Hmm, when I said "on the fly" I meant "when consuming next input 
character". And (to the extent of my knowledge) this is exactly how Earley 
algorithm works: consume next input character, compute Earley item sets 
(active, predicted, completed), repeat. There're many variations 
(prediction/reduction lookahead, Aycock & Horspool trick for empty rules, 
Leo's memoization, LR(0) items), but they don't break general order of 
things.

In Earley's algorithm most of the work must be done at runtime, as opposed 
to e.g. LR-family where most of the work can be done ahead of time, and 
thus no information about input string is encoded in the parser.

What are the other implementations you mentioned?

By the way, do you use lookahead in Marpa?

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