Today we mainly discussed the proof of correctness for our regular expression matcher from the previous lecture. We broke the proof into three parts: termination, soundness, and completeness. Please look at the lecture notes from last time for the full proof. We only did a small part of it in lecture.
At the end of lecture, we briefly discussed a version of the regular expression matcher based on combinators. Combinators help us separate the processing of the regular expression from the actual character matching and continuation-based control flow. This separation facilitates staging: The regular expression pattern matching is in one stage, the character and continuation functions are in another. One can thus produce a matcher for a regular expression without ever seeing any input or continuations.
For a review of staging see Lecture 11.
For the unstaged regular expression matcher see Lecture 14.