From ae5041f376db42f82b4054b715248a1f9d24d834 Mon Sep 17 00:00:00 2001
From: hewigovens <360470+hewigovens@users.noreply.github.com>
Date: Fri, 20 Oct 2023 11:47:56 +0900
Subject: [PATCH] Fix some typos in README

---
 README.md | 18 +++++++++---------
 1 file changed, 9 insertions(+), 9 deletions(-)

diff --git a/README.md b/README.md
index d868db9..938c942 100644
--- a/README.md
+++ b/README.md
@@ -1,5 +1,5 @@
 # circuit-tools
-A lightweit SDK for Halo2 frontend circuit.
+A lightweight SDK for Halo2 frontend circuit.
 ## Features
 ### Logic: Constraint Builder
 Leverage Rust's macro to construct conditional constraints based on execution branching. Build all constraints in on step with Halo2's gate.
@@ -10,9 +10,9 @@ meta.create_gate("Test", |meta| {
     circuit!([meta, cb], {
         ifx!(f!(q_enable) => {
             ifx!{a!(a) => {
-                require!(a!(res) => a!(b) + f!(c)); 
+                require!(a!(res) => a!(b) + f!(c));
             } elsex {
-                require!(a!(res) => a!(b) + c!(r));  
+                require!(a!(res) => a!(b) + c!(r));
             }};
         });
     });
@@ -38,7 +38,7 @@ require!((a.expr(), b.expr()) =>> @TestCellType::Lookup);
 
 ```
 ### Memory: Dynamic Lookup
-Abstraction over using dynamic lookup to prove RW access in RAM. Stores to dynamic table to resemble WRITE and add lookups to represent READ. Lookup operation `(idx, r0, r1) => (rdx, w0, w1)` returns true if and only if the prover access the writen data at anticipated position correctly.
+Abstraction over using dynamic lookup to prove RW access in RAM. Stores to dynamic table to resemble WRITE and add lookups to represent READ. Lookup operation `(idx, r0, r1) => (rdx, w0, w1)` returns true if and only if the prover access the written data at anticipated position correctly.
 ```
 let mut memory = Memory::new();
 memory.add_rw(meta, &mut cb.base, &mut state_cm, MyCellType::Mem1, 1);
@@ -56,11 +56,11 @@ register1.load(cb, &[a0, b1]);
 
 ```
 ### Assignment: Cached Region
-Used to backtrack the intermediate cells queried in by Constrinat Builder during degree reduction. After `a * b * (c + d)` being split into `x = a * b` and `y = c + d`, the system need to account for the assignment of intermediate cells `x` and `y` while the prover only need to assign `a, b, c, d` based on the execution trace. Hence, Cached Region iterates over all stored expressions and recursively find the prover's assignment to calculate the intermediate values.
+Used to backtrack the intermediate cells queried in by Constraint Builder during degree reduction. After `a * b * (c + d)` being split into `x = a * b` and `y = c + d`, the system need to account for the assignment of intermediate cells `x` and `y` while the prover only need to assign `a, b, c, d` based on the execution trace. Hence, Cached Region iterates over all stored expressions and recursively find the prover's assignment to calculate the intermediate values.
 ```
 layouter.get_challenge(self.rand).map(|r| r1 = r);
 layouter.assign_region(
-    || "Test", 
+    || "Test",
     |mut region| {
         let mut region = CachedRegion::new(&mut region, 0.scalar());
         region.push_region(0, 0);
@@ -76,7 +76,7 @@ layouter.assign_region(
 )
 ```
 ## Workflow
-Must specify cell type that implement trait `CellType` to satisfy the generic argument of `ConstraintBuilder<F, C: CellType>`. Can also declear a `TableType` to tag corresponding table for column-to-table lookups.
+Must specify cell type that implement trait `CellType` to satisfy the generic argument of `ConstraintBuilder<F, C: CellType>`. Can also declare a `TableType` to tag corresponding table for column-to-table lookups.
 ```
 pub enum TableTag {
     Fixed,
@@ -108,7 +108,7 @@ impl Default for TestCellType {
     fn default() -> Self {Self::StoragePhase1}
 }
 ```
-Initialize the Constraint Builder and Cell Manager with optional challenge that's used in RLC to conbime multi-columns lookups. The Cell Manager needs a max height and this is usually the height of your Halo2 gate; a offset is also needed to query cell from columns. Offset should be set to 0 in usual case. Load fixed table in to Constraint Builder with corresponding tag and initialized columns with the cell manager with `(cell_type: MyCellType, phase: u8, permuation: bool, num: usize)`.
+Initialize the Constraint Builder and Cell Manager with optional challenge that's used in RLC to combine multi-columns lookups. The Cell Manager needs a max height and this is usually the height of your Halo2 gate; a offset is also needed to query cell from columns. Offset should be set to 0 in usual case. Load fixed table in to Constraint Builder with corresponding tag and initialized columns with the cell manager with `(cell_type: MyCellType, phase: u8, permuation: bool, num: usize)`.
 ```
 let mut cm = CellManager::new(5, 0);
 let mut cb: ConstraintBuilder<F, TestCellType> =  ConstraintBuilder::new(4,  Some(cm), Some(challenge));
@@ -126,4 +126,4 @@ meta.create_gate("Test", |meta| {
 });
 cb.build_lookups(meta);
 ```
-Finally in assingment, initialize `CachedRegion` as demonstrated above and use it to assign values.
+Finally in assignment, initialize `CachedRegion` as demonstrated above and use it to assign values.