x = x a + b
Now use high school algebra
x = x*a + b
x - x*a = b
x*(1-a) = b
x = b / (1-a)
x = b * 1/(1-a)
Now you have to remember that the Taylor series expansion of 1/(1-a) is
1/(1-a) = 1 + a + a^2 + a^3 + a^4 + ...
OK, now put your grammar hat back on. What's
1 | a | aa | aaa | aaaa | ...
it's just an arbitrary number of a:s, i.e., a* (or 'many a' in parsec).
So finally
expr = b a*
nice!-) different viewpoints yield new perspectives.
this made me wonder what those missing algebra operations would mean in terms
of parsing/language generation; it hurts a bit to think about your algebraic manipulations
in that way, but if i got the interpretations right, they might be quite useful
additions:
l1 - l2: things in l1 that are not in l2; generalising elimination of keywords
from valid ids
l1 / l2: things that can be completed to be in l1, via suffixes in l2; standard
tool in ides
thanks for the interesting detour,
claus
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