Fix grammar and style issues in documentation

- Corrected typos (e.g. "delimitor" -> "delimiter",
  "a accepting" -> "an accepting", "so called" -> "so-called").
- Improved grammar and readability in multiple sections:
  - Rephrased awkward or unclear sentences.
  - Added missing articles and adjusted phrasing for clarity.
  - Standardized wording (e.g., "later self" -> "future self").

Author: QuickWrite

docs/sections/first-program.tex

@@ -1,4 +1,4 @@
-In most programming languages the first program people write is the so called ``Hello World'' program.
+In most programming languages the first program people write is the so-called ``Hello World'' program.
 
 The main idea is to show \code{Hello World} to the user.
 
@@ -34,7 +34,7 @@ \subsubsection{The head}
 
 \textbf{So: What can we see?}
 \begin{itemize}
-    \item Every single statement we define has the structure: 
+    \item Each statement follows this structure: 
     \begin{center}
         \code{<name> = <value>}
     \end{center}
@@ -56,11 +56,11 @@ \subsubsection{The head}
     end = HALT
 \end{verbatim}
 
-Now to end the head and start the body we can write any number of \code{-} as a delimitor. For example something like this: \code{----}.
+Now to end the head and start the body we can write any number of \code{-} as a delimiter. For example something like this: \code{----}.
 
 \subsubsection{The body}
 The body contains the state machine. This state machine is the heart of the Turing Machine. 
-So let's visualize how the state machine should look like before we actually implement it:
+So let's visualize how the state machine should look before we actually implement it:
 
 \begin{center}
     \begin{tikzpicture}[->, % makes the edges directed
@@ -163,13 +163,12 @@ \subsection{Executing the program}
     ..., 0, 0, 0, Hello, World, 0, 0, 0, 0, ...
 \end{verbatim}
 
-And now you have written and executed your first Tau program. Yay!
+You have now written and executed your first Tau program. Yay!
 
 \subsection{Comments}
-Comments are an essential aspect of documenting the code so that other people and your later self can understand what the code does
+Comments are an essential aspect of documenting the code so that other people -- and your future self -- can understand what the code does
 if it doesn't work what the intention was.
-
-In Tau there are only single line comments. They start with a \code{\#} and end with the next Line separator (\code{\textbackslash n}).
+In Tau there are only single line comments. They start with a \code{\#} and end with the next line separator (\code{\textbackslash n}).
 
 These comments can be added anywhere and nothing inside the comment will be parsed.
 

docs/sections/flags.tex

@@ -1,4 +1,4 @@
-Some things are not being set up by the program, but rather before executing the program in the command line.
+Some settings are not configured within the program itself, but are instead specified via command-line flags before execution.
 
 These different settings are flags that can be specified with \code{--\{name\} \{value\}}.
 

docs/sections/introduction.tex

@@ -111,8 +111,8 @@ \subsubsection{How a Turing Machine works}
 Repeating these steps twelve times as these are mostly the same steps:
 
 \begin{minipage}{0.45\textwidth}
-After repeating this twelve times we get to this configuration where the Turing Machine is currently
-in the state C and the head currently reads the value $1$. This means that the Turing Machine will now go to state H (\code{HALT}).
+After repeating this twelve times we get to this configuration where the Turing Machine is currently in state C, 
+and the head reads the value $1$. This means that the Turing Machine will now go to state H (\code{HALT}).
 \end{minipage}
 \begin{minipage}{0.50\textwidth}
     \centering
@@ -138,7 +138,7 @@ \subsubsection{How a Turing Machine works}
 \par\noindent\rule{\textwidth}{0.4pt}
 
 \begin{minipage}{0.45\textwidth}
-As the state machine is currently in a accepting state (the double circle) it will stop the Turing Machine and terminate.
+As the state machine is currently in an accepting state (the double circle) it will stop the Turing Machine and terminate.
 It will not go to the next state nor do any modifications on the tape.
 \end{minipage}
 \begin{minipage}{0.50\textwidth}

docs/sections/technical-documentation.tex

@@ -1,9 +1,9 @@
 The programming language Tau is a very simple language. It only implements a Turing Machine and the interface, which is the programming language.
 
 \subsection{EBNF}
-This is how the language is parsed. It does not mean that everything that can be built with this EBNF syntax is also valid.
+This describes how the language is parsed. Not everything that can be expressed in this EBNF syntax is valid
 It is implied that between each token there can be as much whitespace as needed. 
-The tokens are being declared with uppercase letters. Comments are separate as they are just being skipped by the lexer.
+The tokens are being declared with uppercase letters. Comments are handled separately, as they are simply skipped by the lexer.
 
 \begin{verbatim}
     program = head, body;
@@ -45,8 +45,8 @@ \subsubsection{Head Linking}
 It also checks if the blank is a valid symbol.
 
 \subsubsection{Body Linking}
-Any state can be defined in any order. This means that there can be a different state which is being
-referenced that will be parsed. This means that the linking is also being done after the parser finds the end
+Any state can be defined in any order. This means that a state can reference another state that has not yet been parsed.
+This means that the linking is also being done after the parser finds the end
 of the file.
 
 The linker also needs the states to be exhaustive. This means that every single possibility is being covered.