diff --git a/src/backends/plonky2/common.rs b/src/backends/plonky2/common.rs
index 8272a6a..1522f05 100644
--- a/src/backends/plonky2/common.rs
+++ b/src/backends/plonky2/common.rs
@@ -1,12 +1,17 @@
 //! Common functionality to build Pod circuits with plonky2
 
-use crate::middleware::STATEMENT_ARG_F_LEN;
-use crate::middleware::{Params, Value, HASH_SIZE, VALUE_SIZE};
+use crate::backends::plonky2::mock_main::Statement;
+use crate::backends::plonky2::mock_main::{Operation, OperationArg};
+use crate::middleware::{Params, StatementArg, ToFields, Value, F, HASH_SIZE, VALUE_SIZE};
+use crate::middleware::{OPERATION_ARG_F_LEN, STATEMENT_ARG_F_LEN};
+use anyhow::Result;
 use plonky2::field::extension::Extendable;
-use plonky2::field::types::PrimeField64;
+use plonky2::field::types::{Field, PrimeField64};
 use plonky2::hash::hash_types::RichField;
 use plonky2::iop::target::{BoolTarget, Target};
+use plonky2::iop::witness::{PartialWitness, WitnessWrite};
 use plonky2::plonk::circuit_builder::CircuitBuilder;
+use std::iter;
 
 #[derive(Copy, Clone)]
 pub struct ValueTarget {
@@ -15,25 +20,65 @@ pub struct ValueTarget {
 
 #[derive(Clone)]
 pub struct StatementTarget {
-    pub code: [Target; HASH_SIZE + 2],
+    pub predicate: [Target; Params::predicate_size()],
     pub args: Vec<[Target; STATEMENT_ARG_F_LEN]>,
 }
 
 impl StatementTarget {
     pub fn to_flattened(&self) -> Vec<Target> {
-        self.code
+        self.predicate
             .iter()
             .chain(self.args.iter().flatten())
             .cloned()
             .collect()
     }
+
+    pub fn set_targets(
+        &self,
+        pw: &mut PartialWitness<F>,
+        params: &Params,
+        st: &Statement,
+    ) -> Result<()> {
+        pw.set_target_arr(&self.predicate, &st.predicate().to_fields(params))?;
+        for (i, arg) in st
+            .args()
+            .iter()
+            .chain(iter::repeat(&StatementArg::None))
+            .take(params.max_statement_args)
+            .enumerate()
+        {
+            pw.set_target_arr(&self.args[i], &arg.to_fields(params))?;
+        }
+        Ok(())
+    }
 }
 
 // TODO: Implement Operation::to_field to determine the size of each element
 #[derive(Clone)]
 pub struct OperationTarget {
-    pub code: [Target; 6],                        // TODO: Figure out the length
-    pub args: Vec<[Target; STATEMENT_ARG_F_LEN]>, // TODO: Figure out the length
+    pub op_type: [Target; Params::operation_type_size()],
+    pub args: Vec<[Target; OPERATION_ARG_F_LEN]>,
+}
+
+impl OperationTarget {
+    pub fn set_targets(
+        &self,
+        pw: &mut PartialWitness<F>,
+        params: &Params,
+        op: &Operation,
+    ) -> Result<()> {
+        pw.set_target_arr(&self.op_type, &op.op_type().to_fields(params))?;
+        for (i, arg) in op
+            .args()
+            .iter()
+            .chain(iter::repeat(&OperationArg::None))
+            .take(params.max_operation_args)
+            .enumerate()
+        {
+            pw.set_target_arr(&self.args[i], &arg.to_fields(params))?;
+        }
+        Ok(())
+    }
 }
 
 pub trait CircuitBuilderPod<F: RichField + Extendable<D>, const D: usize> {
@@ -70,15 +115,20 @@ impl<F: RichField + Extendable<D>, const D: usize> CircuitBuilderPod<F, D>
 
     fn add_virtual_statement(&mut self, params: &Params) -> StatementTarget {
         StatementTarget {
-            code: self.add_virtual_target_arr::<6>(),
+            predicate: self.add_virtual_target_arr(),
             args: (0..params.max_statement_args)
-                .map(|_| self.add_virtual_target_arr::<STATEMENT_ARG_F_LEN>())
+                .map(|_| self.add_virtual_target_arr())
                 .collect(),
         }
     }
 
     fn add_virtual_operation(&mut self, params: &Params) -> OperationTarget {
-        todo!()
+        OperationTarget {
+            op_type: self.add_virtual_target_arr(),
+            args: (0..params.max_operation_args)
+                .map(|_| self.add_virtual_target_arr())
+                .collect(),
+        }
     }
 
     fn select_value(&mut self, b: BoolTarget, x: ValueTarget, y: ValueTarget) -> ValueTarget {
diff --git a/src/backends/plonky2/main.rs b/src/backends/plonky2/main.rs
index 88e37c2..e419aad 100644
--- a/src/backends/plonky2/main.rs
+++ b/src/backends/plonky2/main.rs
@@ -2,11 +2,14 @@ use crate::backends::plonky2::basetypes::{Hash, Value, D, EMPTY_HASH, EMPTY_VALU
 use crate::backends::plonky2::common::{
     CircuitBuilderPod, OperationTarget, StatementTarget, ValueTarget,
 };
-use crate::backends::plonky2::primitives::merkletree::MerkleProofExistenceCircuit;
+use crate::backends::plonky2::mock_main::Operation;
 use crate::backends::plonky2::primitives::merkletree::{MerkleProof, MerkleTree};
+use crate::backends::plonky2::primitives::merkletree::{
+    MerkleProofExistenceGate, MerkleProofExistenceTarget,
+};
 use crate::middleware::{
-    hash_str, AnchoredKey, NativeOperation, NativePredicate, Operation, Params, PodType, Predicate,
-    Statement, StatementArg, ToFields, KEY_TYPE, SELF, STATEMENT_ARG_F_LEN,
+    hash_str, AnchoredKey, NativeOperation, NativePredicate, Params, PodType, Predicate, Statement,
+    StatementArg, ToFields, KEY_TYPE, SELF, STATEMENT_ARG_F_LEN,
 };
 use anyhow::Result;
 use itertools::Itertools;
@@ -23,9 +26,7 @@ use plonky2::{
     plonk::circuit_builder::CircuitBuilder,
 };
 use std::collections::HashMap;
-
-/// MerkleTree Max Depth
-const MD: usize = 32;
+use std::iter;
 
 //
 // SignedPod verification
@@ -41,7 +42,10 @@ impl SignedPodVerifyGate {
         let id = builder.add_virtual_hash();
         let mut mt_proofs = Vec::new();
         for _ in 0..self.params.max_signed_pod_values {
-            let mt_proof = MerkleProofExistenceCircuit::<MD>::add_targets(builder)?;
+            let mt_proof = MerkleProofExistenceGate {
+                max_depth: self.params.max_depth_mt_gate,
+            }
+            .eval(builder)?;
             builder.connect_hashes(id, mt_proof.root);
             mt_proofs.push(mt_proof);
         }
@@ -68,7 +72,7 @@ struct SignedPodVerifyTarget {
     id: HashOutTarget,
     // The KEY_TYPE entry must be the first one
     // The KEY_SIGNER entry must be the second one
-    mt_proofs: Vec<MerkleProofExistenceCircuit<MD>>,
+    mt_proofs: Vec<MerkleProofExistenceTarget>,
 }
 
 struct SignedPodVerifyInput {
@@ -94,16 +98,22 @@ impl SignedPodVerifyTarget {
 
     fn set_targets(&self, pw: &mut PartialWitness<F>, input: &SignedPodVerifyInput) -> Result<()> {
         assert!(input.kvs.len() <= self.params.max_signed_pod_values);
-        let tree = MerkleTree::new(MD, &input.kvs)?;
-        for (i, (k, v)) in input.kvs.iter().sorted_by_key(|kv| kv.0).enumerate() {
+        let tree = MerkleTree::new(self.params.max_depth_mt_gate, &input.kvs)?;
+
+        // First handle the type entry, then the rest of the entries, and finally pad with
+        // repetitions of the type entry (which always exists)
+        let mut kvs = input.kvs.clone();
+        let key_type = Value::from(hash_str(KEY_TYPE));
+        let value_type = kvs.remove(&key_type).expect("KEY_TYPE");
+
+        for (i, (k, v)) in iter::once((key_type, value_type))
+            .chain(kvs.into_iter().sorted_by_key(|kv| kv.0))
+            .chain(iter::repeat((key_type, value_type)))
+            .take(self.params.max_signed_pod_values)
+            .enumerate()
+        {
             let (_, proof) = tree.prove(&k)?;
-            self.mt_proofs[i].set_targets(pw, tree.root(), proof, *k, *v)?;
-        }
-        // Padding
-        for i in input.kvs.len()..self.params.max_signed_pod_values {
-            // TODO: We need to disable the proofs for the unused slots.  We could add a flag
-            // "enable" to the MerkleTree proof circuit that skips the verification when false.
-            // self.mt_proofs[i].set_targets(pw, false, EMPTY_HASH, proof, *k, *v)?;
+            self.mt_proofs[i].set_targets(pw, tree.root(), proof, k, v)?;
         }
         Ok(())
     }
@@ -125,34 +135,55 @@ impl OperationVerifyGate {
         op: &OperationTarget,
         prev_statements: &[StatementTarget],
     ) -> Result<OperationVerifyTarget> {
+        let _true = builder._true();
+        let _false = builder._false();
+        let one = builder.constant(F::ONE);
+
         // Verify that the operation `op` correctly generates the statement `st`.  The operation
         // can reference any of the `prev_statements`.
         // The verification may require aux data which needs to be stored in the
         // `OperationVerifyTarget` so that we can set during witness generation.
 
-        // TODO: Figure out the right encoding of op.code
+        // For now only support native operations
+        builder.connect(op.op_type[0], one);
+        let native_op = op.op_type[1];
+
+        let mut op_flags = Vec::new();
         let op_none = builder.constant(F::from_canonical_u64(NativeOperation::None as u64));
-        let is_none = builder.is_equal(op.code[0], op_none);
+        let is_none = builder.is_equal(native_op, op_none);
+        op_flags.push(is_none);
         let op_new_entry =
             builder.constant(F::from_canonical_u64(NativeOperation::NewEntry as u64));
-        let is_new_entry = builder.is_equal(op.code[0], op_new_entry);
+        let is_new_entry = builder.is_equal(native_op, op_new_entry);
+        op_flags.push(is_new_entry);
         let op_copy_statement =
             builder.constant(F::from_canonical_u64(NativeOperation::CopyStatement as u64));
-        let is_copy_statement = builder.is_equal(op.code[0], op_copy_statement);
+        let is_copy_statement = builder.is_equal(native_op, op_copy_statement);
+        op_flags.push(is_copy_statement);
         let op_eq_from_entries = builder.constant(F::from_canonical_u64(
             NativeOperation::EqualFromEntries as u64,
         ));
-        let is_eq_from_entries = builder.is_equal(op.code[0], op_eq_from_entries);
-        let op_gt_from_entries =
-            builder.constant(F::from_canonical_u64(NativeOperation::GtFromEntries as u64));
-        let is_gt_from_entries = builder.is_equal(op.code[0], op_gt_from_entries);
+        let is_eq_from_entries = builder.is_equal(native_op, op_eq_from_entries);
+        op_flags.push(is_eq_from_entries);
         let op_lt_from_entries =
             builder.constant(F::from_canonical_u64(NativeOperation::LtFromEntries as u64));
-        let is_lt_from_entries = builder.is_equal(op.code[0], op_lt_from_entries);
-        let op_contains_from_entries = builder.constant(F::from_canonical_u64(
-            NativeOperation::ContainsFromEntries as u64,
+        let is_lt_from_entries = builder.is_equal(native_op, op_lt_from_entries);
+        op_flags.push(is_lt_from_entries);
+        let op_not_contains_from_entries = builder.constant(F::from_canonical_u64(
+            NativeOperation::NotContainsFromEntries as u64,
         ));
-        let is_contains_from_entries = builder.is_equal(op.code[0], op_contains_from_entries);
+        let is_not_contains_from_entries =
+            builder.is_equal(native_op, op_not_contains_from_entries);
+        op_flags.push(is_not_contains_from_entries);
+
+        // One supported operation must be used.  We sum all operation flags and expect the result
+        // to be 1.  Since the flags are boolean and at most one of them is true the sum is
+        // equivalent to the OR.
+        let or_op_flags = op_flags
+            .iter()
+            .map(|b| b.target)
+            .fold(_false.target, |acc, x| builder.add(acc, x));
+        builder.connect(or_op_flags, _true.target);
 
         let ok = builder._true();
         let none_ok = self.eval_none(builder, st, op);
@@ -160,10 +191,9 @@ impl OperationVerifyGate {
         let new_entry_ok = self.eval_new_entry(builder, st, op);
         let ok = builder.select_bool(is_new_entry, new_entry_ok, ok);
 
-        let _true = builder._true();
         builder.connect(ok.target, _true.target);
 
-        todo!()
+        Ok(OperationVerifyTarget {})
     }
 
     fn eval_none(
@@ -184,14 +214,14 @@ impl OperationVerifyGate {
         _op: &OperationTarget,
     ) -> BoolTarget {
         let value_of_st = &Statement::ValueOf(AnchoredKey(SELF, EMPTY_HASH), EMPTY_VALUE);
-        let expected_code =
+        let expected_predicate =
             builder.constants(&Predicate::Native(NativePredicate::ValueOf).to_fields(&self.params));
-        let code_ok = builder.is_equal_slice(&st.code, &expected_code);
+        let predicate_ok = builder.is_equal_slice(&st.predicate, &expected_predicate);
         let expected_arg_prefix = builder.constants(
             &StatementArg::Key(AnchoredKey(SELF, EMPTY_HASH)).to_fields(&self.params)[..VALUE_SIZE],
         );
         let arg_prefix_ok = builder.is_equal_slice(&st.args[0][..VALUE_SIZE], &expected_arg_prefix);
-        builder.and(code_ok, arg_prefix_ok)
+        builder.and(predicate_ok, arg_prefix_ok)
     }
 }
 
@@ -199,13 +229,14 @@ struct OperationVerifyTarget {
     // TODO
 }
 
-struct OperationVerifyInputs {
+struct OperationVerifyInput {
     // TODO
 }
 
 impl OperationVerifyTarget {
-    fn set_targets(&self, pw: &mut PartialWitness<F>, input: &OperationVerifyInputs) -> Result<()> {
-        todo!()
+    fn set_targets(&self, pw: &mut PartialWitness<F>, input: &OperationVerifyInput) -> Result<()> {
+        // TODO
+        Ok(())
     }
 }
 
@@ -246,14 +277,13 @@ impl MainPodVerifyGate {
         // 2. Calculate the Pod Id from the public statements
         let pub_statements_flattened = pub_statements
             .iter()
-            .map(|s| s.code.iter().chain(s.args.iter().flatten()))
+            .map(|s| s.predicate.iter().chain(s.args.iter().flatten()))
             .flatten()
             .cloned()
             .collect();
         let id = builder.hash_n_to_hash_no_pad::<PoseidonHash>(pub_statements_flattened);
 
-        // 3. TODO check that all `input_statements` of type `ValueOf` with origin=SELF have unique
-        //    keys (no duplicates)
+        // 3. TODO check that all `input_statements` of type `ValueOf` with origin=SELF have unique keys (no duplicates).  Maybe we can do this via the NewEntry operation (check that the key doesn't exist in a previous statement with ID=SELF)
 
         // 4. Verify type
         let type_statement = &pub_statements[0];
@@ -324,12 +354,12 @@ impl MainPodVerifyTarget {
     }
 }
 
-struct MainPodVerifyCircuit {
-    params: Params,
+pub struct MainPodVerifyCircuit {
+    pub params: Params,
 }
 
 impl MainPodVerifyCircuit {
-    fn eval(&self, builder: &mut CircuitBuilder<F, D>) -> Result<MainPodVerifyTarget> {
+    pub fn eval(&self, builder: &mut CircuitBuilder<F, D>) -> Result<MainPodVerifyTarget> {
         let main_pod = MainPodVerifyGate {
             params: self.params.clone(),
         }
@@ -338,3 +368,95 @@ impl MainPodVerifyCircuit {
         Ok(main_pod)
     }
 }
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use crate::backends::plonky2::basetypes::C;
+    use crate::backends::plonky2::mock_main;
+    use crate::middleware::OperationType;
+    use plonky2::plonk::{circuit_builder::CircuitBuilder, circuit_data::CircuitConfig};
+
+    #[test]
+    fn test_signed_pod_verify() -> Result<()> {
+        let params = Params::default();
+
+        let config = CircuitConfig::standard_recursion_config();
+        let mut builder = CircuitBuilder::<F, D>::new(config);
+
+        let signed_pod_verify = SignedPodVerifyGate { params }.eval(&mut builder)?;
+
+        let mut pw = PartialWitness::<F>::new();
+        let kvs = [
+            (
+                Value::from(hash_str(KEY_TYPE)),
+                Value::from(PodType::MockSigned),
+            ),
+            (Value::from(hash_str("foo")), Value::from(42)),
+        ]
+        .into();
+        let input = SignedPodVerifyInput { kvs };
+        signed_pod_verify.set_targets(&mut pw, &input)?;
+
+        // generate & verify proof
+        let data = builder.build::<C>();
+        let proof = data.prove(pw)?;
+        data.verify(proof)?;
+
+        Ok(())
+    }
+
+    fn operation_verify(
+        st: mock_main::Statement,
+        op: mock_main::Operation,
+        prev_statements: Vec<mock_main::Statement>,
+    ) -> Result<()> {
+        let params = Params::default();
+
+        let config = CircuitConfig::standard_recursion_config();
+        let mut builder = CircuitBuilder::<F, D>::new(config);
+
+        let st_target = builder.add_virtual_statement(&params);
+        let op_target = builder.add_virtual_operation(&params);
+        let prev_statements_target: Vec<_> = (0..prev_statements.len())
+            .map(|_| builder.add_virtual_statement(&params))
+            .collect();
+
+        let operation_verify = OperationVerifyGate {
+            params: params.clone(),
+        }
+        .eval(
+            &mut builder,
+            &st_target,
+            &op_target,
+            &prev_statements_target,
+        )?;
+
+        let mut pw = PartialWitness::<F>::new();
+        st_target.set_targets(&mut pw, &params, &st)?;
+        op_target.set_targets(&mut pw, &params, &op)?;
+        for (prev_st_target, prev_st) in prev_statements_target.iter().zip(prev_statements.iter()) {
+            prev_st_target.set_targets(&mut pw, &params, prev_st)?;
+        }
+        let input = OperationVerifyInput {};
+        operation_verify.set_targets(&mut pw, &input)?;
+
+        // generate & verify proof
+        let data = builder.build::<C>();
+        let proof = data.prove(pw)?;
+        data.verify(proof)?;
+
+        Ok(())
+    }
+
+    #[test]
+    fn test_operation_verify() -> Result<()> {
+        // None
+        let st: mock_main::Statement = Statement::None.into();
+        let op = mock_main::Operation(OperationType::Native(NativeOperation::None), vec![]);
+        let prev_statements = vec![Statement::None.into()];
+        operation_verify(st, op, prev_statements)?;
+
+        Ok(())
+    }
+}
diff --git a/src/backends/plonky2/mock_main/mod.rs b/src/backends/plonky2/mock_main/mod.rs
index 030ebe4..4583ab5 100644
--- a/src/backends/plonky2/mock_main/mod.rs
+++ b/src/backends/plonky2/mock_main/mod.rs
@@ -260,7 +260,7 @@ impl MockMainPod {
                 .map(|mid_arg| Self::find_op_arg(statements, mid_arg))
                 .collect::<Result<Vec<_>>>()?;
             Self::pad_operation_args(params, &mut args);
-            operations.push(Operation(op.predicate(), args));
+            operations.push(Operation(op.op_type(), args));
         }
         Ok(operations)
     }
diff --git a/src/backends/plonky2/mock_main/operation.rs b/src/backends/plonky2/mock_main/operation.rs
index 460f739..631407a 100644
--- a/src/backends/plonky2/mock_main/operation.rs
+++ b/src/backends/plonky2/mock_main/operation.rs
@@ -1,6 +1,7 @@
 use super::Statement;
-use crate::middleware::{self, OperationType};
+use crate::middleware::{self, OperationType, Params, ToFields, F};
 use anyhow::Result;
+use plonky2::field::types::{Field, PrimeField64};
 use serde::{Deserialize, Serialize};
 use std::fmt;
 
@@ -10,6 +11,16 @@ pub enum OperationArg {
     Index(usize),
 }
 
+impl ToFields for OperationArg {
+    fn to_fields(&self, _params: &Params) -> Vec<F> {
+        let f = match self {
+            Self::None => F::ZERO,
+            Self::Index(i) => F::from_canonical_usize(*i),
+        };
+        vec![f]
+    }
+}
+
 impl OperationArg {
     pub fn is_none(&self) -> bool {
         matches!(self, OperationArg::None)
@@ -20,6 +31,12 @@ impl OperationArg {
 pub struct Operation(pub OperationType, pub Vec<OperationArg>);
 
 impl Operation {
+    pub fn op_type(&self) -> OperationType {
+        self.0.clone()
+    }
+    pub fn args(&self) -> &[OperationArg] {
+        &self.1
+    }
     pub fn deref(&self, statements: &[Statement]) -> Result<crate::middleware::Operation> {
         let deref_args = self
             .1
diff --git a/src/backends/plonky2/mock_main/statement.rs b/src/backends/plonky2/mock_main/statement.rs
index 0bbcf9e..cb0dd6a 100644
--- a/src/backends/plonky2/mock_main/statement.rs
+++ b/src/backends/plonky2/mock_main/statement.rs
@@ -13,6 +13,9 @@ impl Statement {
     pub fn is_none(&self) -> bool {
         self.0 == Predicate::Native(NativePredicate::None)
     }
+    pub fn predicate(&self) -> Predicate {
+        self.0.clone()
+    }
     /// Argument method. Trailing Nones are filtered out.
     pub fn args(&self) -> Vec<StatementArg> {
         let maybe_last_arg_index = (0..self.1.len()).rev().find(|i| !self.1[*i].is_none());
@@ -96,7 +99,7 @@ impl TryFrom<Statement> for middleware::Statement {
 
 impl From<middleware::Statement> for Statement {
     fn from(s: middleware::Statement) -> Self {
-        match s.code() {
+        match s.predicate() {
             middleware::Predicate::Native(c) => Statement(
                 middleware::Predicate::Native(c),
                 s.args().into_iter().collect(),
diff --git a/src/backends/plonky2/primitives/merkletree_circuit.rs b/src/backends/plonky2/primitives/merkletree_circuit.rs
index 6da565b..c907a1a 100644
--- a/src/backends/plonky2/primitives/merkletree_circuit.rs
+++ b/src/backends/plonky2/primitives/merkletree_circuit.rs
@@ -29,11 +29,16 @@ use crate::backends::plonky2::common::{
 };
 use crate::backends::plonky2::primitives::merkletree::MerkleProof;
 
-/// `MerkleProofCircuit` allows to verify both proofs of existence and proofs
+/// `MerkleProofGate` allows to verify both proofs of existence and proofs
 /// non-existence with the same circuit.
-/// If only proofs of existence are needed, use `MerkleProofExistenceCircuit`,
+/// If only proofs of existence are needed, use `MerkleProofExistenceGate`,
 /// which requires less amount of constraints.
-pub struct MerkleProofCircuit<const MAX_DEPTH: usize> {
+pub struct MerkleProofGate {
+    pub max_depth: usize,
+}
+
+pub struct MerkleProofTarget {
+    max_depth: usize,
     pub root: HashOutTarget,
     pub key: ValueTarget,
     pub value: ValueTarget,
@@ -44,16 +49,16 @@ pub struct MerkleProofCircuit<const MAX_DEPTH: usize> {
     pub other_value: ValueTarget,
 }
 
-impl<const MAX_DEPTH: usize> MerkleProofCircuit<MAX_DEPTH> {
+impl MerkleProofGate {
     /// creates the targets and defines the logic of the circuit
-    pub fn add_targets(builder: &mut CircuitBuilder<F, D>) -> Result<Self> {
+    pub fn eval(&self, builder: &mut CircuitBuilder<F, D>) -> Result<MerkleProofTarget> {
         // create the targets
         let key = builder.add_virtual_value();
         let value = builder.add_virtual_value();
         // from proof struct:
         let existence = builder.add_virtual_bool_target_safe();
-        // siblings are padded till MAX_DEPTH length
-        let siblings = builder.add_virtual_hashes(MAX_DEPTH);
+        // siblings are padded till max_depth length
+        let siblings = builder.add_virtual_hashes(self.max_depth);
 
         let case_ii_selector = builder.add_virtual_bool_target_safe();
         let other_key = builder.add_virtual_value();
@@ -107,16 +112,17 @@ impl<const MAX_DEPTH: usize> MerkleProofCircuit<MAX_DEPTH> {
         );
 
         // get key's path
-        let path = keypath_target::<MAX_DEPTH>(builder, &key);
+        let path = keypath_target(self.max_depth, builder, &key);
 
         // compute the root for the given siblings and the computed leaf_hash
         // (this is for the three cases (existence, non-existence case i, and
         // non-existence case ii).
         // This root will be assigned in the `set_targets` method, and it is a
         // public input.
-        let root = compute_root_from_leaf::<MAX_DEPTH>(builder, &path, &leaf_hash, &siblings)?;
+        let root = compute_root_from_leaf(self.max_depth, builder, &path, &leaf_hash, &siblings)?;
 
-        Ok(Self {
+        Ok(MerkleProofTarget {
+            max_depth: self.max_depth,
             existence,
             root,
             siblings,
@@ -127,7 +133,9 @@ impl<const MAX_DEPTH: usize> MerkleProofCircuit<MAX_DEPTH> {
             other_value,
         })
     }
+}
 
+impl MerkleProofTarget {
     /// assigns the given values to the targets
     pub fn set_targets(
         &self,
@@ -143,9 +151,9 @@ impl<const MAX_DEPTH: usize> MerkleProofCircuit<MAX_DEPTH> {
         pw.set_target_arr(&self.value.elements, &value.0)?;
         pw.set_bool_target(self.existence, existence)?;
 
-        // pad siblings with zeros to length MAX_DEPTH
+        // pad siblings with zeros to length max_depth
         let mut siblings = proof.siblings.clone();
-        siblings.resize(MAX_DEPTH, EMPTY_HASH);
+        siblings.resize(self.max_depth, EMPTY_HASH);
         assert_eq!(self.siblings.len(), siblings.len());
 
         for (i, sibling) in siblings.iter().enumerate() {
@@ -173,41 +181,49 @@ impl<const MAX_DEPTH: usize> MerkleProofCircuit<MAX_DEPTH> {
 
 /// `MerkleProofExistenceCircuit` allows to verify proofs of existence only. If
 /// proofs of non-existence are needed, use `MerkleProofCircuit`.
-pub struct MerkleProofExistenceCircuit<const MAX_DEPTH: usize> {
+pub struct MerkleProofExistenceGate {
+    pub max_depth: usize,
+}
+
+pub struct MerkleProofExistenceTarget {
+    max_depth: usize,
     pub root: HashOutTarget,
     pub key: ValueTarget,
     pub value: ValueTarget,
     pub siblings: Vec<HashOutTarget>,
 }
 
-impl<const MAX_DEPTH: usize> MerkleProofExistenceCircuit<MAX_DEPTH> {
+impl MerkleProofExistenceGate {
     /// creates the targets and defines the logic of the circuit
-    pub fn add_targets(builder: &mut CircuitBuilder<F, D>) -> Result<Self> {
+    pub fn eval(&self, builder: &mut CircuitBuilder<F, D>) -> Result<MerkleProofExistenceTarget> {
         // create the targets
         let key = builder.add_virtual_value();
         let value = builder.add_virtual_value();
-        // siblings are padded till MAX_DEPTH length
-        let siblings = builder.add_virtual_hashes(MAX_DEPTH);
+        // siblings are padded till max_depth length
+        let siblings = builder.add_virtual_hashes(self.max_depth);
 
         // get leaf's hash for the selected k & v
         let leaf_hash = kv_hash_target(builder, &key, &value);
 
         // get key's path
-        let path = keypath_target::<MAX_DEPTH>(builder, &key);
+        let path = keypath_target(self.max_depth, builder, &key);
 
         // compute the root for the given siblings and the computed leaf_hash.
         // This root will be assigned in the `set_targets` method, and it is a
         // public input.
-        let root = compute_root_from_leaf::<MAX_DEPTH>(builder, &path, &leaf_hash, &siblings)?;
+        let root = compute_root_from_leaf(self.max_depth, builder, &path, &leaf_hash, &siblings)?;
 
-        Ok(Self {
+        Ok(MerkleProofExistenceTarget {
+            max_depth: self.max_depth,
             root,
             siblings,
             key,
             value,
         })
     }
+}
 
+impl MerkleProofExistenceTarget {
     /// assigns the given values to the targets
     pub fn set_targets(
         &self,
@@ -221,9 +237,9 @@ impl<const MAX_DEPTH: usize> MerkleProofExistenceCircuit<MAX_DEPTH> {
         pw.set_target_arr(&self.key.elements, &key.0)?;
         pw.set_target_arr(&self.value.elements, &value.0)?;
 
-        // pad siblings with zeros to length MAX_DEPTH
+        // pad siblings with zeros to length max_depth
         let mut siblings = proof.siblings.clone();
-        siblings.resize(MAX_DEPTH, EMPTY_HASH);
+        siblings.resize(self.max_depth, EMPTY_HASH);
         assert_eq!(self.siblings.len(), siblings.len());
 
         for (i, sibling) in siblings.iter().enumerate() {
@@ -234,13 +250,14 @@ impl<const MAX_DEPTH: usize> MerkleProofExistenceCircuit<MAX_DEPTH> {
     }
 }
 
-fn compute_root_from_leaf<const MAX_DEPTH: usize>(
+fn compute_root_from_leaf(
+    max_depth: usize,
     builder: &mut CircuitBuilder<F, D>,
     path: &Vec<BoolTarget>,
     leaf_hash: &HashOutTarget,
     siblings: &Vec<HashOutTarget>,
 ) -> Result<HashOutTarget> {
-    assert_eq!(siblings.len(), MAX_DEPTH);
+    assert_eq!(siblings.len(), max_depth);
     // Convenience constants
     let zero = builder.zero();
     let one = builder.one();
@@ -295,12 +312,13 @@ fn compute_root_from_leaf<const MAX_DEPTH: usize>(
 
 // Note: this logic is in its own method for easy of reusability but
 // specially to be able to test it isolated.
-fn keypath_target<const MAX_DEPTH: usize>(
+fn keypath_target(
+    max_depth: usize,
     builder: &mut CircuitBuilder<F, D>,
     key: &ValueTarget,
 ) -> Vec<BoolTarget> {
-    let n_complete_field_elems: usize = MAX_DEPTH / F::BITS;
-    let n_extra_bits: usize = MAX_DEPTH - n_complete_field_elems * F::BITS;
+    let n_complete_field_elems: usize = max_depth / F::BITS;
+    let n_extra_bits: usize = max_depth - n_complete_field_elems * F::BITS;
 
     let path: Vec<BoolTarget> = key
         .elements
@@ -351,41 +369,35 @@ pub mod tests {
 
     #[test]
     fn test_keypath() -> Result<()> {
-        test_keypath_opt::<10>()?;
-        test_keypath_opt::<16>()?;
-        test_keypath_opt::<32>()?;
-        test_keypath_opt::<40>()?;
-        test_keypath_opt::<64>()?;
-        test_keypath_opt::<128>()?;
-        test_keypath_opt::<130>()?;
-        test_keypath_opt::<250>()?;
-        test_keypath_opt::<256>()?;
+        for max_depth in [10, 16, 32, 40, 64, 128, 130, 250, 256] {
+            test_keypath_opt(max_depth)?;
+        }
         Ok(())
     }
 
-    fn test_keypath_opt<const MD: usize>() -> Result<()> {
+    fn test_keypath_opt(max_depth: usize) -> Result<()> {
         for i in 0..5 {
             let config = CircuitConfig::standard_recursion_config();
             let mut builder = CircuitBuilder::<F, D>::new(config);
             let mut pw = PartialWitness::<F>::new();
 
             let key = Value::from(hash_value(&Value::from(i)));
-            let expected_path = keypath(MD, key)?;
+            let expected_path = keypath(max_depth, key)?;
 
             // small circuit logic to check
             // expected_path_targ==keypath_target(key_targ)
-            let expected_path_targ: Vec<BoolTarget> = (0..MD)
+            let expected_path_targ: Vec<BoolTarget> = (0..max_depth)
                 .map(|_| builder.add_virtual_bool_target_safe())
                 .collect();
             let key_targ = builder.add_virtual_value();
-            let computed_path_targ = keypath_target::<MD>(&mut builder, &key_targ);
-            for i in 0..MD {
+            let computed_path_targ = keypath_target(max_depth, &mut builder, &key_targ);
+            for i in 0..max_depth {
                 builder.connect(computed_path_targ[i].target, expected_path_targ[i].target);
             }
 
             // assign the input values to the targets
             pw.set_target_arr(&key_targ.elements, &key.0)?;
-            for i in 0..MD {
+            for i in 0..max_depth {
                 pw.set_bool_target(expected_path_targ[i], expected_path[i])?;
             }
 
@@ -431,40 +443,28 @@ pub mod tests {
 
     #[test]
     fn test_merkleproof_verify_existence() -> Result<()> {
-        test_merkleproof_verify_opt::<10>(true)?;
-        test_merkleproof_verify_opt::<16>(true)?;
-        test_merkleproof_verify_opt::<32>(true)?;
-        test_merkleproof_verify_opt::<40>(true)?;
-        test_merkleproof_verify_opt::<64>(true)?;
-        test_merkleproof_verify_opt::<128>(true)?;
-        test_merkleproof_verify_opt::<130>(true)?;
-        test_merkleproof_verify_opt::<250>(true)?;
-        test_merkleproof_verify_opt::<256>(true)?;
+        for max_depth in [10, 16, 32, 40, 64, 128, 130, 250, 256] {
+            test_merkleproof_verify_opt(max_depth, true)?;
+        }
         Ok(())
     }
 
     #[test]
     fn test_merkleproof_verify_nonexistence() -> Result<()> {
-        test_merkleproof_verify_opt::<10>(false)?;
-        test_merkleproof_verify_opt::<16>(false)?;
-        test_merkleproof_verify_opt::<32>(false)?;
-        test_merkleproof_verify_opt::<40>(false)?;
-        test_merkleproof_verify_opt::<64>(false)?;
-        test_merkleproof_verify_opt::<128>(false)?;
-        test_merkleproof_verify_opt::<130>(false)?;
-        test_merkleproof_verify_opt::<250>(false)?;
-        test_merkleproof_verify_opt::<256>(false)?;
+        for max_depth in [10, 16, 32, 40, 64, 128, 130, 250, 256] {
+            test_merkleproof_verify_opt(max_depth, false)?;
+        }
         Ok(())
     }
 
     // test logic to be reused both by the existence & nonexistence tests
-    fn test_merkleproof_verify_opt<const MD: usize>(existence: bool) -> Result<()> {
+    fn test_merkleproof_verify_opt(max_depth: usize, existence: bool) -> Result<()> {
         let mut kvs: HashMap<Value, Value> = HashMap::new();
         for i in 0..10 {
             kvs.insert(Value::from(hash_value(&Value::from(i))), Value::from(i));
         }
 
-        let tree = MerkleTree::new(MD, &kvs)?;
+        let tree = MerkleTree::new(max_depth, &kvs)?;
 
         let (key, value, proof) = if existence {
             let key = Value::from(hash_value(&Value::from(5)));
@@ -478,9 +478,9 @@ pub mod tests {
         assert_eq!(proof.existence, existence);
 
         if existence {
-            MerkleTree::verify(MD, tree.root(), &proof, &key, &value)?;
+            MerkleTree::verify(max_depth, tree.root(), &proof, &key, &value)?;
         } else {
-            MerkleTree::verify_nonexistence(MD, tree.root(), &proof, &key)?;
+            MerkleTree::verify_nonexistence(max_depth, tree.root(), &proof, &key)?;
         }
 
         // circuit
@@ -488,7 +488,7 @@ pub mod tests {
         let mut builder = CircuitBuilder::<F, D>::new(config);
         let mut pw = PartialWitness::<F>::new();
 
-        let targets = MerkleProofCircuit::<MD>::add_targets(&mut builder)?;
+        let targets = MerkleProofGate { max_depth }.eval(&mut builder)?;
         targets.set_targets(&mut pw, existence, tree.root(), proof, key, value)?;
 
         // generate & verify proof
@@ -501,39 +501,33 @@ pub mod tests {
 
     #[test]
     fn test_merkleproof_only_existence_verify() -> Result<()> {
-        test_merkleproof_only_existence_verify_opt::<10>()?;
-        test_merkleproof_only_existence_verify_opt::<16>()?;
-        test_merkleproof_only_existence_verify_opt::<32>()?;
-        test_merkleproof_only_existence_verify_opt::<40>()?;
-        test_merkleproof_only_existence_verify_opt::<64>()?;
-        test_merkleproof_only_existence_verify_opt::<128>()?;
-        test_merkleproof_only_existence_verify_opt::<130>()?;
-        test_merkleproof_only_existence_verify_opt::<250>()?;
-        test_merkleproof_only_existence_verify_opt::<256>()?;
+        for max_depth in [10, 16, 32, 40, 64, 128, 130, 250, 256] {
+            test_merkleproof_only_existence_verify_opt(max_depth)?;
+        }
         Ok(())
     }
 
-    fn test_merkleproof_only_existence_verify_opt<const MD: usize>() -> Result<()> {
+    fn test_merkleproof_only_existence_verify_opt(max_depth: usize) -> Result<()> {
         let mut kvs: HashMap<Value, Value> = HashMap::new();
         for i in 0..10 {
             kvs.insert(Value::from(hash_value(&Value::from(i))), Value::from(i));
         }
 
-        let tree = MerkleTree::new(MD, &kvs)?;
+        let tree = MerkleTree::new(max_depth, &kvs)?;
 
         let key = Value::from(hash_value(&Value::from(5)));
         let (value, proof) = tree.prove(&key)?;
         assert_eq!(value, Value::from(5));
         assert_eq!(proof.existence, true);
 
-        MerkleTree::verify(MD, tree.root(), &proof, &key, &value)?;
+        MerkleTree::verify(max_depth, tree.root(), &proof, &key, &value)?;
 
         // circuit
         let config = CircuitConfig::standard_recursion_config();
         let mut builder = CircuitBuilder::<F, D>::new(config);
         let mut pw = PartialWitness::<F>::new();
 
-        let targets = MerkleProofExistenceCircuit::<MD>::add_targets(&mut builder)?;
+        let targets = MerkleProofExistenceGate { max_depth }.eval(&mut builder)?;
         targets.set_targets(&mut pw, tree.root(), proof, key, value)?;
 
         // generate & verify proof
@@ -564,19 +558,19 @@ pub mod tests {
         kvs.insert(Value::from(5), Value::from(1005));
         kvs.insert(Value::from(13), Value::from(1013));
 
-        const MD: usize = 5;
-        let tree = MerkleTree::new(MD, &kvs)?;
+        let max_depth = 5;
+        let tree = MerkleTree::new(max_depth, &kvs)?;
         // existence
-        test_merkletree_edgecase_opt::<MD>(&tree, Value::from(5))?;
+        test_merkletree_edgecase_opt(max_depth, &tree, Value::from(5))?;
         // non-existence case i) expected leaf does not exist
-        test_merkletree_edgecase_opt::<MD>(&tree, Value::from(1))?;
+        test_merkletree_edgecase_opt(max_depth, &tree, Value::from(1))?;
         // non-existence case ii) expected leaf does exist but it has a different 'key'
-        test_merkletree_edgecase_opt::<MD>(&tree, Value::from(21))?;
+        test_merkletree_edgecase_opt(max_depth, &tree, Value::from(21))?;
 
         Ok(())
     }
 
-    fn test_merkletree_edgecase_opt<const MD: usize>(tree: &MerkleTree, key: Value) -> Result<()> {
+    fn test_merkletree_edgecase_opt(max_depth: usize, tree: &MerkleTree, key: Value) -> Result<()> {
         let contains = tree.contains(&key)?;
         // generate merkleproof
         let (value, proof) = if contains {
@@ -590,9 +584,9 @@ pub mod tests {
 
         // verify the proof (non circuit)
         if proof.existence {
-            MerkleTree::verify(MD, tree.root(), &proof, &key, &value)?;
+            MerkleTree::verify(max_depth, tree.root(), &proof, &key, &value)?;
         } else {
-            MerkleTree::verify_nonexistence(MD, tree.root(), &proof, &key)?;
+            MerkleTree::verify_nonexistence(max_depth, tree.root(), &proof, &key)?;
         }
 
         // circuit
@@ -600,7 +594,7 @@ pub mod tests {
         let mut builder = CircuitBuilder::<F, D>::new(config);
         let mut pw = PartialWitness::<F>::new();
 
-        let targets = MerkleProofCircuit::<MD>::add_targets(&mut builder)?;
+        let targets = MerkleProofGate { max_depth }.eval(&mut builder)?;
         targets.set_targets(&mut pw, proof.existence, tree.root(), proof, key, value)?;
 
         // generate & verify proof
@@ -617,8 +611,8 @@ pub mod tests {
         for i in 0..10 {
             kvs.insert(Value::from(i), Value::from(i));
         }
-        const MD: usize = 16;
-        let tree = MerkleTree::new(MD, &kvs)?;
+        let max_depth = 16;
+        let tree = MerkleTree::new(max_depth, &kvs)?;
 
         let key = Value::from(3);
         let (value, proof) = tree.prove(&key)?;
@@ -626,11 +620,11 @@ pub mod tests {
         // build another tree with an extra key-value, so that it has a
         // different root
         kvs.insert(Value::from(100), Value::from(100));
-        let tree2 = MerkleTree::new(MD, &kvs)?;
+        let tree2 = MerkleTree::new(max_depth, &kvs)?;
 
-        MerkleTree::verify(MD, tree.root(), &proof, &key, &value)?;
+        MerkleTree::verify(max_depth, tree.root(), &proof, &key, &value)?;
         assert_eq!(
-            MerkleTree::verify(MD, tree2.root(), &proof, &key, &value)
+            MerkleTree::verify(max_depth, tree2.root(), &proof, &key, &value)
                 .unwrap_err()
                 .to_string(),
             "proof of inclusion does not verify"
@@ -641,7 +635,7 @@ pub mod tests {
         let mut builder = CircuitBuilder::<F, D>::new(config);
         let mut pw = PartialWitness::<F>::new();
 
-        let targets = MerkleProofCircuit::<MD>::add_targets(&mut builder)?;
+        let targets = MerkleProofGate { max_depth }.eval(&mut builder)?;
         targets.set_targets(&mut pw, true, tree2.root(), proof, key, value)?;
 
         // generate proof, expecting it to fail (since we're using the wrong
diff --git a/src/frontend/mod.rs b/src/frontend/mod.rs
index 5f92a36..22fd99c 100644
--- a/src/frontend/mod.rs
+++ b/src/frontend/mod.rs
@@ -1091,6 +1091,7 @@ pub mod tests {
             max_operation_args: 5,
             max_custom_predicate_arity: 5,
             max_custom_batch_size: 5,
+            ..Default::default()
         };
 
         let mut alice = MockSigner { pk: "Alice".into() };
diff --git a/src/middleware/custom.rs b/src/middleware/custom.rs
index 6f8d5cb..e71a46a 100644
--- a/src/middleware/custom.rs
+++ b/src/middleware/custom.rs
@@ -5,6 +5,7 @@ use std::{fmt, hash as h, iter, iter::zip};
 use anyhow::{anyhow, Result};
 use plonky2::field::types::Field;
 use schemars::JsonSchema;
+use serde::{Deserialize, Serialize};
 
 use super::{
     hash_fields, AnchoredKey, Hash, NativePredicate, Params, PodId, Statement, StatementArg,
@@ -12,7 +13,6 @@ use super::{
 };
 use crate::backends::plonky2::basetypes::HASH_SIZE;
 use crate::util::hashmap_insert_no_dupe;
-use serde::{Deserialize, Serialize};
 
 // BEGIN Custom 1b
 
@@ -49,9 +49,9 @@ impl fmt::Display for HashOrWildcard {
 }
 
 impl ToFields for HashOrWildcard {
-    fn to_fields(&self, _params: &Params) -> Vec<F> {
+    fn to_fields(&self, params: &Params) -> Vec<F> {
         match self {
-            HashOrWildcard::Hash(h) => h.to_fields(_params),
+            HashOrWildcard::Hash(h) => h.to_fields(params),
             HashOrWildcard::Wildcard(w) => (0..HASH_SIZE - 1)
                 .chain(iter::once(*w))
                 .map(|x| F::from_canonical_u64(x as u64))
@@ -91,7 +91,7 @@ impl StatementTmplArg {
 }
 
 impl ToFields for StatementTmplArg {
-    fn to_fields(&self, _params: &Params) -> Vec<F> {
+    fn to_fields(&self, params: &Params) -> Vec<F> {
         // None => (0, ...)
         // Literal(value) => (1, [value], 0, 0, 0, 0)
         // Key(hash_or_wildcard1, hash_or_wildcard2)
@@ -107,15 +107,15 @@ impl ToFields for StatementTmplArg {
             }
             StatementTmplArg::Literal(v) => {
                 let fields: Vec<F> = iter::once(F::from_canonical_u64(1))
-                    .chain(v.to_fields(_params))
+                    .chain(v.to_fields(params))
                     .chain(iter::repeat_with(|| F::from_canonical_u64(0)).take(HASH_SIZE))
                     .collect();
                 fields
             }
             StatementTmplArg::Key(hw1, hw2) => {
                 let fields: Vec<F> = iter::once(F::from_canonical_u64(2))
-                    .chain(hw1.to_fields(_params))
-                    .chain(hw2.to_fields(_params))
+                    .chain(hw1.to_fields(params))
+                    .chain(hw2.to_fields(params))
                     .collect();
                 fields
             }
@@ -165,7 +165,7 @@ impl StatementTmpl {
             Err(anyhow!(
                 "Cannot check self-referencing statement templates."
             ))
-        } else if self.pred() != &s.code() {
+        } else if self.pred() != &s.predicate() {
             Err(anyhow!("Type mismatch between {:?} and {}.", self, s))
         } else {
             zip(self.args(), s.args())
@@ -318,8 +318,8 @@ impl ToFields for CustomPredicateBatch {
 }
 
 impl CustomPredicateBatch {
-    pub fn hash(&self, _params: &Params) -> Hash {
-        let input = self.to_fields(_params);
+    pub fn hash(&self, params: &Params) -> Hash {
+        let input = self.to_fields(params);
 
         hash_fields(&input)
     }
@@ -399,7 +399,7 @@ impl From<NativePredicate> for Predicate {
 }
 
 impl ToFields for Predicate {
-    fn to_fields(&self, _params: &Params) -> Vec<F> {
+    fn to_fields(&self, params: &Params) -> Vec<F> {
         // serialize:
         // NativePredicate(id) as (0, id, 0, 0, 0, 0) -- id: usize
         // BatchSelf(i) as (1, i, 0, 0, 0, 0) -- i: usize
@@ -410,13 +410,13 @@ impl ToFields for Predicate {
         // in every case: pad to (hash_size + 2) field elements
         let mut fields: Vec<F> = match self {
             Self::Native(p) => iter::once(F::from_canonical_u64(1))
-                .chain(p.to_fields(_params))
+                .chain(p.to_fields(params))
                 .collect(),
             Self::BatchSelf(i) => iter::once(F::from_canonical_u64(2))
                 .chain(iter::once(F::from_canonical_usize(*i)))
                 .collect(),
             Self::Custom(CustomPredicateRef(pb, i)) => iter::once(F::from_canonical_u64(3))
-                .chain(pb.hash(_params).0)
+                .chain(pb.hash(params).0)
                 .chain(iter::once(F::from_canonical_usize(*i)))
                 .collect(),
         };
diff --git a/src/middleware/mod.rs b/src/middleware/mod.rs
index 6d9881c..b07d478 100644
--- a/src/middleware/mod.rs
+++ b/src/middleware/mod.rs
@@ -93,6 +93,8 @@ pub struct Params {
     // in a custom predicate
     pub max_custom_predicate_arity: usize,
     pub max_custom_batch_size: usize,
+    // maximum depth for merkle tree gates
+    pub max_depth_mt_gate: usize,
 }
 
 impl Default for Params {
@@ -107,6 +109,7 @@ impl Default for Params {
             max_operation_args: 5,
             max_custom_predicate_arity: 5,
             max_custom_batch_size: 5,
+            max_depth_mt_gate: 32,
         }
     }
 }
@@ -116,15 +119,27 @@ impl Params {
         self.max_statements - self.max_public_statements
     }
 
-    pub fn statement_tmpl_arg_size() -> usize {
+    pub const fn statement_tmpl_arg_size() -> usize {
         2 * HASH_SIZE + 1
     }
 
-    pub fn predicate_size() -> usize {
+    pub const fn predicate_size() -> usize {
         HASH_SIZE + 2
     }
 
-    pub fn statement_tmpl_size(&self) -> usize {
+    pub const fn operation_type_size() -> usize {
+        HASH_SIZE + 2
+    }
+
+    pub fn statement_size(&self) -> usize {
+        Self::predicate_size() + STATEMENT_ARG_F_LEN * self.max_statement_args
+    }
+
+    pub fn operation_size(&self) -> usize {
+        Self::operation_type_size() + OPERATION_ARG_F_LEN * self.max_operation_args
+    }
+
+    pub const fn statement_tmpl_size(&self) -> usize {
         Self::predicate_size() + self.max_statement_args * Self::statement_tmpl_arg_size()
     }
 
diff --git a/src/middleware/operation.rs b/src/middleware/operation.rs
index da54613..52d3e1c 100644
--- a/src/middleware/operation.rs
+++ b/src/middleware/operation.rs
@@ -1,9 +1,11 @@
 use anyhow::{anyhow, Result};
 use log::error;
+use plonky2::field::types::Field;
 use serde::{Deserialize, Serialize};
 use std::fmt;
+use std::iter;
 
-use super::{CustomPredicateRef, NativePredicate, Statement, StatementArg};
+use super::{CustomPredicateRef, NativePredicate, Statement, StatementArg, ToFields, F};
 use crate::middleware::{AnchoredKey, Params, Predicate, Value, SELF};
 
 #[derive(Clone, Debug, PartialEq, Eq, Serialize, Deserialize)]
@@ -12,6 +14,22 @@ pub enum OperationType {
     Custom(CustomPredicateRef),
 }
 
+impl ToFields for OperationType {
+    fn to_fields(&self, params: &Params) -> Vec<F> {
+        let mut fields: Vec<F> = match self {
+            Self::Native(p) => iter::once(F::from_canonical_u64(1))
+                .chain(p.to_fields(params))
+                .collect(),
+            Self::Custom(CustomPredicateRef(pb, i)) => iter::once(F::from_canonical_u64(3))
+                .chain(pb.hash(params).0)
+                .chain(iter::once(F::from_canonical_usize(*i)))
+                .collect(),
+        };
+        fields.resize_with(Params::operation_type_size(), || F::from_canonical_u64(0));
+        fields
+    }
+}
+
 #[derive(Clone, Copy, Debug, PartialEq, Eq, Serialize, Deserialize)]
 pub enum NativeOperation {
     None = 0,
@@ -31,6 +49,12 @@ pub enum NativeOperation {
     MaxOf = 15,
 }
 
+impl ToFields for NativeOperation {
+    fn to_fields(&self, _params: &Params) -> Vec<F> {
+        vec![F::from_canonical_u64(*self as u64)]
+    }
+}
+
 impl OperationType {
     /// Gives the type of predicate that the operation will output, if known.
     /// CopyStatement may output any predicate (it will match the statement copied),
@@ -91,7 +115,7 @@ pub enum Operation {
 }
 
 impl Operation {
-    pub fn predicate(&self) -> OperationType {
+    pub fn op_type(&self) -> OperationType {
         type OT = OperationType;
         use NativeOperation::*;
         match self {
@@ -178,7 +202,7 @@ impl Operation {
     /// The outer Result is error handling
     pub fn output_statement(&self) -> Result<Option<Statement>> {
         use Statement::*;
-        let pred: Option<Predicate> = self.predicate().output_predicate();
+        let pred: Option<Predicate> = self.op_type().output_predicate();
 
         let st_args: Option<Vec<StatementArg>> = match self {
             Self::None => Some(vec![]),
@@ -401,10 +425,16 @@ impl Operation {
     }
 }
 
+impl ToFields for Operation {
+    fn to_fields(&self, params: &Params) -> Vec<F> {
+        todo!()
+    }
+}
+
 impl fmt::Display for Operation {
     fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
         writeln!(f, "middleware::Operation:")?;
-        writeln!(f, "  {:?} ", self.predicate())?;
+        writeln!(f, "  {:?} ", self.op_type())?;
         for arg in self.args().iter() {
             writeln!(f, "    {}", arg)?;
         }
diff --git a/src/middleware/statement.rs b/src/middleware/statement.rs
index ba879ec..7454f19 100644
--- a/src/middleware/statement.rs
+++ b/src/middleware/statement.rs
@@ -5,11 +5,14 @@ use serde::{Deserialize, Serialize};
 use std::{fmt, iter};
 use strum_macros::FromRepr;
 
-use super::{AnchoredKey, CustomPredicateRef, Params, Predicate, ToFields, Value, F, VALUE_SIZE};
+use super::{
+    AnchoredKey, CustomPredicateRef, Params, Predicate, ToFields, Value, F, HASH_SIZE, VALUE_SIZE,
+};
 
 pub const KEY_SIGNER: &str = "_signer";
 pub const KEY_TYPE: &str = "_type";
 pub const STATEMENT_ARG_F_LEN: usize = 8;
+pub const OPERATION_ARG_F_LEN: usize = 1;
 
 #[derive(Clone, Copy, Debug, FromRepr, PartialEq, Eq, Hash, Serialize, Deserialize, JsonSchema)]
 pub enum NativePredicate {
@@ -53,7 +56,7 @@ impl Statement {
     pub fn is_none(&self) -> bool {
         self == &Self::None
     }
-    pub fn code(&self) -> Predicate {
+    pub fn predicate(&self) -> Predicate {
         use Predicate::*;
         match self {
             Self::None => Native(NativePredicate::None),
@@ -184,16 +187,17 @@ impl Statement {
 }
 
 impl ToFields for Statement {
-    fn to_fields(&self, _params: &Params) -> Vec<F> {
-        let mut fields = self.code().to_fields(_params);
-        fields.extend(self.args().iter().flat_map(|arg| arg.to_fields(_params)));
+    fn to_fields(&self, params: &Params) -> Vec<F> {
+        let mut fields = self.predicate().to_fields(params);
+        fields.extend(self.args().iter().flat_map(|arg| arg.to_fields(params)));
+        fields.resize_with(params.statement_size(), || F::ZERO);
         fields
     }
 }
 
 impl fmt::Display for Statement {
     fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
-        write!(f, "{:?} ", self.code())?;
+        write!(f, "{:?} ", self.predicate())?;
         for (i, arg) in self.args().iter().enumerate() {
             if i != 0 {
                 write!(f, " ")?;