[tex-k] bug in syntax of <numeric primary> in The METAFONTbook
胡亚捷 (Hu Yajie)
2500418497 at qq.com
Mon Jul 13 17:50:54 CEST 2020
The syntax for primaries solves the ambiguity of `-.5[a,b]' by restricting
what can occur in the `t' part of the `t[a,b]' notation: single-token things,
"literal" fractions like 2/3, parenthesized and grouped expressions can occur,
while things with an operator at the left, like -.5, sqrt3, 2/3x etc., cannot.
Therefore, the interpretation `(-.5)[a,b]' is ungrammatical, and it must be
parsed as `-(.5[a,b])'. However, the real reason MF chooses the latter is:
1. Parsing is done from left to right.
2. METAFONT makes each primary as long as possible. In other words, a
<primary> is always extended if it is followed by `[<exp>,<exp>]'.
Thus, you cannot put `-.5' before something like `[a,b]' because `-.5' ends
with an unfinished primary and `[a,b]' happens to finish it, not because
`-.5' begins with an operator. Now, what's the problem if the the two
interpretations explain the same phenomena? The problem is that some `t' parts
begin with an operator and end with a finished primary, such as `-.5[a,b]'
itself occurring before another set of brackets! Try it, and you'll find that
is perfectly grammatical, even though `-.5[a,b]' does not meet the syntax of
<numeric atom>. Thus the syntax rules should be rebalanced to something like
<numeric atom> ::= <numeric variable> | <numeric argument>
| <numeric token primary>
| <internal quantity>
| ( <numeric expression> )
| begingroup <statement list> <numeric expression> endgroup
| length <numeric primary> | length <pair primary>
| length <path primary> | length <string primary>
| ASCII <string primary> | oct <string primary> | hex <string primary>
| <pair part> <pair primary> | <transform part> <transform primary>
| angle <pair primary>
| turningnumber <path primary> | totalweight <picture primary>
| <numeric operator> <numeric primary>
| directiontime <pair expression> of <path primary>
<numeric primary> ::= <numeric atom> [ <numeric expr> , <numeric expr> ]
| <numeric atom not followed by `[ <numeric expr> , <numeric expr> ]'>
Not sure if I got the new syntax right, but it's definitely cleaner if it is.
(You might also want to change the explanation of `sqrt 100(100)' on page 64.)
---------------------------now for some suggestions---------------------------
Page C127, line 19
Concatenation of strings isn't introduced yet for first-time readers.
Page C171, line 4
The parentheses in `round(n)' are superfluous (cf. `round a' and `round x' on
page C66, `round u' and `round 3u' on page 200, etc.)
Page C191, line 2
The `currentpicture' feature isn't introduced yet for first-time readers.
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