Add verifier-datas tree (set) & in-circuit verification (#274)

* containers: add method to create new {Dict,Set,Array} with custom max_depth

* add vds_tree computation, update tree circuit interface

* add VDTree struct, add DEFAULT_VD_TREE, integrate it with MainPod,EmptyPod,frontend,etc.

* adapt frontend/serialization tests to new containers field (max_depth)

* adapt interfaces to allow using custom vd_tree in frontend & backend constructors

* rename VDTree to VDSet (and derivate namings too)

* containers 'new' always with param 'max_depth', use params.max_depth_mt_containers instead of the global constant MAX_DEPTH

* adapt after rebasing the branch to main latest changes

* apply review suggestions from @ed255

* use emptypod vd_mt_proofs (using vd_set as circuit input), merge the two existing set_targets methods of MainPodVerifyTarget

* document VDSet & vds_root

src/frontend/custom.rs

@@ -294,7 +294,7 @@ mod tests {
         backends::plonky2::mock::mainpod::MockProver,
         examples::custom::{eth_dos_batch, eth_friend_batch},
         frontend::MainPodBuilder,
-        middleware::{self, containers::Set, CustomPredicateRef, Params, PodType},
+        middleware::{self, containers::Set, CustomPredicateRef, Params, PodType, DEFAULT_VD_SET},
         op,
     };
 
@@ -328,6 +328,7 @@ mod tests {
     #[test]
     fn test_desugared_gt_custom_pred() -> Result<()> {
         let params = Params::default();
+        let vd_set = &*DEFAULT_VD_SET;
         let mut builder = CustomPredicateBatchBuilder::new(params.clone(), "gt_custom_pred".into());
 
         let gt_stb = StatementTmplBuilder::new(NativePredicate::Gt)
@@ -344,7 +345,7 @@ mod tests {
         let batch_clone = batch.clone();
         let gt_custom_pred = CustomPredicateRef::new(batch, 0);
 
-        let mut mp_builder = MainPodBuilder::new(&params);
+        let mut mp_builder = MainPodBuilder::new(&params, &vd_set);
 
         // 2 > 1
         let s1 = mp_builder.literal(true, Value::from(2))?;
@@ -376,6 +377,7 @@ mod tests {
     #[test]
     fn test_desugared_set_contains_custom_pred() -> Result<()> {
         let params = Params::default();
+        let vd_set = &*DEFAULT_VD_SET;
         let mut builder =
             CustomPredicateBatchBuilder::new(params.clone(), "set_contains_custom_pred".into());
 
@@ -392,10 +394,13 @@ mod tests {
         let batch = builder.finish();
         let batch_clone = batch.clone();
 
-        let mut mp_builder = MainPodBuilder::new(&params);
+        let mut mp_builder = MainPodBuilder::new(&params, &vd_set);
 
         let set_values: HashSet<Value> = [1, 2, 3].iter().map(|i| Value::from(*i)).collect();
-        let s1 = mp_builder.literal(true, Value::from(Set::new(set_values)?))?;
+        let s1 = mp_builder.literal(
+            true,
+            Value::from(Set::new(params.max_depth_mt_containers, set_values)?),
+        )?;
         let s2 = mp_builder.literal(true, Value::from(1))?;
 
         let set_contains = mp_builder.pub_op(op!(set_contains, s1, s2))?;