Onchain decider circuit for Protogalaxy (#145)

* Move r1cs and ccs to standalone folders

* Simplify type bounds of SparseMatrixVar

* Implement `EquivalenceGadget` trait for `FpVar` and `NonNativeUintVar`.

Together with the existing `MatrixGadget` and `VectorGadget`, we can now use the same logic for checking R1CS satisfiability of `R1CSVar` both natively and non-natively.

* Simplify trait bounds

* Implement `ArithGadget` for `R1CSMatricesVar` and `CCSMatricesVar`

* `PedersenGadget::commit` now takes slices as input

* Structs for proofs and auxiliary values in protogalaxy

* `u` in LCCCS should be `z[0]`

* `Inputize` trait

* Generic decider circuits

* Verifier should check the commitments in committed instances

* Update the comments according to the new docs

* Fix examples

* Add `DeciderEnabledNIFS::fold_group_elements_native` to wrap code for folding commitments

* Fix incorrect endian

* Format

* Get rid of `unwrap` when possible

examples/noname_full_flow.rs

@@ -17,9 +17,12 @@ use ark_grumpkin::{constraints::GVar as GVar2, Projective as G2};
 
 use folding_schemes::{
     commitment::{kzg::KZG, pedersen::Pedersen},
-    folding::nova::{
-        decider_eth::{prepare_calldata, Decider as DeciderEth},
-        Nova, PreprocessorParam,
+    folding::{
+        nova::{
+            decider_eth::{prepare_calldata, Decider as DeciderEth},
+            Nova, PreprocessorParam,
+        },
+        traits::CommittedInstanceOps,
     },
     frontend::FCircuit,
     transcript::poseidon::poseidon_canonical_config,
@@ -85,7 +88,6 @@ fn main() {
     // prepare the Nova prover & verifier params
     let nova_preprocess_params = PreprocessorParam::new(poseidon_config, f_circuit.clone());
     let nova_params = N::preprocess(&mut rng, &nova_preprocess_params).unwrap();
-    let pp_hash = nova_params.1.pp_hash().unwrap();
 
     // initialize the folding scheme engine, in our case we use Nova
     let mut nova = N::init(&nova_params, f_circuit.clone(), z_0).unwrap();
@@ -119,8 +121,8 @@ fn main() {
         nova.i,
         nova.z_0.clone(),
         nova.z_i.clone(),
-        &nova.U_i,
-        &nova.u_i,
+        &nova.U_i.get_commitments(),
+        &nova.u_i.get_commitments(),
         &proof,
     )
     .unwrap();
@@ -133,7 +135,6 @@ fn main() {
 
     let calldata: Vec<u8> = prepare_calldata(
         function_selector,
-        pp_hash,
         nova.i,
         nova.z_0,
         nova.z_i,