[rcfox]

Hey, here's a chance to invent some new terminology!

I would say that Norvig's corrector is a first-order spelling corrector, since it works within the context of a single word.

A second-order corrector would take into account the word before or after it to choose the spelling that is more likely to make sense. ("Their coming" would suggest a correction to "They're coming")

Third-, fourth-, (and so on) order expands the distance of words considered.

[dextorious]

"""("Their coming" would suggest a correction to "They're coming")'""

How about: "Her relatives would visit us for Christmas. Their coming filled us with dread!"

[rcfox]

It's valid, but less common, and that's why I specifically chose the wording "suggest a correction" instead of "correct". Spell checkers are still no substitute for actual thought.