Implement HyperNova's IVC into the FoldingScheme trait (#116)

- implement the IVC `FoldingScheme` trait for HyperNova
- refactor Nova's preprocess logic to make it simplier to use
- add to Decider trait (& Nova's DeciderEth) a preprocess method
- get rid of the `init_nova_ivc_params` and `init_ivc_and_decider_params` methods in `examples` since this is achieved with the `FS::preprocess` & `Decider::preprocess` methods
  - (update the examples code to the simplified interface using
    FS::preprocess & Decider::preprocess)

folding-schemes/src/lib.rs

@@ -1,7 +1,6 @@
 #![allow(non_snake_case)]
 #![allow(non_upper_case_globals)]
 #![allow(non_camel_case_types)]
-#![allow(clippy::upper_case_acronyms)]
 
 use ark_ec::{pairing::Pairing, CurveGroup};
 use ark_ff::PrimeField;
@@ -110,13 +109,15 @@ where
     C2::BaseField: PrimeField,
     FC: FCircuit<C1::ScalarField>,
 {
-    type PreprocessorParam: Debug;
-    type ProverParam: Debug;
-    type VerifierParam: Debug;
-    type CommittedInstanceWithWitness: Debug;
-    type CFCommittedInstanceWithWitness: Debug; // CycleFold CommittedInstance & Witness
+    type PreprocessorParam: Debug + Clone;
+    type ProverParam: Debug + Clone;
+    type VerifierParam: Debug + Clone;
+    type RunningInstance: Debug; // contains the CommittedInstance + Witness
+    type IncomingInstance: Debug; // contains the CommittedInstance + Witness
+    type CFInstance: Debug; // CycleFold CommittedInstance & Witness
 
     fn preprocess(
+        rng: impl RngCore,
         prep_param: &Self::PreprocessorParam,
     ) -> Result<(Self::ProverParam, Self::VerifierParam), Error>;
 
@@ -126,7 +127,11 @@ where
         z_0: Vec<C1::ScalarField>, // initial state
     ) -> Result<Self, Error>;
 
-    fn prove_step(&mut self, external_inputs: Vec<C1::ScalarField>) -> Result<(), Error>;
+    fn prove_step(
+        &mut self,
+        rng: impl RngCore,
+        external_inputs: Vec<C1::ScalarField>,
+    ) -> Result<(), Error>;
 
     // returns the state at the current step
     fn state(&self) -> Vec<C1::ScalarField>;
@@ -136,9 +141,9 @@ where
     fn instances(
         &self,
     ) -> (
-        Self::CommittedInstanceWithWitness,
-        Self::CommittedInstanceWithWitness,
-        Self::CFCommittedInstanceWithWitness,
+        Self::RunningInstance,
+        Self::IncomingInstance,
+        Self::CFInstance,
     );
 
     fn verify(
@@ -147,9 +152,9 @@ where
         z_i: Vec<C1::ScalarField>, // last state
         // number of steps between the initial state and the last state
         num_steps: C1::ScalarField,
-        running_instance: Self::CommittedInstanceWithWitness,
-        incoming_instance: Self::CommittedInstanceWithWitness,
-        cyclefold_instance: Self::CFCommittedInstanceWithWitness,
+        running_instance: Self::RunningInstance,
+        incoming_instance: Self::IncomingInstance,
+        cyclefold_instance: Self::CFInstance,
     ) -> Result<(), Error>;
 }
 
@@ -162,16 +167,22 @@ pub trait Decider<
     C1: CurveGroup<BaseField = C2::ScalarField, ScalarField = C2::BaseField>,
     C2::BaseField: PrimeField,
 {
+    type PreprocessorParam: Debug;
     type ProverParam: Clone;
     type Proof;
     type VerifierParam;
     type PublicInput: Debug;
-    type CommittedInstanceWithWitness: Debug;
     type CommittedInstance: Clone + Debug;
 
-    fn prove(
-        pp: Self::ProverParam,
+    fn preprocess(
         rng: impl RngCore + CryptoRng,
+        prep_param: &Self::PreprocessorParam,
+        fs: FS,
+    ) -> Result<(Self::ProverParam, Self::VerifierParam), Error>;
+
+    fn prove(
+        rng: impl RngCore + CryptoRng,
+        pp: Self::ProverParam,
         folding_scheme: FS,
     ) -> Result<Self::Proof, Error>;