Merge pull request #397 from rex4539/typos

Fix typos

book/src/background/fields.md

@@ -11,7 +11,7 @@ numbers $\mathbb{R}$ are an example of a field with uncountably many elements.
 Halo makes use of _finite fields_ which have a finite number of elements. Finite fields
 are fully classified as follows:
 
-- if $\mathbb{F}$ is a finite field, it contains $|\mathbb{F}| = p^k$ elements  for some
+- if $\mathbb{F}$ is a finite field, it contains $|\mathbb{F}| = p^k$ elements for some
   integer $k \geq 1$ and some prime $p$;
 - any two finite fields with the same number of elements are isomorphic. In particular,
   all of the arithmetic in a prime field $\mathbb{F}_p$ is isomorphic to addition and

book/src/background/plonkish.md

@@ -60,7 +60,7 @@ Reference: [Generic Lookups with PLONK (DRAFT)](/LTPc5f-3S0qNF6MtwD-Tdg?view)
 
 ### Vanishing argument
 We want to check that the expressions defined by the gate constraints, permutation
-constraints and loookup constraints evaluate to zero at all elements in the multiplicative
+constraints and lookup constraints evaluate to zero at all elements in the multiplicative
 subgroup. To do this, the prover collapses all the expressions into one polynomial
 $$H(X) = \sum_{i=0}^e y^i E_i(X),$$
 where $e$ is the number of expressions and $y$ is a random challenge used to keep the

book/src/design/protocol.md

@@ -54,7 +54,7 @@ Formally, we use the game $\dlgame$ defined above to capture this problem.
 
 _Interactive proofs_ are a triple of algorithms $\ip = (\setup, \prover,
 \verifier)$. The algorithm $\setup(1^\sec)$ produces as its output some _public
-parameters_ commonly refered to by $\pp$. The prover $\prover$ and verifier
+parameters_ commonly referred to by $\pp$. The prover $\prover$ and verifier
 $\verifier$ are interactive machines (with access to $\pp$) and we denote by
 $\langle \prover(x), \verifier(y) \rangle$ an algorithm that executes a
 two-party protocol between them on inputs $x, y$. The output of this protocol, a

book/src/design/proving-system/circuit-commitments.md

@@ -59,7 +59,7 @@ arguments are independent.)
 
 Let $c$ be the number of columns that are enabled for equality constraints.
 
-Let $m$ be the maximum number of columns that can accomodated by a
+Let $m$ be the maximum number of columns that can accommodated by a
 [column set](permutation.md#spanning-a-large-number-of-columns) without exceeding
 the PLONK configuration's polynomial degree bound.
 

book/src/design/proving-system/lookup.md

@@ -119,7 +119,7 @@ Since we can no longer rely on the wraparound to ensure that the product $Z$ bec
 again at $\omega^{2^k},$ we would instead need to constrain $Z(\omega^u)$ to $1.$ However,
 there is a potential difficulty: if any of the values $A_i + \beta$ or $S_i + \gamma$ are
 zero for $i \in [0, u),$ then it might not be possible to satisfy the permutation argument.
-This occurs with negligble probability over choices of $\beta$ and $\gamma,$ but is an
+This occurs with negligible probability over choices of $\beta$ and $\gamma,$ but is an
 obstacle to achieving *perfect* zero knowledge (because an adversary can rule out witnesses
 that would cause this situation), as well as perfect completeness.
 

book/src/user/dev-tools.md

@@ -29,7 +29,7 @@ sudo apt install cmake libexpat1-dev libfreetype6-dev
 {{#include ../../../examples/circuit-layout.rs:dev-graph}}
 ```
 
-- Columns are layed out from left to right as instance, advice, and fixed. The order of
+- Columns are laid out from left to right as instance, advice and fixed. The order of
   columns is otherwise without meaning.
   - Instance columns have a white background.
   - Advice columns have a red background.
@@ -43,7 +43,7 @@ sudo apt install cmake libexpat1-dev libfreetype6-dev
 ### Circuit structure
 
 `halo2::dev::circuit_dot_graph` builds a [DOT graph string] representing the given
-circuit, which can then be rendered witha variety of [layout programs]. The graph is built
+circuit, which can then be rendered with a variety of [layout programs]. The graph is built
 from calls to `Layouter::namespace` both within the circuit, and inside the gadgets and
 chips that it uses.