test: Add functionality to extract FRI proof from STARK proof

This functionality might belong in the Triton VM repository.

See <TritonVM/triton-vm#258> for thoughts about
this problem.

src/tests_and_benchmarks/ozk/programs/recufier/fri_verify.rs

@@ -1,5 +1,10 @@
 use tasm_lib::prelude::TasmObject;
 use tasm_lib::triton_vm::prelude::*;
+use tasm_lib::triton_vm::stark::StarkProofStream;
+use tasm_lib::triton_vm::table::challenges::Challenges;
+use tasm_lib::triton_vm::table::extension_table::Quotientable;
+use tasm_lib::triton_vm::table::master_table::MasterExtTable;
+use tasm_lib::triton_vm::table::*;
 
 use super::arithmetic_domain::*;
 
@@ -38,9 +43,91 @@ fn main() {
     return;
 }
 
+/// Extracts a proof stream that will work for FRI verification from a proof stream that works for
+/// the whole STARK verification.
+pub(super) fn extract_fri_proof(
+    proof_stream: &StarkProofStream,
+    claim: &Claim,
+) -> StarkProofStream {
+    let mut proof_stream = proof_stream.to_owned();
+    proof_stream
+        .dequeue()
+        .unwrap()
+        .try_into_log2_padded_height()
+        .unwrap();
+    proof_stream.alter_fiat_shamir_state_with(claim);
+
+    // Base-table Merkle root
+    proof_stream
+        .dequeue()
+        .unwrap()
+        .try_into_merkle_root()
+        .unwrap();
+
+    // Extension challenge weights
+    proof_stream.sample_scalars(Challenges::SAMPLE_COUNT);
+
+    // Extension-table Merkle root
+    proof_stream
+        .dequeue()
+        .unwrap()
+        .try_into_merkle_root()
+        .unwrap();
+
+    // Quotient codeword weights
+    proof_stream.sample_scalars(MasterExtTable::NUM_CONSTRAINTS);
+
+    // Quotient codeword Merkle root
+    proof_stream
+        .dequeue()
+        .unwrap()
+        .try_into_merkle_root()
+        .unwrap();
+
+    // Out-of-domain point current row
+    proof_stream.sample_scalars(1);
+
+    // Five out-of-domain values
+    proof_stream
+        .dequeue()
+        .unwrap()
+        .try_into_out_of_domain_base_row()
+        .unwrap();
+    proof_stream
+        .dequeue()
+        .unwrap()
+        .try_into_out_of_domain_ext_row()
+        .unwrap();
+    proof_stream
+        .dequeue()
+        .unwrap()
+        .try_into_out_of_domain_base_row()
+        .unwrap();
+    proof_stream
+        .dequeue()
+        .unwrap()
+        .try_into_out_of_domain_ext_row()
+        .unwrap();
+    proof_stream
+        .dequeue()
+        .unwrap()
+        .try_into_out_of_domain_quot_segments()
+        .unwrap();
+
+    // `base_and_ext_and_quotient_segment_codeword_weights`
+    proof_stream.sample_scalars(NUM_BASE_COLUMNS + NUM_EXT_COLUMNS + NUM_QUOTIENT_SEGMENTS);
+
+    // Deep codeword weights
+    const NUM_DEEP_CODEWORD_COMPONENTS: usize = 3;
+    proof_stream.sample_scalars(NUM_DEEP_CODEWORD_COMPONENTS);
+
+    proof_stream
+}
+
 #[cfg(test)]
 mod test {
     use rand::random;
+    use tasm_lib::triton_vm;
 
     use crate::tests_and_benchmarks::ozk::ozk_parsing;
     use crate::tests_and_benchmarks::ozk::ozk_parsing::EntrypointLocation;
@@ -73,4 +160,22 @@ mod test {
 
         assert_eq!(native_output, vm_output.output);
     }
+
+    #[test]
+    fn extract_fri_proof_works() {
+        let simple_program = triton_program!(halt);
+        let public_input = [];
+        let non_determinism = NonDeterminism::default();
+        let (stark, claim, proof) =
+            triton_vm::prove_program(&simple_program, &public_input, &non_determinism).unwrap();
+        let padded_height = proof.padded_height().unwrap();
+        let fri = stark.derive_fri(padded_height).unwrap();
+
+        let proof_stream = StarkProofStream::try_from(&proof).unwrap();
+        let mut fri_proof_stream = extract_fri_proof(&proof_stream, &claim);
+        assert!(
+            fri.verify(&mut fri_proof_stream, &mut None).is_ok(),
+            "Proof must verify"
+        );
+    }
 }