diff --git a/src/Language/CQL/Instance.hs b/src/Language/CQL/Instance.hs
index 1e94564..3d1296a 100644
--- a/src/Language/CQL/Instance.hs
+++ b/src/Language/CQL/Instance.hs
@@ -49,6 +49,7 @@ import           Data.Set              (Set)
 import qualified Data.Set              as Set
 import           Data.Typeable         hiding (typeOf)
 import           Data.Void
+import           Language.CQL.Collage (Collage(..), attsFrom, fksFrom, typeOf, typeOfCol)
 import           Language.CQL.Common   (elem', intercalate, fromListAccum, mapl, section, sepTup, toMapSafely, Deps(..), Err, Kind(INSTANCE), MultiTyMap, TyMap, type (+))
 import           Language.CQL.Mapping  as Mapping
 import           Language.CQL.Options
diff --git a/src/Language/CQL/Morphism.hs b/src/Language/CQL/Morphism.hs
index f02e9da..9a00d3f 100644
--- a/src/Language/CQL/Morphism.hs
+++ b/src/Language/CQL/Morphism.hs
@@ -44,8 +44,9 @@ import           Data.Map.Strict       as Map hiding (foldr, size)
 import           Data.Maybe
 import           Data.Set              as Set hiding (foldr, size)
 import           Data.Void
+import           Language.CQL.Collage  (Collage(..))
 import           Language.CQL.Common
-import           Language.CQL.Term     (Collage(..), Ctx, Term(..), EQ(..), subst, upp)
+import           Language.CQL.Term     (Ctx, Term(..), EQ(..), subst, upp)
 import           Prelude               hiding (EQ)
 
 
diff --git a/src/Language/CQL/Prover.hs b/src/Language/CQL/Prover.hs
index f348740..571df01 100644
--- a/src/Language/CQL/Prover.hs
+++ b/src/Language/CQL/Prover.hs
@@ -47,6 +47,8 @@ import           Data.Rewriting.Rules        as Rs
 import           Data.Rewriting.Term         as T
 import           Data.Set                    as Set
 import           Language.CQL.Common
+import           Language.CQL.Collage        as Collage (simplify)
+import           Language.CQL.Collage
 import           Language.CQL.Options        as O hiding (Prover)
 import           Language.CQL.Term           as S
 import           Prelude                     hiding (EQ)
@@ -130,7 +132,7 @@ orthProver col ops = if isDecreasing eqs1 || allow_nonTerm
     else   Left $ "Rewriting Error: not orthogonal.  Pairs are " ++ show (findCps eqs2)
   else     Left   "Rewriting Error: not size decreasing"
   where
-    (col', f) = simplifyCol col
+    (col', f) = Collage.simplify col
 
     p _ (EQ (lhs', rhs')) = nf (convert' lhs') == nf (convert' rhs')
 
@@ -272,7 +274,7 @@ kbProver col ops = if allSortsInhabited col || allow_empty
            in pure $ Prover col p'
       else Left "Completion Error: contains uninhabited sorts"
   where
-    (col', f) = simplifyCol col
+    (col', f) = Collage.simplify col
     p ctx (EQ (lhs', rhs')) = normaliseTerm (completed ctx lhs' rhs') (convert col ctx lhs') == normaliseTerm (completed ctx lhs' rhs') (convert col ctx rhs')
     completed g l r = completePure defaultConfig $ addGoal defaultConfig (initState col') (toGoal g l r)
     allow_empty = bOps ops Allow_Empty_Sorts_Unsafe
@@ -297,7 +299,7 @@ congProver col = if eqsAreGround col'
     hidden = decide rules'
     rules' = fmap (\(_, EQ (l, r)) -> (convertCong l, convertCong r)) $ Set.toList $ ceqs col
     doProof l r = hidden (convertCong l) (convertCong r)
-    (col', f) = simplifyCol col
+    (col', f) = Collage.simplify col
 
 convertCong
   :: (MultiTyMap '[Show, Ord, Typeable, NFData] '[var, ty, sym, en, fk, att, gen, sk])
diff --git a/src/Language/CQL/Schema.hs b/src/Language/CQL/Schema.hs
index 5c43f6f..d406e74 100644
--- a/src/Language/CQL/Schema.hs
+++ b/src/Language/CQL/Schema.hs
@@ -45,6 +45,7 @@ import           Data.Maybe
 import           Data.Set              as Set
 import           Data.Typeable
 import           Data.Void
+import           Language.CQL.Collage (Collage(..), typeOfCol)
 import           Language.CQL.Common
 import           Language.CQL.Options
 import           Language.CQL.Prover
diff --git a/src/Language/CQL/Term.hs b/src/Language/CQL/Term.hs
index e8f2c90..674e284 100644
--- a/src/Language/CQL/Term.hs
+++ b/src/Language/CQL/Term.hs
@@ -110,8 +110,8 @@ show' = dropQuotes . show
 deriving instance TyMap Ord '[var, ty, sym, en, fk, att, gen, sk] => Ord (Term var ty sym en fk att gen sk)
 
 -- | A symbol (non-variable).
-data Head ty sym en fk att gen sk =
-    HSym  sym
+data Head ty sym en fk att gen sk
+  = HSym  sym
   | HFk   fk
   | HAtt  att
   | HGen  gen
@@ -172,8 +172,8 @@ vars x = case x of
   Fk  _ a  -> vars a
   Sym _ as -> concatMap vars as
 
-
-occsTerm :: (Ord sym, Ord fk, Ord att, Ord gen, Ord sk)
+occsTerm
+  :: (Ord sym, Ord fk, Ord att, Ord gen, Ord sk)
   => Term var ty sym en fk att gen sk
   -> Map (Head ty sym en fk att gen sk) Int
 occsTerm x = case x of
@@ -186,14 +186,6 @@ occsTerm x = case x of
   where
     m = merge preserveMissing preserveMissing $ zipWithMatched (\_ x y -> x + y)
 
-occs :: (Ord sym, Ord fk, Ord att, Ord gen, Ord sk)
-  => Collage var ty sym en fk att gen sk
-  -> Map (Head ty sym en fk att gen sk) Int
-occs col = foldr (\(_, EQ (lhs, rhs)) x -> m x $ m (occsTerm lhs) $ occsTerm rhs) Map.empty $ ceqs col
-  where
-    m = merge preserveMissing preserveMissing $ zipWithMatched (\_ x y -> x + y)
-
-
 -- | True if sort will be a type.
 hasTypeType :: Term Void ty sym en fk att gen sk -> Bool
 hasTypeType t = case t of
@@ -214,7 +206,6 @@ hasTypeType'' t = case t of
   Gen _   -> False
   Fk  _ _ -> False
 
-
 ----------------------------------------------------------------------------------------------------------
 -- Substitution and simplification of theories
 
@@ -323,19 +314,6 @@ replaceRepeatedly
 replaceRepeatedly [] t        = t
 replaceRepeatedly ((s,t):r) e = replaceRepeatedly r $ replace' s t e
 
--- | Simplify a collage by replacing symbols of the form @gen/sk = term@, yielding also a
--- translation function from the old theory to the new, encoded as a list of (symbol, term) pairs.
-simplifyCol
-  :: (MultiTyMap '[Show, Ord, NFData] '[var, ty, sym, en, fk, att, gen, sk])
-  =>  Collage var ty sym en fk att gen sk
-  -> (Collage var ty sym en fk att gen sk, [(Head ty sym en fk att gen sk, Term var ty sym en fk att gen sk)])
-simplifyCol (Collage ceqs'  ctys' cens' csyms' cfks' catts' cgens'  csks'    )
-  =         (Collage ceqs'' ctys' cens' csyms' cfks' catts' cgens'' csks'', f)
-  where
-    (ceqs'', f) = simplifyFix ceqs' []
-    cgens''     = Map.fromList $ Prelude.filter (\(x,_) -> notElem (HGen x) $ fmap fst f) $ Map.toList cgens'
-    csks''      = Map.fromList $ Prelude.filter (\(x,_) -> notElem (HSk  x) $ fmap fst f) $ Map.toList csks'
-
 -- | Takes in a theory and a translation function and repeatedly (to fixpoint) attempts to simplfiy (extend) it.
 simplifyFix
   :: (MultiTyMap '[Ord] '[var, ty, sym, en, fk, att, gen, sk])
@@ -403,155 +381,3 @@ deriving instance TyMap Eq '[var, sym, fk, att, gen, sk] => Eq (Term var ty sym
 
 hasTypeType' :: EQ Void ty sym en fk att gen sk -> Bool
 hasTypeType' (EQ (lhs, _)) = hasTypeType lhs
-
-data Collage var ty sym en fk att gen sk
-  = Collage
-  { ceqs  :: Set (Ctx var (ty+en), EQ var ty sym en fk att gen sk)
-  , ctys  :: Set ty
-  , cens  :: Set en
-  , csyms :: Map sym ([ty],ty)
-  , cfks  :: Map fk (en, en)
-  , catts :: Map att (en, ty)
-  , cgens :: Map gen en
-  , csks  :: Map sk ty
-  } deriving (Eq, Show)
-
-eqsAreGround :: Collage var ty sym en fk att gen sk -> Bool
-eqsAreGround col = Prelude.null [ x | x <- Set.toList $ ceqs col, not $ Map.null (fst x) ]
-
-fksFrom :: Eq en => Collage var ty sym en fk att gen sk -> en -> [(fk,en)]
-fksFrom sch en' = f $ Map.assocs $ cfks sch
-  where f []               = []
-        f ((fk,(en1,t)):l) = if en1 == en' then (fk,t) : (f l) else f l
-
-attsFrom :: Eq en => Collage var ty sym en fk att gen sk -> en -> [(att,ty)]
-attsFrom sch en' = f $ Map.assocs $ catts sch
-  where f []               = []
-        f ((fk,(en1,t)):l) = if en1 == en' then (fk,t) : (f l) else f l
-
--- | Gets the type of a term that is already known to be well-typed.
-typeOf
-  :: (MultiTyMap '[Show, Ord, NFData] '[var, ty, sym, en, fk, att, gen, sk])
-  => Collage var ty sym en fk att gen sk
-  -> Term Void Void Void en fk Void gen Void -> en
-typeOf col e = case typeOf' col Map.empty (upp e) of
-  Left _ -> error "Impossible in typeOf, please report."
-  Right x -> case x of
-    Left _  -> error "Impossible in typeOf, please report."
-    Right y -> y
-
-
-checkDoms
-  :: (MultiTyMap '[Show, Ord, NFData] '[var, ty, sym, en, fk, att, gen, sk])
-  => Collage var ty sym en fk att gen sk
-  -> Err ()
-checkDoms col = do
-  mapM_ f    $ Map.elems $ csyms col
-  mapM_ g    $ Map.elems $ cfks  col
-  mapM_ h    $ Map.elems $ catts col
-  mapM_ isEn $ Map.elems $ cgens col
-  mapM_ isTy $ Map.elems $ csks  col
-  where
-    f (t1,t2) = do { mapM_ isTy t1 ; isTy t2 }
-    g (e1,e2) = do { isEn e1 ; isEn e2 }
-    h (e ,t ) = do { isEn e ; isTy t }
-    isEn x  = if Set.member x $ cens col
-      then pure ()
-      else Left $ "Not an entity: " ++ show x
-    isTy x  = if Set.member x $ ctys col
-      then pure ()
-      else Left $ "Not a type: "    ++ show x
-
-typeOfCol
-  :: (MultiTyMap '[Show, Ord, NFData] '[var, ty, sym, en, fk, att, gen, sk])
-  => Collage var ty sym en fk att gen sk
-  -> Err ()
-typeOfCol col = do
-  checkDoms col
-  mapM_ (typeOfEq' col) $ Set.toList $ ceqs col
-
-
-----------------------------------------------------------------------------------------------------
--- Checks if all sorts are inhabited
-
--- | Initialize a mapping of sorts to bools for sort inhabition check.
-initGround :: (Ord ty, Ord en) => Collage var ty sym en fk att gen sk -> (Map en Bool, Map ty Bool)
-initGround col = (me', mt')
-  where
-    me  = Map.fromList $ Prelude.map (\en -> (en, False)) $ Set.toList $ cens col
-    mt  = Map.fromList $ Prelude.map (\ty -> (ty, False)) $ Set.toList $ ctys col
-    me' = Prelude.foldr (\(_, en) m -> Map.insert en True m) me $ Map.toList $ cgens col
-    mt' = Prelude.foldr (\(_, ty) m -> Map.insert ty True m) mt $ Map.toList $ csks  col
-
--- | Applies one layer of symbols to the sort to boolean inhabitation map.
-closeGround :: (Ord ty, Ord en) => Collage var ty sym en fk att gen sk -> (Map en Bool, Map ty Bool) -> (Map en Bool, Map ty Bool)
-closeGround col (me, mt) = (me', mt'')
-  where
-    mt''= Prelude.foldr (\(_, (tys,ty)) m -> if and ((!) mt' <$> tys) then Map.insert ty True m else m) mt' $ Map.toList $ csyms col
-    mt' = Prelude.foldr (\(_, (en, ty)) m -> if (!) me' en then Map.insert ty True m else m)            mt  $ Map.toList $ catts col
-    me' = Prelude.foldr (\(_, (en, _ )) m -> if (!) me  en then Map.insert en True m else m)            me  $ Map.toList $ cfks  col
-
--- | Does a fixed point of closeGround.
-iterGround :: (MultiTyMap '[Show, Ord, NFData] '[ty, en]) => Collage var ty sym en fk att gen sk -> (Map en Bool, Map ty Bool) -> (Map en Bool, Map ty Bool)
-iterGround col r = if r == r' then r else iterGround col r'
- where r' = closeGround col r
-
--- | Gets the inhabitation map for the sorts of a collage.
-computeGround :: (MultiTyMap '[Show, Ord, NFData] '[ty, en]) => Collage var ty sym en fk att gen sk -> (Map en Bool, Map ty Bool)
-computeGround col = iterGround col $ initGround col
-
--- | True iff all sorts in a collage are inhabited.
-allSortsInhabited :: (MultiTyMap '[Show, Ord, NFData] '[ty, en]) => Collage var ty sym en fk att gen sk -> Bool
-allSortsInhabited col = t && f
- where (me, mt) = computeGround col
-       t = and $ Map.elems me
-       f = and $ Map.elems mt
-
---------------------------------------------------------------------------------
-
--- I've given up on non string based error handling for now
-typeOf'
-  :: (MultiTyMap '[Show, Ord, NFData] '[var, ty, sym, en, fk, att, gen, sk])
-  => Collage var ty sym en fk att gen sk
-  -> Ctx var (ty + en)
-  -> Term    var ty sym en fk att gen sk
-  -> Err (ty + en)
-typeOf' _ ctx (Var v) = note ("Unbound variable: " ++ show v) $ Map.lookup v ctx
-typeOf' col _ (Gen g) = case Map.lookup g $ cgens col of
-  Nothing -> Left  $ "Unknown generator: " ++ show g
-  Just t  -> Right $ Right t
-typeOf' col _ (Sk s) = case Map.lookup s $ csks col of
-  Nothing -> Left  $ "Unknown labelled null: " ++ show s
-  Just t  -> Right $ Left t
-typeOf' col ctx xx@(Fk f a) = case Map.lookup f $ cfks col of
-  Nothing     -> Left $ "Unknown foreign key: " ++ show f
-  Just (s, t) -> do s' <- typeOf' col ctx a
-                    if (Right s) == s' then pure $ Right t else Left $ "Expected argument to have entity " ++
-                     show s ++ " but given " ++ show s' ++ " in " ++ (show xx)
-typeOf' col ctx xx@(Att f a) = case Map.lookup f $ catts col of
-  Nothing -> Left $ "Unknown attribute: " ++ show f
-  Just (s, t) -> do s' <- typeOf' col ctx a
-                    if (Right s) == s' then pure $ Left t else Left $ "Expected argument to have entity " ++
-                     show s ++ " but given " ++ show s' ++ " in " ++ (show xx)
-typeOf' col ctx xx@(Sym f a) = case Map.lookup f $ csyms col of
-  Nothing -> Left $ "Unknown function symbol: " ++ show f
-  Just (s, t) -> do s' <- mapM (typeOf' col ctx) a
-                    if length s' == length s
-                    then if (Left <$> s) == s'
-                         then pure $ Left t
-                         else Left $ "Expected arguments to have types " ++
-                     show s ++ " but given " ++ show s' ++ " in " ++ (show $ xx)
-                    else Left $ "Expected argument to have arity " ++
-                     show (length s) ++ " but given " ++ show (length s') ++ " in " ++ (show $ xx)
-
-typeOfEq'
-  :: (MultiTyMap '[Show, Ord, NFData] '[var, ty, sym, en, fk, att, gen, sk])
-  => Collage var ty sym en fk att gen sk
-  -> (Ctx var (ty + en), EQ var ty sym en fk att gen sk)
-  -> Err (ty + en)
-typeOfEq' col (ctx, EQ (lhs, rhs)) = do
-  lhs' <- typeOf' col ctx lhs
-  rhs' <- typeOf' col ctx rhs
-  if lhs' == rhs'
-  then Right lhs'
-  else Left  $ "Equation lhs has type " ++ show lhs' ++ " but rhs has type " ++ show rhs'
diff --git a/src/Language/CQL/Typeside.hs b/src/Language/CQL/Typeside.hs
index 502ff20..142b061 100644
--- a/src/Language/CQL/Typeside.hs
+++ b/src/Language/CQL/Typeside.hs
@@ -47,6 +47,7 @@ import           Data.Set              (Set)
 import qualified Data.Set              as Set
 import           Data.Typeable
 import           Data.Void
+import           Language.CQL.Collage  (Collage(..), typeOfCol)
 import           Language.CQL.Common
 import           Language.CQL.Options
 import           Language.CQL.Prover