chore(backend): implement more circuit op logic (#173)

* Add backend MerkleProof type

* Add eval_not_contains

* Remove print statement

* Handle some edge cases

* Add test

* Add missing ?

* Optimisation and stylistic changes

* Code review

src/middleware/mod.rs

@@ -20,6 +20,8 @@ use std::any::Any;
 use std::collections::HashMap;
 use std::fmt;
 
+use crate::backends::plonky2::primitives::merkletree::MerkleProof;
+
 pub const SELF: PodId = PodId(SELF_ID_HASH);
 
 impl fmt::Display for PodId {
@@ -105,6 +107,8 @@ pub struct Params {
     // in a custom predicate
     pub max_custom_predicate_arity: usize,
     pub max_custom_batch_size: usize,
+    // maximum number of merkle proofs
+    pub max_merkle_proofs: usize,
     // maximum depth for merkle tree gadget
     pub max_depth_mt_gadget: usize,
 }
@@ -121,6 +125,7 @@ impl Default for Params {
             max_operation_args: 5,
             max_custom_predicate_arity: 5,
             max_custom_batch_size: 5,
+            max_merkle_proofs: 5,
             max_depth_mt_gadget: 32,
         }
     }

src/middleware/operation.rs

@@ -5,7 +5,10 @@ use serde::{Deserialize, Serialize};
 use std::fmt;
 use std::iter;
 
+use super::Hash;
 use super::{CustomPredicateRef, NativePredicate, Statement, StatementArg, ToFields, F};
+use crate::middleware::EMPTY_HASH;
+use crate::middleware::EMPTY_VALUE;
 use crate::{
     backends::plonky2::primitives::merkletree::{MerkleProof, MerkleTree},
     middleware::{AnchoredKey, Params, Predicate, Value, SELF},

src/middleware/statement.rs

@@ -15,6 +15,7 @@ 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;
+pub const OPERATION_AUX_F_LEN: usize = 1;
 
 #[derive(Clone, Copy, Debug, FromRepr, PartialEq, Eq, Hash, Serialize, Deserialize, JsonSchema)]
 pub enum NativePredicate {