Use predicate hash in statements instead of the literal predicate

Resolve #448 

Previously a predicate was 6 elements.  Now it grows to 8 elements; and the hash is 4 elements.

Some parts of the circuit require only require equality checks with the predicate: that works with the predicate hash.  Other parts require inspecting or working with particular elements in the predicate, those need the preimage of the predicate hash.
Both `StatementTarget` and `StatementTmplTarget` have been updated to include the predicate hash and optionally the predicate.  When the predicate is included, constraints are automatically generated for `pred_hash = hash(pred)`.  We only include the predicate when needed.

src/backends/plonky2/circuits/common.rs

@@ -9,7 +9,7 @@ use plonky2::{
         types::{Field, PrimeField64},
     },
     hash::{
-        hash_types::{HashOutTarget, RichField, NUM_HASH_OUT_ELTS},
+        hash_types::{HashOut, HashOutTarget, RichField, NUM_HASH_OUT_ELTS},
         poseidon::PoseidonHash,
     },
     iop::{
@@ -17,6 +17,7 @@ use plonky2::{
         target::{BoolTarget, Target},
         witness::{PartialWitness, PartitionWitness, Witness, WitnessWrite},
     },
+    plonk::config::Hasher,
     util::serialization::{Buffer, IoResult, Read, Write},
 };
 use serde::{Deserialize, Serialize};
@@ -136,10 +137,99 @@ impl StatementArgTarget {
 
 #[derive(Clone, Serialize, Deserialize)]
 pub struct StatementTarget {
-    pub predicate: PredicateTarget,
+    // If the pred is Some, then the `pred_hash` is constrained to be the `hash(pred)`.
+    pred: Option<PredicateTarget>,
+    pred_hash: HashOutTarget,
     pub args: Vec<StatementArgTarget>,
 }
 
+impl StatementTarget {
+    pub fn pred(&self) -> Option<&PredicateTarget> {
+        self.pred.as_ref()
+    }
+    pub fn pred_hash(&self) -> &HashOutTarget {
+        &self.pred_hash
+    }
+
+    pub fn new(pred_hash: HashOutTarget, args: Vec<StatementArgTarget>) -> Self {
+        Self {
+            pred: None,
+            pred_hash,
+            args,
+        }
+    }
+    pub fn new_with_pred(
+        builder: &mut CircuitBuilder,
+        params: &Params,
+        predicate: impl Build<PredicateTarget>,
+        args: &[StatementArgTarget],
+    ) -> Self {
+        let pred = predicate.build(builder, params);
+        let pred_hash = pred.hash(builder);
+        Self {
+            pred: Some(pred),
+            pred_hash,
+            args: args
+                .iter()
+                .cloned()
+                .chain(iter::repeat_with(|| StatementArgTarget::none(builder)))
+                .take(params.max_statement_args)
+                .collect(),
+        }
+    }
+
+    pub fn new_native(
+        builder: &mut CircuitBuilder,
+        params: &Params,
+        native_predicate: impl Build<NativePredicateTarget>,
+        args: &[StatementArgTarget],
+    ) -> Self {
+        let pred = PredicateTarget::new_native(builder, params, native_predicate);
+        Self::new_with_pred(builder, params, pred, args)
+    }
+
+    pub fn set_targets(
+        &self,
+        pw: &mut PartialWitness<F>,
+        params: &Params,
+        st: &Statement,
+    ) -> Result<()> {
+        if let Some(pred) = &self.pred {
+            pred.set_targets(pw, params, &st.predicate())?;
+        }
+        pw.set_hash_target(self.pred_hash, HashOut::from(st.predicate().hash(params)))?;
+        for (i, arg) in st
+            .args()
+            .iter()
+            .chain(iter::repeat(&StatementArg::None))
+            .take(params.max_statement_args)
+            .enumerate()
+        {
+            self.args[i].set_targets(pw, params, arg)?;
+        }
+        Ok(())
+    }
+
+    pub fn pred_is_blank_intro(&self, builder: &mut CircuitBuilder) -> BoolTarget {
+        let zero_hash = builder.constant_hash(HashOut {
+            elements: [F::ZERO, F::ZERO, F::ZERO, F::ZERO],
+        });
+        let blank_intro = PredicateTarget::new_intro(builder, zero_hash).hash(builder);
+        builder.is_equal_flattenable(&self.pred_hash, &blank_intro)
+    }
+
+    pub fn has_native_type(
+        &self,
+        builder: &mut CircuitBuilder,
+        params: &Params,
+        t: NativePredicate,
+    ) -> BoolTarget {
+        let expected_predicate_hash =
+            builder.constant_hash(HashOut::from(Predicate::Native(t).hash(params)));
+        builder.is_equal_flattenable(&self.pred_hash, &expected_predicate_hash)
+    }
+}
+
 pub trait Build<T> {
     fn build(self, builder: &mut CircuitBuilder, params: &Params) -> T;
 }
@@ -156,57 +246,6 @@ impl<T> Build<T> for T {
     }
 }
 
-impl StatementTarget {
-    /// Build a new native StatementTarget.  Pads the arguments.
-    pub fn new_native(
-        builder: &mut CircuitBuilder,
-        params: &Params,
-        native_predicate: impl Build<NativePredicateTarget>,
-        args: &[StatementArgTarget],
-    ) -> Self {
-        // if native_predicate is const then NativePredicate -> NativePredicateTarget
-        // else just use as is
-        Self {
-            predicate: PredicateTarget::new_native(builder, params, native_predicate),
-            args: args
-                .iter()
-                .cloned()
-                .chain(iter::repeat_with(|| StatementArgTarget::none(builder)))
-                .take(params.max_statement_args)
-                .collect(),
-        }
-    }
-
-    pub fn set_targets(
-        &self,
-        pw: &mut PartialWitness<F>,
-        params: &Params,
-        st: &Statement,
-    ) -> Result<()> {
-        self.predicate.set_targets(pw, params, st.predicate())?;
-        for (i, arg) in st
-            .args()
-            .iter()
-            .chain(iter::repeat(&StatementArg::None))
-            .take(params.max_statement_args)
-            .enumerate()
-        {
-            self.args[i].set_targets(pw, params, arg)?;
-        }
-        Ok(())
-    }
-
-    pub fn has_native_type(
-        &self,
-        builder: &mut CircuitBuilder,
-        params: &Params,
-        t: NativePredicate,
-    ) -> BoolTarget {
-        let expected_predicate = PredicateTarget::new_native(builder, params, t);
-        builder.is_equal_flattenable(&self.predicate, &expected_predicate)
-    }
-}
-
 #[derive(Clone, Serialize, Deserialize)]
 pub struct OperationTypeTarget {
     #[serde(with = "serde_arrays")]
@@ -336,7 +375,7 @@ impl PredicateTarget {
         let id = native_predicate.build(builder, params).0;
         let zero = builder.zero();
         Self {
-            elements: [prefix, id, zero, zero, zero, zero],
+            elements: [prefix, id, zero, zero, zero, zero, zero, zero],
         }
     }
 
@@ -344,7 +383,7 @@ impl PredicateTarget {
         let prefix = builder.constant(F::from(PredicatePrefix::BatchSelf));
         let zero = builder.zero();
         Self {
-            elements: [prefix, index, zero, zero, zero, zero],
+            elements: [prefix, index, zero, zero, zero, zero, zero, zero],
         }
     }
 
@@ -355,8 +394,9 @@ impl PredicateTarget {
     ) -> Self {
         let prefix = builder.constant(F::from(PredicatePrefix::Custom));
         let id = batch_id.elements;
+        let zero = builder.zero();
         Self {
-            elements: [prefix, id[0], id[1], id[2], id[3], index],
+            elements: [prefix, id[0], id[1], id[2], id[3], index, zero, zero],
         }
     }
 
@@ -365,7 +405,7 @@ impl PredicateTarget {
         let vh = vd_hash.elements;
         let zero = builder.zero();
         Self {
-            elements: [prefix, vh[0], vh[1], vh[2], vh[3], zero],
+            elements: [prefix, vh[0], vh[1], vh[2], vh[3], zero, zero, zero],
         }
     }
 
@@ -378,10 +418,30 @@ impl PredicateTarget {
         &self,
         pw: &mut PartialWitness<F>,
         params: &Params,
-        predicate: Predicate,
+        predicate: &Predicate,
     ) -> Result<()> {
         Ok(pw.set_target_arr(&self.elements, &predicate.to_fields(params))?)
     }
+
+    pub fn hash(&self, builder: &mut CircuitBuilder) -> HashOutTarget {
+        // Optimization: if all the predicate values are constants we skip the hash circuit and
+        // return a hash constant
+        let mut predicate_values = [F::ZERO; Params::predicate_size()];
+        let mut predicate_constant = true;
+        for (i, target) in self.elements.iter().enumerate() {
+            if let Some(v) = builder.target_as_constant(*target) {
+                predicate_values[i] = v;
+            } else {
+                predicate_constant = false;
+                break;
+            }
+        }
+        if predicate_constant {
+            builder.constant_hash(PoseidonHash::hash_no_pad(&predicate_values))
+        } else {
+            builder.hash_n_to_hash_no_pad::<PoseidonHash>(self.elements.to_vec())
+        }
+    }
 }
 
 /// Mirrors `middleware::KeyOrWildcard`
@@ -466,18 +526,46 @@ impl StatementTmplArgTarget {
 
 #[derive(Clone, Serialize, Deserialize)]
 pub struct StatementTmplTarget {
-    pub pred: PredicateTarget,
+    pred: Option<PredicateTarget>,
+    pred_hash: HashOutTarget,
     pub args: Vec<StatementTmplArgTarget>,
 }
 
 impl StatementTmplTarget {
+    pub fn new(pred_hash: HashOutTarget, args: Vec<StatementTmplArgTarget>) -> Self {
+        Self {
+            pred: None,
+            pred_hash,
+            args,
+        }
+    }
     pub fn set_targets(
         &self,
         pw: &mut PartialWitness<F>,
         params: &Params,
         st_tmpl: &StatementTmpl,
     ) -> Result<()> {
-        Ok(pw.set_target_arr(&self.flatten(), &st_tmpl.to_fields(params))?)
+        if let Some(pred) = &self.pred {
+            pred.set_targets(pw, params, &st_tmpl.pred)?;
+        }
+        pw.set_hash_target(self.pred_hash, HashOut::from(st_tmpl.pred.hash(params)))?;
+        let arg_pad = StatementTmplArg::None;
+        for (i, arg) in st_tmpl
+            .args
+            .iter()
+            .chain(iter::repeat(&arg_pad))
+            .take(params.max_statement_args)
+            .enumerate()
+        {
+            self.args[i].set_targets(pw, params, arg)?;
+        }
+        Ok(())
+    }
+    pub fn pred(&self) -> Option<&PredicateTarget> {
+        self.pred.as_ref()
+    }
+    pub fn pred_hash(&self) -> &HashOutTarget {
+        &self.pred_hash
     }
 }
 
@@ -494,9 +582,24 @@ impl CustomPredicateTarget {
         &self,
         pw: &mut PartialWitness<F>,
         params: &Params,
-        custom_predicate: &CustomPredicate,
+        custom_pred: &CustomPredicate,
     ) -> Result<()> {
-        Ok(pw.set_target_arr(&self.flatten(), &custom_predicate.to_fields(params))?)
+        pw.set_target(
+            self.conjunction.target,
+            F::from_bool(custom_pred.conjunction),
+        )?;
+        let st_tmpl_pad = custom_pred.pad_statement_tmpl();
+        for (i, st_tmpl) in custom_pred
+            .statements
+            .iter()
+            .chain(iter::repeat(&st_tmpl_pad))
+            .take(params.max_custom_predicate_arity)
+            .enumerate()
+        {
+            self.statements[i].set_targets(pw, params, st_tmpl)?;
+        }
+        pw.set_target(self.args_len, F::from_canonical_usize(custom_pred.args_len))?;
+        Ok(())
     }
 }
 
@@ -507,7 +610,7 @@ pub struct CustomPredicateBatchTarget {
 
 impl CustomPredicateBatchTarget {
     pub fn id(&self, builder: &mut CircuitBuilder) -> HashOutTarget {
-        let flattened = self.predicates.iter().flat_map(|cp| cp.flatten()).collect();
+        let flattened: Vec<_> = self.predicates.iter().flat_map(|cp| cp.flatten()).collect();
         builder.hash_n_to_hash_no_pad::<PoseidonHash>(flattened)
     }
 
@@ -621,7 +724,7 @@ pub struct CustomPredicateVerifyEntryTarget {
 }
 
 impl CustomPredicateVerifyEntryTarget {
-    pub fn new_virtual(params: &Params, builder: &mut CircuitBuilder) -> Self {
+    pub fn new_virtual(params: &Params, builder: &mut CircuitBuilder, with_pred: bool) -> Self {
         let custom_predicate_table_len =
             params.max_custom_predicate_batches * params.max_custom_batch_size;
         CustomPredicateVerifyEntryTarget {
@@ -629,12 +732,12 @@ impl CustomPredicateVerifyEntryTarget {
                 custom_predicate_table_len,
                 builder,
             ),
-            custom_predicate: builder.add_virtual_custom_predicate_entry(params),
+            custom_predicate: builder.add_virtual_custom_predicate_entry(params, with_pred),
             args: (0..params.max_custom_predicate_wildcards)
                 .map(|_| builder.add_virtual_value())
                 .collect(),
             op_args: (0..params.max_operation_args)
-                .map(|_| builder.add_virtual_statement(params))
+                .map(|_| builder.add_virtual_statement(params, false))
                 .collect(),
         }
     }
@@ -897,7 +1000,7 @@ impl Flattenable for PredicateTarget {
 
 impl Flattenable for StatementTarget {
     fn flatten(&self) -> Vec<Target> {
-        self.predicate
+        self.pred_hash
             .flatten()
             .into_iter()
             .chain(self.args.iter().flat_map(|a| &a.elements).cloned())
@@ -906,20 +1009,22 @@ impl Flattenable for StatementTarget {
 
     fn from_flattened(params: &Params, v: &[Target]) -> Self {
         assert_eq!(v.len(), Self::size(params));
-        let predicate = PredicateTarget::from_flattened(params, &v[..Params::predicate_size()]);
+        let predicate_hash = HashOutTarget::from_flattened(params, &v[..HASH_SIZE]);
         let args = (0..params.max_statement_args)
             .map(|i| StatementArgTarget {
-                elements: array::from_fn(|j| {
+                elements: array::from_fn(|j| v[HASH_SIZE + i * STATEMENT_ARG_F_LEN + j]),
-                    v[Params::predicate_size() + i * STATEMENT_ARG_F_LEN + j]
-                }),
             })
             .collect();
 
-        Self { predicate, args }
+        Self {
+            pred: None,
+            pred_hash: predicate_hash,
+            args,
+        }
     }
 
     fn size(params: &Params) -> usize {
-        PredicateTarget::size(params) + params.max_statement_args * StatementArgTarget::size(params)
+        HASH_SIZE + params.max_statement_args * StatementArgTarget::size(params)
     }
 }
 
@@ -957,7 +1062,7 @@ impl Flattenable for CustomPredicateTarget {
 
 impl Flattenable for StatementTmplTarget {
     fn flatten(&self) -> Vec<Target> {
-        self.pred
+        self.pred_hash
             .flatten()
             .into_iter()
             .chain(self.args.iter().flat_map(|sta| sta.flatten()))
@@ -966,21 +1071,24 @@ impl Flattenable for StatementTmplTarget {
 
     fn from_flattened(params: &Params, v: &[Target]) -> Self {
         assert_eq!(v.len(), Self::size(params));
-        let pred_end = Params::predicate_size();
+        let pred_hash_end = HASH_SIZE;
-        let pred = PredicateTarget::from_flattened(params, &v[..pred_end]);
+        let pred_hash = HashOutTarget::from_flattened(params, &v[..pred_hash_end]);
         let sta_size = Params::statement_tmpl_arg_size();
         let args = (0..params.max_statement_args)
             .map(|i| {
-                let sta_v = &v[pred_end + sta_size * i..pred_end + sta_size * (i + 1)];
+                let sta_v = &v[pred_hash_end + sta_size * i..pred_hash_end + sta_size * (i + 1)];
                 StatementTmplArgTarget::from_flattened(params, sta_v)
             })
             .collect();
-        Self { pred, args }
+        Self {
+            pred: None,
+            pred_hash,
+            args,
+        }
     }
 
     fn size(params: &Params) -> usize {
-        PredicateTarget::size(params)
+        HASH_SIZE + params.max_statement_args * StatementTmplArgTarget::size(params)
-            + params.max_statement_args * StatementTmplArgTarget::size(params)
     }
 }
 
@@ -1039,18 +1147,32 @@ pub trait CircuitBuilderPod<F: RichField + Extendable<D>, const D: usize> {
     fn connect_values(&mut self, x: ValueTarget, y: ValueTarget);
     fn connect_slice(&mut self, xs: &[Target], ys: &[Target]);
     fn add_virtual_value(&mut self) -> ValueTarget;
-    fn add_virtual_statement(&mut self, params: &Params) -> StatementTarget;
+    fn add_virtual_statement(&mut self, params: &Params, with_pred: bool) -> StatementTarget;
     fn add_virtual_statement_arg(&mut self) -> StatementArgTarget;
     fn add_virtual_predicate(&mut self) -> PredicateTarget;
     fn add_virtual_operation_type(&mut self) -> OperationTypeTarget;
     fn add_virtual_operation(&mut self, params: &Params) -> OperationTarget;
     fn add_virtual_statement_tmpl_arg(&mut self) -> StatementTmplArgTarget;
-    fn add_virtual_statement_tmpl(&mut self, params: &Params) -> StatementTmplTarget;
+    fn add_virtual_statement_tmpl(
-    fn add_virtual_custom_predicate(&mut self, params: &Params) -> CustomPredicateTarget;
+        &mut self,
-    fn add_virtual_custom_predicate_batch(&mut self, params: &Params)
+        params: &Params,
-        -> CustomPredicateBatchTarget;
+        with_pred: bool,
-    fn add_virtual_custom_predicate_entry(&mut self, params: &Params)
+    ) -> StatementTmplTarget;
-        -> CustomPredicateEntryTarget;
+    fn add_virtual_custom_predicate(
+        &mut self,
+        params: &Params,
+        with_pred: bool,
+    ) -> CustomPredicateTarget;
+    fn add_virtual_custom_predicate_batch(
+        &mut self,
+        params: &Params,
+        with_pred: bool,
+    ) -> CustomPredicateBatchTarget;
+    fn add_virtual_custom_predicate_entry(
+        &mut self,
+        params: &Params,
+        with_pred: bool,
+    ) -> CustomPredicateEntryTarget;
     fn select_value(&mut self, b: BoolTarget, x: ValueTarget, y: ValueTarget) -> ValueTarget;
     fn select_statement_arg(
         &mut self,
@@ -1144,10 +1266,20 @@ impl CircuitBuilderPod<F, D> for CircuitBuilder {
         }
     }
 
-    fn add_virtual_statement(&mut self, params: &Params) -> StatementTarget {
+    /// If `with_pred = true` a predicate is included and its hash constrained.
-        let predicate = self.add_virtual_predicate();
+    /// If `with_pred = false` only the predicate hash is included.
+    fn add_virtual_statement(&mut self, params: &Params, with_pred: bool) -> StatementTarget {
+        let (pred, pred_hash) = if with_pred {
+            let pred = self.add_virtual_predicate();
+            let pred_hash = pred.hash(self);
+            (Some(pred), pred_hash)
+        } else {
+            let pred_hash = self.add_virtual_hash();
+            (None, pred_hash)
+        };
         StatementTarget {
-            predicate,
+            pred,
+            pred_hash,
             args: (0..params.max_statement_args)
                 .map(|_| self.add_virtual_statement_arg())
                 .collect(),
@@ -1188,19 +1320,38 @@ impl CircuitBuilderPod<F, D> for CircuitBuilder {
         }
     }
 
-    fn add_virtual_statement_tmpl(&mut self, params: &Params) -> StatementTmplTarget {
+    /// If `with_pred = true` a predicate is included and its hash constrained.
-        let args = (0..params.max_statement_args)
+    /// If `with_pred = false` only the predicate hash is included.
-            .map(|_| self.add_virtual_statement_tmpl_arg())
+    fn add_virtual_statement_tmpl(
-            .collect();
+        &mut self,
+        params: &Params,
+        with_pred: bool,
+    ) -> StatementTmplTarget {
+        let (pred, pred_hash) = if with_pred {
+            let pred = self.add_virtual_predicate();
+            let pred_hash = pred.hash(self);
+            (Some(pred), pred_hash)
+        } else {
+            let pred_hash = self.add_virtual_hash();
+            (None, pred_hash)
+        };
         StatementTmplTarget {
-            pred: self.add_virtual_predicate(),
+            pred,
-            args,
+            pred_hash,
+            args: (0..params.max_statement_args)
+                .map(|_| self.add_virtual_statement_tmpl_arg())
+                .collect(),
         }
     }
 
-    fn add_virtual_custom_predicate(&mut self, params: &Params) -> CustomPredicateTarget {
+    /// See `add_virtual_statement_tmpl` for the meaning of `with_pred`.
+    fn add_virtual_custom_predicate(
+        &mut self,
+        params: &Params,
+        with_pred: bool,
+    ) -> CustomPredicateTarget {
         let statements = (0..params.max_custom_predicate_arity)
-            .map(|_| self.add_virtual_statement_tmpl(params))
+            .map(|_| self.add_virtual_statement_tmpl(params, with_pred))
             .collect();
         CustomPredicateTarget {
             conjunction: self.add_virtual_bool_target_safe(),
@@ -1209,25 +1360,29 @@ impl CircuitBuilderPod<F, D> for CircuitBuilder {
         }
     }
 
+    /// See `add_virtual_statement_tmpl` for the meaning of `with_pred`.
     fn add_virtual_custom_predicate_batch(
         &mut self,
         params: &Params,
+        with_pred: bool,
     ) -> CustomPredicateBatchTarget {
         CustomPredicateBatchTarget {
             predicates: (0..params.max_custom_batch_size)
-                .map(|_| self.add_virtual_custom_predicate(params))
+                .map(|_| self.add_virtual_custom_predicate(params, with_pred))
                 .collect(),
         }
     }
 
+    /// See `add_virtual_statement_tmpl` for the meaning of `with_pred`.
     fn add_virtual_custom_predicate_entry(
         &mut self,
         params: &Params,
+        with_pred: bool,
     ) -> CustomPredicateEntryTarget {
         CustomPredicateEntryTarget {
             id: self.add_virtual_hash(),
             index: self.add_virtual_target(),
-            predicate: self.add_virtual_custom_predicate(params),
+            predicate: self.add_virtual_custom_predicate(params, with_pred),
         }
     }
 
@@ -1734,7 +1889,8 @@ pub(crate) mod tests {
         let config = CircuitConfig::standard_recursion_config();
         let mut builder = CircuitBuilder::<F, D>::new(config);
 
-        let custom_predicate_batch_target = builder.add_virtual_custom_predicate_batch(params);
+        let custom_predicate_batch_target =
+            builder.add_virtual_custom_predicate_batch(params, false);
 
         // Calculate the id in constraints and compare it against the id calculated natively
         let id_target = custom_predicate_batch_target.id(&mut builder);

src/backends/plonky2/circuits/mainpod.rs

@@ -1396,10 +1396,7 @@ fn make_statement_from_template_circuit(
         })
         .collect();
     measure_gates_end!(builder, measure);
-    StatementTarget {
+    StatementTarget::new(*st_tmpl.pred_hash(), args)
-        predicate: st_tmpl.pred.clone(),
-        args,
-    }
 }
 
 /// Given a custom predicate, a list of operation arguments (statements) and a list of wildcard
@@ -1434,11 +1431,9 @@ fn make_custom_statement_circuit(
             let v = builder.select_flattenable(params, mask, arg, &arg_none);
             StatementArgTarget::wildcard_literal(builder, &v)
         })
-        .collect();
+        .collect_vec();
-    let statement = StatementTarget {
+    let statement_with_pred =
-        predicate: st_predicate,
+        StatementTarget::new_with_pred(builder, params, st_predicate, &st_args);
-        args: st_args,
-    };
 
     // Check the operation arguments
     // From each statement template we generate an expected statement using replacing the
@@ -1470,7 +1465,7 @@ fn make_custom_statement_circuit(
 
     builder.assert_one(is_op_args_ok.target);
     measure_gates_end!(builder, measure);
-    Ok((statement, op_type))
+    Ok((statement_with_pred, op_type))
 }
 
 /// Replace the blank verifier_data_hash slots in intro predicates by `vd_hash`
@@ -1480,19 +1475,13 @@ fn normalize_statement_circuit(
     statement: &StatementTarget,
     vd_hash: &HashOutTarget,
 ) -> StatementTarget {
-    let is_intro = statement.predicate.is_intro(builder);
+    let is_blank_intro = statement.pred_is_blank_intro(builder);
-    let old_pred = statement.predicate.elements;
+    let old_pred_hash = statement.pred_hash();
-    let old = HashOutTarget::try_from(&old_pred[1..1 + HASH_SIZE]).expect("len = 4");
+    let intro_pred_hash = PredicateTarget::new_intro(builder, *vd_hash).hash(builder);
-    let new = builder
+    let new_pred_hash =
-        .select_flattenable(params, is_intro, vd_hash, &old)
+        builder.select_flattenable(params, is_blank_intro, &intro_pred_hash, old_pred_hash);
-        .elements;
 
-    StatementTarget {
+    StatementTarget::new(new_pred_hash, statement.args.clone())
-        predicate: PredicateTarget {
-            elements: [old_pred[0], new[0], new[1], new[2], new[3], old_pred[5]],
-        },
-        args: statement.args.clone(),
-    }
 }
 
 /// `params.num_public_statements_hash` is the total number of statements that will be hashed.
@@ -1538,15 +1527,13 @@ fn normalize_st_tmpl_circuit(
     st_tmpl: &StatementTmplTarget,
     id: HashOutTarget,
 ) -> StatementTmplTarget {
+    let pred = st_tmpl.pred().expect("StatementTmpl contains predicate");
     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 is_batch_self = builder.is_equal(pred.elements[0], prefix_batch_self);
-    let pred_index = st_tmpl.pred.elements[1];
+    let pred_index = 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);
+    let pred = builder.select_flattenable(params, is_batch_self, &custom_pred, pred);
-    StatementTmplTarget {
+    StatementTmplTarget::new(pred.hash(builder), st_tmpl.args.clone())
-        pred,
-        args: st_tmpl.args.clone(),
-    }
 }
 
 /// Build a table of [batch_id, custom_predicate_index, custom_predicate] with queryable part as
@@ -1567,7 +1554,9 @@ fn build_custom_predicate_table_circuit(
             let statements = cp
                 .statements
                 .iter()
-                .map(|st_tmpl| normalize_st_tmpl_circuit(params, builder, st_tmpl, id))
+                .map(|st_with_pred_tmpl| {
+                    normalize_st_tmpl_circuit(params, builder, st_with_pred_tmpl, id)
+                })
                 .collect_vec();
             let cp = CustomPredicateTarget {
                 conjunction: cp.conjunction,
@@ -1625,19 +1614,19 @@ fn verify_main_pod_circuit(
 
         // NOTE: We use an EmptyPod for padding input pod slots.  The EmptyPod is an introduction
         // pod that declares a statement with no arguments.
-        let is_intro = input_pod_self_statements[0].predicate.is_intro(builder);
+        let is_blank_intro = input_pod_self_statements[0].pred_is_blank_intro(builder);
 
         // Introduction pods can only have Introduction or None statements
-        let mut intro_ok = is_intro;
+        let mut intro_ok = is_blank_intro;
         for self_st in &input_pod_self_statements[1..] {
-            let st_is_intro = self_st.predicate.is_intro(builder);
+            let st_is_intro = self_st.pred_is_blank_intro(builder);
             let st_is_none = self_st.has_native_type(builder, params, NativePredicate::None);
             let st_is_intro_or_none = builder.or(st_is_intro, st_is_none);
             intro_ok = builder.and(intro_ok, st_is_intro_or_none);
         }
-        builder.connect(is_intro.target, intro_ok.target);
+        builder.connect(is_blank_intro.target, intro_ok.target);
 
-        let is_main = builder.not(is_intro);
+        let is_main = builder.not(is_blank_intro);
         for self_st in input_pod_self_statements {
             let normalized_st = normalize_statement_circuit(
                 params,
@@ -1750,12 +1739,12 @@ impl MainPodVerifyTarget {
             input_pods_self_statements: (0..params.max_input_pods)
                 .map(|_| {
                     (0..params.max_input_pods_public_statements)
-                        .map(|_| builder.add_virtual_statement(params))
+                        .map(|_| builder.add_virtual_statement(params, false))
                         .collect_vec()
                 })
                 .collect(),
             input_statements: (0..params.max_statements)
-                .map(|_| builder.add_virtual_statement(params))
+                .map(|_| builder.add_virtual_statement(params, false))
                 .collect(),
             operations: (0..params.max_statements)
                 .map(|_| builder.add_virtual_operation(params))
@@ -1781,10 +1770,10 @@ impl MainPodVerifyTarget {
                 })
                 .collect(),
             custom_predicate_batches: (0..params.max_custom_predicate_batches)
-                .map(|_| builder.add_virtual_custom_predicate_batch(params))
+                .map(|_| builder.add_virtual_custom_predicate_batch(params, true))
                 .collect(),
             custom_predicate_verifications: (0..params.max_custom_predicate_verifications)
-                .map(|_| CustomPredicateVerifyEntryTarget::new_virtual(params, builder))
+                .map(|_| CustomPredicateVerifyEntryTarget::new_virtual(params, builder, false))
                 .collect(),
         }
     }
@@ -2084,10 +2073,10 @@ mod tests {
         let config = CircuitConfig::standard_recursion_config();
         let mut builder = CircuitBuilder::new(config);
 
-        let st_target = builder.add_virtual_statement(&params);
+        let st_target = builder.add_virtual_statement(&params, false);
         let op_target = builder.add_virtual_operation(&params);
         let prev_statements_target: Vec<_> = (0..prev_statements.len())
-            .map(|_| builder.add_virtual_statement(&params))
+            .map(|_| builder.add_virtual_statement(&params, false))
             .collect();
 
         let merkle_proofs_target: Vec<_> = aux
@@ -3098,7 +3087,7 @@ mod tests {
         let config = CircuitConfig::standard_recursion_config();
         let mut builder = CircuitBuilder::new(config);
 
-        let st_tmpl_target = builder.add_virtual_statement_tmpl(params);
+        let st_tmpl_target = builder.add_virtual_statement_tmpl(params, false);
         let args_target: Vec<_> = (0..args.len())
             .map(|_| builder.add_virtual_value())
             .collect();
@@ -3109,7 +3098,7 @@ mod tests {
             &args_target,
         );
         // TODO: Instead of connect, assign witness to result
-        let expected_st_target = builder.add_virtual_statement(params);
+        let expected_st_target = builder.add_virtual_statement(params, false);
         builder.connect_flattenable(&expected_st_target, &st_target);
 
         let mut pw = PartialWitness::<F>::new();
@@ -3161,9 +3150,9 @@ mod tests {
         let config = CircuitConfig::standard_recursion_config();
         let mut builder = CircuitBuilder::new(config);
 
-        let custom_predicate_target = builder.add_virtual_custom_predicate_entry(params);
+        let custom_predicate_target = builder.add_virtual_custom_predicate_entry(params, false);
         let op_args_target: Vec<_> = (0..args.len())
-            .map(|_| builder.add_virtual_statement(params))
+            .map(|_| builder.add_virtual_statement(params, false))
             .collect();
         let args_target: Vec<_> = (0..args.len())
             .map(|_| builder.add_virtual_value())
@@ -3455,7 +3444,7 @@ mod tests {
         let mut builder = CircuitBuilder::new(config);
 
         let statements_target = (0..params.max_public_statements)
-            .map(|_| builder.add_virtual_statement(params))
+            .map(|_| builder.add_virtual_statement(params, false))
             .collect_vec();
         let sts_hash_target =
             calculate_statements_hash_circuit(params, &mut builder, &statements_target);

src/backends/plonky2/mainpod/statement.rs

@@ -31,7 +31,7 @@ impl Statement {
 
 impl ToFields for Statement {
     fn to_fields(&self, params: &Params) -> Vec<middleware::F> {
-        let mut fields = self.0.to_fields(params);
+        let mut fields = self.0.hash(params).to_fields(params);
         fields.extend(
             self.1
                 .iter()

src/middleware/basetypes.rs

@@ -169,6 +169,12 @@ pub struct Hash(
     pub [F; HASH_SIZE],
 );
 
+impl From<Hash> for HashOut {
+    fn from(hash: Hash) -> HashOut {
+        HashOut { elements: hash.0 }
+    }
+}
+
 impl ToHex for Hash {
     fn encode_hex<T: std::iter::FromIterator<char>>(&self) -> T {
         self.0

src/middleware/custom.rs

@@ -170,6 +170,7 @@ impl ToFields for StatementTmpl {
 
         let mut fields: Vec<F> = self
             .pred
+            .hash(params)
             .to_fields(params)
             .into_iter()
             .chain(self.args.iter().flat_map(|sta| sta.to_fields(params)))

src/middleware/mod.rs

@@ -809,7 +809,7 @@ impl Params {
     }
 
     pub const fn predicate_size() -> usize {
-        HASH_SIZE + 2
+        8
     }
 
     pub const fn operation_type_size() -> usize {
@@ -817,11 +817,11 @@ impl Params {
     }
 
     pub fn statement_size(&self) -> usize {
-        Self::predicate_size() + STATEMENT_ARG_F_LEN * self.max_statement_args
+        HASH_SIZE + STATEMENT_ARG_F_LEN * self.max_statement_args
     }
 
     pub const fn statement_tmpl_size(&self) -> usize {
-        Self::predicate_size() + self.max_statement_args * Self::statement_tmpl_arg_size()
+        HASH_SIZE + self.max_statement_args * Self::statement_tmpl_arg_size()
     }
 
     pub fn custom_predicate_size(&self) -> usize {

src/middleware/statement.rs

@@ -10,7 +10,8 @@ use serde::{Deserialize, Serialize};
 use strum_macros::FromRepr;
 
 use crate::middleware::{
-    self, AnchoredKey, CustomPredicateRef, Error, Params, Result, ToFields, Value, F, VALUE_SIZE,
+    self, hash_fields, AnchoredKey, CustomPredicateRef, Error, Params, Result, ToFields, Value, F,
+    VALUE_SIZE,
 };
 
 pub const STATEMENT_ARG_F_LEN: usize = 8;
@@ -210,15 +211,15 @@ impl From<PredicatePrefix> for F {
 impl ToFields for Predicate {
     fn to_fields(&self, params: &Params) -> Vec<F> {
         // serialize:
-        // NativePredicate(id) as (1, id, 0, 0, 0, 0) -- id: usize
+        // NativePredicate(id) as (1, id, 0...) -- id: usize
-        // BatchSelf(i) as (2, i, 0, 0, 0, 0) -- i: usize
+        // BatchSelf(i) as (2, i, 0...) -- i: usize
         // CustomPredicateRef(pb, i) as
-        // (3, [hash of pb], i) -- pb hashes to 4 field elements
+        // (3, [hash of pb], i, 0...) -- pb hashes to 4 field elements
-        //                      -- i: usize
+        //                            -- i: usize
         // IntroPredicateRef(vd_hash) as
-        // (4, [vd_hash], 0)
+        // (4, [vd_hash], 0...)
 
-        // in every case: pad to (hash_size + 2) field elements
+        // in every case: pad to `Params::predicate_size()` field elements
         let mut fields: Vec<F> = match self {
             Self::Native(p) => iter::once(F::from(PredicatePrefix::Native))
                 .chain(p.to_fields(params))
@@ -243,6 +244,12 @@ impl ToFields for Predicate {
     }
 }
 
+impl Predicate {
+    pub fn hash(&self, params: &Params) -> middleware::Hash {
+        hash_fields(&self.to_fields(params))
+    }
+}
+
 impl fmt::Display for Predicate {
     fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
         match self {
@@ -497,7 +504,8 @@ impl Statement {
 
 impl ToFields for Statement {
     fn to_fields(&self, params: &Params) -> Vec<F> {
-        let mut fields = self.predicate().to_fields(params);
+        let predicate_hash = hash_fields(&self.predicate().to_fields(params));
+        let mut fields = predicate_hash.0.to_vec();
         fields.extend(self.args().iter().flat_map(|arg| arg.to_fields(params)));
         fields.resize_with(params.statement_size(), || F::ZERO);
         fields