diff --git a/Math/Combinatorics/Species.hs b/Math/Combinatorics/Species.hs
--- a/Math/Combinatorics/Species.hs
+++ b/Math/Combinatorics/Species.hs
@@ -32,6 +32,7 @@
     , madeOf
     , (><), (@@)
     , x, sets, cycles
+    , lists
     , subsets
     , ksubsets
     , elements
@@ -40,7 +41,6 @@
     , pointed
 
       -- ** Derived species
-    , list, lists
     , octopus, octopi
     , partition, partitions
     , permutation, permutations
diff --git a/Math/Combinatorics/Species/AST.hs b/Math/Combinatorics/Species/AST.hs
--- a/Math/Combinatorics/Species/AST.hs
+++ b/Math/Combinatorics/Species/AST.hs
@@ -38,11 +38,11 @@
 --   for that purpose the existential wrapper 'SpeciesAST' is
 --   provided.
 data SpeciesTypedAST s where
-   O        :: SpeciesTypedAST Z
-   I        :: SpeciesTypedAST (S Z)
+   N        :: Integer -> SpeciesTypedAST Z
    X        :: SpeciesTypedAST X
    E        :: SpeciesTypedAST E
    C        :: SpeciesTypedAST C
+   L        :: SpeciesTypedAST L
    Subset   :: SpeciesTypedAST Sub
    KSubset  :: Integer -> SpeciesTypedAST Sub
    Elt      :: SpeciesTypedAST Elt
@@ -63,11 +63,11 @@
    NonEmpty :: SpeciesTypedAST f -> SpeciesTypedAST f
 
 instance Show (SpeciesTypedAST s) where
-  showsPrec _ O                   = showChar '0'
-  showsPrec _ I                   = showChar '1'
+  showsPrec _ (N n)               = shows n
   showsPrec _ X                   = showChar 'X'
   showsPrec _ E                   = showChar 'E'
   showsPrec _ C                   = showChar 'C'
+  showsPrec _ L                   = showChar 'L'
   showsPrec _ Subset              = showChar 'p'
   showsPrec _ (KSubset n)         = showChar 'p' . shows n
   showsPrec _ (Elt)               = showChar 'e'
@@ -112,13 +112,14 @@
   show (SA f) = show f
 
 instance Additive.C SpeciesAST where
-  zero   = SA O
+  zero   = SA (N 0)
   (SA f) + (SA g) = SA (f :+: g)
   negate = error "negation is not implemented yet!  wait until virtual species..."
 
 instance Ring.C SpeciesAST where
   (SA f) * (SA g) = SA (f :*: g)
-  one = SA I
+  one = SA (N 1)
+  fromInteger n = SA (N n)
 
 instance Differential.C SpeciesAST where
   differentiate (SA f) = SA (Der f)
@@ -127,6 +128,7 @@
   singleton               = SA X
   set                     = SA E
   cycle                   = SA C
+  list                    = SA L
   subset                  = SA Subset
   ksubset k               = SA (KSubset k)
   element                 = SA Elt
@@ -142,7 +144,7 @@
 --   example:
 --
 -- > > reify octopus
--- > C . C'+
+-- > C . L+
 -- > > reify (ksubset 3)
 -- > E3 * E
 
@@ -151,11 +153,11 @@
 
 -- | Reflect an AST back into any instance of the 'Species' class.
 reflectT :: Species s => SpeciesTypedAST f -> s
-reflectT O                   = zero
-reflectT I                   = one
+reflectT (N n)               = fromInteger n
 reflectT X                   = singleton
 reflectT E                   = set
 reflectT C                   = cycle
+reflectT L                   = list
 reflectT Subset              = subset
 reflectT (KSubset k)         = ksubset k
 reflectT Elt                 = element
diff --git a/Math/Combinatorics/Species/Class.hs b/Math/Combinatorics/Species/Class.hs
--- a/Math/Combinatorics/Species/Class.hs
+++ b/Math/Combinatorics/Species/Class.hs
@@ -17,6 +17,7 @@
     , x
     , sets
     , cycles
+    , lists
     , subsets
     , ksubsets
     , elements
@@ -29,7 +30,6 @@
       -- * Derived species
       -- $derived
 
-    , list, lists
     , octopus, octopi
     , partition, partitions
     , permutation, permutations
@@ -80,6 +80,13 @@
   -- | The species C of cyclical orderings (cycles/rings).
   cycle     :: s
 
+  -- | The species L of linear orderings (lists): since lists are
+  --   isomorphic to cycles with a hole, we may take L = C' as the
+  --   default implementation; list is included in the 'Species' class
+  --   so it can be special-cased for generation.
+  list :: s
+  list  = oneHole cycle
+
   -- | The species p of subsets is given by p = E * E. 'subset' has a
   --   default implementation of @set * set@, but is included in the
   --   'Species' class so it can be overridden when generating
@@ -186,11 +193,6 @@
 -- $derived
 -- Some species that can be defined in terms of the primitive species
 -- operations.
-
--- | The species L of linear orderings (lists): since lists are
---   isomorphic to cycles with a hole, we may take L = C'.
-list :: Species s => s
-list  = oneHole cycle
 
 lists :: Species s => s
 lists = list
diff --git a/Math/Combinatorics/Species/Generate.hs b/Math/Combinatorics/Species/Generate.hs
--- a/Math/Combinatorics/Species/Generate.hs
+++ b/Math/Combinatorics/Species/Generate.hs
@@ -46,14 +46,14 @@
 --   existentially quantified as well; see 'generate' and
 --   'generateTyped' below.
 generateF :: SpeciesTypedAST s -> [a] -> [StructureF s a]
-generateF O _            = []
-generateF I []           = [Const 1]
-generateF I _            = []
+generateF (N n) []       = map Const [1..n]
+generateF (N _) _        = []
 generateF X [x]          = [Identity x]
 generateF X _            = []
 generateF E xs           = [Set xs]
 generateF C []           = []
 generateF C (x:xs)       = map (Cycle . (x:)) (sPermutations xs)
+generateF L xs           = sPermutations xs
 generateF Subset xs      = map (Set . fst) (pSet xs)
 generateF (KSubset k) xs = map Set (sKSubsets k xs)
 generateF Elt xs         = map Identity xs
@@ -221,6 +221,8 @@
         showsPrecST p t =
           case splitTyConApp t of
             (tycon, [])   -> showString (dropQuals $ tyConString tycon)
+            (tycon, [x])  | tyConString tycon == "[]" 
+                          -> showChar '[' . showsPrecST 11 x . showChar ']'
             (tycon, args) -> showParen (p > 9)
                            $ showString (dropQuals $ tyConString tycon)
                            . showChar ' '
diff --git a/Math/Combinatorics/Species/Labelled.hs b/Math/Combinatorics/Species/Labelled.hs
--- a/Math/Combinatorics/Species/Labelled.hs
+++ b/Math/Combinatorics/Species/Labelled.hs
@@ -39,11 +39,12 @@
   ofSizeExactly s n = (liftEGF . PS.lift1 $ selectIndex n) s
 
 -- | Extract the coefficients of an exponential generating function as
---   a list of Integers.  Since 'EGF' is an instance of
---   'Species', the idea is that 'labelled' can be applied directly to
---   an expression of the Species DSL.  In particular, @labelled s !!
---   n@ is the number of labelled s-structures on an underlying set of
---   size n.  For example:
+--   a list of Integers.  Since 'EGF' is an instance of 'Species', the
+--   idea is that 'labelled' can be applied directly to an expression
+--   of the Species DSL.  In particular, @labelled s !!  n@ is the
+--   number of labelled s-structures on an underlying set of size n
+--   (note that @labelled s@ is guaranteed to be an infinite list).
+--   For example:
 --
 -- > > take 10 $ labelled octopi
 -- > [0,1,3,14,90,744,7560,91440,1285200,20603520]
@@ -51,7 +52,10 @@
 --   gives the number of labelled octopi on 0, 1, 2, 3, ... 9 elements.
 
 labelled :: EGF -> [Integer]
-labelled (EGF f) = map numerator . zipWith (*) (map fromInteger facts) . map unLR 
+labelled (EGF f) = (++repeat 0) 
+                 . map numerator 
+                 . zipWith (*) (map fromInteger facts) 
+                 . map unLR 
                  $ PS.coeffs f
 
 -- A previous version of this module used an EGF library which
diff --git a/Math/Combinatorics/Species/Types.hs b/Math/Combinatorics/Species/Types.hs
--- a/Math/Combinatorics/Species/Types.hs
+++ b/Math/Combinatorics/Species/Types.hs
@@ -60,7 +60,7 @@
       -- * Type-level species
       -- $typespecies
 
-    , Z, S, X, E, C, Sub, Elt, (:+:), (:*:), (:.:), (:><:), (:@:), Der
+    , Z, X, E, C, L, Sub, Elt, (:+:), (:*:), (:.:), (:><:), (:@:), Der
     , StructureF
     ) where
 
@@ -327,10 +327,10 @@
 -- dependently typed language.
 
 data Z
-data S n
 data X
 data E
 data C
+data L
 data Sub
 data Elt
 data (:+:) f g
@@ -346,10 +346,10 @@
 --   @a@, has type @StructureF s a@.
 type family StructureF t :: * -> *
 type instance StructureF Z            = Const Integer
-type instance StructureF (S s)        = Const Integer
 type instance StructureF X            = Identity
 type instance StructureF E            = Set
 type instance StructureF C            = Cycle
+type instance StructureF L            = []
 type instance StructureF Sub          = Set
 type instance StructureF Elt          = Identity
 type instance StructureF (f :+: g)    = Sum (StructureF f) (StructureF g)
diff --git a/Math/Combinatorics/Species/Unlabelled.hs b/Math/Combinatorics/Species/Unlabelled.hs
--- a/Math/Combinatorics/Species/Unlabelled.hs
+++ b/Math/Combinatorics/Species/Unlabelled.hs
@@ -32,12 +32,12 @@
   ofSizeExactly s n = (liftGF . PS.lift1 $ selectIndex n) s
 
 unlabelledCoeffs :: GF -> [Integer]
-unlabelledCoeffs (GF p) = PS.coeffs p
+unlabelledCoeffs (GF p) = PS.coeffs p ++ repeat 0
 
 -- | Extract the coefficients of an ordinary generating function as a
 --   list of Integers.  In particular, @unlabelled s !!  n@ is the
---   number of unlabelled s-structures on an underlying set of size n.
---   For example:
+--   number of unlabelled s-structures on an underlying set of size n
+--   (@unlabelled s@ is guaranteed to be infinite).  For example:
 --
 -- > > take 10 $ unlabelled octopi
 -- > [0,1,2,3,5,7,13,19,35,59]
diff --git a/species.cabal b/species.cabal
--- a/species.cabal
+++ b/species.cabal
@@ -1,5 +1,5 @@
 name:           species
-version:        0.2
+version:        0.2.1
 license:        BSD3
 license-file:   LICENSE
 build-type:     Simple