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If the highest-priority search path (see section 3.2 Path sources) contains an extra colon (i.e., leading, trailing, or doubled), Kpathsea inserts at that point the next-highest-priority search path that is defined. If that inserted path has an extra colon, the same happens with the next-highest. (An extra colon in the compile-time default value has unpredictable results, so installers beware.)
For example, given an environment variable setting
setenv TEXINPUTS /home/karl:
TEXINPUTS value from `texmf.cnf' of
then the final value used for searching will be:
Since Kpathsea looks for multiple configuration files, it would be natural to expect that (for example) an extra colon in `./texmf.cnf' would expand to the path in `$TEXMF/texmf.cnf'. Or, with Dvips' configuration files, that an extra colon in `config.$PRINTER' would expand to the path in `config.ps'. This doesn't happen. It's not clear this would be desirable in all cases, and trying to devise a way to specify the path to which the extra colon should expand seemed truly baroque.
Technicality: Since it would be useless to insert the default value in more than one place, Kpathsea changes only one extra `:' and leaves any others in place (they will eventually be ignored). Kpathsea checks first for a leading `:', then a trailing `:', then a doubled `:'.
You can trace this by debugging "paths" (see section 2.6.3 Debugging). Default expansion is implemented in the source file `kpathsea/kdefault.c'.
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