fix: typos in documentation files

ark-bcs/src/bcs/constraints/transcript.rs

@@ -278,7 +278,7 @@ where
     /// and decision phase.
     ///
     /// **Note**: Since we are not running the actual prover code, verifier
-    /// message is not used `reconstructed_verifer_messages`, so this
+    /// message is not used `reconstructed_verifier_messages`, so this
     /// function returns nothing. TODO: current limitation: sponge
     /// constraints does not support squeeze native elements with size
     pub fn squeeze_verifier_field_elements(
@@ -298,7 +298,7 @@ where
     /// decision phase.
     ///
     /// **Note**: Since we are not running the actual prover code, verifier
-    /// message is not used `reconstructed_verifer_messages`, so this
+    /// message is not used `reconstructed_verifier_messages`, so this
     /// function returns nothing.
     pub fn squeeze_verifier_field_bytes(&mut self, num_bytes: usize) -> Result<(), SynthesisError> {
         let msg = self.sponge.squeeze_bytes(num_bytes)?;
@@ -314,7 +314,7 @@ where
     /// decision phase.
     ///
     /// **Note**: Since we are not running the actual prover code, verifier
-    /// message is not used `reconstructed_verifer_messages`, so this
+    /// message is not used `reconstructed_verifier_messages`, so this
     /// function returns nothing.
     pub fn squeeze_verifier_field_bits(&mut self, num_bits: usize) -> Result<(), SynthesisError> {
         let msg = self.sponge.squeeze_bits(num_bits)?;

ark-bcs/src/bcs/transcript.rs

@@ -141,7 +141,7 @@ where
         }
     }
 
-    /// Register a virtual oracle specfied by coset evaluator.
+    /// Register a virtual oracle specified by coset evaluator.
     /// * `coset_query_evaluator`: a function that takes a coset and constituent
     ///   oracles, and return query responses
     /// * `evaluation_on_domain`: evaluation of this virtual round on evaluation

ark-bcs/src/iop/bookkeeper.rs

@@ -48,7 +48,7 @@ impl NameSpace {
 pub struct MessageBookkeeper {
     /// Store the messages by namespace id
     pub(crate) messages_store: BTreeMap<u64, MessageIndices>,
-    /// An adjacancy list the subspaces called for current namespace, in order.
+    /// An adjacency list the subspaces called for current namespace, in order.
     pub(crate) ns_map: BTreeMap<u64, Vec<u64>>,
     /// Store the namespace details (e.g. trace) by id
     pub(crate) ns_details: BTreeMap<u64, NameSpace>,
@@ -237,7 +237,7 @@ pub trait BookkeeperContainer {
             .len()
     }
 
-    // fetch all sent messages as referecnes
+    // fetch all sent messages as references
 
     /// Return all prover rounds message in the namespace as round reference.
     fn prover_round_refs_in_namespace(&self, namespace: NameSpace) -> &Vec<MsgRoundRef> {

ark-bcs/src/ldt/rl_ldt.rs

@@ -98,7 +98,7 @@ impl<F: PrimeField + Absorb> LDT<F> for LinearCombinationLDT<F> {
                 .map(|_| FieldElementSize::Full)
                 .collect::<Vec<_>>(),
         );
-        transcript.submit_verifier_current_round(namespace, iop_trace!("ldt random coefficeints"));
+        transcript.submit_verifier_current_round(namespace, iop_trace!("ldt random coefficients"));
 
         let mut result_codewords = (0..param.domain.size())
             .map(|_| F::zero())