diff --git a/examples/circuit-layout.rs b/examples/circuit-layout.rs
index 045e50e..ccd9338 100644
--- a/examples/circuit-layout.rs
+++ b/examples/circuit-layout.rs
@@ -283,8 +283,12 @@ fn main() {
              *   ...       ...    ...  0         0
              * ]
              */
-            meta.lookup(&[a.into()], &[sl.into()]);
-            meta.lookup(&[a.into(), b.into()], &[sl.into(), sl2.into()]);
+            let a_ = meta.query_any(a.into(), Rotation::cur());
+            let b_ = meta.query_any(b.into(), Rotation::cur());
+            let sl_ = meta.query_any(sl.into(), Rotation::cur());
+            let sl2_ = meta.query_any(sl2.into(), Rotation::cur());
+            meta.lookup(&[a_.clone()], &[sl_.clone()]);
+            meta.lookup(&[a_, b_], &[sl_, sl2_]);
 
             meta.create_gate("Combined add-mult", |meta| {
                 let d = meta.query_advice(d, Rotation::next());
diff --git a/src/dev.rs b/src/dev.rs
index 02950bf..f11e3fb 100644
--- a/src/dev.rs
+++ b/src/dev.rs
@@ -5,8 +5,8 @@ use ff::Field;
 use crate::{
     arithmetic::{FieldExt, Group},
     plonk::{
-        permutation, Advice, Any, Assignment, Circuit, Column, ColumnType, ConstraintSystem, Error,
-        Fixed,
+        permutation, Advice, Assignment, Circuit, Column, ColumnType, ConstraintSystem, Error,
+        Expression, Fixed,
     },
     poly::Rotation,
 };
@@ -143,7 +143,7 @@ pub enum VerifyFailure {
 /// );
 /// ```
 #[derive(Debug)]
-pub struct MockProver<F: Group> {
+pub struct MockProver<F: Group + Field> {
     n: u32,
     cs: ConstraintSystem<F>,
 
@@ -316,10 +316,21 @@ impl<F: FieldExt> MockProver<F> {
         // Check that all lookups exist in their respective tables.
         for (lookup_index, lookup) in self.cs.lookups.iter().enumerate() {
             for input_row in 0..n {
-                let load = |column: &Column<Any>, row| match column.column_type() {
-                    Any::Fixed => self.fixed[column.index()][row as usize],
-                    Any::Advice => self.advice[column.index()][row as usize],
-                    Any::Instance => self.instance[column.index()][row as usize],
+                let load = |column: &Expression<F>, row| match column {
+                    Expression::Fixed(index) => {
+                        let column_index = self.cs.fixed_queries[*index].0.index();
+                        self.fixed[column_index][row as usize]
+                    }
+                    Expression::Advice(index) => {
+                        let column_index = self.cs.advice_queries[*index].0.index();
+                        self.advice[column_index][row as usize]
+                    }
+                    Expression::Instance(index) => {
+                        let column_index = self.cs.instance_queries[*index].0.index();
+                        self.instance[column_index][row as usize]
+                    }
+                    // TODO: other Expression variants
+                    _ => unreachable!(),
                 };
 
                 let inputs: Vec<_> = lookup
diff --git a/src/plonk.rs b/src/plonk.rs
index 80a05bc..38f9ab4 100644
--- a/src/plonk.rs
+++ b/src/plonk.rs
@@ -467,8 +467,12 @@ fn test_proving() {
              *   ...       ...    ...  0         0
              * ]
              */
-            meta.lookup(&[a.into()], &[sl.into()]);
-            meta.lookup(&[a.into(), b.into()], &[sl.into(), sl2.into()]);
+            let a_ = meta.query_any(a.into(), Rotation::cur());
+            let b_ = meta.query_any(b.into(), Rotation::cur());
+            let sl_ = meta.query_any(sl.into(), Rotation::cur());
+            let sl2_ = meta.query_any(sl2.into(), Rotation::cur());
+            meta.lookup(&[a_.clone()], &[sl_.clone()]);
+            meta.lookup(&[a_, b_], &[sl_, sl2_]);
 
             meta.create_gate("Combined add-mult", |meta| {
                 let d = meta.query_advice(d, Rotation::next());
diff --git a/src/plonk/circuit.rs b/src/plonk/circuit.rs
index bb66484..61b4ed7 100644
--- a/src/plonk/circuit.rs
+++ b/src/plonk/circuit.rs
@@ -15,8 +15,10 @@ pub trait ColumnType: 'static + Sized + std::fmt::Debug {}
 /// A column with an index and type
 #[derive(Clone, Copy, Debug, Eq, PartialEq, Hash)]
 pub struct Column<C: ColumnType> {
-    index: usize,
-    column_type: C,
+    /// Index of column
+    pub index: usize,
+    /// Type of column
+    pub column_type: C,
 }
 
 impl<C: ColumnType> Column<C> {
@@ -362,7 +364,7 @@ pub(crate) struct PointIndex(pub usize);
 /// This is a description of the circuit environment, such as the gate, column and
 /// permutation arrangements.
 #[derive(Debug, Clone)]
-pub struct ConstraintSystem<F> {
+pub struct ConstraintSystem<F: Field> {
     pub(crate) num_fixed_columns: usize,
     pub(crate) num_advice_columns: usize,
     pub(crate) num_instance_columns: usize,
@@ -377,7 +379,7 @@ pub struct ConstraintSystem<F> {
 
     // Vector of lookup arguments, where each corresponds to a sequence of
     // input columns and a sequence of table columns involved in the lookup.
-    pub(crate) lookups: Vec<lookup::Argument>,
+    pub(crate) lookups: Vec<lookup::Argument<F>>,
 }
 
 /// Represents the minimal parameters that determine a `ConstraintSystem`.
@@ -456,19 +458,13 @@ impl<F: Field> ConstraintSystem<F> {
     /// columns are not the same.
     pub fn lookup(
         &mut self,
-        input_columns: &[Column<Any>],
-        table_columns: &[Column<Any>],
+        input_columns: &[Expression<F>],
+        table_columns: &[Expression<F>],
     ) -> usize {
         assert_eq!(input_columns.len(), table_columns.len());
 
         let index = self.lookups.len();
 
-        for input in input_columns {
-            self.query_any_index(*input, Rotation::cur());
-        }
-        for table in table_columns {
-            self.query_any_index(*table, Rotation::cur());
-        }
         self.lookups
             .push(lookup::Argument::new(input_columns, table_columns));
 
diff --git a/src/plonk/lookup.rs b/src/plonk/lookup.rs
index acb76ff..6755d05 100644
--- a/src/plonk/lookup.rs
+++ b/src/plonk/lookup.rs
@@ -1,16 +1,17 @@
-use super::circuit::{Any, Column};
+use super::circuit::Expression;
+use ff::Field;
 
 pub(crate) mod prover;
 pub(crate) mod verifier;
 
 #[derive(Clone, Debug)]
-pub(crate) struct Argument {
-    pub input_columns: Vec<Column<Any>>,
-    pub table_columns: Vec<Column<Any>>,
+pub(crate) struct Argument<F: Field> {
+    pub input_columns: Vec<Expression<F>>,
+    pub table_columns: Vec<Expression<F>>,
 }
 
-impl Argument {
-    pub fn new(input_columns: &[Column<Any>], table_columns: &[Column<Any>]) -> Self {
+impl<F: Field> Argument<F> {
+    pub fn new(input_columns: &[Expression<F>], table_columns: &[Expression<F>]) -> Self {
         assert_eq!(input_columns.len(), table_columns.len());
         Argument {
             input_columns: input_columns.to_vec(),
diff --git a/src/plonk/lookup/prover.rs b/src/plonk/lookup/prover.rs
index 0078322..3b6ad94 100644
--- a/src/plonk/lookup/prover.rs
+++ b/src/plonk/lookup/prover.rs
@@ -1,5 +1,5 @@
 use super::super::{
-    circuit::{Any, Column},
+    circuit::{Advice, Aux, Column, Expression, Fixed},
     ChallengeBeta, ChallengeGamma, ChallengeTheta, ChallengeX, Error, ProvingKey,
 };
 use super::Argument;
@@ -57,7 +57,7 @@ pub(in crate::plonk) struct Evaluated<C: CurveAffine> {
     constructed: Constructed<C>,
 }
 
-impl Argument {
+impl<F: FieldExt> Argument<F> {
     /// Given a Lookup with input columns [A_0, A_1, ..., A_{m-1}] and table columns
     /// [S_0, S_1, ..., S_{m-1}], this method
     /// - constructs A_compressed = \theta^{m-1} A_0 + theta^{m-2} A_1 + ... + \theta A_{m-2} + A_{m-1}
@@ -82,20 +82,27 @@ impl Argument {
         transcript: &mut T,
     ) -> Result<Permuted<'a, C>, Error> {
         // Closure to get values of columns and compress them
-        let compress_columns = |columns: &[Column<Any>]| {
+        let compress_columns = |columns: &[Expression<F>]| {
             // Values of input columns involved in the lookup
             let (unpermuted_columns, unpermuted_cosets): (Vec<_>, Vec<_>) = columns
                 .iter()
-                .map(|&column| {
-                    let (values, cosets) = match column.column_type() {
-                        Any::Advice => (advice_values, advice_cosets),
-                        Any::Fixed => (fixed_values, fixed_cosets),
-                        Any::Instance => (instance_values, instance_cosets),
-                    };
-                    (
-                        &values[column.index()],
-                        &cosets[pk.vk.cs.get_any_query_index(column, Rotation::cur())],
-                    )
+                .map(|column| {
+                    match column {
+                        Expression::Advice(index) => {
+                            let column_index = pk.vk.cs.advice_queries[*index].0.index();
+                            (&advice_values[column_index], &advice_cosets[*index])
+                        }
+                        Expression::Fixed(index) => {
+                            let column_index = pk.vk.cs.fixed_queries[*index].0.index();
+                            (&fixed_values[column_index], &fixed_cosets[*index])
+                        }
+                        Expression::Instance(index) => {
+                            let column_index = pk.vk.cs.instance_queries[*index].0.index();
+                            (&instance_values[column_index], &instance_cosets[*index])
+                        }
+                        // TODO: other Expression variants
+                        _ => unreachable!(),
+                    }
                 })
                 .unzip();
 
diff --git a/src/plonk/lookup/verifier.rs b/src/plonk/lookup/verifier.rs
index 50581ee..9be04cf 100644
--- a/src/plonk/lookup/verifier.rs
+++ b/src/plonk/lookup/verifier.rs
@@ -1,9 +1,9 @@
 use std::iter;
 
-use super::super::circuit::{Any, Column};
+use super::super::circuit::{Advice, Aux, Column, Expression, Fixed};
 use super::Argument;
 use crate::{
-    arithmetic::CurveAffine,
+    arithmetic::{CurveAffine, FieldExt},
     plonk::{ChallengeBeta, ChallengeGamma, ChallengeTheta, ChallengeX, Error, VerifyingKey},
     poly::{multiopen::VerifierQuery, Rotation},
     transcript::TranscriptRead,
@@ -29,7 +29,7 @@ pub struct Evaluated<C: CurveAffine> {
     permuted_table_eval: C::Scalar,
 }
 
-impl Argument {
+impl<F: FieldExt> Argument<F> {
     pub(in crate::plonk) fn read_permuted_commitments<C: CurveAffine, T: TranscriptRead<C>>(
         &self,
         transcript: &mut T,
@@ -101,7 +101,7 @@ impl<C: CurveAffine> Evaluated<C> {
         &'a self,
         vk: &'a VerifyingKey<C>,
         l_0: C::Scalar,
-        argument: &'a Argument,
+        argument: &'a Argument<C::Scalar>,
         theta: ChallengeTheta<C>,
         beta: ChallengeBeta<C>,
         gamma: ChallengeGamma<C>,
@@ -116,15 +116,16 @@ impl<C: CurveAffine> Evaluated<C> {
                 * &(self.permuted_input_eval + &*beta)
                 * &(self.permuted_table_eval + &*gamma);
 
-            let compress_columns = |columns: &[Column<Any>]| {
+            let compress_columns = |columns: &[Expression<C::Scalar>]| {
                 columns
                     .iter()
                     .map(|column| {
-                        let index = vk.cs.get_any_query_index(*column, Rotation::cur());
-                        match column.column_type() {
-                            Any::Advice => advice_evals[index],
-                            Any::Fixed => fixed_evals[index],
-                            Any::Instance => instance_evals[index],
+                        match column {
+                            Expression::Advice(index) => advice_evals[*index],
+                            Expression::Fixed(index) => fixed_evals[*index],
+                            Expression::Instance(index) => instance_evals[*index],
+                            // TODO: other Expression variants
+                            _ => unreachable!(),
                         }
                     })
                     .fold(C::Scalar::zero(), |acc, eval| acc * &*theta + &eval)