Why expl3 booleans values are printed as Γ and ∆ (or as ` and ́ )?

Question

The MWE below points out that expl3 booleans value are printed as Γ and ∆ (or, if \usepackage[T1]{fontenc} is used, as back and forward quotes ` and ́) depending whether they are false or true:

\documentclass{article}
\usepackage{xparse}
\usepackage[T1]{fontenc}
\ExplSyntaxOn
\bool_new:N \falsebool
\bool_new:N \truebool
\bool_set_true:N \truebool
\cs_new_protected:Nn \_boolean_value:n
{
  A~\bool_if:NTF {#1}{true~($=1$)}{false~($=0$)}~ boolean~ is~ printed~ as:~#1
}
\NewDocumentCommand { \displaybooleans } { m }
{
  \_boolean_value:n{#1}
}
\ExplSyntaxOff
\begin{document}
\begin{itemize}
\item \displaybooleans{\falsebool}
\item \displaybooleans{\truebool}
\end{itemize}
\end{document}

Do you know why? Why, outside tests, aren't their values printed as e.g. 0 and 1?

Edit

Here is the background, the real use case: in a package of mine, which is coded thanks to expl3, I provide some (in fact many) options that let the user fix floating points variables, token list variables, boolean variables, etc. And I consider to provide a macro that displays all the options (default ones and user defined ones) in use. The floating points variables and token list variables can be printed in a rather direct way:

• The nice floating point variable is set to: \fp_use:N\g_a_nice_floating_point_variable_fp (though one could expect in a typesetting context, by opposite to a computing context, The nice floating point variable is set to: \g_a_nice_floating_point_variable_fp to be enough, i.e. \fp_use:N to be superfluous),
• The nice token list variable is set to: \g_a_nice_token_list_variable_tl.

And my question is: in order to print the current value of a boolean variable, is it necessary to go through a \bool_if:NTF \g_a_nice_boolean_variable_bool { ... } { ... } test to print its current value or is there a more direct way to do?

Answer 1

This brings up a very old question: “What is truth?” (John, 18:38).

Unfortunately, there is no answer to this question: truth (at least in mathematics) is whatever, so long as it is different from falsehood. Truth has only meaning relative to a model.

LaTeX3 thinks to truth and falsehood in the same way as Perl: 0 is false and 1 is true. Or the other way around. However, one shouldn't rely on the particular implementation, just remain assured that false will always be the same, and truth won't change.

A false conditional is implemented as returning the constant 0 and, similarly, a true conditional returns the constant 1, but this is just implementation. A conditional such as your \falsebool should only be used in the context of a boolean expression and never on its own.

As is usual in TeX, a constant is defined through \chardef, so when it is found in a typesetting context, \falsebool will typeset the character in slot 0 and \truebool the character in slot 1.

In a OT1 encoded font, these are Gamma and Delta respectively. In a T1 encoded font they're the grave and acute accent. More generally, they'll print the characters in slots 0 and 1 of the current font.

If you try \show\falsebool, you'll get

> \falsebool=\char"0.

on the terminal.