Using characters to delimit commands (like markdown)

The basic idea of \DefineShortVerb is that it makes the character in the argument active (\catcode`#1=\active), so that the character behaves like a macro. Then it defines that character to be a verbatim command using the "lowercase trick". You can change that to define the character to a custom macro.

Here's a \DefineShortCommand<char>{<definition>} macro which defines the <char> to expand to <definition>. This eventually does something like \def<char>#1<char>{<definition>}, in which <char> is an active character token. In the <definition>, #1 is the argument, grabbed between the first and the next (brace-balanced) <char>.

\documentclass{article}
\def\DefineShortCommand#1{%
  \catcode`#1=\active
  \begingroup
    \lccode`\~=`#1
    \lowercase{\endgroup
  \def~##1~}}
\begin{document}

\DefineShortCommand\`{\textit{#1}}
`this` and \textit{this} should be the same.

\end{document}

Take care not to activate "dangerous" characters and beware with possible conflicts with babel.

---

To use with Verbatim, the character ` is especially painful because this character is reset by LaTeX's \@noligs to avoid that it forms ligatures in verbatim mode. fancyvrb uses \@noligs after the user's catcode settings, so anything you change to the character ` is overridden. You need to remove it from the verbatim ligature list:

\documentclass{article}
\usepackage{fancyvrb}
\def\DefineShortCommand#1{%
  \catcode`#1=\active
  \begingroup
    \lccode`\~=`#1
    \lowercase{\endgroup
  \def~##1~}}
\begin{document}

\makeatletter
\def\verbatim@nolig@list{\do\<\do\>\do\,\do\'\do\-}
\def\backtickit{\DefineShortCommand\`{\textit{##1}}}
\makeatother

\begin{Verbatim}[codes={\backtickit}]
  x=1/sqrt(z**2) <- This is an `equation`
\end{Verbatim}

\end{document}

---

As Mico noted, when two ` are used (like in ``should'') you usually don't want to apply the special formatting. To detect this case you can check that the argument of active-` is empty and then use the original ` character instead.

Suppose you have a \tlifempty{<token list>}{<empty>}{<not empty>} (shown below) conditional, then this could be accomplished with:

\DefineShortCommand\`{%
  \tlifempty{#1}
    {\char96\char96\relax}
    {\textit{#1}}}

(96 is the ASCII code for `).

To go an extra mile and allow the eventual usage of ` (or other character that you happen to use with \DefineShortCommand) in an expansion-only context, you need to save the original meaning of ` and then retrieve it later with an auxiliary macro.

In the code below, \DefineShortCommand saves the original meaning of the argument as (for example `) \the@char@96. Later you can retrieve it with \thechar{`}. As an extra safety, the code does some normalisation so that both ` or \` retrieve the same character:

\documentclass{article}
\makeatletter
\def\DefineShortCommand#1{%
  \expandafter\edef\csname the@char@\number`#1\endcsname
    {\unless\if\@backslashchar\string#1%
       \string#1\else\expandafter\@gobble\string#1\fi}%
  \catcode`#1=\active
  \begingroup
    \lccode`\~=`#1
    \lowercase{\endgroup
  \def~##1~}}
\def\thechar#1{\csname the@char@\number`#1\endcsname}
% Checking if the argument is empty
\def\tlifempty#1{%
  \if\relax\detokenize{#1}\relax
    \expandafter\@firstoftwo
  \else
    \expandafter\@secondoftwo
  \fi}
\makeatother
\begin{document}
\DefineShortCommand\`{%
  \tlifempty{#1}
    {\thechar{`}\thechar{\`}}
    {\textit{#1}}}

`this` and \textit{this} ``should'' be the same.
\end{document}

I want the text enclosed by [backtick] characters to be displayed in italic

Here's a LuaLaTeX-based solution. It doesn't require making the backtick character, `, "active".

Observe that the "normal" use of double backticks, ``, as in ``that'', is not affected by the processing of material enclosed in pairs of single backticks.

% !TEX TS-program = lualatex
\documentclass{article}
\usepackage{luacode}  
%% Lua-side code:
\begin{luacode}

function backtick2textit ( s )
   s = s:gsub ( "``(.-)''" , "@@@@@%1@@@@@" ) -- save ``...'' cases
   s = s:gsub ( "`(..-)`", "\\textit{%1}" )   -- ignore consecutive backticks
   s = s:gsub ( "@@@@@(.-)@@@@@" , "``%1''" ) -- restore ``...'' cases
   return s
end

\end{luacode}    
%% LaTeX-side code:
\AtBeginDocument{\directlua{luatexbase.add_to_callback( 
   "process_input_buffer", backtick2textit , 
   "backtick2textit" )}}

\begin{document}
\dots\ and `this` and ``that'' and ``why'' and `who` and \dots
\end{document}

---

Addendum to explain how the solution works:

• The Lua function backtick2textit is assigned to the process_input_buffer callback, which operates at a very early stage, i.e., before TeX performs its usual work of expanding macros, etc.

• The function backtick2textit employs the Lua function string.gsub (I believe that "gsub" stands for "global substitution") to perform its job.

  • First, strings enclosed in double-backticks/double apostrophes (non-greedy matching) are set aside.

  • A pattern match occurs if a backtick is encountered, followed by 1 or more arbitrary characters (non-greedy matching), followed by another backtick. If a match occurs, the material enclosed by the backticks is encased in a \textit directive.

  • Finally, the material to rendered in double-quote marks is restored.

• The Lua function will not perform correctly if you use both single and double quote characters to quote material. The code posted above doesn't guard against this eventuality as I assume that you mentioned the use of backtick characters just as an example.