diff --git a/src/Synthesizer/Causal/Process.hs b/src/Synthesizer/Causal/Process.hs
--- a/src/Synthesizer/Causal/Process.hs
+++ b/src/Synthesizer/Causal/Process.hs
@@ -79,7 +79,6 @@
 
 import qualified Synthesizer.Plain.Modifier as Modifier
 
-import qualified Data.StorableVector.Lazy as SVL
 import qualified Data.StorableVector as SV
 
 import Foreign.Storable (Storable, )
@@ -382,7 +381,7 @@
 applyStorableChunk (Cons next start) = Cons
    (\a -> StateT $ \ms ->
       flip fmap ms $ \s ->
-         SVL.crochetLChunk (runStateT . next) s a)
+         SV.crochetLResult (runStateT . next) s a)
    (Just start)
 
 
diff --git a/src/Synthesizer/CausalIO/Gate.hs b/src/Synthesizer/CausalIO/Gate.hs
--- a/src/Synthesizer/CausalIO/Gate.hs
+++ b/src/Synthesizer/CausalIO/Gate.hs
@@ -20,6 +20,7 @@
 
 import qualified Data.StorableVector as SV
 import qualified Data.Monoid as Mn
+import qualified Data.Semigroup as Sg
 import Data.Maybe.HT (toMaybe, )
 
 import qualified Numeric.NonNegative.Class as NonNeg
@@ -60,6 +61,9 @@
 instance CutG.NormalForm (Chunk a) where
    evaluateHead (Chunk dur rel) =
       dur `seq` rel `seq` ()
+
+instance Sg.Semigroup (Chunk a) where
+   (<>) = error "Gate.mappend cannot be defined"
 
 instance Mn.Monoid (Chunk a) where
    mempty = error "Gate.mempty cannot be defined"
diff --git a/src/Synthesizer/CausalIO/Process.hs b/src/Synthesizer/CausalIO/Process.hs
--- a/src/Synthesizer/CausalIO/Process.hs
+++ b/src/Synthesizer/CausalIO/Process.hs
@@ -40,6 +40,7 @@
 import Control.Monad (mplus, )
 
 import Data.Monoid (Monoid, mempty, mappend, )
+import Data.Semigroup (Semigroup, (<>), )
 
 import System.IO.Unsafe (unsafePerformIO, unsafeInterleaveIO, )
 
@@ -194,6 +195,9 @@
    uncurry Zip.Cons ^<< ab &&& ac
 
 
+instance (CutG.Transform a, CutG.Read b, Semigroup b) => Semigroup (T a b) where
+   (<>) = append (<>)
+
 {- |
 @mappend@ should be used sparingly.
 In a loop it will have to construct types at runtime
@@ -204,27 +208,32 @@
       (\ _a () -> return (mempty, ()))
       (return ())
       (\() -> return ())
-   mappend
-         (Cons nextX createX deleteX)
-         (Cons nextY createY deleteY) = Cons
-      (\a s ->
-         case s of
-            Left s0 -> do
-               (b1,s1) <- nextX a s0
-               let lenA = CutG.length a
-                   lenB = CutG.length b1
-               case compare lenA lenB of
-                  LT -> error "CausalIO.Process.mappend: output chunk is larger than input chunk"
-                  EQ -> return (b1, Left s1)
-                  GT -> do
-                     deleteX s1
-                     (b2,s2) <- nextY (CutG.drop lenB a) =<< createY
-                     return (mappend b1 b2, Right s2)
-            Right s0 -> do
-               (b1,s1) <- nextY a s0
-               return (b1, Right s1))
-      (fmap Left createX)
-      (either deleteX deleteY)
+   mappend = append mappend
+
+append ::
+   (CutG.Transform a, CutG.Read b) =>
+   (b -> b -> b) -> T a b -> T a b -> T a b
+append app
+      (Cons nextX createX deleteX)
+      (Cons nextY createY deleteY) = Cons
+   (\a s ->
+      case s of
+         Left s0 -> do
+            (b1,s1) <- nextX a s0
+            let lenA = CutG.length a
+                lenB = CutG.length b1
+            case compare lenA lenB of
+               LT -> error "CausalIO.Process.mappend: output chunk is larger than input chunk"
+               EQ -> return (b1, Left s1)
+               GT -> do
+                  deleteX s1
+                  (b2,s2) <- nextY (CutG.drop lenB a) =<< createY
+                  return (app b1 b2, Right s2)
+         Right s0 -> do
+            (b1,s1) <- nextY a s0
+            return (b1, Right s1))
+   (fmap Left createX)
+   (either deleteX deleteY)
 
 
 data State a b =
diff --git a/src/Synthesizer/Generic/LengthSignal.hs b/src/Synthesizer/Generic/LengthSignal.hs
--- a/src/Synthesizer/Generic/LengthSignal.hs
+++ b/src/Synthesizer/Generic/LengthSignal.hs
@@ -6,6 +6,7 @@
 import qualified Synthesizer.Generic.Cut as CutG
 
 import Data.Monoid (Monoid, mempty, mappend, )
+import Data.Semigroup (Semigroup, (<>), )
 import Data.Tuple.HT (mapSnd, )
 
 import qualified Algebra.Additive       as Additive
@@ -34,6 +35,9 @@
    negate xs = xs{body = SigG.map negate (body xs)}
    (Cons xl xs) + (Cons yl ys) =
       Cons (max xl yl) (SigG.mix xs ys)
+
+instance (Semigroup sig) => Semigroup (T sig) where
+   Cons xl xs <> Cons yl ys = Cons (xl+yl) (xs <> ys)
 
 instance (Monoid sig) => Monoid (T sig) where
    mempty = Cons zero mempty
diff --git a/src/Synthesizer/Generic/Signal.hs b/src/Synthesizer/Generic/Signal.hs
--- a/src/Synthesizer/Generic/Signal.hs
+++ b/src/Synthesizer/Generic/Signal.hs
@@ -52,6 +52,7 @@
 import Data.Function (fix, )
 import Data.Tuple.HT (mapPair, mapFst, fst3, snd3, thd3, )
 import Data.Monoid (Monoid, mappend, mempty, )
+import Data.Semigroup (Semigroup, (<>), )
 
 import qualified Algebra.ToInteger    as ToInteger
 import qualified Algebra.ToRational   as ToRational
@@ -148,9 +149,12 @@
              ToInteger.C, ToRational.C, Absolute.C,
              RealIntegral.C, Integral.C)
 
+instance Semigroup LazySize where
+   LazySize a <> LazySize b = LazySize (a + b)
+
 instance Monoid LazySize where
    mempty = LazySize 0
-   mappend (LazySize a) (LazySize b) = LazySize (a + b)
+   mappend = (<>)
 
 instance Monoid.C LazySize where
    idt = LazySize 0
@@ -363,7 +367,7 @@
    scanL f a x = writeSV (readSV (SV.scanl f a) x)
    {-# INLINE crochetL #-}
    crochetL f a x =
-      writeSV (fst (readSV (SVL.crochetLChunk f a) x))
+      writeSV (fst (readSV (SV.crochetLResult f a) x))
       -- fst . SV.crochetContL f acc
    {-# INLINE zipWithAppend #-}
    zipWithAppend f =
diff --git a/src/Synthesizer/Interpolation/Custom.hs b/src/Synthesizer/Interpolation/Custom.hs
--- a/src/Synthesizer/Interpolation/Custom.hs
+++ b/src/Synthesizer/Interpolation/Custom.hs
@@ -27,8 +27,7 @@
 
 import Synthesizer.Interpolation.Class ((+.*), )
 
-import Control.Applicative.HT (liftA4, )
-import Control.Applicative (liftA2, )
+import qualified Control.Applicative.HT as App
 
 import NumericPrelude.Numeric
 import NumericPrelude.Base
@@ -40,7 +39,7 @@
 linear :: (Interpol.C t y) => T t y
 linear =
    fromPrefixReader "linear" 0
-      (liftA2
+      (App.lift2
           (\x0 x1 phase -> Interpol.combine2 phase (x0,x1))
           getNode getNode)
 
@@ -57,7 +56,7 @@
 {-# INLINE cubic #-}
 cubic :: (Field.C t, Interpol.C t y) => T t y
 cubic =
-   fromPrefixReader "cubicAlt" 1 $ liftA4
+   fromPrefixReader "cubicAlt" 1 $ App.lift4
       (\xm1 x0 x1 x2 t ->
        let (am1, a0, a1) = cubicHalf    t
            ( b2, b1, b0) = cubicHalf (1-t)
diff --git a/src/Synthesizer/Interpolation/Module.hs b/src/Synthesizer/Interpolation/Module.hs
--- a/src/Synthesizer/Interpolation/Module.hs
+++ b/src/Synthesizer/Interpolation/Module.hs
@@ -28,8 +28,7 @@
 import qualified Algebra.Module    as Module
 import qualified Algebra.Field     as Field
 
-import Control.Applicative.HT (liftA4, )
-import Control.Applicative (liftA2, )
+import qualified Control.Applicative.HT as App
 
 import NumericPrelude.Numeric
 import NumericPrelude.Base
@@ -40,7 +39,7 @@
 linear :: (Module.C t y) => T t y
 linear =
    fromPrefixReader "linear" 0
-      (liftA2 Core.linear getNode getNode)
+      (App.lift2 Core.linear getNode getNode)
 
 {- |
 Consider the signal to be piecewise cubic,
@@ -56,13 +55,13 @@
 cubic :: (Field.C t, Module.C t y) => T t y
 cubic =
    fromPrefixReader "cubic" 1
-      (liftA4 Core.cubic getNode getNode getNode getNode)
+      (App.lift4 Core.cubic getNode getNode getNode getNode)
 
 {-# INLINE cubicAlt #-}
 cubicAlt :: (Field.C t, Module.C t y) => T t y
 cubicAlt =
    fromPrefixReader "cubicAlt" 1
-      (liftA4 Core.cubicAlt getNode getNode getNode getNode)
+      (App.lift4 Core.cubicAlt getNode getNode getNode getNode)
 
 
 
diff --git a/src/Synthesizer/Plain/Builder.hs b/src/Synthesizer/Plain/Builder.hs
--- a/src/Synthesizer/Plain/Builder.hs
+++ b/src/Synthesizer/Plain/Builder.hs
@@ -6,6 +6,7 @@
 import qualified Synthesizer.Basic.Binary as BinSmp
 
 import Data.Monoid (Monoid, mempty, mappend, mconcat, Endo(Endo), appEndo, )
+import Data.Semigroup (Semigroup, (<>), )
 
 import qualified Algebra.FloatingPoint as Float
 import qualified Algebra.ToInteger as ToInteger
@@ -21,9 +22,12 @@
 type Put a = a -> T a
 
 
+instance Semigroup (T a) where
+   x <> y = Cons $ decons x <> decons y
+
 instance Monoid (T a) where
    mempty = Cons mempty
-   mappend x y = Cons $ decons x `mappend` decons y
+   mappend = (<>)
 
 put :: Put a
 put = Cons . Endo . (:)
diff --git a/src/Synthesizer/Plain/Filter/Recursive/SecondOrder.hs b/src/Synthesizer/Plain/Filter/Recursive/SecondOrder.hs
--- a/src/Synthesizer/Plain/Filter/Recursive/SecondOrder.hs
+++ b/src/Synthesizer/Plain/Filter/Recursive/SecondOrder.hs
@@ -33,9 +33,8 @@
 
 import qualified Synthesizer.Interpolation.Class as Interpol
 
-import qualified Control.Applicative as App
-import Control.Applicative.HT (liftA4, liftA5, )
-import Control.Applicative (pure, )
+import qualified Control.Applicative.HT as App
+import Control.Applicative (Applicative, pure, (<*>), )
 
 import qualified Data.Foldable as Fold
 import qualified Data.Traversable as Trav
@@ -69,7 +68,7 @@
    fmap f p = Parameter
       (f $ c0 p) (f $ c1 p) (f $ c2 p) (f $ d1 p) (f $ d2 p)
 
-instance App.Applicative Parameter where
+instance Applicative Parameter where
    {-# INLINE pure #-}
    pure x = Parameter x x x x x
    {-# INLINE (<*>) #-}
@@ -83,14 +82,14 @@
 instance Trav.Traversable Parameter where
    {-# INLINE sequenceA #-}
    sequenceA p =
-      liftA5 Parameter
+      App.lift5 Parameter
          (c0 p) (c1 p) (c2 p) (d1 p) (d2 p)
 
 instance Interpol.C a v => Interpol.C a (Parameter v) where
    {-# INLINE scaleAndAccumulate #-}
    scaleAndAccumulate =
       Interpol.runMac $
-         liftA5 Parameter
+         App.lift5 Parameter
             (Interpol.element c0)
             (Interpol.element c1)
             (Interpol.element c2)
@@ -115,7 +114,7 @@
    fmap f p = State
       (f $ u1 p) (f $ u2 p) (f $ y1 p) (f $ y2 p)
 
-instance App.Applicative State where
+instance Applicative State where
    {-# INLINE pure #-}
    pure x = State x x x x
    {-# INLINE (<*>) #-}
@@ -129,7 +128,7 @@
 instance Trav.Traversable State where
    {-# INLINE sequenceA #-}
    sequenceA p =
-      liftA4 State
+      App.lift4 State
          (u1 p) (u2 p) (y1 p) (y2 p)
 
 
@@ -144,7 +143,7 @@
    Storable a => Store.Dictionary (Parameter a)
 storeParameter =
    Store.run $
-   liftA5 Parameter
+   App.lift5 Parameter
       (Store.element c0)
       (Store.element c1)
       (Store.element c2)
@@ -162,7 +161,7 @@
    Storable a => Store.Dictionary (State a)
 storeState =
    Store.run $
-   liftA4 State
+   App.lift4 State
       (Store.element u1)
       (Store.element u2)
       (Store.element y1)
diff --git a/src/Synthesizer/Plain/Filter/Recursive/Universal.hs b/src/Synthesizer/Plain/Filter/Recursive/Universal.hs
--- a/src/Synthesizer/Plain/Filter/Recursive/Universal.hs
+++ b/src/Synthesizer/Plain/Filter/Recursive/Universal.hs
@@ -40,9 +40,8 @@
 import qualified Synthesizer.Interpolation.Class as Interpol
 
 import qualified Control.Monad.Trans.State as MS
-import qualified Control.Applicative as App
-import Control.Applicative.HT (liftA4, liftA6, )
-import Control.Applicative (pure, liftA2, )
+import qualified Control.Applicative.HT as App
+import Control.Applicative (Applicative, pure, (<*>))
 
 import qualified Data.Foldable as Fold
 import qualified Data.Traversable as Trav
@@ -67,7 +66,7 @@
    fmap f p = Parameter
       (f $ k1 p) (f $ k2 p) (f $ ampIn p) (f $ ampI1 p) (f $ ampI2 p) (f $ ampLimit p)
 
-instance App.Applicative Parameter where
+instance Applicative Parameter where
    {-# INLINE pure #-}
    pure x = Parameter x x x x x x
    {-# INLINE (<*>) #-}
@@ -81,7 +80,7 @@
 instance Trav.Traversable Parameter where
    {-# INLINE sequenceA #-}
    sequenceA p =
-      liftA6 Parameter
+      App.lift6 Parameter
          (k1 p) (k2 p) (ampIn p) (ampI1 p) (ampI2 p) (ampLimit p)
 
 instance Interpol.C a v => Interpol.C a (Parameter v) where
@@ -89,7 +88,7 @@
    scaleAndAccumulate =
       Interpol.scaleAndAccumulateApplicative
 {-
-      Interpol.runMac $ liftA6 Parameter
+      Interpol.runMac $ App.lift6 Parameter
          (Interpol.element k1)
          (Interpol.element k2)
          (Interpol.element ampIn)
@@ -108,7 +107,7 @@
    Storable a => Store.Dictionary (Parameter a)
 storeParameter =
    Store.run $
-   liftA6 Parameter
+   App.lift6 Parameter
       (Store.element k1)
       (Store.element k2)
       (Store.element ampIn)
@@ -125,7 +124,7 @@
    fmap f p = Result
       (f $ highpass p) (f $ bandpass p) (f $ lowpass p) (f $ bandlimit p)
 
-instance App.Applicative Result where
+instance Applicative Result where
    {-# INLINE pure #-}
    pure x = Result x x x x
    {-# INLINE (<*>) #-}
@@ -139,7 +138,7 @@
 instance Trav.Traversable Result where
    {-# INLINE sequenceA #-}
    sequenceA p =
-      liftA4 Result
+      App.lift4 Result
          (highpass p) (bandpass p) (lowpass p) (bandlimit p)
 
 instance Additive.C v => Additive.C (Result v) where
@@ -148,8 +147,8 @@
    {-# INLINE (-) #-}
    {-# INLINE negate #-}
    zero   = pure zero
-   (+)    = liftA2 (+)
-   (-)    = liftA2 (-)
+   (+)    = App.lift2 (+)
+   (-)    = App.lift2 (-)
    negate = fmap negate
 {-
    zero = Result zero zero zero zero
@@ -179,7 +178,7 @@
    Storable a => Store.Dictionary (Result a)
 storeResult =
    Store.run $
-   liftA4 Result
+   App.lift4 Result
       (Store.element highpass)
       (Store.element bandpass)
       (Store.element lowpass)
diff --git a/src/Synthesizer/State/Signal.hs b/src/Synthesizer/State/Signal.hs
--- a/src/Synthesizer/State/Signal.hs
+++ b/src/Synthesizer/State/Signal.hs
@@ -35,6 +35,7 @@
 
 import Data.Foldable (Foldable, foldr, )
 import Data.Monoid (Monoid, mappend, mempty, )
+import Data.Semigroup (Semigroup, (<>), )
 
 import qualified Synthesizer.Storable.Signal as SigSt
 import qualified Data.StorableVector.Lazy.Pattern as SVL
@@ -937,6 +938,9 @@
 monoidConcatMap :: Monoid m => (a -> m) -> T a -> m
 monoidConcatMap = foldMap
 
+
+instance Semigroup (T y) where
+   (<>) = append
 
 instance Monoid (T y) where
    mempty = empty
diff --git a/src/Synthesizer/Zip.hs b/src/Synthesizer/Zip.hs
--- a/src/Synthesizer/Zip.hs
+++ b/src/Synthesizer/Zip.hs
@@ -6,6 +6,7 @@
 import Control.Arrow (Arrow, (<<<), (^<<), (<<^), )
 
 import Data.Monoid (Monoid, mempty, mappend, )
+import Data.Semigroup (Semigroup, (<>), )
 
 
 {- |
@@ -108,6 +109,9 @@
 arrowSplitShorten a b =
    arrowFirstShorten a <<< arrowSecondShorten b
 
+
+instance (Semigroup a, Semigroup b) => Semigroup (T a b) where
+   Cons a0 b0 <> Cons a1 b1 = Cons (a0 <> a1) (b0 <> b1)
 
 instance (Monoid a, Monoid b) => Monoid (T a b) where
    mempty = Cons mempty mempty
diff --git a/synthesizer-core.cabal b/synthesizer-core.cabal
--- a/synthesizer-core.cabal
+++ b/synthesizer-core.cabal
@@ -1,5 +1,5 @@
 Name:           synthesizer-core
-Version:        0.8.1.2
+Version:        0.8.2
 License:        GPL
 License-File:   LICENSE
 Author:         Henning Thielemann <haskell@henning-thielemann.de>
@@ -25,7 +25,7 @@
 Stability:      Experimental
 Tested-With:    GHC==6.4.1, GHC==6.8.2, GHC==6.10.4, GHC==6.12.3
 Tested-With:    GHC==7.0.4, GHC==7.2.1, GHC==7.4.2, GHC==7.6.3
-Cabal-Version:  >=1.14
+Cabal-Version:  1.14
 Build-Type:     Simple
 
 Extra-Source-Files:
@@ -38,7 +38,7 @@
 
 
 Source-Repository this
-  Tag:         0.8.1.2
+  Tag:         0.8.2
   Type:        darcs
   Location:    http://code.haskell.org/synthesizer/core/
 
@@ -52,12 +52,13 @@
     sox >=0.1 && <0.3,
     transformers >=0.2 && <0.6,
     non-empty >=0.2 && <0.4,
+    semigroups >=0.1 && <1.0,
     event-list >=0.1 && <0.2,
     non-negative >=0.1 && <0.2,
     explicit-exception >=0.1.6 && <0.2,
     numeric-prelude >=0.4.2 && <0.5,
     numeric-quest >=0.1 && <0.3,
-    utility-ht >=0.0.12 && <0.1,
+    utility-ht >=0.0.14 && <0.1,
     filepath >=1.1 && <1.5,
     bytestring >=0.9 && <0.11,
     binary >=0.1 && <1,
@@ -273,6 +274,8 @@
     Test.Sound.Synthesizer.Generic.Filter
     Test.Sound.Synthesizer.Storable.Cut
     Test.Sound.Synthesizer.Causal.Analysis
+    Synthesizer.Basic.NumberTheory
+    Synthesizer.Generic.Permutation
   Main-Is: Test/Main.hs