TeXbook Exercise 2.4 (triple quotes)

Question

The exercise is to reproduce the two possible typings of ``` (three leftquotes). Immediately beforehand there is an explanation of how to do the same thing with three rightquotes, which I will rewrite in my own words to check I really understand it:

If you type ''', then TeX assumes that this is a double \rq followed by a single \rq, and spaces appropriately. If you group them this way, you have: ''' vs. ''{'}, which I expect to look identical (they do). But if you want a single \rq followed by a double \rq, then grouping does not work: '{''} because the space is too small. So you have to manually insert the \thinspace: to get '\thinspace''

For the exercise, I figured that three leftquotes in a row ``` would be parsed as "double \lq followed by single \lq", and that therefore the spacing would agree with ``\thinspace', but it doesn't. I know from elsewhere that two adjacent backticks get turned into a ligature. I assumed that the spacing between this ligature and the surrounding text was determined dynamically (somehow), but if the `` ligature actually has some space hard-coded (i.e. that it really becomes \thinspace``) then I think I understand (in particular, Don's remarks about spacing in the previous paragraph also seem to make sense). Is this correct?

Answer 1

In cmr10.tfm you find, after transforming it in human readable form with tftopl,

   (LABEL O 47)
   (LIG O 47 O 42)
   (KRN O 77 R 0.111112)
   (KRN O 41 R 0.111112)
   (STOP)

as part of LIGTABLE. This means that if octal 47 (decimal 39, right quote/apostrophe) is followed by the same character, TeX will replace the two characters with the glyph in position octal 42 (decimal 34, double quote/quotation mark). If followed by octal 77 (decimal 63, question mark) or octal 41 (decimal 33, exclamation mark) a kern is added.

The table has no entry for O 42, so no kerning is used after the double quote.

Indeed, if you try

\tracingonline=1
\showboxbreadth=\maxdimen
\showboxdepth=\maxdimen
\tracingoutput=1

\nopagenumbers

'''

\bye

you get

Completed box being shipped out [1]
\vbox(667.20255+0.0)x469.75499
.\vbox(0.0+0.0)x469.75499, glue set 14.0fil
..\glue -22.5
..\hbox(8.5+0.0)x469.75499, glue set 469.75499fil
...\vbox(8.5+0.0)x0.0
...\glue 0.0 plus 1.0fil
..\glue 0.0 plus 1.0fil minus 1.0fil
.\vbox(643.20255+0.0)x469.75499, glue set 633.20255fill
..\glue(\topskip) 3.05556
..\hbox(6.94444+0.0)x469.75499, glue set 441.97719fil
...\hbox(0.0+0.0)x20.0
...\tenrm " (ligature '')
...\tenrm '
...\penalty 10000
...\glue(\parfillskip) 0.0 plus 1.0fil
...\glue(\rightskip) 0.0
..\glue 0.0 plus 1.0fill
.\glue(\baselineskip) 24.0
.\hbox(0.0+0.0)x469.75499, glue set 469.75499fil
..\glue 0.0 plus 1.0fil

showing no kern. However, one has to take into account how the glyphs sit in their bounding box.

\documentclass{article}

\begin{document}

\setlength{\fboxrule}{0.1pt}% hairline
\setlength{\fboxsep}{-\fboxrule}% takes no space

\fbox{''}\fbox{'}

\end{document}

So you see that a “thin space” is somewhat hardwired in the double quote. Different fonts may behave in a different way.