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https://buttondown.email/hillelwayne/archive/why-do-regexes-use-and-as-line-anchors/
Last week I fell into a bit of a rabbit hole: why do regular expressions use $ and ^ as line anchors?1
This talk brings up that they first appeared in Ken Thompson's port of the QED text editor. In his manual he writes: b) "^" is a regular expression which matches character at the beginning of a line.
c) "$" is a regular expression which matches character before the character (usually at the end of a line)
QED was the precursor to ed, which was instrumental in popularizing regexes, so a lot of its design choices stuck.
Okay, but then why did Ken Thompson choose those characters?
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Why Do Regexes Use `$` and `^` as Line Anchors?
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(Score: 3, Interesting) by krishnoid on Thursday March 28, @09:59PM
They don't correspond directly, but understanding a DFA can help understand the shorthand for automata-theoretic regular expressions (Kleene star, et al). That makes it easier to extend DFAs to NFAs, and then add on the additional concepts used in actual programming-language regexes.
For example, DFAs don't have additional storage; the DFA is pretty much just the state machine description and the current state, with no knowledge of previous input. Parentheses and backreferences within a regex require additional storage, which are better understood when considered as a useful programming language extension, to the mathematically-pure DFA and corresponding regular expressions.