hide free text without additional environment

Question

to simplify let us say I have a document with only text and theorems.

I want to display only the text contained in theorems. For instance

    \documentclass[10pt]{book}

\usepackage{amsthm}

\theoremstyle{definition}
\newtheorem{theorem}{Definition}

\begin{document}
\chapter{One}
\section{One}
blah
\section{Two}
\begin{theorem}
Blo
\end{theorem}
\chapter{Two}
Blih

\end{document}

I want only to have displayed: 1.One 1.One 2.Two Theorem:Bloh" 2.Two

Is it possible without having to enclose the text in an additional environment?

One solution would be somehow to suppress the normal output with some trick, e.g. putting font size to 0 (didn't manage to do that), except in the theorems.

Thanks

EDIT: maybe one way to do it would be to automatically collect all the contents of theorems with some packages, not ouput the main document, and only output what has been collected, but I would also like to have chapter and section titles...

Answer 1

The OP stipulates "let us say I have a document with only text and theorems".

I use a tokencycle pseudo-environment named \shothms...\endshothms, one instance of which is wrapped around the whole document, to achieve the result.

As currently EDITED, it will only execute instances of \chapter & \section (without optional arguments) and theorem & proposition environments. Note that optional arguments to these macros/environments can be dealt with via tokcycle, but I did not feel like investing the time and code here. See Parse Argument by Character while Executing Embedded Macros, for an example where it is done.

The macro tests (if one wanted to add additional macros to capture) is performed by the \testmacros macro

\newcommand\testmacros[1]{%
  \ifx\chapter#1\addcytoks{#1}\gdef\addarg{T}\else
  \ifx\section#1\addcytoks{#1}\gdef\addarg{T}\else
    \gdef\addarg{F}\fi\fi
}

The environment tests (if more are needed) are performed by the \testenvs macro, given as

\newcommand\testenvs[1]{%
  \ifx\thmchk#1 1\else
  \ifx\propchk#1 1\else
  0\fi\fi
}

given the preamble definitions

\def\thmchk{theorem}
\def\propchk{proposition}

The MWE:

\documentclass{book}
\usepackage{amsthm}
\usepackage{thmtools}
\usepackage{tokcycle}
\def\addarg{F}
\def\checktheorems{F}
\def\charson{F}
\def\thmchk{theorem}
\def\propchk{proposition}
\declaretheorem{theorem}
\declaretheorem{proposition}
\stripgroupingtrue
\tokcycleenvironment\shothms
  {\if T\charson\addcytoks{##1}\fi}
  {%
    \if T\addarg\addcytoks{{##1}}\gdef\addarg{F}\fi
    \if F\checktheorems
      \if T\charson\addcytoks{{##1}}\fi
    \else
      \gdef\tmp{##1}%
      \ifnum\testenvs{\tmp}=1\relax
        \if B\checktheorems
          \addcytoks{\begin{##1}}\gdef\charson{T}%
        \else
          \addcytoks{\end{##1}}\gdef\charson{F}%
        \fi
      \fi%
    \fi
    \gdef\checktheorems{F}
  }
  {%
    \ifx\begin##1\gdef\checktheorems{B}\else
      \ifx\end##1\gdef\checktheorems{E}\else
        \gdef\checktheorems{F}%
        \if T\charson\addcytoks{##1}\fi%
      \fi
    \fi
    \testmacros{##1}%
  }
  {\if T\charson\addcytoks{##1}\fi}
\newcommand\testmacros[1]{%
  \ifx\chapter#1\addcytoks{#1}\gdef\addarg{T}\else
  \ifx\section#1\addcytoks{#1}\gdef\addarg{T}\else
    \gdef\addarg{F}\fi\fi
}
\newcommand\testenvs[1]{%
  \ifx\thmchk#1 1\else
  \ifx\propchk#1 1\else
  0\fi\fi
}
\begin{document}
\shothms
\chapter{My Chapter}

Chapter text

\section{One}

blah blah
\section{Two}

\begin{theorem}
Bloh \textbf{Blah} \today
\end{theorem}

blih blih \textit{blow}

more blah

\begin{proposition}
Blah$^2$
\end{proposition}
Finis
\endshothms
\end{document}

ADDENDUM

If one wanted less formatting of the sectioning, one could redefine \testmacros as

\newcommand\testmacros[1]{%
  \ifx\chapter#1\addcytoks{\stepcounter{chapter}\par\noindent Chapter 
    \thechapter:~}\gdef\addarg{T}\else
  \ifx\section#1\addcytoks{\stepcounter{section}\par\noindent Section 
    \thesection:~}\gdef\addarg{T}\else
    \gdef\addarg{F}\fi\fi
}

resulting in