van Vliet use of backquote (and backslash)

Tue Feb 10 01:10:34 GMT 2026

Jose, James, and list,

On Mon, Feb 9, 2026 at 6:00 AM Jose E. Marchesi <jemarch@gnu.org> wrote:

>
> > Hello Jose,
> >
> > Thanks for this information.  I had been assuming that since the "e"
> > would only ever be placed between two numbers, such as:
> >
> > a)  1.234e4
> > b)  5.67e-8
> >
> > Then it might be possible to recognize that "e" in these situations
> > could never be confused with other possible tags known as "e".
> >
> > Same can be said for the "i" construct for complex numbers.
> >
> > But, this interpretation of mine is quite naive to the more serious
> > language aspects.
>
> Well, plus-i-times is a monad, we cannot do anything about that :/
>

Warning overly long-winded and rambling "analysis" follows...

I understand that plus-i-times is a monad, here's the rule (RR p. 233):

MONAD{942H) : : or ; and ; ampersand ; differs from ; is at most ;
>   is at least ; over ; percent ; window ; floor ; ceiling ;
>   plus i times ; not ; tilde ; down ; up ; plus ; minus ;
>   style TALLY monad.

Notably not a monad is times-ten-to-the-power.  It appears here (RR p. 109):

times ten to the power choice(g) :
>   times ten to the power symbol{94b} ; letter e symbol(94a)

in §8.1.2 Real denotations.

However there is no such definition of "Complex denotations", at least as
far as I can find.  Pairs of real numbers in a closed collateral clause
show up as "complex numbers" upon occasion; for example in §6.5 Widening we
read:

For example, in z : = J, the yield of 1 is widened to the real number
> 1.0 and then to the complex number (1.0, 0.0);

As far as I can tell though, there is nowhere in the RR that suggests we
should have at hand a "complex denotation" that looks like 3.0⊥2.0

The closest I can find to that is in §10.3.4.5 Complex patterns which
states:

10.3.4.5.1. Syntax
> a) NEST complex pattern(A34lc) : NEST real pattern{A343a},
>       NEST complex frame(A34lj}, NEST real pattern{A343a}.
> b) complex marker{A34lj) : letter i(94a} symbol.

> (Example:
>    a) +.12de+2d 3q"+jx"3", " si +.10de+2d )

> (For the semantics of complex-patterns see 10.3.4.1.2.e.}

> (aa) The modes which are output (input) compatible with a
> 'complex' pattern are those specified by L compl, L real and L int (by ref
> L compl).

> (bb) A value V is converted to a string S using a 'complex' pattern P as
> follows:
> • if necessary, V is widened to a complex number;
> • the element of S controlled by the "i" frame of P is "⊥":
> • the part of S controlled by the first (second) 'real' pattern of P is
> that obtained by converting the first (second) field of V to a string using
> the first (second) 'real' pattern of P (10.3.4.3.1.bb):
> • if either conversion is unsuccessful, the conversion of V is
> unsuccessful.

> (cc) A string is converted to a complex value C suitable for a name
> N, using a ·complex· pattern P, as follows:
> • the part of the string controlled by the first (second) 'real' pattern
> of P is converted to a suitable real number (10.3.4.3.l.cc), which then
> forms the first (second) field of C;
> • if either conversion is unsuccessful, the conversion to C is
> unsuccessful.)

Again, here I don't see any reference to plus i times symbol - just the
bare up tack ⊥

There is also the comment on p. 128 of the RR:

Clearly, these representations have been chosen because of their similarity
> to those of the times-ten-to-the-power-symbol (9.4.1.b) and the
> plus-i-times-symbol (9.4.1.c), but, on media on which these characters are
> not available, other string-items must be chosen (and the letter-e-symbol
> and the letter-i-symbol are obvious candidates).

"these representations" in the quote above refers to subscript-ten ₁₀ and
backslash \ for "times ten to the power symbol" and up tack ⊥ for "plus i
times symbol".

Where am I going with all this?

I don't see a rule (nor even a hint of a rule) that indicates we must use a
"plus i times symbol" anywhere except in the description §10.3.4.5.bb that
indicates 'the element of S controlled by the "i" frame of P is "⊥"', and
that is not referring to the "plus i times symbol" by name.

Furthermore, given the comment I quote from p. 128 of the RR, I feel like
we have the blessings of the RR authors to freely substitute
letter-i-symbol in place of plus-i-times-symbol in formatting.

>
> > At any rate, the backslash (\) as a substitute for "e" could seriously
> > confuse folks and might find better uses elsewhere.
>
> Yes I agree.  I think we should use "e" to represent
> times-ten-to-the-power-symbol.
>
> >
> > On Mon, Feb 9, 2026 at 1:49 PM Jose E. Marchesi <jemarch@gnu.org> wrote:
> >>
> >>
> >> Two problems:
> >>
> >> 1) `plus i times' is a monad. As such, it has to be treated like a
> >>    symbol and thus we cannot use the letter `i' for it, because then the
> >>    tag `min' would be interpreteed as tag `m', symbol `i' tag `n'.  So
> >>    we need a symbol for it, as similar as possible as the one proposed
> >>    by the reference language in 9.4.1.c.
> >>
> >> 2) In rule 812h:
> >>
> >>    h) times ten to the power choice{g} :
> >>      times ten to the power symbol{94b} ; letter e symbol{94a}.
> >>
> >>    So both the letter `e' and some `times ten to the power symbol' are
> >>    allowed in real denotations.  I suppose we could say that the
> >>    representation of `times ten to the power symbol' is also "e".  The
> >>    scanner already recognizes "e" for this purpose.
> >>
> >> > Hello All,
> >> >
> >> > This thread is interesting and I am totally ill-equipped to comment on
> >> > the Vliet aspects.
> >> >
> >> > That said, from a user perspective, the use of "e" in 10.0e3 is so
> >> > ubiquitous that any other denotations would be confusing.  So, seems
> >> > wasteful to use a precious "\" for that.
> >> >
> >> > Regarding 4.7i3.2,  I have never seen it.  But I LOVE IT!  Crisp,
> >> > clean, concise, and without any visual clutter.
> >> >
> >> > Thanks! /James
> >> >
> >> >
> >> >
> >> > On Mon, Feb 9, 2026 at 5:14 AM chris hermansen <clhermansen@gmail.com>
> wrote:
> >> >>
> >> >> Jose and list,
> >> >>
> >> >> On Sat, Feb 7, 2026 at 3:51 PM Jose E. Marchesi <jemarch@gnu.org>
> wrote:
> >> >>>
> >> >>>
> >> >>> > Good evening all
> >> >>> >
> >> >>> > I noticed tonight while poring through van Vliet's transput code
> that he
> >> >>> > appropriates the backquote as "plus_i_times", as part of his
> defining sets
> >> >>> > of characters to be used in transput formatting conversion:
> >> >>> >
> >> >>> > CharBag {ℵ₀} radix10digit = STRINGTOBAG "0123456789",
> >> >>> >         {ℵ₀} radix_2digit = STRINGTOBAG "01",
> >> >>> >         {ℵ₀} radix_4digit = STRINGTOBAG "0123",
> >> >>> >         {ℵ₀} radix_8digit = STRINGTOBAG "01234567",
> >> >>> >         {ℵ₀} radix16digit = STRINGTOBAG "0123456789abcedf",
> >> >>> >         {ℵ₀} time_ten_to_the_power = STRINGTOBAG "\eE",
> >> >>> >         {ℵ₀} flipflop               = STRINGTOBAG (flip + flop),
> >> >>> >         {ℵ₀} plus_i_times           = STRINGTOBAG "`iI",
> >> >>> >         {ℵ₀} signspace              = STRINGTOBAG "+- ",
> >> >>> >         {ℵ₀} plusminus              = STRINGTOBAG "+-",
> >> >>> >         {ℵ₀} point                  = STRINGTOBAG string("."),
> >> >>> >         {ℵ₀} xylpkq                 = STRINGTOBAG "xylpkq";
> >> >>> >
> >> >>> > His CharBag type above is like a Java HashSet<Character> and the
> >> >>> > STRINGTOBAG operator converts a string to a CharBag instance.
> >> >>> >
> >> >>> > This is the only place it appears in the code but of course the
> name
> >> >>> > plus_i_times appears in a few places...
> >> >>> >
> >> >>> > I'm thinking that, given the earlier discussion about whether or
> not
> >> >>> > backquote could be usurped for some other use, maybe better to
> nip this one
> >> >>> > in the bud...
> >> >>>
> >> >>> At the end we are following Hansen's recommendation and using
> apostrophe
> >> >>> for the brief form of OF.
> >> >>>
> >> >>> If/when we support left to right selection, it will most certainly
> be
> >> >>> using the dot character, not the backquote.
> >> >>>
> >> >>> So the backquote is free... do we want to use it for plus_i_times?
> >> >>> Thats the question :)
> >> >>>
> >> >>> >
> >> >>> > The eagle-eyed reader who has yet to fall asleep reading this
> will also
> >> >>> > note that van Vliet has proposed using the backslash as an
> alternative for
> >> >>> > time_ten_to_the_power... which maybe also should be discouraged.
> >> >>>
> >> >>> I have wondered about that one as well.  At the moment backslash is
> also
> >> >>> free, but do we want to spend it on this?
> >> >>>
> >> >>> What are common representation for plus_i_times and
> >> >>> time_ten_to_the_power?  I mean generally.
> >> >>
> >> >>
> >> >> I haven't had a lot of luck with my "favourite" search engine as to
> >> >> finding new denotations for times ten to the power of nor plus i
> >> >> times.  But I did pick this out of the RR:
> >> >>
> >> >> Wherever (in the transput declarations) the representation ₁₀ (\, ⊥)
> >> >> [subscript 10, backslash, tack) occurs within a
> >> >> <bold>character-denotation</bold> or <bold>string-denotation</bold>,
> >> >> it is to be interpreted as the representation of the
> >> >> <bold>string-item</bold> (8.1.4.1.b) used to indicate "times ten to
> >> >> the power" (an alternative form {, if any.} of "times ten to the
> >> >> power", "plus i times") on external media. {Clearly, these
> >> >> representations have been chosen because of their similarity to
> >> >> those of the <bold>times-ten-to-the-power-symbol</bold> (9.4.1.b)
> >> >> and the <bold>plus-i-times-symbol</bold> (9.4.1.c), but, on media on
> >> >> which these characters are not available, other
> >> >> <bold>string-items</bold> must be chosen (and the
> >> >> <bold>letter-e-symbol</bold> and the <bold>letter-i-symbol are
> >> >> obvious candidates</bold>).}
> >> >>
> >> >>
> >> >> I have tried to be very careful above in using <bold>...</bold> to
> >> >> bracket formal grammar terms and I have used the Unicode characters
> >> >> I believe represent the graphical representations of "times ten to
> >> >> the power" and "plus i times".
> >> >>
> >> >> In my opinion, we should at least consider 10.0e3 and 4.7i3.2 as
> >> >> respective denotations, given the stated interest in avoiding
> >> >> characters not available without using the Compose key or other
> >> >> artifices required to select "non-keyboardable" Unicode characters.
> >> >>
> >> >> I dislike the idea of "wasting" \ for "times ten to the power" and `
> >> >> for "plus i times" as neither character is especially evocative of
> >> >> the proposed meaning.  Moreover a casual reader would more likely be
> >> >> familiar with at least 10.0e3 as meaning "ten to the power of 3" and
> >> >> could probably intuit 4.7i3.2 as 4.7 + 3.2i if s/he knew anything
> >> >> about complex numbers.
> >> >>
> >> >> Put another way - if there is any customary use of backslash as
> >> >> "times ten to the power" and ` as "plus i times", I at least have
> >> >> yet to discover it.
> >> >> --
> >> >> Chris Hermansen · clhermansen "at" gmail "dot" com
> >> >>
> >> >> C'est ma façon de parler.
>

-- 
Chris Hermansen · clhermansen "at" gmail "dot" com

C'est ma façon de parler.
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