diff --git a/examples/Examples/Eq.hs b/examples/Examples/Eq.hs
index dce3e323e..78beef5c7 100644
--- a/examples/Examples/Eq.hs
+++ b/examples/Examples/Eq.hs
@@ -7,10 +7,10 @@ import           Prelude                                     hiding (Bool, Eq (.
 
 import           ZkFold.Base.Algebra.Basic.Field             (Zp)
 import           ZkFold.Base.Algebra.EllipticCurve.BLS12_381 (BLS12_381_Scalar)
+import           ZkFold.Symbolic.Class                       (Symbolic)
 import           ZkFold.Symbolic.Compiler
 import           ZkFold.Symbolic.Data.Bool                   (Bool (..))
 import           ZkFold.Symbolic.Data.Eq                     (Eq (..))
-import           ZkFold.Symbolic.Class                       (Symbolic)
 import           ZkFold.Symbolic.Data.FieldElement           (FieldElement)
 
 -- | (==) operation
diff --git a/examples/Examples/LEQ.hs b/examples/Examples/LEQ.hs
index 077a6e112..94ec0e436 100644
--- a/examples/Examples/LEQ.hs
+++ b/examples/Examples/LEQ.hs
@@ -7,13 +7,14 @@ import           Prelude                                     hiding (Bool, Eq (.
 
 import           ZkFold.Base.Algebra.Basic.Field             (Zp)
 import           ZkFold.Base.Algebra.EllipticCurve.BLS12_381 (BLS12_381_Scalar)
+import           ZkFold.Symbolic.Class                       (Symbolic)
 import           ZkFold.Symbolic.Compiler
-import           ZkFold.Symbolic.Data.Bool                   (Bool (..))
+import           ZkFold.Symbolic.Data.Bool                   (Bool)
 import           ZkFold.Symbolic.Data.FieldElement           (FieldElement)
-import           ZkFold.Symbolic.Data.Ord                    (Ord (..))
+import           ZkFold.Symbolic.Data.Ord                    ((<=))
 
 -- | (<=) operation
-leq :: Ord (Bool c) (FieldElement c) => FieldElement c -> FieldElement c -> Bool c
+leq :: Symbolic c => FieldElement c -> FieldElement c -> Bool c
 leq x y = x <= y
 
 exampleLEQ :: IO ()
diff --git a/src/ZkFold/Base/Protocol/ARK/Plonk.hs b/src/ZkFold/Base/Protocol/ARK/Plonk.hs
index c3c3e55e0..a5114b29e 100644
--- a/src/ZkFold/Base/Protocol/ARK/Plonk.hs
+++ b/src/ZkFold/Base/Protocol/ARK/Plonk.hs
@@ -106,11 +106,7 @@ instance forall n l c1 c2 t plonk f g1.
         , KnownNat l
         , KnownNat (PlonkPermutationSize n)
         , KnownNat (PlonkPolyExtendedLength n)
-        , Eq (ScalarField c1)
-        , Scale (ScalarField c1) (ScalarField c1)
-        , BinaryExpansion (ScalarField c1)
-        , Bits (ScalarField c1) ~ [ScalarField c1]
-        , FiniteField (ScalarField c1)
+        , Arithmetic f
         , AdditiveGroup (BaseField c1)
         , Pairing c1 c2
         , ToTranscript t (ScalarField c1)
diff --git a/src/ZkFold/Symbolic/Compiler/ArithmeticCircuit/Combinators.hs b/src/ZkFold/Symbolic/Compiler/ArithmeticCircuit/Combinators.hs
index 7e1fa895b..5e05ae1ec 100644
--- a/src/ZkFold/Symbolic/Compiler/ArithmeticCircuit/Combinators.hs
+++ b/src/ZkFold/Symbolic/Compiler/ArithmeticCircuit/Combinators.hs
@@ -68,7 +68,7 @@ embedVar x = newAssigned $ const (fromConstant x)
 embedAll :: forall a n . (Arithmetic a, KnownNat n) => a -> ArithmeticCircuit a (Vector n)
 embedAll x = circuitF $ Vector <$> replicateM (fromIntegral $ value @n) (newAssigned $ const (fromConstant x))
 
-expansion :: MonadBlueprint i a m => Natural -> i -> m [i]
+expansion :: MonadCircuit i a m => Natural -> i -> m [i]
 -- ^ @expansion n k@ computes a binary expansion of @k@ if it fits in @n@ bits.
 expansion n k = do
     bits <- bitsOf n k
@@ -88,7 +88,7 @@ splitExpansion n1 n2 k = do
     constraint (\x -> x k - x l - scale (2 ^ n1 :: Natural) (x h))
     return (l, h)
 
-bitsOf :: MonadBlueprint i a m => Natural -> i -> m [i]
+bitsOf :: MonadCircuit i a m => Natural -> i -> m [i]
 -- ^ @bitsOf n k@ creates @n@ bits and sets their witnesses equal to @n@ smaller
 -- bits of @k@.
 bitsOf n k = for [0 .. n -! 1] $ \j ->
@@ -97,7 +97,7 @@ bitsOf n k = for [0 .. n -! 1] $ \j ->
         repr :: forall b . (BinaryExpansion b, Bits b ~ [b], Finite b) => b -> [b]
         repr = padBits (numberOfBits @b) . binaryExpansion
 
-horner :: MonadBlueprint i a m => [i] -> m i
+horner :: MonadCircuit i a m => [i] -> m i
 -- ^ @horner [b0,...,bn]@ computes the sum @b0 + 2 b1 + ... + 2^n bn@ using
 -- Horner's scheme.
 horner xs = case reverse xs of
diff --git a/src/ZkFold/Symbolic/Data/Eq/Structural.hs b/src/ZkFold/Symbolic/Data/Eq/Structural.hs
index fbe0ab248..9b57d166e 100644
--- a/src/ZkFold/Symbolic/Data/Eq/Structural.hs
+++ b/src/ZkFold/Symbolic/Data/Eq/Structural.hs
@@ -5,9 +5,9 @@ module ZkFold.Symbolic.Data.Eq.Structural where
 
 import           Prelude                    (type (~))
 
+import           ZkFold.Symbolic.Class
 import           ZkFold.Symbolic.Data.Bool
 import           ZkFold.Symbolic.Data.Class
-import           ZkFold.Symbolic.Class
 import           ZkFold.Symbolic.Data.Eq
 
 newtype Structural a = Structural a
diff --git a/src/ZkFold/Symbolic/Data/Ord.hs b/src/ZkFold/Symbolic/Data/Ord.hs
index 1b999a21b..d26454ae0 100644
--- a/src/ZkFold/Symbolic/Data/Ord.hs
+++ b/src/ZkFold/Symbolic/Data/Ord.hs
@@ -3,28 +3,29 @@
 {-# LANGUAGE TypeApplications    #-}
 {-# LANGUAGE TypeOperators       #-}
 
-module ZkFold.Symbolic.Data.Ord (Ord (..), Lexicographical (..), blueprintGE, circuitGE, circuitGT, getBitsBE) where
-
-import           Control.Monad                                             (foldM)
-import qualified Data.Bool                                                 as Haskell
-import           Data.Foldable                                             (Foldable)
-import           Data.Function                                             ((.))
-import qualified Data.Zip                                                  as Z
-import           GHC.Generics                                              (Par1 (..))
-import           Prelude                                                   (type (~), ($))
-import qualified Prelude                                                   as Haskell
+module ZkFold.Symbolic.Data.Ord (Ord (..), Lexicographical (..), blueprintGE, bitwiseGE, bitwiseGT, getBitsBE) where
+
+import           Control.Monad                                          (foldM)
+import qualified Data.Bool                                              as Haskell
+import           Data.Foldable                                          (Foldable, toList)
+import           Data.Function                                          ((.))
+import           Data.Functor                                           ((<$>))
+import qualified Data.Zip                                               as Z
+import           GHC.Generics                                           (Par1 (..))
+import           Prelude                                                (type (~), ($))
+import qualified Prelude                                                as Haskell
 
 import           ZkFold.Base.Algebra.Basic.Class
-import           ZkFold.Base.Data.HFunctor                                 (hmap)
-import qualified ZkFold.Base.Data.Vector                                   as V
-import           ZkFold.Symbolic.Compiler
-import           ZkFold.Symbolic.Compiler.ArithmeticCircuit.MonadBlueprint (MonadBlueprint (..), circuit)
-import           ZkFold.Symbolic.Data.Bool                                 (Bool (..), BoolType (..))
+import           ZkFold.Base.Data.HFunctor                              (hmap)
+import qualified ZkFold.Base.Data.Vector                                as V
+import           ZkFold.Base.Data.Vector                                (unsafeToVector)
+import           ZkFold.Symbolic.Class                                  (Symbolic (BaseField, symbolicF), symbolic2F)
+import           ZkFold.Symbolic.Compiler.ArithmeticCircuit.Combinators (expansion)
+import           ZkFold.Symbolic.Data.Bool                              (Bool (..))
 import           ZkFold.Symbolic.Data.Class
-import           ZkFold.Symbolic.Data.Conditional                          (Conditional (..))
-import           ZkFold.Symbolic.Data.FieldElement                         (FieldElement (..))
-import           ZkFold.Symbolic.Interpreter                               (Interpreter (..))
-import           ZkFold.Symbolic.MonadCircuit                              (Arithmetic, newAssigned)
+import           ZkFold.Symbolic.Data.Conditional                       (Conditional (..))
+import           ZkFold.Symbolic.Data.FieldElement                      (FieldElement (..))
+import           ZkFold.Symbolic.MonadCircuit                           (MonadCircuit, newAssigned)
 
 -- TODO (Issue #23): add `compare`
 class Ord b a where
@@ -55,79 +56,68 @@ instance Haskell.Ord a => Ord Haskell.Bool a where
 
     min = Haskell.min
 
-toValue :: Interpreter a Par1 -> a
-toValue (Interpreter (Par1 v)) = v
-
-fromValue :: a -> Interpreter a Par1
-fromValue = Interpreter Haskell.. Par1
-
-instance (Arithmetic a, Haskell.Ord a) => Ord (Bool (Interpreter a)) (Interpreter a Par1) where
-    (toValue -> x) <= (toValue -> y) = Haskell.bool false true (x Haskell.<= y)
-    (toValue -> x) <  (toValue -> y) = Haskell.bool false true (x Haskell.<  y)
-    (toValue -> x) >= (toValue -> y) = Haskell.bool false true (x Haskell.>= y)
-    (toValue -> x) >  (toValue -> y) = Haskell.bool false true (x Haskell.>  y)
-    (toValue -> x) `max` (toValue -> y) = fromValue $ Haskell.max x y
-    (toValue -> x) `min` (toValue -> y) = fromValue $ Haskell.min x y
-
 newtype Lexicographical a = Lexicographical a
 -- ^ A newtype wrapper for easy definition of Ord instances
 -- (though not necessarily a most effective one)
 
-deriving newtype instance SymbolicData c x => SymbolicData c (Lexicographical x)
-
-deriving via (Lexicographical (ArithmeticCircuit a Par1))
-    instance Arithmetic a => Ord (Bool (ArithmeticCircuit a)) (ArithmeticCircuit a Par1)
+deriving newtype instance SymbolicData c a => SymbolicData c (Lexicographical a)
 
-deriving newtype instance (Arithmetic a, Haskell.Ord a) => Ord (Bool (Interpreter a)) (FieldElement (Interpreter a))
-deriving newtype instance Arithmetic a => Ord (Bool (ArithmeticCircuit a)) (FieldElement (ArithmeticCircuit a))
+deriving via (Lexicographical (FieldElement c))
+  instance Symbolic c => Ord (Bool c) (FieldElement c)
 
 -- | Every @SymbolicData@ type can be compared lexicographically.
 instance
-    ( Arithmetic a
-    , SymbolicData (ArithmeticCircuit a) x
-    , Support (ArithmeticCircuit a) x ~ ()
-    , TypeSize (ArithmeticCircuit a) x ~ 1
-    ) => Ord (Bool (ArithmeticCircuit a)) (Lexicographical x) where
+    ( Symbolic c
+    , SymbolicData c x
+    , Support c x ~ ()
+    , TypeSize c x ~ 1
+    ) => Ord (Bool c) (Lexicographical x) where
 
     x <= y = y >= x
 
     x <  y = y > x
 
-    x >= y = circuitGE (getBitsBE x) (getBitsBE y)
+    x >= y = bitwiseGE (getBitsBE x) (getBitsBE y)
 
-    x > y = circuitGT (getBitsBE x) (getBitsBE y)
+    x > y = bitwiseGT (getBitsBE x) (getBitsBE y)
 
-    max x y = bool @(Bool (ArithmeticCircuit a)) x y $ x < y
+    max x y = bool @(Bool c) x y $ x < y
 
-    min x y = bool @(Bool (ArithmeticCircuit a)) x y $ x > y
+    min x y = bool @(Bool c) x y $ x > y
 
-getBitsBE :: forall c a x . (Arithmetic a, c ~ ArithmeticCircuit a, SymbolicData c x, Support c x ~ (), TypeSize c x ~ 1) => x -> c (V.Vector (NumberOfBits a))
+getBitsBE ::
+  forall c x .
+  (Symbolic c, SymbolicData c x, Support c x ~ (), TypeSize c x ~ 1) =>
+  x -> c (V.Vector (NumberOfBits (BaseField c)))
 -- ^ @getBitsBE x@ returns a list of circuits computing bits of @x@, eldest to
 -- youngest.
-getBitsBE x = let expansion = binaryExpansion $ hmap (Par1 . V.item) (pieces @c @x x ())
-               in expansion { acOutput = V.reverse $ acOutput expansion }
+getBitsBE x =
+  hmap unsafeToVector
+    $ symbolicF (pieces x ()) (binaryExpansion . V.item)
+      $ expansion (numberOfBits @(BaseField c)) . V.item
 
-circuitGE :: forall a f . (Arithmetic a, Z.Zip f, Foldable f) => ArithmeticCircuit a f -> ArithmeticCircuit a f -> Bool (ArithmeticCircuit a)
+bitwiseGE :: forall c f . (Symbolic c, Z.Zip f, Foldable f) => c f -> c f -> Bool c
 -- ^ Given two lists of bits of equal length, compares them lexicographically.
-circuitGE xs ys = Bool $ circuit $ do
-  is <- runCircuit xs
-  js <- runCircuit ys
-  blueprintGE is js
+bitwiseGE xs ys = Bool $
+  symbolic2F xs ys
+    (\us vs -> Par1 $ Haskell.bool zero one (toList us Haskell.>= toList vs))
+    $ \is js -> Par1 <$> blueprintGE is js
 
-blueprintGE :: (MonadBlueprint i a m, Z.Zip f, Foldable f) => f i -> f i -> m i
+blueprintGE :: (MonadCircuit i a m, Z.Zip f, Foldable f) => f i -> f i -> m i
 blueprintGE xs ys = do
   (_, hasNegOne) <- circuitDelta xs ys
   newAssigned $ \p -> one - p hasNegOne
 
-circuitGT :: forall a f . (Arithmetic a, Z.Zip f, Foldable f) => ArithmeticCircuit a f -> ArithmeticCircuit a f -> Bool (ArithmeticCircuit a)
+bitwiseGT :: forall c f . (Symbolic c, Z.Zip f, Foldable f) => c f -> c f -> Bool c
 -- ^ Given two lists of bits of equal length, compares them lexicographically.
-circuitGT xs ys = Bool $ circuit $ do
-  is <- runCircuit xs
-  js <- runCircuit ys
-  (hasOne, hasNegOne) <- circuitDelta is js
-  newAssigned $ \p -> p hasOne * (one - p hasNegOne)
-
-circuitDelta :: forall i a m f . (MonadBlueprint i a m, Z.Zip f, Foldable f) => f i -> f i -> m (i, i)
+bitwiseGT xs ys = Bool $
+  symbolic2F xs ys
+    (\us vs -> Par1 $ Haskell.bool zero one (toList us Haskell.> toList vs))
+    $ \is js -> do
+      (hasOne, hasNegOne) <- circuitDelta is js
+      Par1 <$> newAssigned (\p -> p hasOne * (one - p hasNegOne))
+
+circuitDelta :: forall i a m f . (MonadCircuit i a m, Z.Zip f, Foldable f) => f i -> f i -> m (i, i)
 circuitDelta l r = do
     z1 <- newAssigned (Haskell.const zero)
     z2 <- newAssigned (Haskell.const zero)
diff --git a/src/ZkFold/Symbolic/Data/UInt.hs b/src/ZkFold/Symbolic/Data/UInt.hs
index 7514f3ee3..8ba35eae8 100644
--- a/src/ZkFold/Symbolic/Data/UInt.hs
+++ b/src/ZkFold/Symbolic/Data/UInt.hs
@@ -293,12 +293,12 @@ instance (Arithmetic a, KnownNat n, KnownRegisterSize r, KnownNat (NumberOfRegis
     u1 >= u2 =
         let ByteString rs1 = from u1 :: ByteString n (ArithmeticCircuit a)
             ByteString rs2 = from u2 :: ByteString n (ArithmeticCircuit a)
-         in circuitGE rs1 rs2
+         in bitwiseGE rs1 rs2
 
     u1 > u2 =
         let ByteString rs1 = from u1 :: ByteString n (ArithmeticCircuit a)
             ByteString rs2 = from u2 :: ByteString n (ArithmeticCircuit a)
-         in circuitGT rs1 rs2
+         in bitwiseGT rs1 rs2
 
     max x y = bool @(Bool (ArithmeticCircuit a)) x y $ x < y
 
diff --git a/src/ZkFold/Symbolic/MonadCircuit.hs b/src/ZkFold/Symbolic/MonadCircuit.hs
index abeacf73e..b4de5df48 100644
--- a/src/ZkFold/Symbolic/MonadCircuit.hs
+++ b/src/ZkFold/Symbolic/MonadCircuit.hs
@@ -9,6 +9,7 @@ import           Data.Eq                         (Eq)
 import           Data.Function                   (id)
 import           Data.Functor                    (Functor)
 import           Data.Functor.Identity           (Identity (..))
+import           Data.Ord                        (Ord)
 import           Data.Type.Equality              (type (~))
 
 import           ZkFold.Base.Algebra.Basic.Class
@@ -105,8 +106,9 @@ class Monad m => MonadCircuit i a m | m -> i, m -> a where
     newAssigned :: ClosedPoly i a -> m i
     newAssigned p = newConstrained (\x i -> p x - x i) p
 
--- | Field of witnesses with decidable equality is called an ``arithmetic'' field.
-type Arithmetic a = (WitnessField a, Eq a)
+-- | Field of witnesses with decidable equality and ordering
+-- is called an ``arithmetic'' field.
+type Arithmetic a = (WitnessField a, Eq a, Ord a)
 
 -- | An example implementation of a @'MonadCircuit'@ which computes witnesses
 -- immediately and drops the constraints.
diff --git a/tests/Tests/Arithmetization/Test3.hs b/tests/Tests/Arithmetization/Test3.hs
index 4ff746804..e1726dc6e 100644
--- a/tests/Tests/Arithmetization/Test3.hs
+++ b/tests/Tests/Arithmetization/Test3.hs
@@ -9,16 +9,17 @@ import           Test.Hspec
 
 import           ZkFold.Base.Algebra.Basic.Class   (fromConstant)
 import           ZkFold.Base.Algebra.Basic.Field   (Zp)
+import           ZkFold.Symbolic.Class             (Symbolic)
 import           ZkFold.Symbolic.Compiler
 import           ZkFold.Symbolic.Data.Bool         (Bool (..))
 import           ZkFold.Symbolic.Data.FieldElement (FieldElement)
-import           ZkFold.Symbolic.Data.Ord          (Ord (..))
+import           ZkFold.Symbolic.Data.Ord          ((<=))
 import           ZkFold.Symbolic.Interpreter       (Interpreter (Interpreter))
 
 type R = ArithmeticCircuit (Zp 97)
 
 -- A comparison test
-testFunc :: Ord (Bool c) (FieldElement c) => FieldElement c -> FieldElement c -> Bool c
+testFunc :: Symbolic c => FieldElement c -> FieldElement c -> Bool c
 testFunc x y = x <= y
 
 specArithmetization3 :: Spec
diff --git a/tests/Tests/Arithmetization/Test4.hs b/tests/Tests/Arithmetization/Test4.hs
index cb3e9a7eb..4ffc79725 100644
--- a/tests/Tests/Arithmetization/Test4.hs
+++ b/tests/Tests/Arithmetization/Test4.hs
@@ -18,11 +18,11 @@ import           ZkFold.Base.Protocol.ARK.Plonk              (Plonk (..), PlonkP
                                                               plonkVerifierInput)
 import           ZkFold.Base.Protocol.ARK.Plonk.Internal     (getParams)
 import           ZkFold.Base.Protocol.NonInteractiveProof    (NonInteractiveProof (..))
+import           ZkFold.Symbolic.Class
 import           ZkFold.Symbolic.Compiler                    (ArithmeticCircuit (..), acValue, applyArgs, compile)
 import           ZkFold.Symbolic.Data.Bool                   (Bool (..))
 import           ZkFold.Symbolic.Data.Eq                     (Eq (..))
 import           ZkFold.Symbolic.Data.FieldElement           (FieldElement)
-import           ZkFold.Symbolic.Class
 
 type N = 1