diff --git a/src/Algebra/Expr.hs b/src/Algebra/Expr.hs
new file mode 100644
index 0000000..649ec51
--- /dev/null
+++ b/src/Algebra/Expr.hs
@@ -0,0 +1,138 @@
+
+-- | Polynomial expressions
+--
+
+{-# LANGUAGE StrictData, RecordWildCards #-}
+module Algebra.Expr where
+
+--------------------------------------------------------------------------------
+
+import Data.Array
+import Data.Char
+
+import Text.Show
+
+import Algebra.Goldilocks
+import Algebra.GoldilocksExt
+
+import Gate.Base
+
+--------------------------------------------------------------------------------
+-- * Polynomial expressions
+
+data Expr v
+  = VarE   v              -- ^ a variable
+  | LitE   F              -- ^ constant literal
+  | ScaleE F (Expr v)     -- ^ linear scaling by a constant
+  | ImagE  (Expr v)       -- ^ multiplies by the field extension generator X
+  | SumE   [Expr v]       -- ^ sum of expressions
+  | ProdE  [Expr v]       -- ^ product of expressions
+  | PowE   (Expr v) Int   -- ^ exponentiation
+  deriving (Eq) -- ,Show)
+
+instance Pretty var => Show (Expr var) where show = pretty
+
+-- | Degree of the expression
+exprDegree :: Expr var -> Int
+exprDegree = go where
+  go expr = case expr of
+    VarE   _   -> 1
+    LitE   _   -> 0
+    ScaleE _ e -> go e
+    ImagE    e -> go e
+    SumE   es  -> if null es then 0 else maximum (map go es)
+    ProdE  es  -> sum (map go es)
+    PowE   e n -> n * go e
+
+instance Num (Expr var) where
+  fromInteger = LitE . fromInteger
+  negate = negE
+  (+) = addE
+  (-) = subE
+  (*) = mulE
+  abs    = error "Expr/abs"
+  signum = error "Expr/signum"
+
+negE :: Expr var -> Expr var
+negE (ScaleE s e) = ScaleE (negate s) e
+negE e            = ScaleE (-1)       e
+
+addE :: Expr var -> Expr var -> Expr var
+addE (SumE es) (SumE fs) = SumE (es++fs )
+addE e         (SumE fs) = SumE (e : fs )
+addE (SumE es) f         = SumE (es++[f])
+addE e         f         = SumE [e,f]
+
+subE :: Expr var -> Expr var -> Expr var
+subE e f = addE e (negate f)
+
+sclE :: F -> Expr var -> Expr var
+sclE s (ScaleE t e) = sclE (s*t) e
+sclE s e            = ScaleE s e
+
+mulE :: Expr var -> Expr var -> Expr var
+mulE (ScaleE s e) (ScaleE t f) = sclE (s*t) (mulE e f)
+mulE (ScaleE s e) f            = sclE  s    (mulE e f)
+mulE (LitE s) f                = sclE s f
+mulE e            (LitE t)     = sclE t e
+mulE e            (ScaleE t f) = sclE    t  (mulE e f)
+mulE (ProdE es)   (ProdE fs)   = ProdE (es++fs )
+mulE e            (ProdE fs)   = ProdE (e : fs )
+mulE (ProdE es)   f            = ProdE (es++[f])
+mulE e            f            = ProdE [e,f]
+
+--------------------------------------------------------------------------------
+-- * pretty printing
+
+-- | TODO: maybe move this somewhere else
+class Pretty a where
+  prettyPrec :: Int -> a -> (String -> String)
+
+pretty :: Pretty a => a -> String
+pretty x = prettyPrec 0 x ""
+
+instance Pretty F    where prettyPrec _ x = shows x
+instance Pretty FExt where prettyPrec _ x = shows x
+
+instance Pretty var => Pretty (Expr var) where
+  prettyPrec d expr = 
+    case expr of
+      VarE   v   -> prettyPrec 0 v
+      LitE   x   -> prettyPrec 0 x
+      ScaleE s e -> prettyPrec 0 s . showString " * " . showParen (d > mul_prec) (prettyPrec mul_prec e)
+      ImagE    e ->                  showString "X*"  . showParen (d > mul_prec) (prettyPrec mul_prec e)
+      SumE   es  -> showParen (d > add_prec) $ intercalates " + " $ map (prettyPrec add_prec) es 
+      ProdE  es  -> showParen (d > mul_prec) $ intercalates " * " $ map (prettyPrec mul_prec) es
+      PowE   e k -> showParen (d > pow_prec) $ (prettyPrec pow_prec e) . showString ("^" ++ show k)
+    where
+      add_prec = 5
+      mul_prec = 6
+      pow_prec = 7
+      intercalates sep = go where
+        go []     = id
+        go [x]    = x
+        go (x:xs) = x . showString sep . go xs
+
+--------------------------------------------------------------------------------
+-- * Evaluation
+
+{-
+class (Eq a, Show a, Num a, Fractional a) => EvalField a where
+  fromGoldilocks :: Goldilocks -> a
+
+instance EvalField F    where fromGoldilocks = id
+instance EvalField FExt where fromGoldilocks = fromBase
+-}
+
+evalExprWith :: (var -> FExt) -> Expr var -> FExt
+evalExprWith evalVar expr = go expr where
+  go e = case e of
+    VarE   v   -> evalVar v
+    LitE   x   -> fromBase x
+    ScaleE s e -> fromBase s * go e
+    ImagE    e -> (MkExt 0 1) * go e
+    SumE  es   -> sum     (map go es)
+    ProdE es   -> product (map go es) 
+    PowE   e n -> powExt (go e) (fromIntegral n)
+
+--------------------------------------------------------------------------------
diff --git a/src/Goldilocks.hs b/src/Algebra/Goldilocks.hs
similarity index 99%
rename from src/Goldilocks.hs
rename to src/Algebra/Goldilocks.hs
index 1649808..2290b1c 100644
--- a/src/Goldilocks.hs
+++ b/src/Algebra/Goldilocks.hs
@@ -2,7 +2,7 @@
 -- | Reference (simple, but very slow) implementation of the Goldilocks prime field
 
 {-# LANGUAGE BangPatterns, NumericUnderscores #-}
-module Goldilocks where
+module Algebra.Goldilocks where
 
 --------------------------------------------------------------------------------
 
diff --git a/src/GoldilocksExt.hs b/src/Algebra/GoldilocksExt.hs
similarity index 97%
rename from src/GoldilocksExt.hs
rename to src/Algebra/GoldilocksExt.hs
index 4f0d967..2809287 100644
--- a/src/GoldilocksExt.hs
+++ b/src/Algebra/GoldilocksExt.hs
@@ -6,7 +6,7 @@
 -- (@X^2 - 7@ is the smallest such irreducible polynomial over Goldilocks)
 --
 
-module GoldilocksExt where
+module Algebra.GoldilocksExt where
 
 --------------------------------------------------------------------------------
 
@@ -15,7 +15,7 @@ import Data.Ratio
 
 import Data.Aeson ( ToJSON(..), FromJSON(..) )
 
-import Goldilocks
+import Algebra.Goldilocks
 
 --------------------------------------------------------------------------------
 
diff --git a/src/Challenge/FRI.hs b/src/Challenge/FRI.hs
index d135787..2a3371c 100644
--- a/src/Challenge/FRI.hs
+++ b/src/Challenge/FRI.hs
@@ -10,8 +10,8 @@ import Control.Monad
 
 import Data.Bits
 
-import Goldilocks
-import GoldilocksExt
+import Algebra.Goldilocks
+import Algebra.GoldilocksExt
 import Hash
 import Digest
 import Types
diff --git a/src/Challenge/Monad.hs b/src/Challenge/Monad.hs
index b671742..dad332f 100644
--- a/src/Challenge/Monad.hs
+++ b/src/Challenge/Monad.hs
@@ -13,7 +13,7 @@ import Control.Monad.Identity
 import qualified Control.Monad.State.Strict as S
 import Control.Monad.IO.Class
 
-import Goldilocks
+import Algebra.Goldilocks
 import Digest
 import Challenge.Pure ( DuplexState, Squeeze, Absorb )
 import qualified Challenge.Pure as Pure
diff --git a/src/Challenge/Pure.hs b/src/Challenge/Pure.hs
index 255ef92..5a32704 100644
--- a/src/Challenge/Pure.hs
+++ b/src/Challenge/Pure.hs
@@ -15,8 +15,8 @@ module Challenge.Pure
 
 import Data.Array
 
-import Goldilocks
-import GoldilocksExt
+import Algebra.Goldilocks
+import Algebra.GoldilocksExt
 import Poseidon
 import Digest
 import Types
diff --git a/src/Challenge/Verifier.hs b/src/Challenge/Verifier.hs
index 8caf535..50c8148 100644
--- a/src/Challenge/Verifier.hs
+++ b/src/Challenge/Verifier.hs
@@ -6,8 +6,8 @@ module Challenge.Verifier where
 
 --------------------------------------------------------------------------------
 
-import Goldilocks
-import GoldilocksExt
+import Algebra.Goldilocks
+import Algebra.GoldilocksExt
 import Hash
 import Digest
 import Types
diff --git a/src/Constants.hs b/src/Constants.hs
index ac3475b..6527344 100644
--- a/src/Constants.hs
+++ b/src/Constants.hs
@@ -8,7 +8,8 @@ module Constants where
 --------------------------------------------------------------------------------
 
 import Data.Array
-import Goldilocks
+
+import Algebra.Goldilocks
 
 --------------------------------------------------------------------------------
 
diff --git a/src/Digest.hs b/src/Digest.hs
index a6e7670..1ea4a0f 100644
--- a/src/Digest.hs
+++ b/src/Digest.hs
@@ -11,7 +11,7 @@ import Data.Bits
 import GHC.Generics
 import Data.Aeson ( FromJSON(..) , ToJSON(..) , object , withObject , (.=) , (.:) )
 
-import Goldilocks
+import Algebra.Goldilocks
 
 --------------------------------------------------------------------------------
 
diff --git a/src/Gate/Base.hs b/src/Gate/Base.hs
index 89c8b40..ee74802 100644
--- a/src/Gate/Base.hs
+++ b/src/Gate/Base.hs
@@ -11,7 +11,7 @@ import Data.Word
 import Data.Aeson
 import GHC.Generics
 
-import Goldilocks
+import Algebra.Goldilocks
 
 --------------------------------------------------------------------------------
 
diff --git a/src/Gate/Constraints.hs b/src/Gate/Constraints.hs
index 474f001..12d701b 100644
--- a/src/Gate/Constraints.hs
+++ b/src/Gate/Constraints.hs
@@ -15,8 +15,9 @@ import Data.Char
 
 import Text.Show
 
-import Goldilocks
-import GoldilocksExt
+import Algebra.Goldilocks
+import Algebra.GoldilocksExt
+import Algebra.Expr
 
 import Gate.Base
 
@@ -31,103 +32,12 @@ data Var
   | PIV    Int        -- ^ public input hash variable
   deriving (Eq,Ord,Show)
 
-data Expr 
-  = VarE   Var        -- ^ a variable
-  | LitE   F          -- ^ constant literal
-  | ScaleE F Expr     -- ^ linear scaling by a constant
-  | ImagE  Expr       -- ^ multiplies by the field extension generator X
-  | SumE   [Expr]     -- ^ sum of expressions
-  | ProdE  [Expr]     -- ^ product of expressions
-  | PowE   Expr Int   -- ^ exponentiation
-  deriving (Eq) -- ,Show)
-
-instance Show Expr where show = pretty
-
--- | Degree of the expression
-exprDegree :: Expr -> Int
-exprDegree = go where
-  go expr = case expr of
-    VarE   _   -> 1
-    LitE   _   -> 0
-    ScaleE _ e -> go e
-    ImagE    e -> go e
-    SumE   es  -> if null es then 0 else maximum (map go es)
-    ProdE  es  -> sum (map go es)
-    PowE   e n -> n * go e
-
-instance Num Expr where
-  fromInteger = LitE . fromInteger
-  negate = negE
-  (+) = addE
-  (-) = subE
-  (*) = mulE
-  abs    = error "Expr/abs"
-  signum = error "Expr/signum"
-
-negE :: Expr -> Expr
-negE (ScaleE s e) = ScaleE (negate s) e
-negE e            = ScaleE (-1)       e
-
-addE :: Expr -> Expr -> Expr
-addE (SumE es) (SumE fs) = SumE (es++fs )
-addE e         (SumE fs) = SumE (e : fs )
-addE (SumE es) f         = SumE (es++[f])
-addE e         f         = SumE [e,f]
-
-subE :: Expr -> Expr -> Expr
-subE e f = addE e (negate f)
-
-sclE :: F -> Expr -> Expr
-sclE s (ScaleE t e) = sclE (s*t) e
-sclE s e            = ScaleE s e
-
-mulE :: Expr -> Expr -> Expr
-mulE (ScaleE s e) (ScaleE t f) = sclE (s*t) (mulE e f)
-mulE (ScaleE s e) f            = sclE  s    (mulE e f)
-mulE (LitE s) f                = sclE s f
-mulE e            (LitE t)     = sclE t e
-mulE e            (ScaleE t f) = sclE    t  (mulE e f)
-mulE (ProdE es)   (ProdE fs)   = ProdE (es++fs )
-mulE e            (ProdE fs)   = ProdE (e : fs )
-mulE (ProdE es)   f            = ProdE (es++[f])
-mulE e            f            = ProdE [e,f]
-
---------------------------------------------------------------------------------
--- * pretty printing
-
-class Pretty a where
-  prettyPrec :: Int -> a -> (String -> String)
-
-pretty :: Pretty a => a -> String
-pretty x = prettyPrec 0 x ""
-
-instance Pretty F    where prettyPrec _ x = shows x
-instance Pretty FExt where prettyPrec _ x = shows x
-
 instance Pretty Var where
   prettyPrec _ v = case v of
     SelV   k -> showString ("s" ++ show k)
     ConstV k -> showString ("c" ++ show k)
     WireV  k -> showString ("w" ++ show k)
     PIV    k -> showString ("h" ++ show k)
-instance Pretty Expr where
-  prettyPrec d expr = 
-    case expr of
-      VarE   v   -> prettyPrec 0 v
-      LitE   x   -> prettyPrec 0 x
-      ScaleE s e -> prettyPrec 0 s . showString " * " . showParen (d > mul_prec) (prettyPrec mul_prec e)
-      ImagE    e ->                  showString "X*"  . showParen (d > mul_prec) (prettyPrec mul_prec e)
-      SumE   es  -> showParen (d > add_prec) $ intercalates " + " $ map (prettyPrec add_prec) es 
-      ProdE  es  -> showParen (d > mul_prec) $ intercalates " * " $ map (prettyPrec mul_prec) es
-      PowE   e k -> showParen (d > pow_prec) $ (prettyPrec pow_prec e) . showString ("^" ++ show k)
-    where
-      add_prec = 5
-      mul_prec = 6
-      pow_prec = 7
-      intercalates sep = go where
-        go []     = id
-        go [x]    = x
-        go (x:xs) = x . showString sep . go xs
 
 --------------------------------------------------------------------------------
 
@@ -145,29 +55,19 @@ data EvaluationVars a = MkEvaluationVars
 --------------------------------------------------------------------------------
 -- * Evaluation
 
-class (Eq a, Show a, Num a, Fractional a) => EvalField a where
-  fromGoldilocks :: Goldilocks -> a
-
-instance EvalField F    where fromGoldilocks = id
-instance EvalField FExt where fromGoldilocks = fromBase
-
-evalExpr :: EvalField a => Expr -> EvaluationVars a -> a
-evalExpr expr (MkEvaluationVars{..}) = go expr where
-  go e = case e of
-    VarE  v  -> case v of
-      SelV   k -> local_selectors !  k
-      ConstV k -> local_constants !  k
-      WireV  k -> local_wires     !  k
-      PIV    k -> fromGoldilocks (public_inputs_hash !! k)
-    LitE  x  -> fromGoldilocks x
-    SumE  es -> sum     (map go es)
-    ProdE es -> product (map go es) 
-
+evalExpr :: Expr Var -> EvaluationVars FExt -> FExt
+evalExpr expr (MkEvaluationVars{..}) = evalExprWith f expr where
+  f v = case v of
+    SelV   k -> local_selectors !  k
+    ConstV k -> local_constants !  k
+    WireV  k -> local_wires     !  k
+    PIV    k -> fromBase (public_inputs_hash !! k)
+ 
 --------------------------------------------------------------------------------
 -- * Gate constraints
 
 -- | Returns the (symbolic) constraints for the given gate
-gateConstraints :: Gate -> [Expr]
+gateConstraints :: Gate -> [Expr Var]
 gateConstraints gate = 
   case gate of
 
diff --git a/src/Gate/Parser.hs b/src/Gate/Parser.hs
index f00e870..0064072 100644
--- a/src/Gate/Parser.hs
+++ b/src/Gate/Parser.hs
@@ -18,7 +18,7 @@ import GHC.Generics
 
 import "parsec1" Text.ParserCombinators.Parsec
 
-import Goldilocks
+import Algebra.Goldilocks
 import Gate.Base
 
 --------------------------------------------------------------------------------
diff --git a/src/Hash.hs b/src/Hash.hs
index 84ff044..2bc040d 100644
--- a/src/Hash.hs
+++ b/src/Hash.hs
@@ -7,7 +7,7 @@ import Data.Array
 import Data.Word
 import Data.Bits
 
-import Goldilocks
+import Algebra.Goldilocks
 import Poseidon
 import Digest
 
diff --git a/src/Poseidon.hs b/src/Poseidon.hs
index d685590..c87b2fe 100644
--- a/src/Poseidon.hs
+++ b/src/Poseidon.hs
@@ -14,7 +14,7 @@ import Data.Word
 import Data.Array (Array)
 import Data.Array.IArray
 
-import Goldilocks
+import Algebra.Goldilocks
 import Constants
 import Digest
 
diff --git a/src/Types.hs b/src/Types.hs
index 69e833f..d19c706 100644
--- a/src/Types.hs
+++ b/src/Types.hs
@@ -15,8 +15,8 @@ import qualified Data.ByteString.Lazy.Char8 as L
 
 import GHC.Generics
 
-import Goldilocks
-import GoldilocksExt
+import Algebra.Goldilocks
+import Algebra.GoldilocksExt
 import Digest
 import Gate.Base
 import Gate.Parser
diff --git a/src/testmain.hs b/src/testmain.hs
index f8efbde..dacdd50 100644
--- a/src/testmain.hs
+++ b/src/testmain.hs
@@ -8,7 +8,7 @@ import Data.Aeson
 import Types
 import Hash
 import Digest
-import Goldilocks
+import Algebra.Goldilocks
 import Challenge.Verifier
 
 import qualified Data.ByteString.Char8      as B
@@ -28,7 +28,7 @@ main = do
   let Just common_data   = decode text_common :: Maybe CommonCircuitData
   let Just verifier_data = decode text_vkey   :: Maybe VerifierOnlyCircuitData
   let Just proof_data    = decode text_proof  :: Maybe ProofWithPublicInputs
-  
+
   let challenges = proofChallenges common_data verifier_data proof_data
 
   print challenges
\ No newline at end of file