Add NIFSGadgetTrait, implement Mova's NIFSGadget, adapt Nova NIFSGadg…

…et into NIFSGadgetTrait

* add new NIFSGadgetTrait

* implement Mova's NIFSGadget

* refactor Nova NIFSGadget to fit into the new NIFSGadgetTrait

* abstract NIFSGadget related tests for all implementors of
  NIFSGadgetTrait to avoid duplicated code in the tests between the
  different Nova variants gadget tests

examples/full_flow.rs

@@ -78,7 +78,7 @@ impl<F: PrimeField> FCircuit<F> for CubicFCircuit<F> {
 }
 
 fn main() {
-    let n_steps = 10;
+    let n_steps = 2;
     // set the initial state
     let z_0 = vec![Fr::from(3_u32)];
 

folding-schemes/src/arith/r1cs/circuits.rs

@@ -121,8 +121,8 @@ pub mod tests {
             nonnative::uint::NonNativeUintVar,
         },
         nova::{
-            circuits::CommittedInstanceVar, decider_eth_circuit::WitnessVar, CommittedInstance,
-            Witness,
+            decider_eth_circuit::WitnessVar, nifs::nova_circuits::CommittedInstanceVar,
+            CommittedInstance, Witness,
         },
     };
     use crate::frontend::{

folding-schemes/src/folding/circuits/decider/mod.rs

@@ -150,7 +150,7 @@ pub mod tests {
     use ark_std::UniformRand;
 
     use super::*;
-    use crate::folding::nova::{circuits::CommittedInstanceVar, CommittedInstance};
+    use crate::folding::nova::{nifs::nova_circuits::CommittedInstanceVar, CommittedInstance};
     use crate::transcript::poseidon::poseidon_canonical_config;
 
     // checks that the gadget and native implementations of the challenge computation match

folding-schemes/src/folding/circuits/decider/off_chain.rs

@@ -28,7 +28,7 @@ use crate::{
             nonnative::affine::NonNativeAffineVar,
             CF1, CF2,
         },
-        nova::{circuits::CommittedInstanceVar, decider_eth_circuit::WitnessVar},
+        nova::{decider_eth_circuit::WitnessVar, nifs::nova_circuits::CommittedInstanceVar},
         traits::{CommittedInstanceOps, CommittedInstanceVarOps, Dummy, WitnessOps, WitnessVarOps},
     },
 };