Henry Spencer's Regular Expression library for support of REGEXP function.
This is the copyrighted product of Henry Spencer from the University of Toronto. It's a fairly-well-known implementation of the requirements of POSIX 1003.2 Section 2.8. The library is bundled with Apache and is the default implementation for regular-expression handling in BSD Unix. MySQL's Monty Widenius has made minor changes in three programs (debug.c, engine.c, regexec.c) but this is not a MySQL package. MySQL calls it only in order to support two MySQL functions: REGEXP and RLIKE.
Some of Mr Spencer's documentation for the regex library can be found in the README and WHATSNEW files.
One MySQL program which uses regex is \cmd-line-utils\libedit\search.c
This program calls the 'regcomp' function, which is the entry point in \regex\regexp.c.