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Finally the prototype parser has produced the first correct forest.
It is my first time to generate a correct forest, in fact, ever since
the beginning of this project.
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I have an ostensibly working prototype now.
Further tests are needed to make sure that the algorithm meets the
time complexity requirement, though.
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Now the grammar will record the left-linear expansions when generating
the nondeterministic finite automaton frmo its rules, and will record
whether an edge in the nondeterministic finite automaton comes from a
left-linear expansion. The latter is needed because while performing
a chain-rule derivation, we do not need the left-linear expanded
derivations in the "first layer". This might well have been the root
cause of the bad performance of the previous version of this package.
Also I have figured out how to properly generate and handle parse
forests while manipulating the "chain-rule machine".
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I put functionalities that are not strictly core to separate crates,
so that the whole package becomes more modular, and makes it easier to
try other parsing algorithms in the future.
Also I have to figure the forests out before finishing the core
chain-rule algorithm, as the part about forests affects the labels of
the grammars directly. From my experiences in writing the previous
version, it is asking for trouble to change the labels type
dramatically at a later point: too many places need to be changed.
Thus I decide to figure the rough part of forests out.
Actually I only have to figure out how to attach forests fragments to
edges of the underlying atomic languages, and the more complex parts
of putting forests together can be left to the recorders, which is my
vision of assembling semi-ring values during the chain-rule machine.
It should be relatively easy to produce forests fragments from
grammars since we are just trying to extract some information from the
grammar, not to manipulate those information in some complicated way.
We have to do some manipulations in the process, though, in order to
make sure that the nulling and epsilon-removal processes do not
invalidate these fragments.
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