Why can't cleveref determine if the reference is at the beginning of a sentence?

Question

I was reading the documentation on the cleveref package, which can be found here, when I stumbled upon a side remark on page six (can be found in the paragraph for \Cref), which says

As it is very difficult³ for LATEX to determine whether a cross-reference appears at the beginning of a sentence or not, [...]

³ Actually, very likely impossible!

(Changed the original Latex sign generated by \LaTeX to LATEX)

I'd like to know why this is the case?

Answer 1

Here's a LuaLaTeX-based implementation of the preprocessor-based approach I outlined in the comments above. It replaces instances of \cref with \Cref (and of \crefrange with \Crefrange) if they occur either at the very start of a line of input or are preceded by a sentence-ending punctuation mark (., ?, or !) followed by one of more whitespaces. The main work is performed by the cref2Cref Lua function, which gets assigned to the process_input_buffer callback, thus acting as a preprocessor before TeX starts its normal work.

The main, crucial assumption about the input is that there are no line-breaks inside sentences. If this assumption isn't satisfied, the approach is not guaranteed to work. A second, hopefully trivially-true, assumption is that only macros of the cleveref package start with the string \cref. If, for whatever reason, your code defines macros named \crefx or \crefzzz, be prepared for some unpleasant surprises. The approach also ignores the possibility that non-sentence-ending periods are followed immediately by \cref. Thus, a (highly questionable!) sentence fragment such as "Mr. and Mrs. \cref{fig:a} are pleased to announce" will trip up the algorithm. Do let me know if your document contains such passages...

The code used to generate the following screenshot loads the hyperref package and loads the cleveref package with the option nameinlink in order to make it easy for the eye to detect cross-references. Observe that two of the four instances of \cref were replaced with \Cref "on the fly".

Finally, note that cleveref itself does no extra work here: It only ever gets to see, and process, instances of \cref and \Cref. cleveref has no way of knowing which instances of \Cref and \Crefrange were provided by the author and which ones were created on-the-fly by the Lua function cref2Cref.

% !TEX TS-program = lualatex
\documentclass{article}
\usepackage{amsmath} % for 'gather' env.
\usepackage[colorlinks]{hyperref} % optional
\usepackage[nameinlink,noabbrev]{cleveref}
\usepackage{luacode}
\begin{luacode}

function cref2Cref ( s )
   s = s:gsub ( "^\\cref", "\\Cref" )
   s = s:gsub ( "([%.%!%?])%s*\\cref" , "%1 \\Cref" )
   return s
end

\end{luacode}
%% Assign the Lua function to the 'process_input_buffer' callback:
\AtBeginDocument{\directlua{luatexbase.add_to_callback( 
  "process_input_buffer" , cref2Cref , "cref2Cref" )}}

\begin{document}
%% Set up a few equations and figures.
\begin{gather} 
1+1=2 \label{eq:1} \\
2+2=4 \label{eq:2} \\
3+3=6 \label{eq:3} 
\end{gather}
\begin{figure}[h!] 
\caption{AAA} \label{fig:a} \smallskip
\caption{BBB} \label{fig:b} \smallskip 
\caption{CCC} \label{fig:c} 
\end{figure}

% Now generate a few cross-references.
Is this a cross-reference to \cref{eq:1}? \cref{eq:2,eq:3} show that\dots

\crefrange{fig:a}{fig:c} illustrate\dots\ As \crefrange{fig:b}{fig:c} demonstrate, \dots
\end{document}