (t2 IO Int -> t2 IO Int)
+    -> ([t2 IO Int] -> t2 IO Int)
     -> Spec
-bindAndComposeHierarchy tl g = do
+bindAndComposeHierarchy t1 t2 g = do
     it "Bind and compose nested" $
-        (tl bindComposeNested >>= return . sort)
+        ((A.toList . t1) bindComposeNested >>= return . sort)
             `shouldReturn` (sort (
                    [12, 18]
                 ++ replicate 3 13
@@ -489,12 +523,11 @@ bindAndComposeHierarchy tl g = do
 --         in m
          in b
 
-    tripleCompose a b c = g [a, b, c]
+    tripleCompose a b c = adapt . t2 $ g [a, b, c]
     tripleBind mx my mz =
-        mx `f` \x -> my
-           `f` \y -> mz
-           `f` \z -> return (x + y + z)
-    f = (>>=)
+        mx >>= \x -> my
+           >>= \y -> mz
+           >>= \z -> return (x + y + z)
 
 mixedOps :: Spec
 mixedOps = do
@@ -512,14 +545,14 @@ mixedOps = do
         x <- return 1
         y <- return 2
         z <- do
-                x1 <- return 1 <|> return 2
+                x1 <- adapt . parallely $ return 1 <> return 2
                 liftIO $ return ()
                 liftIO $ putStr ""
-                y1 <- return 1 <| return 2
+                y1 <- adapt . asyncly $ return 1 <> return 2
                 z1 <- do
                     x11 <- return 1 <> return 2
-                    y11 <- return 1 <| return 2
-                    z11 <- return 1 <=> return 2
+                    y11 <- adapt . asyncly $ return 1 <> return 2
+                    z11 <- adapt . interleaving $ return 1 <> return 2
                     liftIO $ return ()
                     liftIO $ putStr ""
                     return (x11 + y11 + z11)
diff --git a/test/Prop.hs b/test/Prop.hs
index 33cd80c3..fb17b0a6 100644
--- a/test/Prop.hs
+++ b/test/Prop.hs
@@ -15,8 +15,12 @@ import Test.QuickCheck.Monadic (run, monadicIO, monitor, assert, PropertyM)
 import Test.Hspec
 
 import Streamly
+import Streamly.Prelude ((.:), nil)
 import qualified Streamly.Prelude as A
 
+singleton :: IsStream t => a -> t m a
+singleton a = a .: nil
+
 sortEq :: Ord a => [a] -> [a] -> Bool
 sortEq a b = sort a == sort b
 
@@ -203,20 +207,19 @@ transformOpsWord8 constr desc t = do
 
 -- XXX concatenate streams of multiple elements rather than single elements
 semigroupOps
-    :: (IsStream t, MonadPlus (t IO)
+    :: (IsStream t
 
 #if __GLASGOW_HASKELL__ < 804
        , Semigroup (t IO Int)
 #endif
        , Monoid (t IO Int))
-    => String -> (t IO Int -> t IO Int) -> Spec
-semigroupOps desc t = do
-    prop (desc ++ " <>") $ foldFromList (foldMapWith (<>) return) t (==)
-    prop (desc ++ " mappend") $ foldFromList (foldMapWith mappend return) t (==)
-    prop (desc ++ " <=>") $ foldFromList (foldMapWith (<=>) return) t (==)
-    prop (desc ++ " <|>") $ foldFromList (foldMapWith (<|>) return) t sortEq
-    prop (desc ++ " mplus") $ foldFromList (foldMapWith mplus return) t sortEq
-    prop (desc ++ " <|") $ foldFromList (foldMapWith (<|) return) t sortEq
+    => String
+    -> (t IO Int -> t IO Int)
+    -> ([Int] -> [Int] -> Bool)
+    -> Spec
+semigroupOps desc t eq = do
+    prop (desc ++ " <>") $ foldFromList (foldMapWith (<>) singleton) t eq
+    prop (desc ++ " mappend") $ foldFromList (foldMapWith mappend singleton) t eq
 
 applicativeOps
     :: (IsStream t, Applicative (t IO))
@@ -330,8 +333,12 @@ main = hspec $ do
         functorOps folded "zippingAsync folded" zippingAsync (==)
 
     describe "Semigroup operations" $ do
-        semigroupOps "serially" serially
-        semigroupOps "interleaving" interleaving
+        semigroupOps "serially" serially (==)
+        semigroupOps "interleaving" interleaving (==)
+        semigroupOps "asyncly" asyncly sortEq
+        semigroupOps "parallely" parallely sortEq
+        semigroupOps "zipping" zipping (==)
+        semigroupOps "zippingAsync" zippingAsync (==)
 
     describe "Applicative operations" $ do
         -- The tests using sorted equality are weaker tests