Fe contains (#145)

* Contains should take three arguments (root, key, value)

* Add a test for frontend Dictionaries

* Separate frontend and middleware operations

* Make tests pass: add arg to contains

* Cargo fmt

* Merkleproof verify circuit (#143)

* merkletree: add keypath circuit

* merkletree-circuit: implement proof of existence verification in-circuit

* parametrize max_depth at the tree circuit

* Constrain selectors in-circuit

* implement merketree nonexistence proof circuit, and add edgecase tests

* add non-existence proofs documentation in the mdbook, mv EMPTY->EMPTY_VALUE & NULL->EMPTY_HASH, dependency clean and public exposure methods

* review comments, some extra polishing and add a test that expects wrong proofs to fail

* Add circuit to check only merkleproofs-of-existence

With this, the merkletree_circuit module offers two different circuits:
- `MerkleProofCircuit`: allows to verify both proofs of existence and proofs
non-existence with the same circuit.
- `MerkleProofExistenceCircuit`: allows to verify proofs of existence only.

In this way, if only proofs of existence are needed,
`MerkleProofExistenceCircuit` should be used, which requires less amount
of constraints than `MerkleProofCircuit`.

* Code review

---------

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

* Towards Contains/NotContains in middleware and backend

* Fix build

* Adding error handling to deal with op compile introduce extra ops

* Incorporate Merkle proofs into MockMainPod

* Merkleproof verify circuit (#143)

* merkletree: add keypath circuit

* merkletree-circuit: implement proof of existence verification in-circuit

* parametrize max_depth at the tree circuit

* Constrain selectors in-circuit

* implement merketree nonexistence proof circuit, and add edgecase tests

* add non-existence proofs documentation in the mdbook, mv EMPTY->EMPTY_VALUE & NULL->EMPTY_HASH, dependency clean and public exposure methods

* review comments, some extra polishing and add a test that expects wrong proofs to fail

* Add circuit to check only merkleproofs-of-existence

With this, the merkletree_circuit module offers two different circuits:
- `MerkleProofCircuit`: allows to verify both proofs of existence and proofs
non-existence with the same circuit.
- `MerkleProofExistenceCircuit`: allows to verify proofs of existence only.

In this way, if only proofs of existence are needed,
`MerkleProofExistenceCircuit` should be used, which requires less amount
of constraints than `MerkleProofCircuit`.

* Code review

---------

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

* Towards Contains/NotContains in middleware and backend

* Frontend compound types -- allow one frontend operation to produce multiple middleware statements (in progress)

* Incorporate Merkle proofs into MockMainPod

* Incorporate Merkle proof op arg into frontend

* Compile one statement to many, in progress

* Fix remaining tests

* Minor clean-up

* Oops I did a bunch of work in the middle of a rebase, committing

* Incorporate Merkle proof op arg into frontend

* still working on frontend compound types, refactor compile() to output multiple statements

* Contains statements for frontend types: code compiles

* Tests pass

* Examples use front-end compound types

* Remove old Contains and NotContains from frontend

* Add nin to typos

* Code review

---------

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

src/backends/plonky2/circuits/mainpod.rs

@@ -491,7 +491,10 @@ impl MainPodVerifyCircuit {
 mod tests {
     use super::*;
     use crate::backends::plonky2::mock::mainpod;
-    use crate::backends::plonky2::{basetypes::C, mock::mainpod::OperationArg};
+    use crate::backends::plonky2::{
+        basetypes::C,
+        mock::mainpod::{OperationArg, OperationAux},
+    };
     use crate::middleware::{OperationType, PodId};
     use plonky2::plonk::{circuit_builder::CircuitBuilder, circuit_data::CircuitConfig};
 
@@ -571,20 +574,29 @@ mod tests {
     fn test_operation_verify() -> Result<()> {
         // None
         let st: mainpod::Statement = Statement::None.into();
-        let op = mainpod::Operation(OperationType::Native(NativeOperation::None), vec![]);
+        let op = mainpod::Operation(
+            OperationType::Native(NativeOperation::None),
+            vec![],
+            OperationAux::None,
+        );
         let prev_statements = vec![Statement::None.into()];
         operation_verify(st.clone(), op, prev_statements.clone())?;
 
         // NewEntry
         let st1: mainpod::Statement =
             Statement::ValueOf(AnchoredKey(SELF, "hello".into()), 55.into()).into();
-        let op = mainpod::Operation(OperationType::Native(NativeOperation::NewEntry), vec![]);
+        let op = mainpod::Operation(
+            OperationType::Native(NativeOperation::NewEntry),
+            vec![],
+            OperationAux::None,
+        );
         operation_verify(st1.clone(), op, vec![])?;
 
         // Copy
         let op = mainpod::Operation(
             OperationType::Native(NativeOperation::CopyStatement),
             vec![OperationArg::Index(0)],
+            OperationAux::None,
         );
         operation_verify(st, op, prev_statements)?;
 
@@ -602,6 +614,7 @@ mod tests {
         let op = mainpod::Operation(
             OperationType::Native(NativeOperation::EqualFromEntries),
             vec![OperationArg::Index(0), OperationArg::Index(1)],
+            OperationAux::None,
         );
         let prev_statements = vec![st1.clone(), st2];
         operation_verify(st, op, prev_statements)?;
@@ -620,6 +633,7 @@ mod tests {
         let op = mainpod::Operation(
             OperationType::Native(NativeOperation::LtFromEntries),
             vec![OperationArg::Index(0), OperationArg::Index(1)],
+            OperationAux::None,
         );
         let prev_statements = vec![st1.clone(), st2];
         operation_verify(st, op, prev_statements)?;