diff --git a/src/lib.rs b/src/lib.rs
index a3a0bafc..55e9275a 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -63,7 +63,7 @@ pub struct R1CSWithArity<E: Engine> {
 impl<E: Engine> SimpleDigestible for R1CSWithArity<E> {}
 
 impl<E: Engine> R1CSWithArity<E> {
-  /// Create a new `CircuitShape`
+  /// Create a new `R1CSWithArity`
   pub fn new(r1cs_shape: R1CSShape<E>, F_arity: usize) -> Self {
     Self {
       F_arity,
@@ -71,7 +71,7 @@ impl<E: Engine> R1CSWithArity<E> {
     }
   }
 
-  /// Return the [CircuitShape]' digest.
+  /// Return the [R1CSWithArity]' digest.
   pub fn digest(&self) -> E::Scalar {
     let dc: DigestComputer<'_, <E as Engine>::Scalar, R1CSWithArity<E>> = DigestComputer::new(self);
     dc.digest().expect("Failure in computing digest")
diff --git a/src/supernova/Readme.md b/src/supernova/Readme.md
index deb73832..11b43d6e 100644
--- a/src/supernova/Readme.md
+++ b/src/supernova/Readme.md
@@ -76,7 +76,7 @@ At each step, the prover needs to:
 
 In pseudocode, `prove_step` looks something like:
 
-```ignore
+```text
 if i = 0 {
 	U[] = [ø;l]
 
@@ -189,7 +189,7 @@ The inputs of provided to the augmented step circuit $F'_j$ are:
 	- **Secondary**: Always `None`, and interpreted as $\mathsf{pc}_i \equiv 0$, since there is only a single circuit.
 - $z_0 \in \mathbb{F}^a$: inputs for the first iteration of $F$
 - $z_i \in \mathbb{F}^a$: inputs for the current iteration of $F$
-	- **Base case**: Set to `None`, in which case it is allocated as $[0]$, and $z_0$ is used as $z_i$.
+	- **Base case**: Set to `None`, in which case it is allocated as $\[0\]$, and $z_0$ is used as $z_i$.
 - $U_i[\ ] \in \mathbb{R}'^\ell$: list of relaxed R1CS instances on the other curve
 	- **Primary**: Since there is only a single circuit on the secondary curve, we have $\ell = 0$ and therefore $U_i[\ ]$ only contains a single `RelaxedR1CSInstance`.
 	- **Secondary**: The list of input relaxed instances $U_i[\ ]$ is initialized by passing a slice `[Option<RelaxedR1CSInstance<G>>]`, one for each circuit on the primary curve.
diff --git a/src/supernova/mod.rs b/src/supernova/mod.rs
index 5dbcf36e..8c3313fb 100644
--- a/src/supernova/mod.rs
+++ b/src/supernova/mod.rs
@@ -71,7 +71,7 @@ impl<E: Engine> CircuitDigests<E> {
   }
 }
 
-/// A vector of [CircuitParams] corresponding to a set of [PublicParams]
+/// A vector of [R1CSWithArity] adjoined to a set of [PublicParams]
 #[derive(Clone, Serialize, Deserialize)]
 #[serde(bound = "")]
 pub struct PublicParams<E1, E2, C1, C2>
@@ -288,7 +288,7 @@ where
     (circuit_shapes, aux_params)
   }
 
-  /// Create a [PublicParams] from a vector of raw [CircuitShape] and auxiliary params.
+  /// Create a [PublicParams] from a vector of raw [R1CSWithArity] and auxiliary params.
   pub fn from_parts(circuit_shapes: Vec<R1CSWithArity<E1>>, aux_params: AuxParams<E1, E2>) -> Self {
     let pp = PublicParams {
       circuit_shapes,
@@ -312,7 +312,7 @@ where
     pp
   }
 
-  /// Create a [PublicParams] from a vector of raw [CircuitShape] and auxiliary params.
+  /// Create a [PublicParams] from a vector of raw [R1CSWithArity] and auxiliary params.
   /// We don't check that the `aux_params.digest` is a valid digest for the created params.
   pub fn from_parts_unchecked(
     circuit_shapes: Vec<R1CSWithArity<E1>>,
@@ -335,7 +335,7 @@ where
   }
 
   /// Compute primary and secondary commitment keys sized to handle the largest of the circuits in the provided
-  /// `CircuitShape`.
+  /// `R1CSWithArity`.
   fn compute_primary_ck(
     circuit_params: &[R1CSWithArity<E1>],
     ck_hint1: &CommitmentKeyHint<E1>,