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> A better formatting would be
>
> \bool_if:nTF {
>     \bool_pred:n{\l_my_first_bool} && (
>        \bool_pred:n{\l_my_second_bool} &&
>        ! \bool_pred:n{\l_my_third_bool}
>     )
> }

information, and are just there to make TeX happy. Since we can avoid
them altogether, let's do it.

\bool_if:nTF
{
\l_my_first_bool
&& (
\l_my_second_bool
&& ! \l_my_third_bool
)
}

> :) But maybe the problem is that &&, (, ), !, and || do not really stand out
> from the background of braces and backslashes (far less than against the
> background of alphanumeric identifiers you'd encounter in C)? Fortanish
> .AND., .OR., and .NOT. would be more eye-catching, but the parentheses are
> probably a lost cause readability-wise.

I find && and || to be more visible than AND and OR in fact (probably
a matter of syntax highlighting in the editor).

> Well, it depends on the parsing scheme one uses. If instead going for
> delimited-argument style subformula grabbing, then it wouldn't matter how
> many tokens an expression terminal (predicate) consists of, and as a
> side-effect operation priority becomes straightforward (the operation you
> split at first gets the lowest priority). What would be tricky for this
> approach is the handling of parentheses, since in that case there are two
> distinct possibilities for "the next token of interest here", but I think it
> is doable (first split on one, then try to split on the second, and treat
> the combination of the outcomes as a case).

The other problem with this approach is that my working copy with
Church booleans is now catcode agnostic, while delimited arguments
would require one particular catcode. You are right on the other
arguments for that approach.

> I believe one could preferably structure the whole thing as an expand-only
> rewrite of infix boolean expression to Church-style compositions of
> booleans. It probably wouldn't be good at catching certain syntax errors,
> though.

That's a pretty big change. I need some time to ponder it. (And in any
case, changes won't happen before a few weeks from now.)

> Consider a command whose role is similar to that of the 2e \makelabel: A
> user-definable command which gets its argument(s) from more basic levels of
> LaTeX, and is supposed to do something in a configurable way. ((In the
> future all such commands should be template keys, you say? Why, yes, it may
> well be. Template instances will often be defined with \ExplSyntaxOff, I
> think.)) Suppose further that one of these arguments is a boolean. ((Poor
> design? Well, such things will happen; it's an open system.)) Now, if said
> boolean is a Church boolean (effectively \use_i:nn or \use_ii:nn), then it
> can be used directly to select between two pieces of code, e.g. like
>
> \def\makesomething#1#2{% Assuming \ExplSyntaxOff
>     % #1 is some text
>     % #2 is the boolean
>     #1%
>     #2{ \thetheorem}{}%
>     .\ %
> }

What about \let \ifthenelse \bool_if:nTF ? That doesn't assume
anything about the internals, and allows precisely what you describe
(and is slightly more general, since the user can now use boolean
expressions).

> Here, \makesomething{Theorem}{\use_i:nn} will produce e.g. "Theorem 3.4. ",
> whereas \makesomething{Theorem}{\use_ii:nn} produces "Theorem. "
>
> Yes, templates tend to handle these situations by having two separate keys
> for the two cases. No, I don't think that package authors will therefore
> never decide to pass booleans to these kinds of commands.

I still haven't caught up on the whole template business, so I can't
follow you there yet. Does giving a user level alias for \bool_if:nTF
solve that problem? Another relevan function (which I discovered when
changing the implementation) is \bool_set:Nn.

>> If the issue is with
>> preserving spaces, then \ExplNames(On|Off) is also provided,
>
> No, and using that adds even further complications.

You have a point, both for \ExplSyntaxOn and \ExplNamesOn.

>> and (infix) boolean expressions work there as well.
>
> Within \ExplNamesOn, you mean? Making sure that *all* stray spaces are
> *always* gobbled could be difficult to prove, but I can see that there at
> least is a fair chance of this happening (thanks to undelimited macro
> arguments skipping spaces).

With the current approach, it is clear: everything is either grabbed
as an undelimited argument, or expanded with \number, except when we
skip the end of a parenthesis group, in which case the delimited
argument is meant to be dropped eventually. So no stray space remains.

>> We could provide \bool_and:nn etc. (or some variation thereof). One
>> problem is where to stop: here you've used the three argument variant
>> \add:nnn, but we should then provide a four argument variant, etc.
>
> Even if you include everything up to the nine argument forms, you'll end up
> with fewer macros in total than for the alternative. ;-)

True with the current code, I think, but my new code doesn't need two
separate branches, so that statement becomes false :). Then it _is_
true that 18 cs is not that much. However,

\bool_if:nTF
{
\bool_and:nnnnnnn % n?
\l_i_bool
\l_ii_bool
\l_iii_bool
\l_iv_bool
\l_v_bool
\l_vi_bool
\l_vii_bool
\l_viii_bool
}

is not exactly obvious to update if a boolean is added. The && version

> A couple of years ago, the Tcl community faced a similar situation:
> Arithmetic had always been expressed in an infix fashion (using the [expr]
> command, which is very similar semantically to these \XX_eval:n), even
> though the language as such is strongly prefix in nature. Proposals were
> made to add prefix arithmetic commands as a supplement. Some argued against,
> etc.), but in the end the prefix forms were added. In the years since, they
> have proven to be quite useful at times, even though hardly anyone uses them
> exclusively.

My position is that infix notation should definitely remain. Adding
prefix notation may make sense, perhaps.

> Well, count this as brainstorming. It occurred to me that in the vast
> majority of cases, it wouldn't matter to me whether I got
> \YesValue{<argument>} or simply <argument>.

Thanks a lot for proposing ideas. It helps clarify what is needed, and
how to improve things.

Regards,
Bruno