Fix custom predicate circuits and add tests for them (#235)

* add tests, fix custom predicates

* wip

* wip

* fix custom predicates

* modularize code

* fix typos

* remove scratch file

* update

* Update src/backends/plonky2/circuits/mainpod.rs

Co-authored-by: Ahmad Afuni <root@ahmadafuni.com>

---------

Co-authored-by: Ahmad Afuni <root@ahmadafuni.com>

book/src/statements.md

@@ -24,18 +24,19 @@ The following table summarises the natively-supported statements, where we write
 
 | Code | Identifier    | Args                | Meaning                                                           |
 |------|---------------|---------------------|-------------------------------------------------------------------|
-| 0    | `None`        |                     | no statement (useful for padding)                                 |
+| 0    | `None`        |                     | no statement, always true (useful for padding)                    |
-| 1    | `ValueOf`     | `ak`, `value`       | `value_of(ak) = value`                                            |
+| 1    | `False`       |                     | always false (useful for padding disjunctions)                    |
-| 2    | `Eq`          | `ak1`, `ak2`        | `value_of(ak1) = value_of(ak2)`                                   |
+| 2    | `ValueOf`     | `ak`, `value`       | `value_of(ak) = value`                                            |
-| 3    | `NEq`         | `ak1`, `ak2`        | `value_of(ak1) != value_of(ak2)`                                  |
+| 3    | `Eq`          | `ak1`, `ak2`        | `value_of(ak1) = value_of(ak2)`                                   |
-| 4    | `Gt`          | `ak1`, `ak2`        | `value_of(ak1) > value_of(ak2)`                                   |
+| 4    | `NEq`         | `ak1`, `ak2`        | `value_of(ak1) != value_of(ak2)`                                  |
-| 5    | `LEq`         | `ak1`, `ak2`        | `value_of(ak1) <= value_of(ak2)`                                  |
+| 5    | `Gt`          | `ak1`, `ak2`        | `value_of(ak1) > value_of(ak2)`                                   |
-| 6    | `Contains`    | `ak1`, `ak2`        | `(key_of(ak2), value_of(ak2)) ∈ value_of(ak1)` (Merkle inclusion) |
+| 6    | `LEq`         | `ak1`, `ak2`        | `value_of(ak1) <= value_of(ak2)`                                  |
-| 7    | `NotContains` | `ak1`, `ak2`        | `(key_of(ak2), value_of(ak2)) ∉ value_of(ak1)` (Merkle exclusion) |
+| 7    | `Contains`    | `ak1`, `ak2`        | `(key_of(ak2), value_of(ak2)) ∈ value_of(ak1)` (Merkle inclusion) |
-| 8    | `SumOf`       | `ak1`, `ak2`, `ak3` | `value_of(ak1) = value_of(ak2) + value_of(ak3)`                   |
+| 8    | `NotContains` | `ak1`, `ak2`        | `(key_of(ak2), value_of(ak2)) ∉ value_of(ak1)` (Merkle exclusion) |
-| 9    | `ProductOf`   | `ak1`, `ak2`, `ak3` | `value_of(ak1) = value_of(ak2) * value_of(ak3)`                   |
+| 9    | `SumOf`       | `ak1`, `ak2`, `ak3` | `value_of(ak1) = value_of(ak2) + value_of(ak3)`                   |
-| 10   | `MaxOf`       | `ak1`, `ak2`, `ak3` | `value_of(ak1) = max(value_of(ak2), value_of(ak3))`               |
+| 10   | `ProductOf`   | `ak1`, `ak2`, `ak3` | `value_of(ak1) = value_of(ak2) * value_of(ak3)`                   |
-| 11   | `HashOf`      | `ak1`, `ak2`, `ak3` | `value_of(ak1) = hash(value_of(ak2), value_of(ak3))`              |
+| 11   | `MaxOf`       | `ak1`, `ak2`, `ak3` | `value_of(ak1) = max(value_of(ak2), value_of(ak3))`               |
+| 12   | `HashOf`      | `ak1`, `ak2`, `ak3` | `value_of(ak1) = hash(value_of(ak2), value_of(ak3))`              |
 
 ### Frontend statements
 

src/backends/plonky2/circuits/common.rs

@@ -153,7 +153,7 @@ impl<T> Build<T> for T {
 }
 
 impl StatementTarget {
-    /// Build a new native StatementTarget
+    /// Build a new native StatementTarget.  Pads the arguments.
     pub fn new_native(
         builder: &mut CircuitBuilder<F, D>,
         params: &Params,
@@ -311,7 +311,7 @@ impl NativePredicateTarget {
 
 #[derive(Clone)]
 pub struct PredicateTarget {
-    elements: [Target; Params::predicate_size()],
+    pub(crate) elements: [Target; Params::predicate_size()],
 }
 
 impl PredicateTarget {
@@ -520,8 +520,35 @@ impl CustomPredicateEntryTarget {
     ) -> Result<()> {
         pw.set_target_arr(&self.id.elements, &predicate.batch.id().0)?;
         pw.set_target(self.index, F::from_canonical_usize(predicate.index))?;
-        self.predicate
+
-            .set_targets(pw, params, predicate.predicate())?;
+        // Replace statement templates of batch-self with (id,index)
+        let batch = &predicate.batch;
+        let predicate = predicate.predicate();
+        let statements = predicate
+            .statements
+            .clone()
+            .into_iter()
+            .map(|st_tmpl| {
+                let pred = match st_tmpl.pred {
+                    Predicate::BatchSelf(i) => Predicate::Custom(CustomPredicateRef {
+                        batch: batch.clone(),
+                        index: i,
+                    }),
+                    p => p,
+                };
+                StatementTmpl {
+                    pred,
+                    args: st_tmpl.args,
+                }
+            })
+            .collect_vec();
+        let predicate = CustomPredicate {
+            name: predicate.name.clone(),
+            conjunction: predicate.conjunction,
+            statements,
+            args_len: predicate.args_len,
+        };
+        self.predicate.set_targets(pw, params, &predicate)?;
         Ok(())
     }
 }
@@ -570,6 +597,7 @@ impl CustomPredicateVerifyEntryTarget {
             self.custom_predicate_table_index,
             F::from_canonical_usize(cpv.custom_predicate_table_index),
         )?;
+        // Replace statement templates of batch-self with (id,index)
         self.custom_predicate
             .set_targets(pw, params, &cpv.custom_predicate)?;
         let pad_arg = WildcardValue::None;
@@ -1439,7 +1467,7 @@ pub(crate) mod tests {
         let params = Params::default();
         let config = CircuitConfig::standard_recursion_config();
 
-        let custom_predicate_batch = eth_friend_batch(&params)?;
+        let custom_predicate_batch = eth_friend_batch(&params, false)?;
 
         for (i, cp) in custom_predicate_batch.predicates().iter().enumerate() {
             let mut builder = CircuitBuilder::<F, D>::new(config.clone());
@@ -1502,10 +1530,10 @@ pub(crate) mod tests {
         helper_custom_predicate_batch_target_id(&params, &custom_predicate_batch).unwrap();
 
         // Some cases from the examples
-        let custom_predicate_batch = eth_friend_batch(&params)?;
+        let custom_predicate_batch = eth_friend_batch(&params, false)?;
         helper_custom_predicate_batch_target_id(&params, &custom_predicate_batch).unwrap();
 
-        let custom_predicate_batch = eth_dos_batch(&params)?;
+        let custom_predicate_batch = eth_dos_batch(&params, false)?;
         helper_custom_predicate_batch_target_id(&params, &custom_predicate_batch).unwrap();
 
         let custom_predicate_batch =

src/backends/plonky2/circuits/mainpod.rs

@@ -14,10 +14,10 @@ use crate::{
         circuits::{
             common::{
                 CircuitBuilderPod, CustomPredicateBatchTarget, CustomPredicateEntryTarget,
-                CustomPredicateVerifyEntryTarget, CustomPredicateVerifyQueryTarget, Flattenable,
+                CustomPredicateTarget, CustomPredicateVerifyEntryTarget,
-                MerkleClaimTarget, OperationTarget, OperationTypeTarget, PredicateTarget,
+                CustomPredicateVerifyQueryTarget, Flattenable, MerkleClaimTarget, OperationTarget,
-                StatementArgTarget, StatementTarget, StatementTmplArgTarget, StatementTmplTarget,
+                OperationTypeTarget, PredicateTarget, StatementArgTarget, StatementTarget,
-                ValueTarget,
+                StatementTmplArgTarget, StatementTmplTarget, ValueTarget,
             },
             signedpod::{SignedPodVerifyGadget, SignedPodVerifyTarget},
         },
@@ -30,8 +30,8 @@ use crate::{
     },
     middleware::{
         AnchoredKey, CustomPredicate, CustomPredicateBatch, CustomPredicateRef, NativeOperation,
-        NativePredicate, Params, PodType, Statement, StatementArg, ToFields, Value, WildcardValue,
+        NativePredicate, Params, PodType, PredicatePrefix, Statement, StatementArg, ToFields,
-        F, KEY_TYPE, SELF, VALUE_SIZE,
+        Value, WildcardValue, F, KEY_TYPE, SELF, VALUE_SIZE,
     },
 };
 
@@ -188,8 +188,7 @@ impl OperationVerifyGadget {
         .concat();
 
         let ok = builder.any(op_checks);
-
+        builder.assert_one(ok.target);
-        builder.connect(ok.target, _true.target);
 
         Ok(())
     }
@@ -813,6 +812,7 @@ impl CustomOperationVerifyGadget {
         // expected_sts.len() == self.params.max_custom_predicate_arity
         // op_args.len() == self.params.max_operation_args;
         assert!(self.params.max_custom_predicate_arity <= self.params.max_operation_args);
+
         let sts_eq: Vec<_> = expected_sts
             .iter()
             .zip(op_args.iter())
@@ -837,6 +837,119 @@ struct MainPodVerifyGadget {
 }
 
 impl MainPodVerifyGadget {
+    // Replace predicates of batch-self with the corresponding global custom predicate batch_id and
+    // index
+    fn normalize_st_tmpl(
+        &self,
+        builder: &mut CircuitBuilder<F, D>,
+        st_tmpl: &StatementTmplTarget,
+        id: HashOutTarget,
+    ) -> StatementTmplTarget {
+        let params = &self.params;
+        let prefix_batch_self = builder.constant(F::from(PredicatePrefix::BatchSelf));
+        let is_batch_self = builder.is_equal(st_tmpl.pred.elements[0], prefix_batch_self);
+        let pred_index = st_tmpl.pred.elements[1];
+        let custom_pred = PredicateTarget::new_custom(builder, id, pred_index);
+        let pred = builder.select_flattenable(params, is_batch_self, &custom_pred, &st_tmpl.pred);
+        StatementTmplTarget {
+            pred,
+            args: st_tmpl.args.clone(),
+        }
+    }
+    /// Build a table of [batch_id, custom_predicate_index, custom_predicate] with queryable part as
+    /// hash([batch_id, custom_predicate_index, custom_predicate]).  While building the table we
+    /// calculate the id of each batch.
+    fn build_custom_predicate_table(
+        &self,
+        builder: &mut CircuitBuilder<F, D>,
+    ) -> Result<(Vec<HashOutTarget>, Vec<CustomPredicateBatchTarget>)> {
+        let params = &self.params;
+        let mut custom_predicate_table =
+            Vec::with_capacity(params.max_custom_predicate_batches * params.max_custom_batch_size);
+        let mut custom_predicate_batches = Vec::with_capacity(params.max_custom_predicate_batches);
+        for _ in 0..params.max_custom_predicate_batches {
+            let cpb = builder.add_virtual_custom_predicate_batch(params);
+            let id = cpb.id(builder); // constrain the id
+            for (index, cp) in cpb.predicates.iter().enumerate() {
+                let statements = cp
+                    .statements
+                    .iter()
+                    .map(|st_tmpl| self.normalize_st_tmpl(builder, st_tmpl, id))
+                    .collect_vec();
+                let cp = CustomPredicateTarget {
+                    conjunction: cp.conjunction,
+                    statements,
+                    args_len: cp.args_len,
+                };
+                let entry = CustomPredicateEntryTarget {
+                    id,                                                      // output
+                    index: builder.constant(F::from_canonical_usize(index)), // constant
+                    predicate: cp.clone(),                                   // input
+                };
+
+                let in_query_hash = entry.hash(builder);
+                custom_predicate_table.push(in_query_hash);
+            }
+            custom_predicate_batches.push(cpb); // We keep this for witness assignment
+        }
+        Ok((custom_predicate_table, custom_predicate_batches))
+    }
+
+    /// Build table of [batch_id, custom_predicate_index, custom_predicate, args, st, op, op_args]
+    /// with queryable part as hash([st, op, op_args]).  While building the table we verify each
+    /// custom predicate against the operation and statement.
+    fn build_custom_predicate_verification_table(
+        &self,
+        builder: &mut CircuitBuilder<F, D>,
+        custom_predicate_table: &[HashOutTarget],
+    ) -> Result<(Vec<HashOutTarget>, Vec<CustomPredicateVerifyEntryTarget>)> {
+        let params = &self.params;
+        let mut custom_predicate_verifications =
+            Vec::with_capacity(params.max_custom_predicate_verifications);
+        let mut custom_predicate_verification_table =
+            Vec::with_capacity(params.max_custom_predicate_verifications);
+        for _ in 0..params.max_custom_predicate_verifications {
+            let custom_predicate_table_index = builder.add_virtual_target();
+            let custom_predicate = builder.add_virtual_custom_predicate_entry(params);
+            let args = (0..params.max_custom_predicate_wildcards)
+                .map(|_| builder.add_virtual_value())
+                .collect_vec();
+            let op_args = (0..params.max_operation_args)
+                .map(|_| builder.add_virtual_statement(params))
+                .collect_vec();
+
+            // Verify the custom predicate operation
+            let (statement, op_type) = CustomOperationVerifyGadget {
+                params: params.clone(),
+            }
+            .eval(builder, &custom_predicate, &op_args, &args)?;
+
+            // Check that the batch id is correct by querying the custom predicate batches table
+            let table_query_hash =
+                builder.vec_ref(params, custom_predicate_table, custom_predicate_table_index);
+            let out_query_hash = custom_predicate.hash(builder);
+            builder.connect_array(table_query_hash.elements, out_query_hash.elements);
+
+            let entry = CustomPredicateVerifyEntryTarget {
+                custom_predicate_table_index, // input
+                custom_predicate,             // input
+                args,                         // input
+                query: CustomPredicateVerifyQueryTarget {
+                    statement, // output
+                    op_type,   // output
+                    op_args,   // input
+                },
+            };
+            let in_query_hash = entry.query.hash(builder);
+            custom_predicate_verification_table.push(in_query_hash);
+            custom_predicate_verifications.push(entry); // We keep this for witness assignment
+        }
+        Ok((
+            custom_predicate_verification_table,
+            custom_predicate_verifications,
+        ))
+    }
+
     fn eval(&self, builder: &mut CircuitBuilder<F, D>) -> Result<MainPodVerifyTarget> {
         let params = &self.params;
         // 1. Verify all input signed pods
@@ -851,12 +964,17 @@ impl MainPodVerifyGadget {
 
         // Build the statement array
         let mut statements = Vec::new();
+        // Statement at index 0 is always None to be used for padding operation arguments in custom
+        // predicate statements
+        let st_none =
+            StatementTarget::new_native(builder, &self.params, NativePredicate::None, &[]);
+        statements.push(st_none);
         for signed_pod in &signed_pods {
             statements.extend_from_slice(signed_pod.pub_statements(builder, false).as_slice());
         }
         debug_assert_eq!(
             statements.len(),
-            self.params.max_input_signed_pods * self.params.max_signed_pod_values
+            1 + self.params.max_input_signed_pods * self.params.max_signed_pod_values
         );
         // TODO: Fill with input main pods
         for _main_pod in 0..self.params.max_input_main_pods {
@@ -895,73 +1013,13 @@ impl MainPodVerifyGadget {
             .map(|pf| pf.into())
             .collect();
 
-        // Table of [batch_id, custom_predicate_index, custom_predicate] with queryable part as
+        // Table of custom predicate batches with batch_id calculation
-        // hash([batch_id, custom_predicate_index, custom_predicate]).  While building the table we
+        let (custom_predicate_table, custom_predicate_batches) =
-        // calculate the id of each batch.
+            self.build_custom_predicate_table(builder)?;
-        let mut custom_predicate_table =
-            Vec::with_capacity(params.max_custom_predicate_batches * params.max_custom_batch_size);
-        let mut custom_predicate_batches = Vec::with_capacity(params.max_custom_predicate_batches);
-        for _ in 0..params.max_custom_predicate_batches {
-            let cpb = builder.add_virtual_custom_predicate_batch(&self.params);
-            let id = cpb.id(builder); // constrain the id
-            for (index, cp) in cpb.predicates.iter().enumerate() {
-                let entry = CustomPredicateEntryTarget {
-                    id,                                                      // output
-                    index: builder.constant(F::from_canonical_usize(index)), // constant
-                    predicate: cp.clone(),                                   // input
-                };
-                let in_query_hash = entry.hash(builder);
-                custom_predicate_table.push(in_query_hash);
-            }
-            custom_predicate_batches.push(cpb); // We keep this for witness assignment
-        }
 
-        // Table of [batch_id, custom_predicate_index, custom_predicate, args, st, op, op_args]
+        // Table of custom predicate statements verification against operations
-        // with queryable part as hash([st, op, op_args]).  While building the table we verify each
+        let (custom_predicate_verification_table, custom_predicate_verifications) =
-        // custom predicate against the operation and statement.
+            self.build_custom_predicate_verification_table(builder, &custom_predicate_table)?;
-        let mut custom_predicate_verifications =
-            Vec::with_capacity(params.max_custom_predicate_verifications);
-        let mut custom_predicate_verification_table =
-            Vec::with_capacity(params.max_custom_predicate_verifications);
-        for _ in 0..params.max_custom_predicate_verifications {
-            let custom_predicate_table_index = builder.add_virtual_target();
-            let custom_predicate = builder.add_virtual_custom_predicate_entry(&self.params);
-            let args = (0..params.max_custom_predicate_wildcards)
-                .map(|_| builder.add_virtual_value())
-                .collect_vec();
-            let op_args = (0..params.max_operation_args)
-                .map(|_| builder.add_virtual_statement(&self.params))
-                .collect_vec();
-
-            // Verify the custom predicate operation
-            let (statement, op_type) = CustomOperationVerifyGadget {
-                params: params.clone(),
-            }
-            .eval(builder, &custom_predicate, &op_args, &args)?;
-
-            // Check that the batch id is correct by querying the custom predicate batches table
-            let table_query_hash = builder.vec_ref(
-                &self.params,
-                &custom_predicate_table,
-                custom_predicate_table_index,
-            );
-            let out_query_hash = custom_predicate.hash(builder);
-            builder.connect_array(table_query_hash.elements, out_query_hash.elements);
-
-            let entry = CustomPredicateVerifyEntryTarget {
-                custom_predicate_table_index, // input
-                custom_predicate,             // input
-                args,                         // input
-                query: CustomPredicateVerifyQueryTarget {
-                    statement, // output
-                    op_type,   // output
-                    op_args,   // input
-                },
-            };
-            let in_query_hash = entry.query.hash(builder);
-            custom_predicate_verification_table.push(in_query_hash);
-            custom_predicate_verifications.push(entry); // We keep this for witness assignment
-        }
 
         // 2. Calculate the Pod Id from the public statements
         let pub_statements_flattened = pub_statements.iter().flat_map(|s| s.flatten()).collect();
@@ -2193,7 +2251,7 @@ mod tests {
         custom_predicate: CustomPredicateRef,
         op_args: Vec<Statement>,
         args: Vec<WildcardValue>,
-        expected_st: Statement,
+        expected_st: Option<Statement>,
     ) -> Result<()> {
         let config = CircuitConfig::standard_recursion_config();
         let mut builder = CircuitBuilder::<F, D>::new(config);
@@ -2226,22 +2284,22 @@ mod tests {
             arg_target.set_targets(&mut pw, &Value::from(arg.raw()))?;
         }
         // Expected Output
-        st_target.set_targets(&mut pw, params, &expected_st.into())?;
+        if let Some(expected_st) = expected_st {
+            st_target.set_targets(&mut pw, params, &expected_st.into())?;
+        }
 
         let expected_op_type = OperationType::Custom(custom_predicate);
         op_type_target.set_targets(&mut pw, params, &expected_op_type)?;
 
         // generate & verify proof
         let data = builder.build::<C>();
-        let proof = data.prove(pw).unwrap();
+        let proof = data.prove(pw)?;
-        data.verify(proof.clone()).unwrap();
+        Ok(data.verify(proof.clone())?)
-
-        Ok(())
     }
 
     // TODO: Add negative tests
     #[test]
-    fn test_custom_operation_verify_gadget() -> frontend::Result<()> {
+    fn test_custom_operation_verify_gadget_positive() -> frontend::Result<()> {
         // We set the parameters to the exact sizes we have in the test so that we don't have to
         // pad.
         let params = Params {
@@ -2298,7 +2356,7 @@ mod tests {
             custom_predicate,
             op_args,
             args,
-            expected_st,
+            Some(expected_st),
         )
         .unwrap();
 
@@ -2322,7 +2380,7 @@ mod tests {
             custom_predicate,
             op_args,
             args,
-            expected_st,
+            Some(expected_st),
         )
         .unwrap();
 
@@ -2349,10 +2407,190 @@ mod tests {
             custom_predicate,
             op_args,
             args,
-            expected_st,
+            Some(expected_st),
         )
         .unwrap();
 
         Ok(())
     }
+
+    #[test]
+    fn test_custom_operation_verify_gadget_negative() -> frontend::Result<()> {
+        // We set the parameters to the exact sizes we have in the test so that we don't have to
+        // pad.
+        let params = Params {
+            max_custom_predicate_arity: 2,
+            max_custom_predicate_wildcards: 2,
+            max_operation_args: 2,
+            max_statement_args: 2,
+            ..Default::default()
+        };
+
+        use NativePredicate as NP;
+        use StatementTmplBuilder as STB;
+        let mut builder = CustomPredicateBatchBuilder::new(params.clone(), "batch".into());
+        let stb0 = STB::new(NP::ValueOf)
+            .arg(("id", key("score")))
+            .arg(literal(42));
+        let stb1 = STB::new(NP::Equal)
+            .arg(("id", "secret_key"))
+            .arg(("id", key("score")));
+        let _ = builder.predicate_and(
+            "pred_and",
+            &["id"],
+            &["secret_key"],
+            &[stb0.clone(), stb1.clone()],
+        )?;
+        let _ = builder.predicate_or("pred_or", &["id"], &["secret_key"], &[stb0, stb1])?;
+        let batch = builder.finish();
+
+        let pod_id = PodId(hash_str("pod_id"));
+
+        // AND (0) Sanity check with correct values
+        let custom_predicate = CustomPredicateRef::new(batch.clone(), 0);
+        let op_args = vec![
+            Statement::ValueOf(
+                AnchoredKey::new(pod_id, Key::from("score")),
+                Value::from(42),
+            ),
+            Statement::Equal(
+                AnchoredKey::new(pod_id, Key::from("foo")),
+                AnchoredKey::new(pod_id, Key::from("score")),
+            ),
+        ];
+        let args = vec![
+            WildcardValue::PodId(pod_id),
+            WildcardValue::Key(Key::from("foo")),
+        ];
+        let expected_st = Statement::Custom(
+            custom_predicate.clone(),
+            vec![args[0].clone(), WildcardValue::None],
+        );
+
+        helper_custom_operation_verify_gadget(
+            &params,
+            custom_predicate,
+            op_args,
+            args,
+            Some(expected_st),
+        )
+        .unwrap();
+
+        // AND (1) Different pod_id for same wildcard
+        let custom_predicate = CustomPredicateRef::new(batch.clone(), 0);
+        let op_args = vec![
+            Statement::ValueOf(
+                AnchoredKey::new(pod_id, Key::from("score")),
+                Value::from(42),
+            ),
+            Statement::Equal(
+                AnchoredKey::new(PodId(hash_str("BAD")), Key::from("foo")),
+                AnchoredKey::new(pod_id, Key::from("score")),
+            ),
+        ];
+        let args = vec![
+            WildcardValue::PodId(pod_id),
+            WildcardValue::Key(Key::from("foo")),
+        ];
+
+        assert!(helper_custom_operation_verify_gadget(
+            &params,
+            custom_predicate,
+            op_args,
+            args,
+            None,
+        )
+        .is_err());
+
+        // AND (2) key doesn't match template
+        let custom_predicate = CustomPredicateRef::new(batch.clone(), 0);
+        let op_args = vec![
+            Statement::ValueOf(AnchoredKey::new(pod_id, Key::from("BAD")), Value::from(42)),
+            Statement::Equal(
+                AnchoredKey::new(pod_id, Key::from("foo")),
+                AnchoredKey::new(pod_id, Key::from("score")),
+            ),
+        ];
+        let args = vec![
+            WildcardValue::PodId(pod_id),
+            WildcardValue::Key(Key::from("foo")),
+        ];
+
+        assert!(helper_custom_operation_verify_gadget(
+            &params,
+            custom_predicate,
+            op_args,
+            args,
+            None,
+        )
+        .is_err());
+
+        // AND (3) literal doesn't match template
+        let custom_predicate = CustomPredicateRef::new(batch.clone(), 0);
+        let op_args = vec![
+            Statement::ValueOf(
+                AnchoredKey::new(pod_id, Key::from("score")),
+                Value::from(0xbad),
+            ),
+            Statement::Equal(
+                AnchoredKey::new(pod_id, Key::from("foo")),
+                AnchoredKey::new(pod_id, Key::from("score")),
+            ),
+        ];
+        let args = vec![
+            WildcardValue::PodId(pod_id),
+            WildcardValue::Key(Key::from("foo")),
+        ];
+
+        assert!(helper_custom_operation_verify_gadget(
+            &params,
+            custom_predicate,
+            op_args,
+            args,
+            None,
+        )
+        .is_err());
+
+        // AND (4) predicate doesn't match template
+        let custom_predicate = CustomPredicateRef::new(batch.clone(), 0);
+        let op_args = vec![
+            Statement::ValueOf(
+                AnchoredKey::new(pod_id, Key::from("score")),
+                Value::from(42),
+            ),
+            Statement::NotEqual(
+                AnchoredKey::new(pod_id, Key::from("foo")),
+                AnchoredKey::new(pod_id, Key::from("score")),
+            ),
+        ];
+        let args = vec![
+            WildcardValue::PodId(pod_id),
+            WildcardValue::Key(Key::from("foo")),
+        ];
+
+        assert!(helper_custom_operation_verify_gadget(
+            &params,
+            custom_predicate,
+            op_args,
+            args,
+            None,
+        )
+        .is_err());
+
+        // OR (1) Two Nones
+        let custom_predicate = CustomPredicateRef::new(batch.clone(), 1);
+        let op_args = vec![Statement::None, Statement::None];
+        let args = vec![WildcardValue::PodId(pod_id), WildcardValue::None];
+
+        assert!(helper_custom_operation_verify_gadget(
+            &params,
+            custom_predicate,
+            op_args,
+            args,
+            None
+        )
+        .is_err());
+
+        Ok(())
+    }
 }

src/backends/plonky2/circuits/mod.rs

@@ -1,3 +1,4 @@
 pub mod common;
 pub mod mainpod;
 pub mod signedpod;
+pub mod utils;

src/backends/plonky2/circuits/utils.rs

@@ -0,0 +1,73 @@
+use plonky2::{
+    field::extension::Extendable,
+    hash::hash_types::RichField,
+    iop::{
+        generator::{GeneratedValues, SimpleGenerator},
+        target::Target,
+        witness::{PartitionWitness, Witness},
+    },
+    plonk::circuit_data::CommonCircuitData,
+    util::serialization::{Buffer, IoResult, Read, Write},
+};
+
+/// Plonky2 generator that allows debugging values assigned to targets.  This generator doesn't
+/// actually generate any value and doesn't assign any witness.  Instead it can be registered to
+/// monitor targets and print their values once they are available.
+///
+/// Example usage:
+/// ```rust,ignore
+/// builder.add_simple_generator(DebugGenerator::new(
+///     format!("values_{}", i),
+///     vec![v1, v2, v3],
+/// ));
+/// ```
+#[derive(Debug, Default)]
+pub struct DebugGenerator {
+    pub(crate) name: String,
+    pub(crate) xs: Vec<Target>,
+}
+
+impl DebugGenerator {
+    pub fn new(name: String, xs: Vec<Target>) -> Self {
+        Self { name, xs }
+    }
+}
+
+impl<F: RichField + Extendable<D>, const D: usize> SimpleGenerator<F, D> for DebugGenerator {
+    fn id(&self) -> String {
+        "DebugGenerator".to_string()
+    }
+
+    fn dependencies(&self) -> Vec<Target> {
+        self.xs.clone()
+    }
+
+    fn run_once(
+        &self,
+        witness: &PartitionWitness<F>,
+        _out_buffer: &mut GeneratedValues<F>,
+    ) -> anyhow::Result<()> {
+        let xs = witness.get_targets(&self.xs);
+
+        println!("debug: values of {}", self.name);
+        for (i, x) in xs.iter().enumerate() {
+            println!("- {:03}: {}", i, x);
+        }
+        Ok(())
+    }
+
+    fn serialize(&self, dst: &mut Vec<u8>, _common_data: &CommonCircuitData<F, D>) -> IoResult<()> {
+        dst.write_usize(self.name.len())?;
+        dst.write_all(self.name.as_bytes())?;
+        dst.write_target_vec(&self.xs)
+    }
+
+    fn deserialize(src: &mut Buffer, _common_data: &CommonCircuitData<F, D>) -> IoResult<Self> {
+        let name_len = src.read_usize()?;
+        let mut name_buf = vec![0; name_len];
+        src.read_exact(&mut name_buf)?;
+        let name = unsafe { String::from_utf8_unchecked(name_buf) };
+        let xs = src.read_target_vec()?;
+        Ok(Self { name, xs })
+    }
+}

src/backends/plonky2/mainpod/mod.rs

@@ -87,7 +87,7 @@ pub(crate) fn extract_custom_predicate_verifications(
                 .find_map(|(i, cpb)| (cpb.id() == cpr.batch.id()).then_some(i))
                 .expect("find the custom predicate from the extracted unique list");
             let custom_predicate_table_index =
-                batch_index * params.max_custom_predicate_batches + cpr.index;
+                batch_index * params.max_custom_batch_size + cpr.index;
             CustomPredicateVerification {
                 custom_predicate_table_index,
                 custom_predicate: cpr.clone(),
@@ -150,20 +150,18 @@ pub(crate) fn extract_merkle_proofs(
 
 /// Find the operation argument statement in the list of previous statements and return the index.
 fn find_op_arg(statements: &[Statement], op_arg: &middleware::Statement) -> Result<OperationArg> {
-    match op_arg {
+    // NOTE: The `None` `Statement` always exists as a constant at index 0
-        middleware::Statement::None => Ok(OperationArg::None),
+    statements
-        _ => statements
+        .iter()
-            .iter()
+        .enumerate()
-            .enumerate()
+        .find_map(|(i, s)| {
-            .find_map(|(i, s)| {
+            (&middleware::Statement::try_from(s.clone()).ok()? == op_arg).then_some(i)
-                (&middleware::Statement::try_from(s.clone()).ok()? == op_arg).then_some(i)
+        })
-            })
+        .map(OperationArg::Index)
-            .map(OperationArg::Index)
+        .ok_or(Error::custom(format!(
-            .ok_or(Error::custom(format!(
+            "Statement corresponding to op arg {} not found",
-                "Statement corresponding to op arg {} not found",
+            op_arg
-                op_arg
+        )))
-            ))),
-    }
 }
 
 /// Find the operation auxiliary data in the list of auxiliary data and return the index.
@@ -179,15 +177,21 @@ fn find_op_aux(
     op: &middleware::Operation,
 ) -> Result<OperationAux> {
     let op_aux = op.aux();
-    let op_type = op.op_type();
+    if let (middleware::Operation::Custom(cpr, op_args), Some(cpvs)) =
-    if let (OperationType::Custom(cpr), Some(cpvs)) = (op_type, custom_predicate_verifications) {
+        (op, custom_predicate_verifications)
+    {
         return Ok(cpvs
             .iter()
             .enumerate()
             .find_map(|(i, cpv)| {
                 (cpv.custom_predicate.batch.id() == cpr.batch.id()
-                    && cpv.custom_predicate.index == cpr.index)
+                    && cpv.custom_predicate.index == cpr.index
-                    .then_some(i)
+                    && cpv
+                        .op_args
+                        .iter()
+                        .zip_eq(op_args.iter())
+                        .all(|(a0, a1)| a0.0 == a1.predicate() && a0.1 == a1.args()))
+                .then_some(i)
             })
             .map(OperationAux::CustomPredVerifyIndex)
             .expect("custom predicate verification in the list"));
@@ -228,6 +232,10 @@ fn pad_operation_args(params: &Params, args: &mut Vec<OperationArg>) {
 pub(crate) fn layout_statements(params: &Params, inputs: &MainPodInputs) -> Vec<Statement> {
     let mut statements = Vec::new();
 
+    // Statement at index 0 is always None to be used for padding operation arguments in custom
+    // predicate statements
+    statements.push(middleware::Statement::None.into());
+
     // Input signed pods region
     let none_sig_pod_box: Box<dyn Pod> = Box::new(NonePod {});
     let none_sig_pod = none_sig_pod_box.as_ref();
@@ -531,10 +539,16 @@ pub mod tests {
             primitives::signature::SecretKey,
             signedpod::Signer,
         },
-        examples::{zu_kyc_pod_builder, zu_kyc_sign_pod_builders},
+        examples::{
-        frontend::{self},
+            eth_dos_pod_builder, eth_friend_signed_pod_builder, zu_kyc_pod_builder,
+            zu_kyc_sign_pod_builders,
+        },
+        frontend::{
+            key, literal, CustomPredicateBatchBuilder, MainPodBuilder, StatementTmplBuilder as STB,
+            {self},
+        },
         middleware,
-        middleware::RawValue,
+        middleware::{CustomPredicateRef, NativePredicate as NP, RawValue},
         op,
     };
 
@@ -644,4 +658,109 @@ pub mod tests {
         let pod = (kyc_pod.pod as Box<dyn Any>).downcast::<MainPod>().unwrap();
         pod.verify().unwrap()
     }
+
+    #[test]
+    fn test_main_ethdos() -> frontend::Result<()> {
+        let params = Params {
+            max_input_signed_pods: 2,
+            max_input_main_pods: 1,
+            max_statements: 26,
+            max_public_statements: 5,
+            max_signed_pod_values: 8,
+            max_statement_args: 6,
+            max_operation_args: 4,
+            max_custom_predicate_arity: 4,
+            max_custom_batch_size: 3,
+            max_custom_predicate_wildcards: 12,
+            max_custom_predicate_verifications: 8,
+            ..Default::default()
+        };
+
+        let mut alice = Signer(SecretKey(RawValue::from(1)));
+        let bob = Signer(SecretKey(RawValue::from(2)));
+        let mut charlie = Signer(SecretKey(RawValue::from(3)));
+
+        // Alice attests that she is ETH friends with Charlie and Charlie
+        // attests that he is ETH friends with Bob.
+        let alice_attestation =
+            eth_friend_signed_pod_builder(&params, charlie.public_key().0.into())
+                .sign(&mut alice)?;
+        let charlie_attestation =
+            eth_friend_signed_pod_builder(&params, bob.public_key().0.into()).sign(&mut charlie)?;
+
+        let alice_bob_ethdos_builder = eth_dos_pod_builder(
+            &params,
+            false,
+            &alice_attestation,
+            &charlie_attestation,
+            bob.public_key().0.into(),
+        )?;
+
+        let mut prover = MockProver {};
+        let pod = alice_bob_ethdos_builder.prove(&mut prover, &params)?;
+        assert!(pod.pod.verify().is_ok());
+
+        let mut prover = Prover {};
+        let alice_bob_ethdos = alice_bob_ethdos_builder.prove(&mut prover, &params)?;
+        let pod = (alice_bob_ethdos.pod as Box<dyn Any>)
+            .downcast::<MainPod>()
+            .unwrap();
+
+        Ok(pod.verify()?)
+    }
+
+    #[test]
+    fn test_main_mini_custom_1() -> frontend::Result<()> {
+        let params = Params {
+            max_input_signed_pods: 0,
+            max_input_main_pods: 0,
+            max_statements: 9,
+            max_public_statements: 4,
+            max_statement_args: 3,
+            max_operation_args: 3,
+            max_custom_predicate_arity: 3,
+            max_custom_batch_size: 3,
+            max_custom_predicate_wildcards: 4,
+            max_custom_predicate_verifications: 2,
+            ..Default::default()
+        };
+
+        let mut cpb_builder = CustomPredicateBatchBuilder::new(params.clone(), "cpb".into());
+        let stb0 = STB::new(NP::ValueOf)
+            .arg(("id", key("score")))
+            .arg(literal(42));
+        let stb1 = STB::new(NP::Equal)
+            .arg(("id", "secret_key"))
+            .arg(("id", key("score")));
+        let _ = cpb_builder.predicate_and(
+            "pred_and",
+            &["id"],
+            &["secret_key"],
+            &[stb0.clone(), stb1.clone()],
+        )?;
+        let _ = cpb_builder.predicate_or("pred_or", &["id"], &["secret_key"], &[stb0, stb1])?;
+        let cpb = cpb_builder.finish();
+
+        let cpb_and = CustomPredicateRef::new(cpb.clone(), 0);
+        let _cpb_or = CustomPredicateRef::new(cpb.clone(), 1);
+
+        let mut pod_builder = MainPodBuilder::new(&params);
+
+        let st0 = pod_builder.priv_op(op!(new_entry, ("score", 42)))?;
+        let st1 = pod_builder.priv_op(op!(new_entry, ("foo", 42)))?;
+        let st2 = pod_builder.priv_op(op!(eq, st1.clone(), st0.clone()))?;
+
+        let _st3 = pod_builder.priv_op(op!(custom, cpb_and.clone(), st0, st2))?;
+
+        let mut prover = MockProver {};
+        let pod = pod_builder.prove(&mut prover, &params)?;
+        assert!(pod.pod.verify().is_ok());
+
+        let mut prover = Prover {};
+        let pod = pod_builder.prove(&mut prover, &params)?;
+
+        let pod = (pod.pod as Box<dyn Any>).downcast::<MainPod>().unwrap();
+
+        Ok(pod.verify()?)
+    }
 }

src/backends/plonky2/mock/mainpod.rs

@@ -57,11 +57,14 @@ impl fmt::Display for MockMainPod {
         writeln!(f, "MockMainPod ({}):", self.id)?;
         // TODO print input signed pods id and type
         // TODO print input main pods id and type
+        let offset_input_signed_pods = Self::offset_input_signed_pods();
         let offset_input_main_pods = self.offset_input_main_pods();
         let offset_input_statements = self.offset_input_statements();
         let offset_public_statements = self.offset_public_statements();
         for (i, st) in self.statements.iter().enumerate() {
-            if (i < self.offset_input_main_pods()) && (i % self.params.max_signed_pod_values == 0) {
+            if (i >= offset_input_signed_pods && i < offset_input_main_pods)
+                && ((i - offset_input_signed_pods) % self.params.max_signed_pod_values == 0)
+            {
                 writeln!(
                     f,
                     "  from input SignedPod {}:",
@@ -125,8 +128,12 @@ fn fmt_statement_index(
 /// - private Statements
 /// - public Statements
 impl MockMainPod {
+    fn offset_input_signed_pods() -> usize {
+        1
+    }
     fn offset_input_main_pods(&self) -> usize {
-        self.params.max_input_signed_pods * self.params.max_signed_pod_values
+        Self::offset_input_signed_pods()
+            + self.params.max_input_signed_pods * self.params.max_signed_pod_values
     }
     fn offset_input_statements(&self) -> usize {
         self.offset_input_main_pods()

src/backends/plonky2/mock/signedpod.rs

@@ -19,7 +19,7 @@ pub struct MockSigner {
 }
 
 impl MockSigner {
-    pub fn pubkey(&self) -> Hash {
+    pub fn public_key(&self) -> Hash {
         hash_str(&self.pk)
     }
 }
@@ -27,7 +27,7 @@ impl MockSigner {
 impl MockSigner {
     fn _sign(&mut self, _params: &Params, kvs: &HashMap<Key, Value>) -> Result<MockSignedPod> {
         let mut kvs = kvs.clone();
-        let pubkey = self.pubkey();
+        let pubkey = self.public_key();
         kvs.insert(Key::from(KEY_SIGNER), Value::from(pubkey));
         kvs.insert(Key::from(KEY_TYPE), Value::from(PodType::MockSigned));
 

src/backends/plonky2/primitives/signature/mod.rs

@@ -55,7 +55,7 @@ pub struct VerifierParams(pub(crate) VerifierCircuitData<F, C, D>);
 pub struct SecretKey(pub(crate) RawValue);
 
 #[derive(Clone, Debug)]
-pub struct PublicKey(pub(crate) RawValue);
+pub struct PublicKey(pub RawValue);
 
 #[derive(Clone, Debug)]
 pub struct Signature(pub(crate) Proof);

src/backends/plonky2/signedpod.rs

@@ -36,6 +36,10 @@ impl Signer {
             dict,
         })
     }
+
+    pub fn public_key(&self) -> PublicKey {
+        self.0.public_key()
+    }
 }
 
 impl PodSigner for Signer {

src/examples/custom.rs

@@ -11,7 +11,12 @@ use crate::{
 };
 
 /// Instantiates an ETH friend batch
-pub fn eth_friend_batch(params: &Params) -> Result<Arc<CustomPredicateBatch>> {
+pub fn eth_friend_batch(params: &Params, mock: bool) -> Result<Arc<CustomPredicateBatch>> {
+    let pod_type = if mock {
+        PodType::MockSigned
+    } else {
+        PodType::Signed
+    };
     let mut builder = CustomPredicateBatchBuilder::new(params.clone(), "eth_friend".into());
     let _eth_friend = builder.predicate_and(
         "eth_friend",
@@ -24,7 +29,7 @@ pub fn eth_friend_batch(params: &Params) -> Result<Arc<CustomPredicateBatch>> {
             // there is an attestation pod that's a SignedPod
             STB::new(NP::ValueOf)
                 .arg(("attestation_pod", key(KEY_TYPE)))
-                .arg(literal(PodType::MockSigned)), // TODO
+                .arg(literal(pod_type)),
             // the attestation pod is signed by (src_or, src_key)
             STB::new(NP::Equal)
                 .arg(("attestation_pod", key(KEY_SIGNER)))
@@ -41,8 +46,8 @@ pub fn eth_friend_batch(params: &Params) -> Result<Arc<CustomPredicateBatch>> {
 }
 
 /// Instantiates an ETHDoS batch
-pub fn eth_dos_batch(params: &Params) -> Result<Arc<CustomPredicateBatch>> {
+pub fn eth_dos_batch(params: &Params, mock: bool) -> Result<Arc<CustomPredicateBatch>> {
-    let eth_friend = Predicate::Custom(CustomPredicateRef::new(eth_friend_batch(params)?, 0));
+    let eth_friend = Predicate::Custom(CustomPredicateRef::new(eth_friend_batch(params, mock)?, 0));
     let mut builder =
         CustomPredicateBatchBuilder::new(params.clone(), "eth_dos_distance_base".into());
 

src/examples/mod.rs

@@ -69,10 +69,7 @@ pub fn zu_kyc_pod_builder(
 
 // ETHDoS
 
-pub fn eth_friend_signed_pod_builder(
+pub fn eth_friend_signed_pod_builder(params: &Params, friend_pubkey: Value) -> SignedPodBuilder {
-    params: &Params,
-    friend_pubkey: TypedValue,
-) -> SignedPodBuilder {
     let mut attestation = SignedPodBuilder::new(params);
     attestation.insert("attestation", friend_pubkey);
 
@@ -81,13 +78,14 @@ pub fn eth_friend_signed_pod_builder(
 
 pub fn eth_dos_pod_builder(
     params: &Params,
+    mock: bool,
     alice_attestation: &SignedPod,
     charlie_attestation: &SignedPod,
-    bob_pubkey: &TypedValue,
+    bob_pubkey: Value,
 ) -> Result<MainPodBuilder> {
     // Will need ETH friend and ETH DoS custom predicate batches.
-    let eth_friend = CustomPredicateRef::new(eth_friend_batch(params)?, 0);
+    let eth_friend = CustomPredicateRef::new(eth_friend_batch(params, mock)?, 0);
-    let eth_dos_batch = eth_dos_batch(params)?;
+    let eth_dos_batch = eth_dos_batch(params, mock)?;
     let eth_dos_base = CustomPredicateRef::new(eth_dos_batch.clone(), 0);
     let eth_dos_ind = CustomPredicateRef::new(eth_dos_batch.clone(), 1);
     let eth_dos = CustomPredicateRef::new(eth_dos_batch.clone(), 2);

src/frontend/custom.rs

@@ -274,12 +274,12 @@ mod tests {
         params.print_serialized_sizes();
 
         // ETH friend custom predicate batch
-        let eth_friend = eth_friend_batch(&params)?;
+        let eth_friend = eth_friend_batch(&params, true)?;
 
         // This batch only has 1 predicate, so we pick it already for convenience
         let eth_friend = Predicate::Custom(CustomPredicateRef::new(eth_friend, 0));
 
-        let eth_dos_batch = eth_dos_batch(&params)?;
+        let eth_dos_batch = eth_dos_batch(&params, true)?;
         let eth_dos_batch_mw: middleware::CustomPredicateBatch =
             Arc::unwrap_or_clone(eth_dos_batch);
         let fields = eth_dos_batch_mw.to_fields(&params);

src/frontend/mod.rs

@@ -793,7 +793,7 @@ pub mod build_utils {
         (max_of, $($arg:expr),+) => { $crate::frontend::Operation(
             $crate::middleware::OperationType::Native($crate::middleware::NativeOperation::MaxOf),
             $crate::op_args!($($arg),*), $crate::middleware::OperationAux::None) };
-        (custom, $op:expr, $($arg:expr),+) => { $crate::frontend::Operation(
+        (custom, $op:expr, $($arg:expr),*) => { $crate::frontend::Operation(
             $crate::middleware::OperationType::Custom($op),
             $crate::op_args!($($arg),*), $crate::middleware::OperationAux::None) };
         (dict_contains, $dict:expr, $key:expr, $value:expr) => { $crate::frontend::Operation(
@@ -925,18 +925,19 @@ pub mod tests {
         // Alice attests that she is ETH friends with Charlie and Charlie
         // attests that he is ETH friends with Bob.
         let alice_attestation =
-            eth_friend_signed_pod_builder(&params, charlie.pubkey().into()).sign(&mut alice)?;
+            eth_friend_signed_pod_builder(&params, charlie.public_key().into()).sign(&mut alice)?;
         check_kvs(&alice_attestation)?;
         let charlie_attestation =
-            eth_friend_signed_pod_builder(&params, bob.pubkey().into()).sign(&mut charlie)?;
+            eth_friend_signed_pod_builder(&params, bob.public_key().into()).sign(&mut charlie)?;
         check_kvs(&charlie_attestation)?;
 
         let mut prover = MockProver {};
         let alice_bob_ethdos = eth_dos_pod_builder(
             &params,
+            true,
             &alice_attestation,
             &charlie_attestation,
-            &bob.pubkey().into(),
+            bob.public_key().into(),
         )?
         .prove(&mut prover, &params)?;
 

src/frontend/serialization.rs

@@ -276,16 +276,17 @@ mod tests {
         // Alice attests that she is ETH friends with Charlie and Charlie
         // attests that he is ETH friends with Bob.
         let alice_attestation =
-            eth_friend_signed_pod_builder(&params, charlie.pubkey().into()).sign(&mut alice)?;
+            eth_friend_signed_pod_builder(&params, charlie.public_key().into()).sign(&mut alice)?;
         let charlie_attestation =
-            eth_friend_signed_pod_builder(&params, bob.pubkey().into()).sign(&mut charlie)?;
+            eth_friend_signed_pod_builder(&params, bob.public_key().into()).sign(&mut charlie)?;
 
         let mut prover = MockProver {};
         let alice_bob_ethdos = eth_dos_pod_builder(
             &params,
+            true,
             &alice_attestation,
             &charlie_attestation,
-            &bob.pubkey().into(),
+            bob.public_key().into(),
         )?
         .prove(&mut prover, &params)?;
 

src/middleware/custom.rs

@@ -276,9 +276,9 @@ impl CustomPredicate {
     pub fn pad_statement_tmpl(&self) -> StatementTmpl {
         StatementTmpl {
             pred: Predicate::Native(if self.conjunction {
-                NativePredicate::False
-            } else {
                 NativePredicate::None
+            } else {
+                NativePredicate::False
             }),
             args: vec![],
         }