diff --git a/mwc-probability-transition.cabal b/mwc-probability-transition.cabal
--- a/mwc-probability-transition.cabal
+++ b/mwc-probability-transition.cabal
@@ -1,5 +1,5 @@
 name:                mwc-probability-transition
-version:             0.1.0.0
+version:             0.2.0.0
 synopsis:            A Markov stochastic transition operator with logging
 description:
             .
@@ -31,8 +31,6 @@
                      , primitive
                      , transformers
 
-
-
 test-suite spec
   default-language:    Haskell2010
   ghc-options:         -Wall
@@ -40,6 +38,7 @@
   hs-source-dirs:      test
   main-is:             LibSpec.hs
   build-depends:       base
+                     , mwc-probability
                      , mwc-probability-transition
                      , hspec
                      , QuickCheck
diff --git a/src/System/Random/MWC/Probability/Transition.hs b/src/System/Random/MWC/Probability/Transition.hs
--- a/src/System/Random/MWC/Probability/Transition.hs
+++ b/src/System/Random/MWC/Probability/Transition.hs
@@ -1,5 +1,6 @@
 {-# language OverloadedStrings #-}
 {-# language DeriveFunctor, GeneralizedNewtypeDeriving #-}
+{-# language FlexibleContexts #-}
 module System.Random.MWC.Probability.Transition (
   -- * Transition
     Transition
@@ -7,10 +8,10 @@
   , runTransition
   -- ** Helper functions
   , withSeverity
-  -- * Re-exported from `logging-effect`
-  , Handler
-  , WithSeverity(..), Severity(..)
-  -- , withFDHandler, defaultBatchingOptions
+  -- -- * Re-exported from `logging-effect`
+  -- , Handler
+  -- , WithSeverity(..), Severity(..)
+  -- -- , withFDHandler, defaultBatchingOptions
   ) where
 
 import Control.Monad
@@ -33,6 +34,9 @@
   Gen (PrimState m) -> StateT s (LoggingT message m) a
   ) deriving (Functor)
 
+instance Show (Transition msg s m a) where
+  show _ = "<Transition>"
+
 -- | Construct a 'Transition' from sampling, state transformation and logging functions.
 --
 -- NB: The three function arguments are used in the order in which they appear here:
@@ -45,7 +49,7 @@
 mkTransition :: Monad m =>
         (s -> Prob m t)     -- ^ Random generation
      -> (s -> t -> (a, s))  -- ^ (Output, Next state)
-     -> (a -> s -> message) -- ^ Log message generation
+     -> (a -> s -> message) -- ^ Log message construction
      -> Transition message s m a
 mkTransition fm fs flog = Transition $ \gen -> do
   s <- S.get
@@ -62,12 +66,14 @@
       -> Int                      -- ^ Number of iterations 
       -> s                        -- ^ Initial state
       -> Gen (PrimState m)        -- ^ PRNG
-      -> m [(a, s)]
+      -> m ([a], s)               -- ^ (Outputs, Final state)
 runTransition logf (Transition fm) n s0 g =
-  runLoggingT (replicateM n (runStateT (fm g) s0)) logf
+  runLoggingT (runStateT (replicateM n (fm g)) s0) logf
 
 
 
+
+-- * Helpers
   
 bracketsUpp :: Show a => a -> String
 bracketsUpp p = unwords ["[", map toUpper (show p), "]"]
diff --git a/test/LibSpec.hs b/test/LibSpec.hs
--- a/test/LibSpec.hs
+++ b/test/LibSpec.hs
@@ -3,14 +3,30 @@
 import Test.Hspec
 import Test.Hspec.QuickCheck
 
+import System.Random.MWC.Probability
+import System.Random.MWC.Probability.Transition
 
+
 main :: IO ()
 main = hspec spec
 
 spec :: Spec
 spec =
-  describe "Lib" $ do
-    it "works" $ do
-      True `shouldBe` True
+  describe "System.Random.MWC.Probability.Transition" $ do
+    it "computes the final state of a sequence of deterministic transitions" $ do
+      (_, z) <- runT01
+      z `shouldBe` 5
     -- prop "ourAdd is commutative" $ \x y ->
     --   ourAdd x y `shouldBe` ourAdd y x
+
+
+runT01 :: IO ([Double], Double)
+runT01 = create >>= runTransition (putStrLn . withSeverity id) t01 5 0
+
+t01 :: Monad m => Transition (WithSeverity String) Double m Double
+t01 = mkTransition modelf statef logf where
+  modelf _ = pure (1 :: Double)
+  statef s t = (t, s + 1)
+  logf _ s = WithSeverity Informational (show s)
+
+