The amazing page computes binary relations between pairs of regular expressions and shows a graphical representation of the DFA.
It’s a really incredible demonstration of some highly non-trivial operations on regular expressions.
It’s a really incredible demonstration of some highly non-trivial operations on regular expressions.
The standard theory of regular expressions focuses entirely on regex matching, rather than searching. For matching, ^ and $ don't really mean anything. In particular, regexp theory is defined in terms of the "language of" a regexp: the set of strings which match it. What's the set of strings that "^" matches? Well, it's the empty string, but only if it comes at the beginning of a line (or sometimes the beginning of the document). This beginning-of-line constraint doesn't fit nicely into the "a regexp is defined by its language/set of strings" theory, much the same way lookahead/lookbehind assertions don't quite fit the theory of regular expressions.
The standard workaround is to augment your alphabet with special beginning/end-of-line characters (or beginning/end-of-document), and say that "^" matches the beginning-of-line character.
More interesting is word boundaries:
`\b` is just `\<|\>` though that should be bubbled up and usually only one side will actually produce a matchable regex.
`A\<B` is just `(A&\W)(\w&B)`, and similar for `\>`.
(a|b|^)(c|d|^)foo
((a|b)?(c|d)|c|d)?foo
((.*a|.*b)(c|d)|c|d)?foo
In an engine supporting ^ and $, searching for this
(a|b|^)(c|d|^)foo
^((.*a|.*b)(c|d)|c|d)?foo.*$