diff --git a/src/spartan/batched.rs b/src/spartan/batched.rs
index ebcc5508d..d04017eb1 100644
--- a/src/spartan/batched.rs
+++ b/src/spartan/batched.rs
@@ -17,7 +17,7 @@ use super::{
   math::Math,
   polys::{eq::EqPolynomial, multilinear::MultilinearPolynomial},
   powers,
-  snark::batch_eval_prove,
+  snark::batch_eval_reduce,
   sumcheck::SumcheckProof,
   PolyEvalInstance, PolyEvalWitness,
 };
@@ -348,7 +348,7 @@ impl<E: Engine, EE: EvaluationEngineTrait<E>> BatchedRelaxedR1CSSNARKTrait<E>
     };
 
     let (batched_u, batched_w, sc_proof_batch, claims_batch_left) =
-      batch_eval_prove(u_vec, &w_vec, &mut transcript)?;
+      batch_eval_reduce(u_vec, &w_vec, &mut transcript)?;
 
     let eval_arg = EE::prove(
       ck,
diff --git a/src/spartan/polys/power.rs b/src/spartan/polys/power.rs
index 55bd2a4ad..fc0bb6996 100644
--- a/src/spartan/polys/power.rs
+++ b/src/spartan/polys/power.rs
@@ -27,7 +27,7 @@ impl<Scalar: PrimeField> PowPolynomial<Scalar> {
 
   /// Create powers the following powers of `t`:
   /// [t^{2^0}, t^{2^1}, ..., t^{2^{ell-1}}]
-  pub(in crate::spartan) fn squares(t: &Scalar, ell: usize) -> Vec<Scalar> {
+  pub fn squares(t: &Scalar, ell: usize) -> Vec<Scalar> {
     successors(Some(*t), |p: &Scalar| Some(p.square()))
       .take(ell)
       .collect::<Vec<_>>()
diff --git a/src/spartan/ppsnark.rs b/src/spartan/ppsnark.rs
index 711f80039..aba5a98be 100644
--- a/src/spartan/ppsnark.rs
+++ b/src/spartan/ppsnark.rs
@@ -584,10 +584,11 @@ impl<E: Engine, EE: EvaluationEngineTrait<E>> RelaxedR1CSSNARKTrait<E> for Relax
     let u: PolyEvalInstance<E> =
       PolyEvalInstance::batch(&comm_vec, tau_coords.clone(), &eval_vec, &c);
 
-    // we now need to prove three claims
+    // we now need to prove four claims
     // (1) 0 = \sum_x poly_tau(x) * (poly_Az(x) * poly_Bz(x) - poly_uCz_E(x)), and eval_Az_at_tau + r * eval_Bz_at_tau + r^2 * eval_Cz_at_tau = (Az+r*Bz+r^2*Cz)(tau)
     // (2) eval_Az_at_tau + c * eval_Bz_at_tau + c^2 * eval_Cz_at_tau = \sum_y L_row(y) * (val_A(y) + c * val_B(y) + c^2 * val_C(y)) * L_col(y)
     // (3) L_row(i) = eq(tau, row(i)) and L_col(i) = z(col(i))
+    // (4) Check that the witness polynomial W is well-formed e.g., it is padded with only zeros
     let gamma = transcript.squeeze(b"g")?;
     let r = transcript.squeeze(b"r")?;
 
diff --git a/src/spartan/snark.rs b/src/spartan/snark.rs
index 3b82c3e57..fed756059 100644
--- a/src/spartan/snark.rs
+++ b/src/spartan/snark.rs
@@ -250,7 +250,7 @@ impl<E: Engine, EE: EvaluationEngineTrait<E>> RelaxedR1CSSNARKTrait<E> for Relax
     ];
 
     let (batched_u, batched_w, sc_proof_batch, claims_batch_left) =
-      batch_eval_prove(u_vec, &w_vec, &mut transcript)?;
+      batch_eval_reduce(u_vec, &w_vec, &mut transcript)?;
 
     let eval_arg = EE::prove(
       ck,
@@ -415,8 +415,8 @@ impl<E: Engine, EE: EvaluationEngineTrait<E>> RelaxedR1CSSNARKTrait<E> for Relax
   }
 }
 
-/// Proves a batch of polynomial evaluation claims using Sumcheck
-/// reducing them to a single claim at the same point.
+/// Reduces a batch of polynomial evaluation claims using Sumcheck
+/// to a single claim at the same point.
 ///
 /// # Details
 ///
@@ -429,7 +429,7 @@ impl<E: Engine, EE: EvaluationEngineTrait<E>> RelaxedR1CSSNARKTrait<E> for Relax
 ///
 /// We allow the polynomial Pᵢ to have different sizes, by appropriately scaling
 /// the claims and resulting evaluations from Sumcheck.
-pub(in crate::spartan) fn batch_eval_prove<E: Engine>(
+pub(in crate::spartan) fn batch_eval_reduce<E: Engine>(
   u_vec: Vec<PolyEvalInstance<E>>,
   w_vec: &[PolyEvalWitness<E>],
   transcript: &mut E::TE,